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 Semiconductor Measurement Technology:
Spreading Resistance Symposium

Proceedings of a Symposium
Held at the National Bureau of Standards
Gaithersburg, Maryland
June 13-14, 1974

James R. Ehrstein, Editor

Electronic Technology Division

Institute for Applied Technology
National Bureau of Standards
Washington, B.C. 20234

Under the Sponsorship of

Committee F-l of the
American Society for Testing and Materials

and

The National Bureau of Standards

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued December 1974

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 National Bureau of Standards Special Publication 400-10
Nat. Bur. Stand. (U.S.), Spec. Publ. 400-10, 293 pages (Dec. 1974)
CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1974
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402
(Order by SD Catalog No. C13.10:400-10). Price $3.55.
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 PREFACE

This Symposium on Spreading Resistance measurements was held on June 13-14, 1974 at the
National Bureau of Standards under the cosponsorship of this Bureau and Committee F-l of the
American Society for Testing and Materials. It consisted of three sessions as detailed in
the Contents on pp. vi to viii. -
The objective of the Symposium was to expose the state of the art with respect to the
theory, practice and applications of the electrical spreading resistance measurement tech-
nique. This technique which has seen rapidly increasing interest and use over the last 10
or more years, has noteworthy versatility for profiling dopant concentrations over many
orders of magnitude in multiple layer semiconductor structures. Nevertheless, the ever in-
creasing demand on all measurement methods, caused by device fabrication utilizing active
regions often less than 1 um. in thickness, taxes the theory, practice and successful appli-
cation of all techniques, including the electrical spreading resistance.
It is hoped that this symposium, by illustrating the successful applications which
have been made of the technique, and by indicating some of the areas where limitations
have been found to exist, will encourage further effort by interested parties, to find
solutions to those limitations.
Finally, by compiling a store of well documented measurement practice in one volume,
it is hoped that the beginner in this technique will find rapid solutions to possible
basic problems, so that he too may make rapid and successful use of this technique.

James R. Ehrstein
Editor

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 SPREADING RESISTANCE SYMPOSIUM

ABSTRACT

This Proceedings contains the information presented at the Spreading Resistance

Symposium held at the National Bureau of Standards on June 13-14, 1974.
This Symposium covered the state of the art of the theory, practice and applications
of the electrical spreading resistance measurement technique as applied to characterization
of dopant density in semiconductor starting materials and semiconductor device structures.
In addition to the presented papers, the transcripts of the discussion sessions which were
held directly after the Theory, Practice and Applications sessions are also included.
These transcripts, which were reviewed by the respective respondents for clarity, are
essentially as presented at the symposium.

Key words: Dopant concentration, dopant profiles, metal-semiconductor contacts,

resistivity, semiconductor surface preparation, silicon, spreading resistance.

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 SYMPOSIUM COMMITTEE

P. LANGER, Symposium Chairman

Bell Telephone Laboratories
Allentown, Pennsylvania

R. E. BENSON, Cochairman - Theory Session

Bell Telephone Laboratories
Allentown, Pennsylvania

F. VIEWEG-GUTBERLET, Cochairman - Theory Session

Wacker Chemitronic
Burghausen, West Germany

B. MORRIS, Cochairman - Practice Session

Bell Telephone Laboratories
Allentown, Pennsylvania

P. LANGER, Cochairman - Practice Session

Bell Telephone Laboratories
Allentown, Pennsylvania*

A. MAYER, Cochairman - Application Session

RCA Corporation
Someryille, New Jersey

F. PADOVANI, Cochairman - Application Session

Texas Instruments, Inc.
Dallas, Texas

J. R. EHRSTEIN, Chairman - Publicity, Arrangements, Publication

National Bureau of Standards
Washington, D. C. 20234

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 CONTENTS

Paper No. Page No.

1-1. Welcome from NBS

Judson C. French, Chief, Electronic Technology Division
National Bureau of Standards, Gaithersburg, Maryland 1

1-2. Welcome from ASTM

Robert I. Scace, Chairman, ASTM Committee F-l
General Electric Company, Syracuse, New York 3

1-3. Keynote Address

Robert G. Mazur
Solid State Measurements, Monroeville, Pennsylvania 5

SESSION I - THEORY

T-l. The Physics of Spreading Resistance Measurements

S. J. Fonash, Engineering Science Department
Pennsylvania State University
University Park, Pennsylvania 17

T-2. Formal Comparison of Correction Formulae for Spreading Resistance

Measurements on Layered Structures
P. J. Severin, Philips Research Laboratories
Eindhoven, The Netherlands 27

T-3. Two-Point Probe Correction Factors

D. H. Dickey, Bell and Howell Research Laboratory
Pasadena, California 45

T-4. On the Validity of Correction Factors Applied to Spreading

Resistance Measurements on Bevelled Structures
P. M. Pinchon, R. T. C. La Radiotechnique Compelec
14 Caen, France 51

T-5. SRPROF, A Fast and Simple Program for Analyzing Spreading Resistance
Profile Data
B. L. Morris and P. H. Langer, Bell Telephone Laboratories
Allentown, Pennsylvania 63

T-6. Multilayer Analysis of Spreading Resistance Measurements

Gregg A. Lee, Texas Instruments Incorporated
Dallas, Texas 75

SESSION II - PRACTICE

P-l. An Automated Spreading Resistance Test Facility

J. C. White, Western Electric Company
Allentown, Pennsylvania 95

P-2. Angle Bevelling Silicon Epitaxial Layers, Technique and Evaluation

P. J. Severin, Philips Research Laboratories
Eindhoven, The Netherlands 99

P-3. Spreading Resistance Measurements on Silicon with Non-blocking

Aluminum-Silicon Contacts
J. byKrausse,
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Paper No. Page No.

P-4. The Preparation of Bevelled Surfaces for Spreading Resistance Probing

by Diamond Grinding and Laser Measurement of Bevel Angles
A. Mayer and S. Shwartzman, RCA, Solid State Division
Somerville, New Jersey 123

P-5. Spreading Resistance Correction Factors for (111) and (100) Samples
H. Murrmann and F. Sedlak, Siemens AG
Munich, F. R. Germany 137

P-6. On the Calibration and Performance of a Spreading Resistance Probe

H. J. Ruiz and F. W. Voltmer, Texas Instruments Incorporated
Dallas, Texas 145

P-7. Comparison of the Spreading Resistance Probe with Other Silicon

Characterization Techniques
W. J. Schroen, G. A. Lee, and F. W. Voltmer, Texas Instruments, In-
corporated, Dallas, Texas 155

P-8. Preparation of Lightly Loaded, Closely Spaced Spreading Resistance

Probe and Its Application to the Measurement of Doping Profiles in
Silicon
J. L. Deines, E. F. Gorey, A. E. Michel, and M. R. Poponiak
IBM, Systems Products Division, East Fishkill Facility
Hopewell Junction, New York 169

SESSION III - APPLICATIONS

A-l. A Direct Comparison of Spreading Resistance and MOS C-V Measurements

of Radial Resistivity Inhomogeneities on PICTUREPHONE R Wafers
J. R. Edwards and H. E. Nigh, Bell Telephone Laboratories
Allentown, Pennsylvania 179

A-2. Investigation of Local Oxygen Distribution in Silicon Single Crystals

by Means of the Spreading Resistance Technique
F. Vieweg-Gutberlet, Wacker Chemitronic
Burghausen, F. R. Germany 185

A-3. Use of the Spreading Resistance Probe for the Characterization of

Microsegregation in Silicon Crystals
F. W. Voltmer and H. J. Ruiz, Texas Instruments Incorporated
Dallas, Texas 191

A-4. Effects of Oxygen and Gold in Silicon Power Devices

J. Assour, RCA, Solid State Division
Somerville, New Jersey 201

A-5. The Evaluation of Thin Silicon Layers by Spreading Resistance

Measurements
G. Gruber and R. Pfeiffer, Solid State Measurements, Incorporated
Monroeville, Pennsylvania 209

A-6. Evaluation of Effective Epilayer Thickness by Spreading Resistance

Measurement
H. Murrmann and F. Sedlak, Siemens AG
Munich, F. R. Germany 217

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Paper No. Page No.

A-7. The Experimental Investigation of Two-Point Spreading Resistance

Correction Factors for Diffused Layers
N. Goldsmith, R. V. D'Aiello, and R. A. Sunshine, RCA Laboratories
Princeton, New Jersey 223

A-8. Applications of the Spreading Resistance Technique to Silicon

Characterization for Process and Device Modeling
W. H. Schroen, Texas Instruments Incorporated
Dallas, Texas 235

LATE NEWS PAPER

Improved Surface Preparation for Spreading Resistance Measurements

on p—Type Silicon
J. R. Ehrstein, National Bureau of Standards
Gaithersburg, Maryland 249

DISCUSSION SESSION

List of Participants 257

Discussion - Theory 259

Discussion - Practice 262

Discussion - Applications 268

Concluding Remarks
P. H. Langer - Symposium Chairman 278

Appendix - Bibliography 279

Certain commercial materials and equipment are identified in this paper in order to
adequately specify the experimental procedure. In no case does such identification imply
recommendation or endorsement by the National Bureau of Standards, nor does it imply
that the material or equipment identified is necessarily the best available for the
purpose.

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 AUTHOR INDEX

Author Page No.

Assour, J. 201

Deines, J. L. 169

Dickey, D. H. 45

Ehrstein, J. R. 249

Edwards, J. R. 179

Fonash, S. J. 17

Goldsmith, N. 223

Gruber, G. 209

Krausse, J. 109

Lee, G. A. 75

Mayer, A. 123

Morris, B. L. 63

Murrmann, H. 137

Murrmann, H. 217

Pinchon, P. M. 51

Ruiz, H. J. 145

Schroen, W. J. 155

Schroen, W. J. 235

Severin, P. J. 27

Severin, P. J. 99

Vieweg-Gutberlet, F. 185

Voltmer, F. W. 191

White, J. C. 95

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ix
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 WELCOMING REMARKS
AT THE
ASTM/NBS SYMPOSIUM ON SPREADING RESISTANCE MEASUREMENTS
. GAITHERSBURG, MARYLAND
JUNE 13, 1974
BY JUDSON C. FRENCH, CHIEF
ELECTRONIC TECHNOLOGY DIVISION
NATIONAL BUREAU OF STANDARDS

Good morning. It is a real pleasure for me to bid you welcome to the ASTM/NBS Symposium
on Spreading Resistance Measurements on behalf of the National Bureau of Standards and, in
particular, on behalf of the Bureau's Electronic Technology Division. I welcome also your
co-host Bob Scace, Chairman of Committee F-l on Electronics of the American Society for
Testing and Materials.
Sharing this period of welcome with Bob is, I believe, representative of the long con-
tinuing cooperation between NBS and ASTM in many fields, always with the common interests of
improvements in technology, in methods of measurement and specifications, and in the pro-
motion of sound and effective voluntary standards.
Many of you are old friends of NBS and our Division but some are becoming acquainted
with us for the first time at this Symposium. I would like to address my first few remarks
to these new visitors. I am sure you are aware of the NBS role in maintaining and dissem-
inating the primary standards of measurement for this Nation. But the Bureau carries on an
amazingly wide variety of activities in other fields as diverse as pollution control and
building research, dental materials and cryogenics, standard reference data and computer
research, all stemming from the broad charter established by Congress nearly three quarters
of a century ago. Here again in its breadth and subject matter the Bureau's interests par-
allel those of ASTM to a surprising degree.
Closest to the interests of this audience and of much of ASTM's Committee on Electronics
is the work of our Electronic Technology Division. This 'Division focuses its resources on
solving critical measurement and standardization problems associated with the manufacture,
procurement, and application of essential electronic components.
Most of the work of this Division is devoted to semiconductor electronics. This comes
as a surprise to many who ask: Why does the Bureau need to work in a field which so sophis-
ticated, so technologically advanced, and so innovative? The answer is that the sophisti-
cation and innovative abilities of the semiconductor industry have led to the development
of new processes and new devices much faster than the measurement techniques for their con-
trol and characterization have been developed.
In the fifteen years or more that our staff has worked with the semiconductor industry
and its customers we have seen increasing need for improvements in practical methods of
measurement for analysis, control, and specifications in this field. And we have learned
that the Bureau can be especially helpful in this field because of its neutrality in eval-
uating measurement methods, and associated technology, and because its charter encourages it
to work in the area of generic measurement for industry-wide use and market-place application.
This is an area where individual companies understandably find less incentive for extensive
research than in areas leading to new and proprietary processes and designs.
As a result, the NBS Semiconductor Technology Program has been established, having as
its goal the development and standardization of improved methods of measurement for use in
specifying materials and devices and in control of device fabrication processes: methods
that have been well documented and tested for technical adequacy, are of demonstrated pre-
cision of an industrially acceptable level, and are acceptable to both users and suppliers.

1
 If such methods are used by the electronics industry, they are expected to provide a
more consistent set of measured results and interpretations and, hence, lead to improved
quality control and yield in the manufacturer's plant, and to improved reliability and
economy in the customer's applications.

But even when NBS is successful in providing such methods how does it assure the in-
dustry will use them? Only by working closely with the industry and its customers in the
first place to ascertain for what measurements improvements are needed, then to carry on
interlaboratory, or round robin, evaluation of the improved methods to show their practical
value and precision, and finally to inform the electronics community of the resulting meth-
ods and to encourage their adoption as voluntary standards. This last step is important
because NBS has no enforcement or regulatory authority in this field.

And here again we find ourselves working closely with ASTM which can so effectively
provide an avenue to accomplishing these NBS aims, aims which are, of course, common to those
of ASTM's Committee on Electronics.

Our Program now encompasses work on selected measurements, ranging from those needed to
characterize silicon and oxides and interface states, through those for photolithography,
process control using test structures, bonding and die attachment, and hermeticity; on to
thermal and electrical properties of finished devices. And we report our output not only
through ASTM but through many other channels including a special series of NBS publications
with which many of you are familiar.

But I would like to reminisce for a moment, back to 1960 when our program was not so
extensive and when our first project in the semiconductor materials measurement field was
undertaken.

It was undertaken at the request of ASTM's Committee F-l and the subject was measure-
ment of resistivity. I have a very personal interest in this subject because I learned of
the need in my first day of attendance at an F-l meeting. And ASTM and NBS have done a lot
together on this subject in the intervening years. We developed an improved four-probe
method, improved in precision by an order of magnitude as a matter of fact, and the method
and its various correction factors and other aspects now play a part in five ASTM standards.
Later a scanning photovoltaic technique for convenient, essentially non-contacting, radial
profiling was developed. Most recently we have issued a Standard Reference Material, com-
prising two boron doped silicon wafers with certified resistivity values for checking mea-
surements; and their stability is now being tested in a long term cooperative experiment
with the industry. These are the first Standard Reference Materials issued for the semi-
conductor industry's use.

But sophistication in the industrial development of devices has raised new problems
which can only be solved by new techniques for resistivity measurements yielding resolution
far beyond the capability of the currently standard four-probe technique. Where the four-
probe method is limited to resolution of the order of millimeters, resolution of the order
of micrometers and better is needed now for determination of crystal uniformity and for con-
trol of junction profiles.

The spreading resistance measurement method you will be discussing today and tomorrow
is a leading contender in this field. We are working, as are many of you, to develop this
method to a level of repeatability and understanding, both in and between laboratories, to
meet the industry's needs. We are anxious to learn of the new developments to be reported
here today and tomorrow.

So I will say no more now, except that it is a pleasure to be able to provide the
facilities of the Bureau for this Symposium and to join with ASTM in encouraging the ex-
change of information in this rather new and very important field.

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 WELCOMING REMARKS FROM ASTM

Robert I. Scace

General Electric Company

Syracuse, New York

Good morning. On behalf of ASTM Committee F-l, the other sponsor of this meeting, I
want to welcome you all. Spreading resistance measurements are only one of many measure-
ment techniques with which Committee F-l is concerned. To give some perspective, let me
describe a little of ASTM's background in electronics for you.

ASTM is a large association of professional people who are engaged in developing stan-
dards on subjects ranging from railroad rails to surgical implants, and electronics is just
one of over 120 such topics. Committee F-l was established in 1955, developing out of work
on electron tube materials which had previously been in a committee on copper. One of our
major efforts has been in the development of ways to measure the properties of semiconductor
silicon.

As Judson French has mentioned, NBS and ASTM have collaborated closely in this work,
especially in resistivity measurements. Fifteen years ago we were lucky if two different
people could measure the resistivity of a piece of silicon to within a factor of two, but
now with the use of ASTM'methods it is possible to do this measurement to an accuracy of a
couple of percent. Similar progress could be cited for many other measurements essential
to good process control in our industry.

Achievements such as these are one of the professional satisfactions of work in ASTM.
We can all do our jobs better with better measurement tools and techniques. Another more
personal reward is in the relationships established over the years with the people in ASTM.
Committee F-l meets three times a year to do its work, and this frequent contact on common
technical problems results in close friendships with fellow professionals.

For the next two days we will be discussing spreading resistance measurements on sili-
con. This is a very powerful technique for analysis of structures and control of processes
which is now mature enough to discuss at length. I hope you all find these sessions valu-
able, and I also encourage you to come to future Committee F-l meetings to participate and
to contribute further to the development of spreading resistance techniques.

3
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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Keynote Address
Symposium on Spreading Resistance
Gaithersburg, Maryland
June 13-14, 1974

Robert G. Mazur
Solid State Measurements, Inc.
600 Seco Road
Monroeville, Pennsylvania 15146

1. Introduction

This is the first symposium ever to be held on the subject of spreading resistance
measurements. As I see it, the purpose in having this meeting is to gather together those
who are currently using the spreading resistance measurement technique in their work on
semiconductor processing problems along with others who would like to be able to do some-
thing about the same or similar problems, in the hope that, by sharing our knowledge and ex-
perience, we may all be better able to use the spreading resistance technique to our own ad-
vantage. I hope and believe that we will achieve this particular goal and that therefore in
the future this meeting will be referred to as "The First Symposium on Spreading Resistance
Measurements."
In deciding what I should talk about in a keynote speech for such an occasion, two re-
lated subjects came to mind. First, a number of individuals who haven't worked in the semi-
conductor industry from its earliest days have expressed an interest in the questions of
where the technique came from as well as why and how it came about. Therefore, in the first
part of my talk today I would like to relate the background of the spreading resistance tech-
nique as I know it.
The second subject that came to mind is also in response to certain people that I've
met over the years. These are the people who, when first exposed to the spreading resis-
tance technique, rapidly developed a "hang-up" with respect to the mechanics of the contacts
used. In an attempt to shed some light in this area, I will devote the second part of this
morning's talk to what I know about the achievement of reproducible, known-geometry, metal-
semiconductor, small-area pressure contacts. These contacts are what I have often referred
to in past discussions as "conditioned" contacts.

2. The Spreading Resistance Technique: Who, What, Why, Where and When.
The Spreading Resistance Technique is a method used to obtain quantitative measurement
of the local resistivity of certain semiconductor materials. Currently, the technique is
used most extensively on silicon. An essential feature of the technique is the achievement
of sufficiently high spatial resolution so as to allow detailed evaluation of those varia-
tions in dopant concentration which are important to the manufacture of semiconductor de-
vices. The technique is based on measurement of the "spreading resistance" or "constriction
resistance" of small-area metal-semiconductor pressure contacts. It is currently in wide
use in mapping inhomogeneities in silicon crystals and in obtaining thickness profiles of
many of the diffused, epitaxial and ion-implanted layers produced during semiconductor de-
vice processing.

Small area metal-semiconductor pressure contacts are historically somewhat loosely

called "point" contacts. The spreading resistance effect associated with such contacts has
a distinguished place in the history of semiconductor technology. Certainly one of the
earliest practical applications of a semiconductor device was the use of a point-contact
rectifier in "crystal" radios during the early days of the radio age (I)1. Later, the

1
Figures in brackets refer to literature citations at the end of this paper.
5
desire to understand and thus to improve point-contact diode detectors used in early World
War II radar equipment sparked the efforts of a number of research groups in work on ger-
manium and silicon. This work eventually led to the discovery of the transistor effect in
late 1947 by Bardeen, Brattain and Shockley at the Bell Telephone Laboratories in Murray
Hill, New Jersey (2).

However, there is an even closer relationship between spreading resistance measurements

and the invention of the transistor. From the beginning of my work with the spreading re-
sistance technique, I have been impressed by the fact that a key step in the Bardeen,
Brattain and Shockley transistor invention involved a spreading resistance measurement (3).
The experiment is detailed in the Physical Review for 1948 immediately following the note
describing the transistor effect. This crucial experiment established the existence of ad-
ditional charge carriers produced by injection from a metal-germanium point-contact identi-
cal to the emitter used in the first point-contact transistor. Brattain and Bardeen showed
that the potential associated with a current flow through a metal-semiconductor point con-
tact did not fall off with increasing distance from the point in accordance with a standard
spreading resistance calculation but rather exhibited an anomalous decrease in the rate-of-
change of potential in the immediate vicinity of the contact. This behavior was explained
as being due in part to the injection of additional charge carriers into the semiconductor
with a consequent lowering of the resistivity near the contact.

At this time, I'd like to call your attention to an interesting aspect of this
Brattain-Bardeen injecting point-contact experiment, specifically that, to the best of my
knowledge, the experiment has never been repeated. Not that I am suggesting that their work
needs corroboration but I consider it surprising that such an elegant experiment which so
nicely illustrates a basic phenomenon in semiconductor physics should not have been repeated
many times over if for no other reason than for its educational effect.

This situation stands out even more in contrast with the often-repeated Haynes-Shockley
experiment (4) which provides a measurement of the drift mobility of charge carriers in a
semiconductor by timing the arrival of a pulse of injected carriers at a point down the
electric field relative to the original point of injection into the bar. Because of its
fundamental nature and its simplicity, the Haynes-Shockley experiment has been repeated many
times over in a number of university and industrial laboratories since the description of
the experiment was first published. Now, the question is: why has the equally fundamental
and simple Brattain-Bardeen spreading resistance experiment not been repeated as many times?
I would like to suggest that the main reason is the experimental difficulty of the Brattain-
Bardeen measurement; it is no easy job to do a potential probe within micrometers of a
metal-semiconductor point contact. I believe that the significance to us of the familiarity
of the Haynes-Shockley experiment and the relative obscurity of the Brattain-Bardeen experi-
ment is that our experimental problems with spreading resistance contacts are not trivial
ones.

Before leaving this subject, I'd also like to point out that Brattain and Bardeen
credit W. L. Bond with construction of their micromanipulator. If we should ever need to
produce a name for an award of the like in conjunction with spreading resistance measure-
ments, I think that the name of Bond should be a front-runner.

Returning to the history of spreading resistance after Bardeen, Brattain and Shockley,
I must admit that I have no firsthand knowledge of developments during the 1950's. However,
the relationship between semiconductor resistivity and point-contact spreading resistance
must have been used off and on in semiconductor materials evaluation, at least sufficiently
so as to warrant inclusion in several publications, including volume 6, Part B of the book
"Methods of Experimental Physics", edited by K. Lark-Horovitz and V. A. Johnson (5). The
basic spreading resistance measurement method is described under the heading "Spreading
Resistance Measurements" in the chapter entitled "Conductivity Measurements on Solids".
The treatment, while brief, is complete in that it indicates both the high spatial resolu-
tion of the technique as well as its primary problem—that of determining true contact
dimensions.

My personal experience with the spreading resistance technique dates to the first job
I was assigned on beginning work at the Westinghouse R & D Center in June of 1959. At that
time, Westinghouse was in the middle of an extensive program to make use of germanium and
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silicon dendrites, produced by growth from a supercooled melt. The end product of the den-
dritic growth process was a ribbon or strip of semiconductor single crystal, having a width
of about 1 mm and a thickness of about 0.1 mm. The dendritic ribbon could be grown at a
rate of several feet per minute and produced in lengths of up to several hundred feet with
the dendrite being rolled up on a reel located above the crystal puller for storage and
later use. The plan was to make use of the nearly perfect surfaces of this material for
automatic device fabrication with no lapping, etching or other surface treatment of chips
needed. My job was to measure the resistivity of as-grown dendrites using a traveling one-
point potential probe.
Very soon after I began work (or perhaps even before that time) someone began to sus-
pect that the dendrite material being grown was too inhomogeneous in resistivity to be of
use in practical device manufacture. This later turned out to be the case and, unfortunate-
ly for the dendrite program, the inhomogeneities turned out to be inescapably associated
with the fundamental growth habit of dendrites.

However, before the demise of the dendrite program became certain, I was given the
additional task of developing some way of quantitatively evaluating dendrite cross-
sectional resistivity variations. I began with the point-contact voltage breakdown tech-
nique which had already come into use for evaluating N on N"*" epitaxial silicon (6). Figure
1 shows some raw data obtained on a dendrite cross-section which was grown from a melt con-
taining both P-type and N-type impurities. The conductivity type and the point-contact
breakdown voltages measured at various points on the cross-section are shown. The data show
that the central part of the dendrite (which grows first) is P-type of relatively lower re-
sistivity as compared to the "arms" of the H-structure pattern in which such dendrites grow.
The material between the "arms" of the H-structure solidifies last and is N-type. Although
the point-contact breakdown technique did work more or less, I eventually abandoned it be-
cause of inadequate reproducibility as well as the fact that it was difficult to obtain
absolute resistivity values over the wide range of both P- and N-type resistivities found
in the dendritic material.
I next tried to use free-carrier infrared absorption with a small diameter lightbeam
but soon found that, at least for me, this approach yielded a better thickness gauge than
it did a dopant-level monitor.
Meanwhile, the reproducibility of I-V characteristics observed during point-contact
breakdown voltage measurements as well as during low voltage point-contact rectification
type testing was so good that I was led to consider the possibility of making spreading
resistance measurements as described in the Lark-Horovitz book (5). I tried the technique,
using the same traveling one-point probe apparatus that I had inherited on coming to
Westinghouse, along with a Keithley 610A Electrometer. The 610A had an ohmmeter function
built in via a constant current generator and an electrometer measurement of the total volt-
age across the current output terminals. The key feature for me was that this instrument
had a useful sensitivity extending down to below one millivolt so that I was able to use low
enough currents for a given resistivity sample such that the spreading resistance meas-re-
ment could always be done with a total applied voltage in the vicinity of 10 millivolts.
With such a low bias level, significant change in sample resistivity due to injection of
excess carriers was avoided along with several other undesirable effects normally associated
with voltages much greater than kT/q (e.g., high-field mobility modification and contact
heating).

Figure 2 shows the probe and the 610A Electrometer as well as the stack of brass wash-
ers used to load the probe to 25 grams. This loading was used for germanium — I later
used 45 grams for silicon measurements. These load values were dictated by the desire to
have the load large with respect to frictional force in the distorted ball bearings used to
pivot the probe arm and yet not so large as to crack samples during probing. The probes
used were standard (at the time) phonograph needles.
Early results were encouraging. The spreading resistance values measured on a given
sample were reproducible to within a few percent and furthermore, the size of the micro-
cracked region left on the sample after a spreading resistance measurement agreed rather
well with the circular contact size expected on the basis of a Hertz formula calculation
for the case of a spherical surface having the radius of curvature of the phonograph needle
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mating with a plane surface (7). For the case of a silicon to osmium contact with a loading
of 45 grams, I calculated just under 4 micrometers for the value of "a" where "a" is the
radius of the contact spot.

The fact that the Hertz formula used in calculating contact size is based on the
assumption of elastic stress in the materials involved while the micro-cracking in itself
clearly indicated the existence of an inelastic situation didn't bother me much. A lot of
physical situations behave even when the underlying assumptions are violated somewhat.

What did cause me to pause for a long while in the early development of the technique
was the inability to fit a single value of "a" into the classical spreading resistance for-
mula for both P-type and N-type material. According to my understanding of the situation,
the simple formula Rg = p/4a should have applied (7). Thus, the calculated and observed
value for "a" should have been verified by a spreading resistance measurement on a single
sample of known resistivity. However, and unfortunately, things were not so simple. Mea-
surements on samples of different resistivities or of opposite conductivity types with the
same resistivity led to inconsistent results when compared to the values expected from the
simple Rs = p/4a relationship. At first, it appeared that the calculated value for "a"
would fit the experimental data if a proportionality constant "k" = about 3 were to be in-
serted for N-type material; i.e.

for P-type,

and for N-type,

However, with more careful measurements over a wider range(of P- and N-type resistivities,
I found that, in fact, k was not a constant at all but rather a complicated function of p
and that, furthermore, the k(p) function for P-type material differed from the k(p) for N-
type samples.

This situation led others then and later involved in spreading resistance measurements
to talk in terms of an "effective contact radius". I rejected the effective radius concept
from the beginning for two reasons: 1) it didn't make sense physically—I just couldn't
believe that impurity levels of one part per million or less could radically alter the hard-
ness of silicon and germanium; 2) a much simpler explanation was available in that osmium
has a larger work-function than silicon and should therefore make a rectifying contact on
N-type silicon and an ohmic contact on P-type. Thus, even at zero bias, an additional re-
sistance should be observed for the osmium, N-type contact as compared to the osmium, P-type
contact. The measured resistances for N-type and P-type samples were in the right direc-
tion—with the measured spreading resistance on 1 ohm-cm N-type silicon, for instance, being
about a factor of three larger than that measured on P-type 1 ohm-cm silicon. Furthermore,
a work-function barrier effect would cause a variation in measured spreading resistance with
change in sample resistivity in qualitative agreement with the shape of the k(p) function.

The work function-determined zero-bias barrier model even fitted the fact that I sub-
sequently found that "k" was not only a function of semiconductor material, conductivity
type and resistivity but that it also depended on the mechanical finish of a sample surface
and even the time elapsed between surface preparation and measurement. This behavior would
be consistent with a model based on a property such as the work function which would be ex-
pected to have some dependence on the physical and chemical nature of the surface.

Despite the magnitude of the problem involved in understanding the contacts used in
these early spreading resistance measurements, the high degree of reproducibility which was
experimentally observed suggested that I could get on with the job that needed doing by
generating a calibration curve of spreading resistance vs. resistivity through making mea-
surements on known resistivity samples. With this approach, the complications posed by the
complex dependence of the k-function on conductivity type and surface finish could be han-
dled by generating separate calibration curves for P- and N-silicon with a particular sur-
face finishing procedure that could be kept constant for both known-resistivity samples and
the unknown test samples.

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 With calibration curves so generated, measurement results were at least good enough to
successfully establish that germanium and silicon dendrites were extremely inhomogeneous in
dopant concentrations.
Another result of generating the calibration curves was the fact that I became con-
vinced that nothing other than a strongly empirical approach would suffice for further mea-
surements with the spreading resistance technique. This conviction grew out of the discovery
that the calibration curves for lapped and polished N-type silicon samples crossed each
other in the vicinity of 1 ohm-cm. This result (and the surface "aging" effects) clearly
indicated that spreading resistance measurements were affected by the electrical properties
of the silicon surface and that therefore, a satisfactory theoretical understanding was
beyond reach for some time to come.
Thus, my development work on the technique subsequent to this time was concentrated on
making the contacts as reproducibly as possible and on achieving the highest degree of re-
producibility possible in sample surface preparation.
Development work on the spreading resistance technique continued despite the close-out
of the dendrite programs because new programs arose in which high spatial resolution mea-
surements were needed, especially in research and development into the growth of multilayer
homo-epitaxial silicon structures for use in high-power devices. This work was primarily
under the direction of T, L. Chu who then headed the epitaxial growth work at the
Westinghouse R & D Center. Without his early support, the spreading resistance work at
Westinghouse might easily have ended in its infancy.
The state of development achieved during this part of the work at Westinghouse is
illustrated by the data and remarks presented as oral papers by myself and by Dave Dickey
at the ECS Meeting in Pittsburgh in 1963 (8).
The 1963 "state-of-the-art" is also well illustrated by the 1966 paper, co-authored by
Dave Dickey and me (9). This is so because this paper was my first and it took a couple of
years to actually get into print.
As is made clear in the 1966 paper, by the middle of the 1960's we had a useful and
practical technique. We knew that it involved three basic requirements:
1) Reproducible contacts; these had to be mechanically generated in such a way
that they were reproducible over periods of months or longer. They had to be
produced without even microscopic sliding or other motion during contact-make
and had to be capable of positioning within ±1 micrometer of a given standard
placement.
2) Low applied voltage; the voltage across spreading resistance contacts had to
be small enough so as to avoid significant amounts of carrier injection, con-
tact heating or the like.

3) Calibration; the spreading resistance technique is a comparison technique.

Unknown resistivity samples must be evaluated through the use of calibration
curves produced by making spreading resistance measurements on samples of known
resistivity (these calibration samples are generally measured with a 4-point
probe and are prepared so as to have the same surface finish as the unknown
resistivity material to be measured).
N.B. Because of this dependence on calibration, the results obtainable with
the spreading resistance technique are limited in accuracy only by the qual-
ity and the quantity of the calibration work done.
While the technique practiced up until 1966 was a manual one, it was useful and prac-
tical. This is illustrated by Figure 3 which is a resistivity profile produced by the man-
ual spreading resistance technique as of about 1962. Figures 4 and 5 illustrate early use
of the automatic spreading resistance probe at Westinghouse in profiling thick epitaxial
structures then under development for power device use. A typical process-control problem

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which illustrates the need for spreading resistance data is shown by the defective profile
of Figure 5. Figure 6 illustrates a typical N on P+ epitaxial structure.
The main drawback to our measurements at the time involved the need to correct the raw
data in order to obtain true resistivity/impurity concentration values in thin layers of
interest. This need arose because of the existence of two basic assumptions in the deriva-
tion of the equation Rg = p/4a, i.e.:
1) all sample boundaries are at "infinity", i.e., far away from the contact as
compared to the size of the contact (see Holm (7)).
2) the resistivity in the semiconductor sample is uniform throughout.
The paper by Dickey (8) gives a theoretical solution to the boundary condition imposed
by the presence of an (insulating) p-n junction within several contact diameters or less of
the probe. The results and limitations of this and several other correction schemes will
be the subject of several papers to be presented here in the next two days. Suffice it to
say that the correction factors are probably the greatest problem in the use of spreading
resistance measurements today.

3. The Nature of the "Conditioned" Probe

Rather than getting into any discussion at all of correction factors, I'd like to use
my remaining time to get into the second part of this talk. This involves abandoning the
historical approach in order to present a contact model and some remarks which will reflect
my best current understanding of the mechanical and physical aspects of what I call
"conditioned" probes.

I believe that this aspect of the spreading resistance technique is worth taking the
time for now for three reasons:

1) "conditioned" contacts are the primary requirement for a practical spreading

resistance measurement technique;

2) the mechanical aspects of spreading resistance contacts have not been dis-
cussed in detail in the published literature;
3) I believe that a realistic picture of the contacts used for spreading resis-
tance measurements is fundamental to proper understanding and use of measure-
ment results.

In my early attempts to get around the problem posed by not being certain of the true
dimensions of the spreading resistance contacts, I elected to proceed by first assuming that
the Hertzian value for "a" as calculated was correct. This then suggested that 1 fi*em P-
type silicon involved a barrier free contact and led to the selection of 1 fl»cm P-type
samples for use in checking probes. On such samples, measurements should depend only on
geometrical spreading resistance. These standard samples eventually became our "QTA"
samples, with "QTA" being an abbreviation for "Qualification, Test and Alignment".

During subsequent checking of probes on these samples, I found that, despite the fact
that new probes would have a variable and relatively high measured spreading resistance when
first run, they would subsequently show a lower and quite uniform value after being used in
making spreading resistance measurements on lapped (bevelled) samples. Typically, new
probes would give values of up to three or four thousand ohms on the QTA sample, but, after
running on lapped samples for one or two thousand measurement points, the probes would con-
sistently show a decrease of measured QTA resistance to about 600 fi.

This behavior, when viewed in the light of the known inability of simple cleaning pro-
cesses to remove all residual abrasive from lapped silicon samples, led me to begin thinking
of the probes as undergoing some kind of "conditioning" process. This process was not at all
well understood but the results were so reproducible from one probe to another that I felt
justified in using probes so "conditioned" for routine measurements—depending, of course,
on calibration curves for absolute results.
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 My understanding of the conditioning process has increased only slowly over the years<—
mostly as a result of using hundreds of probes on many individual pieces of spreading re-
sistance apparatus over a long period of time. While I still cannot claim complete under-
standing of the process, the attainment of stabilized measured spreading resistance values
on a standard (QTA) sample for many different probe tips strongly suggests the achievement
of a mechanically reproducible contact situation subsequently involving only elastic defor-
mation of the metal probe.
Furthermore, while it is well known that the true electrical contact area between con-
tact members is small as compared to the size of the apparent contact region (7), experi-
mental evidence shows that even the apparent area of the spreading resistance contacts being
used for measurements is very small — for the 45 gm probes used in my early work, the over-
all contact area was 5 * 10~7 cm2. It seemed obvious that there had to be some limit to the
"normal" orders-of-magnitude difference between apparent contact size and the actual
electrically-conducting contact size; i.e., given a conducting region small enough and with
sufficiently high pressures, the electrically-conducting contact size should approximate the
apparent contact size. This idea eventually became embodied in a definition of a useable
and practical "conditioned" spreading resistance contact.
Basically, by a "conditioned" probe, I mean one which is so contoured and chemically
treated that, despite the fact that the surface of the probe is rough on a micro-scale, the
micro-contacts made by it when it is set down on a silicon surface are sufficient in number
and grouped closely enough so that the overall effect is as if there is a single circular
contact of specific, reproducible radius "a". A corollary idea is that, under these condi-
tions, "a" is large enough relative to the load applied that the pressure at the metal semi-
conductor interface will be within the elastic range of the metal involved and the contact
will therefore be mechanically reproducible.
A rather complete treatment of the geometrical concept behind this definition of a
"conditioned" contact is contained in the work of J. A. Greenwood (10).
I can also offer a few further remarks relative to the details of spreading resistance
contacts and probes which may aid you in becoming comfortable with the idea of a
"conditioned" probe.

The probes used for spreading resistance measurements are initially imperfectly
contoured—they are nominally of a one mil (25 ym) radius of curvature at the tip and are
otherwise contoured as shown in Figure 7. The probe tips are rough on the micro-scale,
having a surface roughness of approximately 1 urn. Thus, when set down on a smooth silicon
surface, they initially contact the silicon at several randomly-scattered points correspond-
ing to high-spots in the tip-contact region. As the load on the probe increases, the con-
tact area increases, both by enlargement of the first contact spots and contact-make at new
spots.

The initial contact points are the regions under which the applied pressure first ex-
ceeds the fracture stress of the silicon material and are therefore the points from which
micro-cracks will radiate upon lifting the probe. Note that it may be possible for the
stress at some of the later contact points to be large enough to crack and displace the
brittle silicon oxide layer while not becoming great enough to cause cracking in the silicon.
This would result in no micro-cracks radiating from these points and hence no way to visually
tell afterwards that electrical contact was made at such a point.

Furthermore, current density is quite non-uniform in a flat circular contact—very

little current flows through the center of the contact. Therefore, lack of true electrical
contact in the central region of a contact pattern will in general not appreciably affect
the measured spreading resistance. One way of looking at this is to observe that in using
contacts for spreading resistance measurements, we are primarily concerned with the
perimeter of the contact.

The model as described here also suggests that the individualized patterns of micro-
cracks observed for a particular probe are primarily indicative of the detailed micro-
topography of that probe tip and are not necessarily directly related to the electrical
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properties of the final contact. Therefore, detailed study of contact-spot micro-crack
patterns may well turn out to be a study of the micro-metallurgy of osmium-tungsten (or
whatever other material the probe is fabricated from) rather than anything else.
Thus, I now see the "conditioning" process as one wherein the probe tip is so con-
toured and roughened (on a micro-scale) that, when properly placed on a silicon surface,
it produces a contact which may well be a cluster of micro-contacts but, if so, the cluster
is so grouped that the result is the same as if the electrically-conducting area was a
single spot with the radius "a" given by the Hertz relationship for the probe radius of
curvature and the load and materials involved.
Given acceptance of this "conditioned" probe concept and definition and the equipment
capable of producing such contacts without sliding or other mechanical problems, the prac-
tical problem becomes one of knowing when the "conditioned" contact situation is reached.
I believe that the primary criterion for assessing contact quality must be a repro-
ducibility check on a standard sample. In line with this approach, we use slices taken
from a common batch of 1 ohm-cm, p-type silicon wafers which were "chem-mechanically"
polished years ago. Through direct experience, we have been able to establish practical
limits for spreading resistance values obtained on these standard samples for conditioned
probes under normal conditions.
The criteria and limits that we now suggest are the following:

Table 1

a) Probe Load 45 gms 20 gms

b) Measured resistance per probe on
UNREFINISHED QTA sample 300-700 ohm 600-1000 ohm
c) Diameter of Circumscribed Circle
around contact spot pattern 8-9 ym 5-6 ym
In addition to these criteria there are several other "characteristics" of conditioned
probes that may be useful in your evaluation of the suitability of particular probes for
spreading resistance measurements. These are:

1) conditioned probes make contacts whose measured spreading resistance on QTA

samples is relatively stable in time. Where vibration is not unusually severe,
measurement values on QTA samples will remain stable within several percent or
less after a typical initial increase of approximately 5%.
2) conditioned probes yield measured values on QTA samples which are much more
uniform from one point to the next than are the values obtained with uncon-
ditioned probes.

3) conditioned probes are more easily seen in the microscope than are uncondi-
tioned probes, probably because of a larger number of micro-contacts with a
resultant increase in light scattered from the (111) plane facets produced
by fracture.

The remarks that I offer here are based on my own attempts to rationalize the behavior
of spreading resistance probe contacts during measurements over a period of some 13-14 years.
I hope that these comments will assist others in increasing their understanding of the
physics and mechanics of the "point" contact used in the spreading resistance measurement
technique.

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 References

1. H. C. Torrey and C. A. Whitmer "Crystal Rectifiers", 1st ed., McGraw-Hill Book Co

New York (1948).

2. J. Bardeen and W. H. Brattain, Phys. Rev. 74, 230 (1948).

3. W. H. Brattain and J. Bardeen, Phys. Rev. 74, 231 (1948).

4. J. R. Haynes and W. Shockley, Phys. Rev. 75, 691 (1949).

5. "Methods of Experimental Physics" V. 6, Part B, Solid State Physics, ed. by K Lark-

Horovitz and V. A. Johnson, Academic Press (1959).

6. J. Brownson, J. Electrochem. Soc. Ill, 919 (1964).

7. R. Holm, "Electric Contacts Handbook", 3rd ed. Springer, Berlin (1958).

8. R. G. Mazur, Abs. No. 56 and D. H. Dickey, Abs. No. 57, Papers presented at the
Pittsburgh Meeting of the Electrochemical Society, Spring, 1963. See Extended
Abstracts of the Electronics Div. Vol. 12, No. 1.

9. R. G. Mazur and D. H. Dickey, J. Electrochem. Soc. 113, No. 3 (255-259) March 1966.

10. J. A. Greenwood, Brit. J. Appl. Phys., 17, 1621-1631 (1966).

Figure 1 - Map of a three-zone dendrite cross-section, showing the experimentally-

determined conductivity type and point contact breakdown voltage as a function
of position on the cross-sectional surface. Vertical:approximately 0.25 mm;
Horizontal:approximately 0.9 mm.

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Figure 2. The first Westinghouse spreading re-
sistance probe apparatus.

Figure 3. Spreading resistance - derived resis-

tivity profile of a defective epitaxial thyristor
structure: manual probe data, circa 1962.

Figure 4. Early automatic spreading resistance

profile of a P+ NN+ epitaxial power device
structure.

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Figure 5 - Early automatic spreading resistance profile of _
a P+ NN epitaxial structure with an anomalous profile due to
lack of epi-dopant control during the early stages of growth.

Figure 6. A typical N on P+ epitaxial structure

as profiled with the automatic spreading resis-
tance probe.

Figure 7. Shadow graph of two spreading resis-

tance probe tips with a 10 ym stage micrometer
scale.

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 This page intentionally left blank

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

The Physics of Spreading Resistance Measurements

Stephen J. Fonash
Engineering Science Department
Pennsylvania State University, University Park, Pennsylvania 16802

The spreading resistance method is uniquely suitable for the deter-

mination of electrical resistivities in a number of situations. However
the technique does not simply measure the resistivity beneath the con-
tacts. Considering the two probe configuration, what is actually meas-
ured is the ratio AV/I. Here AV is the difference between the Fermi
levels of the probes necessary to maintain the sampling current I. This
difference in the Fermi levels of the probes depends on the zero bias re-
sistance of the probe - semiconductor contacts, the effective resistivity
of the layers in a multilayer structure, and the configuration of the
structure. The zero bias resistance depends on temperature and details
of the metal-semiconductor contact including surface history. Effective
resistivities enter into the measurement - and not the actual resistivi-
ties - because of the fact that the use of pressure probes creates a
stress field under the contacts. This field falls off with a character-
istic length of the order of the contact radius. Thus piezoreslstivity
effects - well known for Si - can be operative under the contacts. As a
consequence of these various effects the interpretation of what AV/I is
actually measuring is not straightforward. Practical application of the
spreading resistance technique necessitates making certain simplifying
assumptions. In light of the various phenomena involved in-a spreading
resistance measurement it is imperative that the implications of these
assumptions to the accuracy of the measurement be understood.

Key words: Correction factor; crystallographic orientations; effective

contact radius; interfaces; metal-semiconductor contacts; multilayered
structure; piezoresistivity; resistivity; spreading resistance; stress;
zero bias resistance.

1. Introduction

The use of the spreading resistance technique 11-5] for resistivity measurements in
homogeneous and inhomogeneous semiconductor materials is finding increasing popularity.
Ostensibly this method is quite simple and straightforward. However, due to geometrical

Figures in brackets indicate the literature references at the end of this paper

17
effects, the presence of material interfaces, the presence of space charge regions, and the
presence of stress fields, there are a number of physical phenomena which come into play
when this measurement is made. An understanding and appreciation of these various phenomena
involved in a spreading resistance measurement is necessary for a meaningful application of
this technique.
To determine what physical phenomena are playing a role in spreading resistance measure-
ments and to determine how they influence the measurement a simple two probe configuration
t2j will be assumed for this discussion. (See figure 1) Obviously the conclusions that will
be reached can be applied to other configurations used in spreading resistance measurements.
As is shown in this figure, it is also assumed that this measurement is"being made on a lay-
ered structure for generality.
In the configuration depicted, a current I is flowing into probe contact one and flow-
ing out of probe contact two. These metal probe-semiconductor contacts are, ideally, flat
circular areas whose radii are determined by the force on the probe and the Young's moduli
of the metal and the semiconductor C3,(G • The electrostatic potential ty which is set up by
this current flow must be such that

(all r)

and

(all r not under the contacts)

Under the contacts, since there is a current flowing,

In addition, since no current flows out the sides of the structure,

where X is a coordinate normal to any lateral surface under consideration.

These four statements constitute very general constraints on 1^1, the electrostatic
potential. However ty as a function of position in the structure must actually be found
since the potential difference AV between the probes, necessary to drive I, is to be com-
puted. Really it is the ratio AV/I which is to be found since this is the quantity measured
by the spreading resistance technique

2. The Physical Phenomena Involved

To beby more
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where the subscripts refer to a polar (r ,6) coordinate system situated, for convenience in
discussing this integral, at the center of circular contact one. This expression assumes
that, just beneath the metal probe-semiconductor contact, the current is carried by drift
in the semiconductor. The need for an effective resistivity - instead of the actual re-
sistivity p - will become apparent; p ff reduces to p in the absence of a mechanical stress
field. The fundamental question, what does AV/I measure, can be answered by a study of
eq. (5)
It is clear that eq. (5) underscores the necessity of finding the electrostatic
potential ty - i|;(r ,0 ,Z) in the semiconductor. At first glance this is straightforward since
\l> should satisfy Laplace's equation in the semiconductor and it is known to be subject to
the boundary conditions given by eq. (1) - (A). However, the potential difference measured
between probe one and probe two, the quantity AV, is the difference between the Fermi levels
(electrochemical potentials) of the two metal probes. Thus, if ty is to be written in terms
of AV as it must be to obtain an answer from eq. (5) which depends only on the structure, it
is necessary to relate the Fermi level in metal one to fy in the semiconductor beneath con-
tact one. Correspondingly it is necessary to relate the Fermi level in metal two to ty in
the semiconductor beneath contact two.
With a layered structure such as that shown in figure 1, a second problem becomes
apparent: ^ does not satisfy Laplace's equation in the interface regions. In these inter-
face regions (1 - between layers I and II, 2 - between layers II and III, and 3 - between
III and IV) there is an assumed abrupt change in resistivity. That is, in the interface
regions, a transition occurs from one value of doping density to another. Figure 2 shows,
in cross-section, some region of interface 1, for example; figure 3 shows the band diagram
for this cross-section. In general these transition layers are of width w. where j = 1,2,3.
From figure 3 it is seen that a charge density a. exists in these interface regions.
Consequently

may be assumed valid for layers I, II, III, and IV; it can not be assumed valid for the
interface regions.
Considering the first problem, it is apparent that a boundary condition at the contacts
relating the Fermi levels of the metals and fy is needed £7]. If the electrostatic potential
in the semiconductor is measured (see figure 4) henceforth with respect to the Fermi level

2
The electrostatic potential in the semiconductor is measured positively down, from the
Fermi level of probe two, to the position of the Fermi level in the semiconductor in this
analysis. See figure 4.

19
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of metal probe two, then it follows that the current density normal to the contact at some
point ( r 2 > 6 a ) in the metal-semiconductor boundary two is continuous at the boundary and that
D,<3

Here 1^2 is the value of fy under this contact (ie, Z = 0) at some general (r^a) > this polar
coordinate system at contact two is defined analogously to (rl56i). A similar condition may
be developed for contact one; ie, £7,8}

where 4>i is the value of ip under contact one (ie, Z = 0) at some general (ri*6fc). Of course
AV is the difference between the Fermi levels of the probes, as stated previously.

The quantity C is the reciprocal of the zero bias resistance of the contacts per unit
area. They have been assumed to be identical. Equations (7) and (8) - as well as the re-
maining analysis - assume that the bias AV is small compared to kT so that the J-V
characteristics of the metal-semiconductor contacts may be linearized.^ Equations (7) and
(8) may be written in integral form as

and

These constraints are placed on the solution to eq. (6).

Having related fy to the metal Fermi levels through eq (7) and (8) - a necessity since
it is the difference between these Fermi levels which is actually measured - it is now
possible to turn to the problem posed by the interfacial regions between layers. Rather
than finding the electrostatic potential in these space charge regions DQ, an alternative
approach is to relate the solutions for ^ in two adjacent layers. If these interfaces are
sufficiently thin, the current normal to these transitions regions is constant through the
regions (9,10). Thus it follows that (see fig. 2 and 3)

3As is discussed in ref. 00, the current density depends on the difference in the Fermi
levels between the metal and the semiconductor. If the general expression for this current
density given in ref. DO is linearized about zero bias, (7) and (8) result. That is, the
right hand sides of (7) and (8) are just Taylor series expansions of the J-V characteristics.
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is one such relation joining solutions in adjacent layers. Since eq. (6) is second order,
another joining relation is needed OJ,10j. Following reasoning similar to that which led to
eq. (7) and (8), it is seen that this relation is provided by

where all of these quantities in eq. (12) can depend on position in the boundary planes Z =h
and Z = h. + w. of interface region j . -*

Of course, rather than using eq. (11) and (12), one could determine the electrostatic
potential in the interface regions by solving Poisson's equation C?D • Boundary conditions
would then be imposed on the electrostatic potential and its normal derivative (the electric
field) at h. and h. + w., if this approach were selected. Such an approach is, of course,
an exact one as opposed to the approximations (eq. (11) and (12)) involved in the alternative.
From a practical point of(view, one is forced to select eq. (11) and (12) in dealing with
these interface regions £9j.
With either approach ^ is completely specified in the semiconductor. Further, it must
obey eq. (l)-(A) as well as conditions (9) and (10). Thus in principle ij> can bfi completely
determined and the resistance measured experimentally (ie, eq. (5)) can be evaluated in terms
of the material parameters of the semiconductor structure. That is, it is possible to
establish what is being measured by the ratio AV/I. Unfortunately, examination of the
conditions on fy as developed above demonstrates that the ratio AV/I can not just depend on
the resistivity beneath the contacts since ty does not. From this development presented it
is clear that AV/I will depend on C, the parameter characterizing the probe-semiconductor
contacts, on the geometry, the interfacial regions and the effective resistivity p ff.

At this point it is necessary to establish why it is an effective resistivity that

enters into ijj and, therefore, into AV/I. This effective resistivity that appears in the
conditions imposed on i|> (see eq. (7),(8),(11) and (12)) arises from the presence of stress
fields in the material. As is well known, in the presence of a stress field the resistivity
must be expressed as a second rank tensor p [11,123; thus

where p is the scalar resistivity (in the absence of any stress). The second rank tensor.^
is related to the stress tensor Jj;. by the fourth rank piezoresistance tensor J^*[jll»l2J Of
course A vanishes if there is no stress field. Obviously there is a stress field under the
probes [3,13J. This could even extend down (see figure 1) to at least the first interfacial
region.

So it is an effective resistivity - determined from eq. (13) - which enters into if;. If
the probe has a pressure p applied to it, then for a {100} plane on Si (n or p type) p
e
under the contacts is given, after some manipulation, by

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For contacts on a {ill} plane, the corresponding expression is

for n or p type Si. Here the II.. are components of a collapsed H.

Using data for the It in the literature D-1,1^ and p .= 10 dynes/cm2 results in the
determination that, for • {100} planes, under the contacts

for n-type Si

and

for p - type Si

For {111} planes, under the contacts

for n - type Si

and

for p - type Si

Unfortunately these are just estimates since data at high stress levels are not avail-
able for the II . and the II . depend on doping. However, the point has been made that an
effective resistivity - duetto stress - enters into ty. Whether or not p differs signifi-
cantly from p depends on the stress and the crystallographic orientationf On the basis of
eq. (18) and (19) alone one would estimate that the measured resistance AV/I, for a given
resistivity, would be lower for p-type material than for n-type if both had a {ill}
orientation and identical contacts and geometry. This piezoresistance effect may also be
at least partially responsible for correction factors of less than unity which are seen on
p-type Si. D-4J.

The zero bias resistance per area of the probe - semiconductor contacts, which enters
into \p and, therefore, into AV/I, also depends on stress. In fact C is a function of the
stress, temperature, doping, and crystallographic orientation flA-Kj). The quantity C de-
pends, in addition, on surface history. D-4,16] Thus, in a spreading resistance measure-
ment, AV/I depends on considerably more than just the resistivity of the material beneath
the contact, as this above development has indicated.

3. Practical Considerations

The measured quantity AV/I depends on the contacts, mechanical stress, temperature, and
the geometrical configuration of the layers as well as their resistivity and transition
regions. Therefore, it is not surprising that, to employ the spreading resistance technique,
it is necessary to assume that the resistivity of layer I (see figure 1) is related to the
22
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measured AV/I by

where K is a correction factor and the remaining terms are the ideal spreading resistance
for a semi-infinite slab using the two probe configuration £17} . The quantity a f should
be the radius of the contacts - a quantity depending only on the mechanical properties of
the probe - semiconductor system. In actual fact, if K is used to correct for structure
(that is, used in some manner to account for eq. (11) and (12) as is done in ref. D-7]), it
is found that a ff is an effective radius not a geometrical radius. It can vary by a factor
of more than 2 with resistivity D-7J and in practical applications is determined from a
calibration curve obtained from a body of uniform resistivity. Obviously the effective
radius is attempting to account for the various other phenomena involved in a spreading
resistance measurement which were discussed in section 2.

It is interesting to establish how eq. (2) may be obtained from eq. (5), a statement
which is fundamentally correct. If eq. (5), (7), and (8) are manipulated, it follows from
some straightforward algebra that eq. (5) can be written as

where the probes have been assumed identical. In the term involving ipi and ^2 » it is
necessary to evaluate these quantities at equivalent points under the contacts in integrating.
Obviously the first term on the right may be interpreted as a resistance arising from the
contacts only. The second term involves (through the conditions on ty) the contacts, the
geometry of the layered configuration, the interfacial regions, and the piezoresistivity
effects.

If C is assumed constant and very large (ie, ohmic contacts between the probes and the
semiconductor) the metal Fermi levels line up with the Fermi level of the semiconductor just
beneath the contact. Thus in this case, ^2 * 0 and ty\ = AV replace eq. (7) and (8) and eq.
(21) reduces to

Using an approximation in eq. (22) for ij) proposed by Schumann and Gardner [<Q allows eq. (21)
to be finally reduced to

where K is a function of the various layer resistivities (which may actually depend on stress
at least for the first layer), the radius a, and the geometry RJ . Of course, here a is the
radius of the contacts.

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23
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 The approximation for TJJ used to obtain eq. (23) assumes the C. of eq. (12) are infinite.
Further it does not obey the conditions ij^i = AV and tyz = 0 applicable in the assumed case of
ohmic contacts but rather fits a postulated current distribution under the contacts - an
expediency used to avoid mixed boundary conditions [9j . Thus if the K of Schumann and
Gardner is used in eq. (2), a ff is attempting to account for piezoresistivity and the zero
bias resistance of the contacts. It can not account for the C, quantities of the inter-
face layers since it is usually obtained from a calibration curve for uniform material.

Thus using eq. (21) and a K developed as indicated is beset with assumptions and
simplifications. This fact has led Hu pjQ , in commenting on the limits of accuracy one
could expect from eq. (21) , to note that this "mathematical model of the multilayer
spreading resistance rests on a number of simplifying assumptions, most of which are not
accurate . "

4. C onclus ions

From eq. (21), it can be seen that the quantity being measured for the structure shown
in fig. 1 is

where R is a measure of the contact resistance only and R depends on the contacts, the
resistivities, and the geometry of the structure. If eq. (20) is used for R, the accuracy
of the measurement is limited obviously by the choice of K and a ; that is, the accuracy
is limited by the approximation used for ty in the term

In practice the term involving R in eq. (24) is frequently neglected.

5 . References

(1) Holm, R., Electric Contacts Handbook, (10) Brook, P. and Smith, J.G., Electronics
Springer, Berlin (1967). Lett., £, 253 (1973).
(2) Gardner, E.E., Hallenback, J.F., and (11) Smith, C.S., Phys. Rev. 94, 42 (1954).
Schumann, P. A., Solid-St. Electron, j6, (12) Smith, C.S., Solid St. Physics (F.
311 (1963). Seitz and D. Turnbull, Eds.) 6^, 175.
(3) Mazur, R.G. and Dickey, D.H., J. Academic Press, Inc. N.Y. (1958).
Electrochem. Soc. 113, 255(1966). (13) Severin, P.J., Solid St. Electron.
(4) Gupta, D.C. and Chan, J.Y., Rev. Sci. 14, 247 (1971).
Instr. 41, 176 (1970). (14) Kramer, P. and Van Ruyven, L.J., Solid
(5) Schumann, P. A., Gorey, E.F., and St. Electron. 15, 757 (1972).
Schneider, C.P., Solid St. Tech. 15, (15) Kramer, P. and Van Ruyven, L.J., Appl.
50 (1972). Phys. Lett. 20, 420 (1972)
(6) Kramer, P. and Van Ruyven, L. , Solid (16) Fonash, S.J., J. Appl. Phys., 45_, 496
St. Electron, 15_, 757 (1972). (1974).
(7) Foxhall, G.F. and Lewis, J.A. , Bell (17) Hu, S.M., Solid-St. Electron. 15_, 809
System Tech. Journal. 43_, 1609 (1964). (1972).
(8) Fonash, S.J., Solid St. Electron, 15,
783 (1972).
(9) Schumann, P. A. and Gardner, E.E., J.
Electrochem. Soc: Solid St. Sci. 116,
87 (196by
Copyright 9).
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 Figure 1. Configuration for Spreading Resistance Measurements on a Layered Structure.
The Two-probe setup is shown.

Figure 2. The Transition -or Interface- Region Between Two Ideally Uniform Layers.

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 Figure 3. An Energy Band Diagram Through an Interface Region Such as That
Shown in Figure 2. Bias Drop Across this Region is Indicated.

Figure 4. Diagram Showing the Energy Band Bending Under the Contacts. Also
indicated is the reference electrostatic Potential.

26

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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

FORMAL COMPARISON OF CORRECTION

FORMULAE FOR SPREADING RESISTANCE
MEASUREMENTS ON LAYERED STRUCTURES

P.J. Severin

Philips Research Laboratories

Eindhoven, The Netherlands

The spreading resistance of a metal contact on a

semiconductor sample is analysed for infinite geometry, with
three different boundary conditions: a specified potential
of the contact, a uniform contact current density and a
current density dependent on contact resistance. The cases
of a thin layer on a perfec'tly conducting substrate and on
a non-conducting substrate are analysed each for the
boundary conditions of uniform current density and of the
current density distribution valid for the infinite
geometry. With a perfectly conducting substrate the two
boundary conditions yield about 1O$ difference. With a
non-conducting substrate calculations based on both
current density distributions produce in the thin layer
approximation the same In r dependence required. The
constant terms in both approaches are different by 5%
and the constant current density result in addition agrees
with the result obtained with a totally different trans-
mission-lbe approach. The actual three-point-probe
measurement situation is discussed. The danger of correcting
the precise spreading resistance measurement results with
an error of 1$, with formulae derived on the basis of a
formal model which is sensitive to the choice of the
boundary conditions by up to 10$, is stressed. The effects
of undefined thickness, bevel edge and transition layer
curving upwards are mentioned as further complications.

Key words: Contact resistance, correction formulae,

sheet resistance, silicon, spreading resistance.

1. Introduction

Spreading resistance measured on a structure of infinite lateral ex-

tent, but finite layer thickness d is different from the spreading
resistance measured on an infinite geometry. Their ratio is generally
referred to as a correction formula for a finite thickness measurement
result. Such formulae have been derived by Sphumann and Gardner[1], initial-
ly for a two-layer system and extended later (2Jto a. graded structure. This
theory has been used in computer solutions by Yeh[3j, Kokhani [^) ,. Hu [5j
Some preliminary studies are available in the form of reports [6, 7] •
In the standard solution for infinite geometry a constant potential
V of the contact of radius A is specified and the potential V(r,z) and
the current density distribution J (r,o) over the contact are calculated.
In the approach followed by Schumann et al.ftjto solve the potential for
finite layer thickness d the same current density distribution J (r,o) is
2

figures in brackets indicate the literature references at the end of this paper.
27
used to calculate V(r,o). The potential V of the probe is obtained by
averaging V(r,o) over the contact area. This problem is solved for any
ratio of the resistivities ^ of the layer and p^ of the substrate. In
order to check the validity of this approach we have studied the sensitivi-
ty of the solutions for the two limiting cases p^ - O and f^ = o» to the
choice of the boundary conditions. In particular we studied the cases
d /A « 1 and d/A » 1,which have well known solutions.
In the next section the case of infinite geometry is investigated
using the conventional approach (2.1) and assuming a uniform current
density over the contact (2.3). The effect of the boundary condition
resulting from contact resistance which modifies the current density
distribution over the contact, is also examined (2.2). In the fchird section,
devoted to the case O, = O, the approach of Brooks and Mattes [8]is shown
to be incorrect (3-1) and the approach with uniform current density over
the contact (3.2) is compared to the results obtained by Schumann et al.[l]
(3.3). In the fourth section, devoted to the"case j>% - oo , the same two
approached are again compared,(4.1) and (k.2),and both approximations are
found to yield divergent integrals for v(r,z). When the difference between
the potential V of the contact and the potential V(r,o) is introduced
the malignant terms cancel. With both approaches in the thin layer approxi-
mation the satisfying result is found that the potential depends on r as
In r ,(4.l) and (4.2). This is also the experimentally verified result of
an elementary consideration (4.3). A transmission-line approach, valid for
thin layers with a contact resistance whish influences the current distri-
bution at the contact, described earlier[9}, is compared with the present
results (4.3). In the approximation of dominant contact resistance this
transmission-line approach produces exactly the same expression as did the
uniform currrent density approach (4.1). Schumann's approach yields a
slightly different result. Spreading resistance measurements are essential-
ly three-point-probe measurements. Two different probe configurations are
currently in use with^different but related formulae. The difference in
particular for thin layers is discussed in the fifth section.
The experimental results of spreading resistance measurements are
extremely precise fio], about 1$. The conversion to the local resistivity,
let alone to the local dope atom concentration, is hindered by the uncer-
tainties originating from the choice of a not sufficiently realistic model
for a thin layer structure. In addition to this, the effective contact
resistance due to micro-contacts, deeper damage or barrier-resistance,
should be taken into account. Furthermore, the effects of the bevel edge,
of the finite transition layer at the interface and of the modification of
the transition layer due to the exposure at the bevel are mentioned in
the summary.

2. Infinite geometry
The potential distribution due to a circular metal disk of radius A
at potential V on a semi-infinite medium of resistivity g has been
discussed by various authors. Formulated in this way or as the problem of
a charged disk on top of an isolating medium it is a classical text book
example of the application of mixed boundary conditions [11 , 12]
2.1. Mixed boundary conditions solution
In cylindrical coordinates,shown in figure 1,the potential V(r,z) is
a solution of Laplace's equation, which reads for circular symmetry

28
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The solution can be easily obtained with separation of variables to be
given in terms of a Bessel function J (kr)

In this solution as a first boundary condition has been used

V(r, «o ) = 0, and the second boundary condition at z = O is of
a mixed nature"[12], for the potential of the contact

for
and for the electric field strength

for
To this set of dual integral equations

7T -A
is known to be the solution because

for

for
and
for

for
so that the potential becomes

The current i flowing into the metal contact is given by

which with eqs (6) and (5t>) becomes

or

the well known spreading resistance formula for infinite geometry. It is

interesting to note that the electric field has infinite strength at
r = A, which is physically unrealistic.

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 2.2. The influence of contact resistance
on the current density distribution.
In practice the ideal spreading resistance as given by eq. (8a) is
seldom or never measured. The contact to the semi-conductor is not as
perfect as it is supposed to be in formulating the problem: usually- an
extra voltage drop -is noted due to zero-bias-barrier resistance fl3t1^], a
multitipped[lO ^ 15 , 16] or otherwise incomplete contact. This effect is
usually taken into account by calibrating the probe so that the effective
spreading resistance

or introducing a series contact resistance R to

However, it is not self evident that the extra voltage drop can be
considered as being due to a series resistance which does not influence
the current density distribution over the contact area. This problem can
be analysed as follows. The boundary condition which incorporates the
1
specific contact resistance Rc ( Si. cm ), is

which with and

gives

The contact resistance makes the mixed boundary conditions quite

complicated, but by choosing an oblate spheroidal coordinate system the
same boundary conditions can be formulated conventionally [17 ]• With the
coordinates shown in figure 2,

Laplacefs equation can be separated by putting

into

The solution to eqs (l2b) and (l2c) in terms of Legendre polynomials

P (x) and Q (x) reads

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From the boundary conditions it follows that some coefficients are zero,
because with r, z -»o» likewise -»j -^ oo , and P (z) —> o» as z , the
coefficients c =O to satisfy V -* O, for r,z -»o«. Because at £ = O
the electric fieldj

the solution should be even inj. Finally Qn (5) has a singular point at
*~ 1 so that the coefficient bn must be zero. Hence the solution is

When this solution is subj ected to the newly formulated boundary condition,
eq. (lOb), the condition to be satisfied reads

This condition can be converted into an infinite system of linear equations

for the unknowns a_ , which upon proper truncation can be numerically
solved to the required precision. The total current iQ can then be easily
calculated from

The calculation of a has been done and the surprising result is that
for the parameter A/A assuming the values 0, 0.1, 1 and 1O the resis-
tance is, by at most a few percent larger than the resistance obtained by
simply adding G^/irf)* and ^/V/9 in series. The parameter A/A,
apart from a factor w/V , is equal to the ratio of these two resistances
and the range investigated covers any practical situation. Hence in the
infinite geometry the separation implied in eqs (9) and (9a) turns out to
be allowed. However, the effect of contact resistance R on spreading
resistance is more complicated in a finite geometry. An example is treated
in sec. k.k
2.3. Solution with uniform contact current density distribution

An alternative way to avoid the mixed boundary conditions and the

infinite field strength at r = A is to specify the electric field, instead
of the potential at the contact. The electric field corresponding to a
uniform current density distribution at the contact is given by
for 0 < r < A
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and, as before,

for r > A.
The potential of eq. (2) then yields

for

for
and f(k) follows from comparison with

for

for
so that the potential reads

According to this equation the potential at z=O of the contact depends

on r. This is a direct consequence of the choice of the uniform current
density boundary condition. By averaging the potential V(r,o) over the
contact area Vo', expressed
^ in R s = Vo/io'. is found to be

It is to be concluded that at least for the infinite geometry this

approximation of an uniform current density at the contact is a fairly
good one, differing by only 8$ from the result in eq. (8a).
It is worth noting here that R has never yet been verified with
sufficient precision to be able to decide unequivocally between eqs (8a)
and (20). Generally, spreading resistance measurements are hampered by a
large contact resistance, which has not been determined separately with
sufficient precision and accuracy. An experimental determination of R /O
within a few percent error, was done recently with a mercury probe [18].
Because the mercury probe has a much larger contact diameter 2A=1 mm than
any conventional probe and should be applied on a carefully prepared
surface, the contact resistance does not play a role. The spreading
resistance on bulk material has been found to satisfy eq. (8a) or (2O) over
a range of four decades of resistivity on N-type Si, as shown in figure 3«

3- Thin layer on infinitely conducting substrate

3.1. The Brooks and Mattes approach

A structure to which a spreading resistance measurement is frequently

applied, consists of a thin layer of thickness d ^ A on a much better
conducting substrate. Considering the substrate as a perfect conductor
this problem has been treated by Brooks and Mattes(8jL Unfortunately, they
made an error and the problem should be formulated as follows.

32
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The potential again is a solution of Laplace's equation

which, because V(r,d)=O and hence

can be simplified to

The mixed boundary conditions corresponding to eqs (4a) and (4b) now
read as

for
and

for

There is no known analytical solution to these dual integral equations and

this line of reasoning cannot be pursued.
Brookes and Mattes arrive at the mixed boundary conditions on the
surface in the form

for
and, with the correction of an obvious misprint,

for
to which

would be a solution were it not that C and C_ are functions of k, which

they derive later, and not constants as they appear to suggest. Their
final result, which has been computed and is plotted in figure 4, is however
remarkably close to the results obtained otherwise.

3.2. Solution with uniform contact current density distribution

As discussed in sec. 3 » 1 » the potential cannot be solved analytically

assuming a constant potential of the contact V . However, an analytic
solution
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uniform over the contact area, as done for the infinite geometry in sec.
2.3- , x
Application of the boundary condition eq. (17) and the relation
eq. (18) to the non-zero field strength of eq. (24b) yields

and hence

Now the average value of V(r,o) over the contact area, the applied
potential V , with um of//J and X = -4 /? , expressed in Rg=Vo/io, is

The validity of this equation can be checked by considering the two extreme
cases of a very thick and a very thin layer. With a very thick layer,
y ^ oo , and R approximates the expression for infinite geometry eq.(20)
For a very thin layer the integral eq. (28) yields as expected

Eq. (28) has been computed and is presented as a plot of

( oo ) vs d/A in figure k.

3.3. Solution with infinite geometry contact current density distribution

The choice of a uniform electric field is one of several possibilities

to avoid the mixed boundary conditions by specifying the electric field
at the top side of the structure. Schumann et. al.fljhave based their
analysis on the choice of the field strength at the contact that exists
with an infinite geometry

and. as before,

The potential, subjected to the boundary condition V(r,d)=O, as before, is

given by eq. (23). Now applying to the non-zero field strength of eq.(24b)
the boundary conditions eq. (3O)» it can be seen fromeq. (5*>) that

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Hence the potential reads

R v The
i average
vields value of V(r,o) over the contact area, V , expressed in
s= o/ o'

Making the approximation for a thick layer directly from the potential
e<i» (32) at *ne surface % =O, it is found th* the potential equals the
potential .for the infinite geometry eq. (6). The spreading resistance
eq. (33)t in the same approximation correctly yields R as in eq. (8a).
For a thin layer the spreading resistance is found to Be given as expec-
ted by eq. (29)* Eq. (33) has also been computed and plotted in figure k.
3*^. An experimental approach
An experimental approach has been followed by Cox and Strack[l9] who
studied the resistance in the case in point as a function of contact
radius A. They assumed that the resistance is composed of the contribu-
tions due to contact resistance, spreading resistance corrected for
finite thickness and residual resistance:

By plotting the total resistance R vs 1/A the three different components

can be separated. From electrolytic tank experiments they concluded that
the function f obeys the empirical relation

which has the correct value in the extremes d -^ o and d -^ oo

Eq, (35) has also been plotted in figure 4.

4. Thin layer on zero-conductivity substrate

4.1. Solution with uniform contact current density distribution
4

Another structure for which it is of interest to know the spreading

resistance as a function of the thickness d ^ A is a thin layer on a
non-conducting substrate or separated from a conducting substrate by an
isolating layer.
The potential is again given by eq. (21) and the electric field at
z=d equals

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Because should be valid for all r

and hence the electric field at z=O is

Applying the boundary condition eq. (1?) and eq. (18), eq. (38) yields

The average value of V(r,o) over the contact area, VQ, with
y = d/A and x = kA is found to be

For a very thick layer the potential and the spreading resistance
approximate the expressions for infinite geometry eqs (19) and (2O). For
any other layer, and mathematically for any layer, the integral eqs. (39)
and (4o) do not exist. However, when the potential at the distance r at
the surface z=O is referred to the averaged potential V of the contact, a
non-divergent integral is found because the malignant terms cancel

For a very thin layer, y -^ o, the integral in eq. (^1) can be solved
exactly. Then for z=O eq. (39) can be approximated as

and invoking the expression

it follows that

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This is a satisfying result because this dependence on r is exactly the
dependence which follows from an irrefutable elementary consideration
eqs (49) and (50), which, moreover, has been verified experimentally with
nigh precision by us. Using eq. (44) the non-divergent integral eq.
can be written as

Because the integral equals 1/8, eq. (45) can be written as

In this way it has been shown that by considering the potential

difference the divergency of the integral is removed, that the correct
dependence of the thin layer resistance on the distance r is obtained and
that the resistance between the contact and r=A equals p/8 tf d. In
sec. 4..3 it will be recapitulated that this value has also been obtained
earlierf 9} from a very different transmission-line model. In the absence
of a zero-voltage reference at infinity, R should be defined from a three
point-probe system to be discussed in sec.5»

4.2. Solution with infinite geometry contact current density distribution

Applying" the Schumann et al.[1 ] approximation to this structure, by

imposing the boundary condition eq. (30) and the relation eq. (5a) to eq.
(38) it is found that

Hence the average value of V(r,o) over the contact area, V , yields

For a very thick layer this expression approximates the expression

for infinite geometry eq. (6^. For any other,and mathematically for any
layer, the integrals eqs (46) and (4y) are divergent. Again referring the
potential at the distance r at the surface z=O to the averaged potential
V , a non-divergent integral is found

For a very thin layer, y -=> o, eq. (48) reads

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which can be solved exactly to yield

This result cannot experimentally be distinguished from eq. (^5a) obtained

with the constant current density approach.

4.3. Solution with transmission-line approach

From elementary considerations it is clear, that at a distance r

from the centre E (r,z)=0, that the total current i is related to

and that hence for a. thin layer the potential difference between points
at r=A and r equals

The difference between the potential V of the contact and the

potential at r=A should be added to the potential eq. (50). However, this
potential is only independent of z when the layer is very thin with
respect to the probe, radius. For this geometry a transmission-line model
has been worked out [9j»where the current is assumed to flow in the z-
direction only through the contact resistance R at the metal-silicon
interface and radially anywhere else. The resistance R between the
contact and the cylinder wall at r=A has been calculated to be

(51)
w, _ . The function F(U) = I (u)/ul (u), where I and
I1 are modified Bessel functions of the first kind, is plotted in figure
5. An essentially similar approach with a linear geometry has been
followed fo^ many years to derive the contact potential based on an
expression [9]given ^Y Shockley. Eq. (51) can be used for the same purpose.
This approach can be compared to that followed in sec. 4.1 only when
R is dominant, so that the contact resistance can be considered as a
series resistance which does not affect the current density distribution.
Under these conditions

exactly and almost the same result as obtained in eqs (45a) and (48b)
respectively, along totally different lines.

38

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 5. Three-point-probe configurations
For spreading resistance measurements two different three-point-
probe configurations are currently in use each with different, but
related correction formulae. They are presented in figure 6, as parts of
an in-line four-point-probe arrangement with three equal probe distances a,
because the two configurations can be easily related in this way.
It will be shown that the two configurations yield very different
measurement results with thin layers in particular. The three probes are
referred to as voltage, current and common probe. The spreading resistance
is measured below the common probe.
From superposition of the potentials due to the input and output
currents the potential differences measured in configurations A and B can
easily be shown to be

and

where V is the potential drop of the common probe due to spreading

resistance. Reversing the current in B and superimposing this configura-
tion onto A the normal four-point—probe arrangement is obtained, that is

The four-point-probe measured potential for a thin layer on an isolating

substrate is given by

and for bulk material by

Comrjaring the voltage drop due to the spreading\resistance i j> /kA. to

V^q ', it is evident that the contribution V£~ ' is negligible for bul
material (s ^> A). For a thin layer the sheet resistance generally
seriously reduces the precision of the desired information which is in
the spreading resistance term.
The next problem to be treated is whether the voltage or the current
probes can be replaced by a bottom contact.
When the structure to be investigated is such that the support is
thick or highly doped so that it can be considered as an equipotential
surface, a voltage or current contact can be connected to^it. Calling the
bottom potential V, the potential difference reads in configuration A1 of
figure 6 as

39
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565-448 O - 75 - 4
and in configuration B1 as

which is identical to eq. (j?Jf) of configuration B. The difference

between eqs (53) and (58) amounts to half the four-point-probe value.
When in configurations A1 and ~B the voltage probe is displaced towards
infinity^the measurement result is evidently the same as with a bottom
Voltage contact.
In figure 6D the configurations A and B are presented with bottom
current contacts. ¥hen the configurations C and -C are superimposed on
D the voltages read

and

Hence in configuration D

(A )
which is equal to V^_ ' yand in configuration C

which is half the four-point-probe value. Upon applying a bottom current

contact the potential is reduced in configuration A and is increased in
configuration B by half the normal four-point-probe value.

6. Summary and conclusions

The resistance between a metal contact of radius A at uniform

potential and an electrode at infinity to material of resistivity J> of
infinite extent is the spreading resistance ,£ /4A. An extremely thin
top layer representing a contact resistance is generally considered as a
series resistance. It turns out to influence the potential distribution
itself and to increase the resistance by h% over the series combination.
Imposing the boundary condition of a uniform current density distribution
over the contact area instead of a uniform potential yields a spreading
resistance higher by at most 8% over the series combination.
The potential problem for a layer of finite thickness d is solved for
a perfectly conducting and a non-conducting substrate. For both problems
the boundary conditions of uniform current density and of the current
density distribution found with infinite thickness are tried.
For the first problem a difference of about 10$ is found with both

40
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boundary conditions. Another published solution is found to be
mathematically incorrect. For the second problem both boundary conditions
yield divergent integrals for the potential. However, the difference
between the potential of the contact and the potential at some point r
yields a finite integral. With the boundary condition of uniform current
density at the contact the In r-dependence of the. voltage is found which
follows from elementary considerations and which has been verified expe-
rimentally. Moreover, the other voltage term representing the geometrical-
ly constrained spreading resistance for a thin layer turns out to be
equal to the value obtained from a completely different approach based on
a transmission-line model. The other boundary condition of the same
density distribution as found for infinite geometry also yields the In r-
dependence and a constant term smaller by 5$»
The latter approach has been followed by Schumann et al.[l]in their
calculation of the spreading resistance not only as a function of d/A, as
done here, but also as a function of the ratio of layer to substrate
resistivity $11$1, » of which only the two extremes have been studied
here. It is evident that all results are only valid as far as the model
is valid and it is the pertinent conclusion of this contribution that
equally reasonable boundary conditions yield results which are different
by about 10$. Agreement with experimental results of this precision
exists only for the In r-dependence, which is found with both approaches.
The infinite geometry expression j> /kA has been verified with about this
precision with a Hg probefl8] and experiments in which probes with small
contact area are used, are troubled by contact resistance., Schumann's
choice of the boundary conditions is a logical one because the infinite
geometry with ff* / $3, = 1 can be used as a reference in this way.
Nevertheless, in view of the results obtained above it appears worth
repeating Schumann*s computer exercise with various conditions. It is
probably safe to say that in interpreting thin layer spreading resistance
measurements, which may be precise with in 1$, the precision drops to
about 1O$.
It would, moreover, also be better to include from the very beginning
the influence of-the contact resistance, which influences the current
density distribution at the contact, particularly for a thin layer on a
less conducting substrate. When all this preliminary mathematical work
for spreading resistance on a non-bevelled structure has been done
correctly, the influence of the edge on a bevelled surface should be
included, as with four-point-probe correction formulae for finite geometry,
Furthermore, it should be realized that on any layered structure the
transition is not abrupt but extends over a finite length, due to dope
atom gradient, space charge or both. Therefore in spreading resistance
correction formulae the thickness obtained with the infrared multiple
interference method should be used with caution £21 , 22 J .
Finally on a bevelled structure the complication arises that the
charge carrier distribution is perturbed by the exposure of the transi-
tion on the bevel. In a PN-junction the zero-bias depletion layer
extends so far to both sides of the junction that the net charge
vanishes. In a bevelled PN-junction therefore the lower«ide boundary of
the depletion layer curves upwards where the top-side boundary would
intersect the bevel surface. The top-side boundary then must also curve
upwards and a modified space charge pattern results suggesting a smaller
depth of the interface. These effects are well known to give rise to
lower surface break-down voltages, as discussed by Davies and Gentry [23J »
Similar effects occur, on a smaller scale, with an NN junction where
charge spills over a few Debye lengths into the lowly doped layer, but
may show a different space charge distribution near the bevelled surface.
It is the author*s opinion that sufficiently reproducible and precise
spreading resistance measurements can be done, but that for the interpre-
tation of the data to extract explicit and accurate information on the
resistivity of layered or bevelled structures theory is seriously deficient.
41
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 Acknowledgement

The assistance of Prof.Dr. C.J. Bouwkamp in some analytical

problems, of Ir. ¥. Fontein in some numerical problems and of
Dr. J.D. Wasscher in carefully reveiwing the manuscript is gratefully
acknowledged.

References

1 P.A. Schumann and E.E. Gardner, 13 R.G. Mazur and D.H. Dickey,
J.Electrochem.Soc. 116 (1969) J.Electrochem.Soc. 113
87. 0966) 255.
2 P.A. Schumann and E.E. Gardner, 14 ¥.A. Keenan, P.A. Schumann,
SolSt.Electr.12 (1969) 371. R.P.Phillips and A.H. Tong,
3 T.H. Yeh, Silicon Device Ohmic contacts to semiconduc-
Processing, NBS Spec.Publ. tors, ed. B. Schwartz, Elec-
337 (1970) 1 1 1 . trochem.Soc. (1969) 263.
4 T.H. Yeh and K.H. Kokhani, J. 15 P.J. Severin, Silicon Device
Electrochem.Soc.116 (1969) Processing, NBS Spec.Publ.
1461. 337 (1970) 224.
5 S.M. Hu, Sol.St.Electr. 15 16 P.J. Severin, Sol.St.Electr,
(1972) 809. 14 (1971) 24?.
6 E.E. Gardner and P.A. Schumann 17 C.J. Bouwkamp, IEEE Transact.
IBMTR 22191, July 1965. Antennas and Propagation, AP-
7 E.E. Gardner, P.A. Schumann 18 (1970) 152.
and E.F. Gorey, IBMTR 22394, 18 P.J. Severin, Paper 75 presented
May 1967. at the Chicago, Illinois, Meeting
8 R.D. Brooks .and H.G. Mattes, of the Electrochemical Society,
BSTJ 50 (1971) 775. May 13-18, 1973.
9 P.J. Severin, Philips Res. 19 R.H. Cox and H. Strack,So'l.
Repts 26 (1971) 359. St.Electr. 10 (1969) 1213.
10 P.J. Severin, Symposium on 20 I.S. Gradshteyn and I.M. Ryzhik,
spreading resistance measu- Table of integrals, series and
rements, NBS (1974). products, Acad.Press, 1965»
11 R. Holm, Electrical contacts 6. 533.
handbook, Springer Verlag, 21 P.J. Severin, Appl.Opt. 2
Berlin, 1958. (1970) 2381; JJ_ (1972) 691.
12 J.N. Sneddon, Mixed boundary 22 P.J. Severin, J.Electrochem.Soc.
value problems in potential 121 (1974) 150.
theory, North-Holland Publ. 23 R.L. Davies and F.E. Gentry,
Co. Amsterdam ,1966. IEEE .Transact. Electron Devices
ED 11 (1964) 313.

Figure 1. The geometry of the contact and the two-layer structure.

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 Figure 2. The oblate spheroidal
coordinate system schematically
drawn.

Figure 3. The spreading resistance R2H3 ™ V2i/ii3

(fig. 6B) plotted vs the four-point-probe resis-
tance R23i«t> both measured with mercury probes,
on bulk samples. The solid line represents
R = P/4A, where 1 ft corresponds to p = 0.2 ficm

Figure 4. The spreading resistance R, normalized by the spreading resistance on infinite geometry
ROD =« P/4A, plotted vs the normalized thickness d/A, as calculated by Brooks and Mattes (sec. 3.1), by
Schumann (sec. 3.3), by Severin (sec. 3.2) and measured by Cox and Strack (sec. 3.4). The two ranges
are noted on the horizontal axis.

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 Figure 5. The. function F(u)
with u2 = A2 p/R'd.
c

Figure 6. The two alternative three-point-probe arrangements for spreading resis-

tance measurements (A and B), modified with bottom voltage probe (Aj and BI), and
modified for bottom current probe (D), with two arrangements used in the text (Cand -C)

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NATIONAL BUREAÜ OF STANDARDS SPECIAL PUBLICATION 400-10, Spreadlng Resistance Synposium,
Proceedings of a. Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Two-Point Probé Correction Factors

D. H. Dickey
Bell and Howell Research Laboratory
Pasadera, California

The effects of sample boundaries on resistivity measurements made

with a two-point spreading resistance probé are calculated for various
boundary conditions. The results are presented in the form of dimen-
sionless correction factors. The problem of depth-dependent resistivity
in a thin layer is considered, and a method for correcting measurements
on such layers is described.

Key words: Boundary correction; calculations; electrostatic analogue;

resistivity; semiconductor; spreading resistance.

1. Introduction

The two-point spreading resistance probé as originally developed [1]^ was characterized
by a sampling volume substantially smaller than then-current resistivity probes. The accur-
acy available with the technique did not justify correction for sample boundaries when it
was used for bulk samples of even moderately small size. Improvements in the accuracy of
the technique in recent years, coupled with the desire for probing smaller and smaller
samples has made correction for sample boundaries a necessity. The purpose of this paper
is to present correction factors for a variety of boundary conditions, including conducting
and non-conducting edge, end and subsurface boundaries. A simplified approach to the prob-
lem of a depth-dependent variation in resistivity in a thin layer wi11 also be presented.

2. Method of Calculation

The resistivity of a sample is assumed to be related to the resistance measured between

the two probes according to

P = 2aR/F ohn-cm (1)

where ¿ is the contact radius and F is a dimensionless factor that contains the correction
for sample boundaries.
The following development is similar in many respects to that used by Uhlir [2] for the
conventional four-point resistivity probé, and makes use of his results for those cases

Figures in brackets indícate the literature references at the end of this paper.

45
involving image sources. The basic approach is to invoke the electrostatic analogue of the
current flow problem, in which equipotential contacts are replaced by capacitor plates and
current sources are replaced by electrostatic charges.
A point charge in free space establishes the same potential distribution as that of a
current I flowing from a point into an infinite medium of homogeneous resistivity if the
charge has magnitude

In practicality, current flows from a surface contact into a half-space of resistive

.medium, so the current required to establish a certain potential distribution is one-half
that implied by equation 2. Rewriting equation 1 for F in terms of the potential difference
between the two probes, we find

Combining equations 2 and 3, the correction factor we seek for two probes on the surface of
a half-space can be written in terms of the electrostatic analogue as

where q is the charge on one contact, -q is on the other and AV is the potential difference
between them.
To illustrate, we take the simple case of a semi-infinite solid with the probes sepa-
rated by a distance £. We replace the contacts with two capacitor plates having charges +q
and -q and calculate the potential difference between them. The potential on the first
plate is

where the first term is owing to the charge on the first plate (the capacitance of a disc is
2a/Tr esu) and the second term is the contribution from the negative charge on the other
plate; assumed to be concentrated in a point. The potential on the second plate is equal to
that on the first, but opposite in sign, so the potential difference is

and the correction factor, from equation 4, is

This expression represents a negligible correction for very large values of s/a, and
should be valid for any practically attainable smaller probe separations.

46
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 3. Calculations for Abrupt Boundaries
3.1. The Infinite Slab
The method of images may be used to calculate the correction factor for the case in which
the probes are on one surface of a thin slab. The arrangement of the image plates in the
electrostatic analogue is illustrated in figure 1. Each plate has associated with it an
infinite array of images, which ensure that the normal derivative of the potential will
vanish in the planes corresponding to the upper and lower boundaries of the slab. As before,
we write the potential on the first plate as a sum of contributions from each of the real
and image charges. Fortunately, the contribution from exactly such an array of image
charges has been conveniently summed by Uhlir. Using his result, we find

where the first two terms are the potentials owing to the charges on the two real plates, t
is the slab thickness and M(x) is a function tabulated by Uhlir. The M-function has the
limiting form for large s/t:

The potential on the second plate is again equal but opposite in sign to that on the first,
so from equation 4 we obtain

This result is valid for slab thickness greater than the contact radius, but breaks down
somewhat for smaller thicknesses because the image charges can no longer be assumed to be
concentrated in a point.
For very small sample thicknesses, the resistance model is equivalent to one in which
the equipotential contacts extend through the entire thickness of the sample. The problem
therefore becomes two-dimensional and can be solved in many ways. An electrostatic analogue
is the two-parallel-wire transmission line, for which the capacitance per length t is

The capacitance is just q/AV, and since this problem is not confined to a half-space the
correction factor is one-half that given by equation 4. The result is

Equations 10 and 12, valid for large and small sample thicknesses, respectively, are graphed
versus t/a for s/a = 100 in figure 2. The two formulas are in excellent agreement for
t - a.
In the case where the lower surface of the slab is a conducting boundary, the electro-
static analogue consists of the same array of images as shown in figure 1 but with different
signs. The lower set of signs indicated in figure 1 apply in this case. These images can
be considered to be made up of two superimposed sets: those about PI being a set with
charge -q and spacing 2t superimposed on a set with charge +2q and spacing 4t. This
arrangement satisfies the requirement that the tangential component of the field must
vanish in the plane corresponding to the lower boundary. Again using the results of Uhlir
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for the potential owing to the image charges, assuming they can be represented by point
sources, the potential on P-j is

\/2 is the same, but with opposite sign, so

This formula is useful for sample thickness greater than the contact radius.
For very thin layers on a conducting substrate the measured spreading resistance should
be independent of probe separation s^ The electrostatic analogue is the parallel disc
capacitor with plate separation 2t. The capacitance in electrostatic units, including the
effects of fringing, is

Again, this model is not confined to a half-space, so the correction factor is one-half
that given by equation 4:

Equations 14 and 16 are graphed as a function of t/a in figure 3. The agreement at

t = a is not exact, but close enough that we can assume the validity of equation 16 for
t < a» and equation 14 for t > a.
3.2. The Quarter-Infinite Solid
The case in which the probes are near and parallel to the edge of a thick sample
requires only two image contacts instead of the infinite arrays encountered with a thin
sample. The potential on each plate is therefore the sum of four terms, and the potential
difference is

where w is the distance from the line between the probes and the sample edge. The upper
set of signs apply when the edge is insulated, and the lower set applies when the edge is
a conducting boundary. The correction factor is:

If the line between the probes is perpendicular to a sample boundary, the potentials on
the two contacts are not equal and opposite since there is no longer a symmetry plane mid-
way between them. The potentials can however be immediately written, and the resulting
correction factor is

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where t is the distance from the boundary to the nearest probe. Again, the upper set of
signs apply if the edge is insulated, and the lower set applies for a conducting boundary.
3.3. The Semi-Infinite Slab
For the case in which the probes are parallel to the edge of a thin slice, four infinite
arrays of images are required. The potential on one of the contacts can be obtained from the
superposition of three pairs of arrays of the type shown in figure 1. If the probes are
parallel to the edge, the potential on the positive contact "is

where w is the distance from the edge and the upper signs are used if the edge is insulated,
The potential oh the negative contact has the same magnitude so the correction factor is

This result is valid only for sample thickness greater than the contact radius. For
thinner samples, a model similar to that used to obtain equation 12 is useful. Other
correction factors for more complicated boundary conditions can be obtained by using the
process outlined in the preceding cases.

4. Inhomogeneous Resistivity
The final case to be considered is the one in which resistivity varies with distance
from the surface of an infinite slab. If the resistivity is a monotonically increasing
function of depth, the profile can be approximated by dividing the sample into a number of
superimposed electrically parallel bodies, each with a different thickness. For illustra-
tion, consider the rectilinear resistivity profile shown in figure 4. This profile is the
result of superimposing three bodies of thickness tg, ti and t2, each having uniform
resistivity 3p. The relation between p, the surface resistivity, and the spreading
resistance measured at the surface is in this example:

where Fn is the correction factor calculated from the thickness t«. In practice, one must
estimate the thicknesses t] and t2, these being the depth at which the resistivity is 3p
and 3p/2, respectively. If measurements are made at various depths on an angle-lapped
sample, the tn's can be estimated with increasing accuracy by considering first the
deepest measurements and working out to the original surface.
In general, the surface resistivity obtained by this method from a division of the
sample into N superimposed parts each with resistivity Np is

where FQ is calculated from the total sample thickness, Fn from the depth at which the
resistivity is approximately Np/n, and R is the spreading resistance measured at the
surface.
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 5.References
[1J R.G. Mazur and D.H. Dickey, Electro-Chem. [2] A. Uhlir, Bell Syst. Tech. J., .34, 105 (1955)
Soc. Abstracts, 12. N. 148 (1963)

Figure 2. Correction factor, F, versus the

ratio of sample thickness to contact radius
for insulated boundaries and probe separ-
Figure 1. Arrangement of image contacts ation s - 100 a.
for an infinite slab. Upper and lower signs
are for insulated and conducting lower
boundary, respectively.

Figure 3. Correction factor, F, (formed by

splicing equations 14 and 16) versus the ratio of
Figure 4. Resistivity profile re-
sample thickness to contact radius for a slab with
sulting from the superposition of
conducting lower boundary. Probe separation s =
three layers of different thickness
100 a. The dotted lines are the continuation of
but uniform resistivity 3p.
the individual equations beyond the point of
joining.

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NATIONAL BUREAD OF STANDARES SPECIAL PÜBLICATION 400-10, Spreadlng Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

On the Talidity of Correction Factors

applied to Spreading Sesistanee Measurements
on Bevelled Structures

P. K. PINCHÓN
R.T.C La Radiotechnique Compelec
Route de la Délivrande
B.P. 6025 - U Caen Prance

The correction factors in spreading reaistance measurements

are generally detennined by using a plan-parallel model of &
single or multi-layer strueture. This paper will discuss the
applicability of these factors to the profiling measurements on a
bevel, and cali attention to poasible systematic errors which can
appear in the case of an insulated layer or a low/high type of
structure.
After a short discussion on the spacial resolution of the
spreading resiscanee probé, the case of a homogeneous isolated
layer is examined in more detall. A simplified expression for the
valué of spreading resistance was calibrated against published
data using fitting coefficients.
It is then easy to show that the use of a correction derived
for párallel structures is not correct for the case of a thin,
isolated layer, when the measurement is made on a bevel.
Indications are also given on the parameters which could
minimise the problem
The experimental part of this paper shows a series of profi-
les tnade with P-type epitaxial layers.
After the applicatíon of the usual corrections, the varlous
electrical boundaries or geometrical conditions are seen to affect
the results in accordance with the discussion. An edge effect which
is significant even at great distance from the edge, is also described.
In the absence of a three dimensional theory for correction,
the use of small spacing is recotmnended in conjunction with a small
radius of contact and a shallow bevelling angle.

Key words: Accuracy; bevelled structures; correction application;

correction factors; edge effect; profiles; resistivity profiling;
small spacing; spreading resistance.

1. Introduction
According to Mazur 03» the spreading resistance teehnique has been increaaingly poputer
in the last years for resistivity measurements mainly due to its high spaeial resolution
coopared to other methods. But in the case of measurements on thin layers, the measurement
valúesfflustbe oorrected to give the actual resistlvity depending on geometrical factors
and on the nature of the layer toundary»

51
 Theoretical models have been used to derive these correction factors in the simple
case of a two-layer system £2,33 and later, extended to a graded structure, £4} using a
nrultilayered approach. Up to now these calculations of corrections have always been based
on a plan-parallel structure having infinitely wide lateral dimensions.
The aim of the present paper is to examine in which conditions these correction factors
can be applied to measurements made on bevelled structures where the lateral homogeneity is
evidently not maintained at large scale (compared to the contact radius) and what kind of
errors are involved in doing so.

2. Qualitative background
We shall assume that the probe has a plain, circular contact with the material, of no
contact resistance*
The figure 1 shows qualitatively what shape of current streams and equipotential lines
are involved in three distinct cases, under a spreading resistance probe : a) thin layer on
shorting substrate, b) infinitely thick sample, c) thin layer on insulating substrate.
In all cases the current sink is considered located at infinity, and the layers or the bulk
supposed to be homogeneous in resistivity.
In the case of thick samples, figure 1b the equipotential surfaces tend rapidly to be
hemispherical as the distance increases from the probe. Using this approximation it can
easily be shown that 95$ of the voltage drop is obtained at a distance x related to the
radius of contact, r<> by :

In the case of a highly conducting boundary, figure 1a» it is evident that the volta-
ge drop is confined in a very small space, smaller than that of the thick sample. On the
contrary, the case of the insulating boundary, figure 1c, indicates that the voltage drop is
practically in the lateral direction, and closely related to the sheet resistance of the
layer. It will be seen later how this lateral voltage drop can still be of importance at
distances greater than 20 ro.
Let us take as reference, the spacial resolution of the thick homogeneous sample. Thus,
the fact of the non homogeneity at large scale in the lateral direction in the case of a
bevelled layer becomes important in structures of the low/high type and very pronounced for
an insulated layer.

3. Semiquantitative model
Let us restrict our discussion to the case of homogeneous thin layer, of thickness : t,
resistivity :^ , limited by an insulating boundary.
Elementary theory shows that the lateral resistance of a disc, having an inner contact
of radius : r^ , an outer contact of raidus : rx , figure 2, is given by

r
Figures in brackets indicate the literature references at the end of this paper.

52
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 With an arbitrary geometry of 3 point contacts, as shown in figure 3» the circumferen-
ce of the contact of radius : r, being the common electrode, it is easy to obtain the
voltage drop between the circumferential contact and the voltage probe : (V-To), assuming
that the distances : a, b and c are large compared to rv :

For thin layers, the graph in figure 1 suggests that the spreading resistance is domi-
nated by the lateral sheet resistance. Thus, by comparison with the spreading resistance of
the infinitely thick material it becomes :

If we relate r^ to ro, introducing a fitting parameter such as rfe =o(ro, a linear re-
lation of the correction factor (C.F) is found versus (t/ro)~1 this being confirmed by the
published data of Gardner £3! obtained by more accurate derivation, for the range of
t/r0<1.
Using the in-line geometry, with a spacing : s, the common electrode on one. side, the
fitting parameter is obtained by comparison with Gardner's curve and found : 0(3;0.8.
The value of the spreading resistance for thin layer is then approximated, for t/ro <1 by :

This indicates that the spreading resistance is mainly equivalent to the resistance of
a sheet having a side injection contact of 0.8 rQ radius.
For thicker layers, using again approximate models including fitting parameters we may
decompose the spreading resistance into

total spreading resistance

"local" resistance
"lateral" resistance

where A and 0 are fitting parameters;

A t represents the radius of a: hemisphere in which the "local"resistance is expressed,
and
yt represents the radius of a ring from which the "lateral" sheet resistance starts to
become of importance*
By fitting with Gardner's curve, an agreement of<±10$ is obtained for t/ro>0.5»
making :

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 Using these semi-empirical relations the correction factor (C.P.), for a variety of
2s/ro and t/rQ values can be derived.
Table 1 gives a set of (C.F.) values ranging from large spacing (2s/rQ = 2000) to rela-
tively small spacing (2s/rQ = 20) and for three relative thicknesses :t/r0 = 0.5, 2 and 5,
The values in table 1 agree reasonably well with those reported by Schumann, Gorey and
Schneider [5] taking into account of the appropriate probe geometry,
CF — PF
These values are rewritten in the form —; (20) in table 2, in order to illustrate
the relative importance of the lateral (20) resistance outside a radius of 20r0,
tfhere CF/2o)is the correction factor for 2s = 20.
r
o

Table 1. Evaluated correction factors in the case of an insulated, homogeneous layer :

2s/rQ relative probe spacing ;. t/r = relative thickness ; probe geometry
3 pt. in-line, common probe on one side

(2s/r0)
2000 500 ° 100 20
0.5 9.9 8.2 6.1 4.1
(t/r 0 ) 2 2.8 2.4 1.9 1.35
5 1.6 1.4 1.2 1.024

Table 2. Ratio of the resistance outside a distance of 20 r to the resistance

at 20r0: CF - CF (20)
CF
(20)
(2s/r0)
2000 500 100
0.5 1.4 1.0 0.5
(t/r0) 2 1.1 0.8 0.4
5 0.55 0.37 0.17

Prom table 2 it is obvious that it is not correct to apply the standard correction
factors as determined for laterally homogeneous models in the case of a bevelled layer.

Let us take a numerical example, as may be found in practice :

tangent of the bevel angle : 1/50

The length of the bevelled part of the layer is only 500|jm, length over which the sheet
resistance varies from nominal to infinity. But from table 2 it is seen that a very signifi-
cant part of the spreading resistance comes from the lateral part included from SO^un (=20r
to 1000pm (=s) outside the measuring probe*

Thus in general, a three dimensional model is needed for correction factor calculation
in the case of an insulating limit or more generally in the case of low/high resistivity
structures. In view of the complexity of this task it seems more practical to look at the
conditions for which the error involved in the application of classical correction would
be minimised.
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 Obviously a small spacing arrangement is favourable in conjunction with a low bevel
angle in such a way that the sheet resistance variation in the direction of the slope may
be small compared to the probe spacing distance.
However the very last portion of the bevel can never fulfill the right conditions even
with a small probe spacing . Of course the error is confined to a thinner portion of the
layer in this case*

4. Experimental procedure
Experiments have been done using an automatic S.R prober of our construction which
prints on a semi-log paper, the uncorrected resistance values versus distance. The system
works in the constant voltage mode (lOrnV) with a dual polarity print at each point ; it
has a 3 pt. in-line probe made 'with tungsten carbide needles , having a tip radius of
» 20pm. The applied contact force is 20 - 25 grams.
For the experimental part shown hereafter, P type silicon layers have been selected.
We found, as others have, that the contact resistance is lower for P-type material. Thus
the measurements are more sensitive to bulk properties (i.e. proximity of an interface).
When measuring a bevel, we always apply a metallic shorting strip on which the two
accessory probes make contact directly. This shorting is made of indium-gallium paint
applied together with a mechanical scratching. Only the common probe is working outside
the strip at a distance : d which is recorded after the measurement. This arrangement is
depicted in figure 4.
The correction procedure has been done as follows : r is deduced in each series of
experiments from the measurement- itself on a thick part or known resistivity (substrate
or average resistivity of a thick layer) according to :

where : Rm is the measured resistance in opposition to RSR, the theoretical one

and where Re is the contact resistance supposed to be independent of the layer thickness.
A value of K = 1.2 has been used for all corrections on P type material.
Thus the applied correction : M, is related to the calculated correction : (C.F.),
corresponding to the simple one-layer system and a plan-parallel structure as mentioned
in the previous section, by :

Trials with K = 1.0 or K = 1.4 instead of 1.2 gave very minorchanges in the corrected
results and hardly any for the part of the layer thicker than 2 microns*

5. Results
5.1. Edge effect
In order to illustrate a boundary effect which may be observed at large geometrical
scales, in accordance with the discussion given in section 3» an edge effect has been
tentatively looked for in the case of an insulating boundary. An experimental result of
this nature has been already given by Severin £6} at the edge of a heterotype epitaxial
slice . Here, we used a P layer : 8\m thick, resistivity : 4ncm, on an N-type substrate.
We first recorded the surface measurements over a length of 1 cm at the center of the
slice, and found it essentially flat. Then the slice was cleaved in two parts and
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565-448 O - 75 - 5
re-measured on one half, in the same region as before and. in the direction perpendicular to
the broken edge, the probes being parallel to it* The probe spacing was s = 3mm*
The result is shown in figure 5 which illustrates clearly the expected edge effect. It
amounts to a 20$ increase at a distance as large as •£" mm. Also on figure 5 is plotted, for
comparison, the calculated effect using an image method and the approximate relations given
in section 3- (The calculated curve has been drawn arbitrarily at a level of 10Kn).

5.2 Comparison of Corrected Profiles

Having Different Boundary Conditions
In these series of measurements, the depth profiles of resistivity are compared as a
function of the boundary nature. In the same epitaxial run three different substrates
have been coated with a P type layer, in order to compare the effects of boundaries in the
case of : F/N, P/P and P/P+ configurations.
In the P/P case the choice of the substrate was such that its resistivity would approach
the one expected for the layer, thus allowing a profile which does not require a correction
(substrate resistivity : 3*95ncm). f

The uncorrected measurements are given in figure 6, The corrected P/N and P/P+ profiles
are compared to the P/P, uncorrected, in figure 7. It can been seen that the agreement with
the P/P profile is better for the P/P+ corrected profile than for the P/N profile.
In any case the slope of the P layer on the N substrate is wrong according to the two
others and the possible autodoping contribution which would have led to the reverse tenden-
cy. This is attributed to the use of a correction factor which does not fulfil the condi-
tions of bevel measurements.

5.3 Experiments Using Thickness and Probe Spacing Variations

Here, a rather thick (26.5M&0 P type layer on N substrate has been profiled using three
distinct values of the distance d, between the probe track and the shorting strip (see fig4)
The layer has an average resistivity of 5.8ncm as measured by the 4 pt probe method.
The actual measurements are shown on figure 8 and the corrected profiles, figure 9.
Now the measurements are taken at a short distance from each other, on the same bevel, and
thus the differences in profiles are likely to be due to the correction errors. They are
smaller for the smaller spacing (d s 120|jm). Then, on the other half of the same slice the
layer has been thinned down to Q\m by etching, bevelled and measured in the same manner as
the previous portion, again using three different spacings d.
The corrected profiles are shown on figure 10. It can be observed that the profile
slopes differ markedly, and the one obtained with the smaller spacing (d = 120nm) is consi-
dered to be more accurate than the others.
If we admit that there must be an agreement between the profiles of figures 9 and 10,
and that this would be optimum for the smaller spacing, then a downward shift of 20$ is
necessary for the last experiment* This is attributed to a small change in the experimen-
tal conditions between the two experiments (which were not done in the same day). By doing
so, we obtained figure 11, which shows the comparison of the six corrected profiles.

6. Discussion
The errors involved by using the common correction factors in the case of an insulated
layer can be sketched as in figure 12 where the practical situation is represented in dark
lines and the situation for which the usual C.F has been calculated is in dotted lines.
The discussion is also restricted to homogeneous layers, for simplicity.

562016
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 At the starting point (fig 12a) the measurement is higher than it would be for a con-
tinuous layer because an edge effect occurs, this being roughly equivalent to that of a
vertically cut layer at half the level length. Then the corrected value is too high.
At a point near to the middle of the bevel (fig 12b) the higher conductance (two
times higher) of the left hand part compensates for the absence of layer at the right. Then
the usual C.F. is nearly correct for all probe spacings.
At the last position close to the junction (fig 12c), the very high conductance of the
left hand side overcompensates for the absence of the layer at the right. Then the measure-
ment is too low after correction.
This qualitative behaviour is clearly observed in figures 7, 9, 10 and 11.

7. Conclusion
The errors involved by the application of correction factors determined for plan
parallel models in the case of bevel measurements have been discussed in a semi quantitative
manner and the behaviour verified by a few experiments.
A three dimentional model is in principle required to derive the correction factors in
the case of low/high configuration. Using the common C.F., the errors after correction can
be minimized using a contact radius, a probe spacing and a bevel angle as small as possible.
The general benefit in using a small probe spacing has already been reported [5].
The present work leads to the same conclusion explaining by simple models the physical
nature of the benefit in layer profiling.

8. References
[l] Mazur, R. G., Dickey, D.H. [2] Dickey, D. H., Electrochem. Soc. Conf.
J.Electrochem. Soc. HI 255 0966) Pittsburg, Abstr. No 57, April (1963)
[3] Gardner, E. E., Symposium on Hanufactu- [4} Schumann, P. A., Gardner, E. E.
ring In-Process Control and Measuring Solid-State Electron. 12 371 (1969)
Techniques for Semiconductors, Vol II,
p 19. Manufacturing Technology Division, [6] Severin, P. J.
A.P. Materials Lab. (1966) Philips Res. Repts. 26_ 359 (1971)
[5] Schumann, P. A., Gorey, E. F.,
Schneider, C. P., Solid-State Technology
50 (March 1972)

57 EST 2016
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 Figure 1. Qualitative shape of current flows and equipotential lines, a) short-circuiting
boundary; b) thick homogeneous sample; c) insulating boundary.

I*
00

Figure 2. Lateral resistance of a disc.

Figure 3. Resistance of a disc measured with three contacts

of arbitrary location. The ring of radius r, is the common
contact.
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 Figure 5. Measurements at the surface of a P layer on N sub-
strate, in a direction X, perpendicular to a cleaved edge.
Figure 4. Contacting set-up used in our Layer thickness - 8ym
measurements on bevels. Layer resistivity • 4ftcm
Interprobe distance - 3mm

in Figure 6. Uncorrected profiles of three

<o P-type layers coming out of the same epi-
taxial run, (resistivity of the P-type
substrate « 3.95ftcm).

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 Figure 8. Uncorrected profiles of one P-
layer on N-substrate. The distance, d,
from the probe to the strip is the param-
eter.

Figure 9. Same profiles as in figure 8,

after correction, using k - 1.2, r » 5.2pm
and d as indicated for 2d/rQ.

Figure 10. Corrected profiles for a

portion of the same slice as figure 9, but
after thickness reduction of the layer to
8pm prior to measurements.

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 Figure 11. Comparison between the profiles of figures 9 and 10 (the data of figure 10:
curves a', b1 and c* have been shifted downwards by 20% for better agreement).

Figure 12. Qualitative effect of the bevel geometry: the usual correction factor is:
too small in a) (edge effect) nearly adequate in b) too large in c)

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 This page intentionally left blank

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

SRPROF, A Fast and Simple Program for

Analyzing Spreading Resistance Profile Data

B. L. Morris and P. H. Langer

Bell Telephone Laboratories, Incorporated
Allentown, Pennsylvania
and
J. C. White, Jr.
Western Electric Company
Allentown, Pennsylvania

The spreading resistance technique is an excellent

method of measuring epitaxial resistivity profiles. In
many cases it is the only method by which the complete
profile may be measured. However, thin film correction
factors must be used to convert the spreading resistance
into a corrected resistivity. Previous calculations of
these correction factors have emphasized a mathemati-
cally complex solution which necessitates the use of a
large computer. The correction factors used here are
calculated from a relatively simple alg6rithm which
allows the use of a minicomputer. A documented program
is presented which uses these algorithms. This program,
written in FOCAL for use on the PDP8 series of mini-
computers, is fast, accurate, easy to use, and provides
a complete data reduction system. Examples of corrected
spreading resistance profiles are presented, and com-
pared with independent results such as diode C-V and
four point probe measurements.

Key words: Resistivity profiles; spreading resistance;

thin film correction factors.

1. Introduction
If a flat circular probe of radius a is brought into contact with a
semi-infinite material of resistivity p, and a current I is passed through
this structure, practically all of the potential drop will occur within
1.5 x a of the point of contact.[I]1 This is shown schematically in
Figure 1. For a contact in which the surface barrier resistance (Schottky
resistance) can be neglected, the resistance of the structure is

This is known as the spreading resistance. Since real metal-semiconductor

1
Figures in brackets indicate the literature references at the end of this
paper.

63
contacts can have appreciable barrier resistance, an empirical calibration
of R vs. p is necessary. These calibration curves are constructed for sil-
icon by measuring R and p on a large number of samples, both N and P type,
<100> and <111> orientations, with resistivities from 0.001 ohm-cm to
100 ohm-cm.
The spreading resistance set used in this work is the model ASR-100
built by Solid State Measurements, Inc.[2] This unit measures the total
contact resistance between two probes, each of which have a radius of con-
tact of approximately 3 microns. For the two-probe case, eq (1) is modified
to read

or

The assumption that the material is infinitely thick, i.e., that

t/a » 1, is not true for most of the structures used in semiconductor de-
vices. In particular, epitaxial films, which are grown on substrates of
different resistivity, usually have thicknesses which are of the same order
of magnitude as the probe radius. For these thin films, the equipotential
lines shown in figure 1 will be distorted, and the relation between R and p
will be subject to a thin film correction factor (CF):

The CF depends upon the relative resistivities of the film (p,) and substrate
(p2)r as well as the film thickness. If p 2 > p,, the potential lines will
tend to be pushed out of the substrate. In the limit where Pi/P? = 0, which
is the effective ratio when the film-substrate boundary is an insulating one
(i.e., a p-n junction), the potential lines are unable to penetrate the
boundary. In this case the measured value of Rg for a given p will be higher
than predicted by eq (2a), and the CF in eq (3) should be greater than unity.
If the boundary is a conducting one, potential lines will be drawn into the
substrate, making the value of R too low. In this case the CF will be less
s
than unity.

2. Previous Work
A great deal of effort has gone into the problem of calculating the
exact solution of the potential distribution for a real (i.e., multilayer)
semiconductor material under a charged circular disc.[3-5] For the simple
case of a two probe measurement on a two layer system, with a layer of
resistivity p, and thickness t, and an infinitely thick substrate of
resistivity p 2 , the spreading resistance is [3]

where RS is the spreading resistance,

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S = 2s/a (s is the spacing between the two probes), x is an integration
parameter, and J and J, are Bessel functions. The term within the square
bracket is the CF. These CFs are shown schematically in figure 2.

Unfortunately/ the relatively simple calculation of eq (4) is not always

a proper representation of the complex structure of a real epitaxial profile,
a more realistic approach is the multilayer concept.[3-4] This method in-
volves a numerical solution, in which the determinant of a (2N + 2)
x (2N + 2) matrix must be calculated in order to compute the correction fac-
tors of a profile with N points.[4] This calculation takes approximately
10 minutes of CPU time on an IBM Model 360/85 to correct a profile of
25 points,[4-5] although a recent paper by Hu[5] states that it is possible
to reduce this time by a factor of about 30.

3. Calculation of CF Algorithms
If spreading resistance profiles are to be used to evaluate epitaxial
material on a routine basis, the data reduction scheme, which includes cal-
culation of the thin film CF, should have the following properties; accuracy,
ease of utilization, and low cost. In the final analysis, the accuracy of
the calculated CF can only be determined by comparing the corrected spreading
resistance profile with a profile determined by an independent measurement
technique. While this comparison includes all of the other possible sources
of error inherent in a spreading resistance profile measurement, and of
course in the "other" technique, it is the ultimate test of the entire sys-
tem, which is really what is important. The ease of utilization includes
total effort needed to reduce the "raw" data produced by the apparatus into
a final profile. Since our ASR-100 is equipped with a data acquisition sys-
tem which reproduces the data on punched paper tape, it was advantageous to
use a system which could read this tape as a primary input. This factor,
combined with the need for an easily accessed low cost system, led us to
consider writing a program which could be used on a PDP8 minicomputer cur-
rently in our laboratory.

A minicomputer using an interactive language such as FOCAL runs at a

much slower speed than a large computer using FORTRAN, therefore it was felt
that the only method by which a reasonable calculating speed could be ob-
tained would be to fit the results of eq (4) to a simple mathematical
expression, and then modify this function until the results agreed with
independent profile measurements.
Initial attempts to fit a simple polynomial function were not success-
ful due to the extreme non-linear behavior of the CF, as seen in figure 2.
For the insulating boundary condition (K = +1), a function of the type
CF = A + Bex was then tried. The limits of this CF, as t/a approaches zero
and infinity, are respectively infinity and unity, suggesting a function of
the form

where m = m (t/a). The best fit of this CF to the values of eq (4) was
found for the case where B = 1.4 and m (t/a) is shown in Table 1.

Equation (5) assumes that the p-n junction is a perfectly insulating

boundary. As the junction is approached, and the resistivity of the layer
rises toward that at the junction, this assumption is no longer true, and
results in over-correction of these last points*[5] Experimental data ob-
tained from profiling heavily doped (* 10 cm ) p-type epi on an n-type
substrate were used to derive an empirical correction eq (5). The best
solution, one that did not produce over correction was found to be:
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where

Table 1

t/a Insulating boundary "m" Conducting boundary "n"

0.1 34.32 -0.0637
0.2 13.55 -0.1174
0.3 7.587 -0.1622
0.4 4.905 -0.1995
0.5 3.426 -0.2303
0.6 2.511 -0.2558
0.7 1.899 -0.2767
0.8 1.466 -0.2943
0.9 1.149 -0.3091
1 0.9087 -0.3216
2 0.0248 -0.3830
3 -0.1599 -0.4041
4 -0.2169 -0.4142
5 -0.2355 -0.4199
6 -0.2399 -0.4239
7 -0.2372 -0.4277
8 -0.2330 -0.4306
9 -0.2267 -0.4331
10 -0.2207 -0.4354
20 -0.1706 -0.4431
50 -0.1381 -0.4430
100 -0.1842 -0.4789

All of the corrections discussed so far have applied to one-dimensional,

semi-infinite material. In fact there is a two-dimensional effect in the CF,
analogous to that of the four point probe. In this latter measurement, the
sheet resistance of a large wafer is R = (Tr/£n2) • V/I, but if the probes
are on the edge of the wafer, the relation is R = 1/2 (ir/fcn2) • V/I. In
spreading resistance measurements, this limit il arrived at as the p-n
junctionc on the beveled wafer is approached by the probes. This 2-dimension
factor, F2j-j/ must be multiplied by the one-dimensional CF. to get the
proper resultant. CF9n depends upon the spacing between tfte two probes, and
the lateral distance or the probes from the junction. This factor was
experimentally determined for our probe spacing of 0.6 mm, and is shown in
Table 2.
The conducting boundary condition has a CF_n with the following proper-
ties:
CF
1. CD< 1 in all cases
2. CFCD ->- 1 as t/a -»• <»
3. CFCD -> 1 as K -»• 0 .

As in the case of the insulating boundary, a simple polynomial could not be

found to fit. Equation (4) was used to generate values of CFC_ as a func-
tion of t/a and K. The best fit was found to be
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where n = n (t/a) is given in Table 1.

Table 2.

Two-Dimensional Correction Factor for Finite Sheet Size

X (urn)
(Lateral distance from edge)
CF 2D = R (x)/R (~)

0 2.00
10 1.72
20 1.60
30 1.46
40 1.39
50 1.33
60 1.29
80 1.22
100 1.17
120 1.14
140 1.10
160 1.08
180 1.06
200 1.04
1,000 1.00

Equation (7) is strictly valid only for the single layer approximation.
Schumann and Gardner[3] have shown that the multilayer approach is quite
important for N/N /P structures, where the insulating N /P boundary can have
a large effect on the N/N CF. This effect becomes more pronounced as:
1. the N layer becomes £hin, 2. the resistivity of the point on the N layer
approaches that of the N layer. An empirical correction for this double
layer case has been incorporated into our conducting CF, this is:

where RJ = resistivity of last point in N layer

UR = uncorrected resistivity of the point to be corrected
TP = (X + TK (N )/a
X = depth of point to be corrected
TK (N ) = thickness of N layer

and
At the N/N boundary where UR = RJ and X =0, this factor reduces to the
insulating boundary CF. For points on the N layer haying relatively high
resistivity (UR > 100 x RJ), or for the very thick N layers (TK (N ) >
10 x a), this factor approaches unity.

4. Programming of SRPROF (Spreading Resistance PROFile)

The complete program utilizing the correction factor algorithms dis-

cussed in the previous section is shown in Appendix I. Comment "cards" and a
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variable list are shown in Appendix II. The programming language is 8K
FOCAL, an interactive language developed by Digital Equipment Corporation for
use on the PDP8 series of minicomputers. It is quite similar to BASIC,
which, in various forms, is used on many large and small computers. A flow
chart of the program is shown in figure 3.
The initial parameters entered on the keyboard are wafer identification,
scale factor, orientation, points on oxide (i.e., not on the beveled sur-
face) , thickness and conductivity type of J layers. This data is terminated
by entering a thickness of zero.
The data tape generated by the data acquisition system of the ASR-100 is
then entered into the tape reader, a 9999 entered from the keyboard termi-
nates the data. Any "bad" points can be edited at this step by manually
entering the point number and the "correct" resistance of that point.

Starting with the first layer (J = 1) the program calculates the number
of points in this layer, the uncorrected resistivity of the last point in
this layer, calculates the relevant CF, and prints out all data for this
point. A typical output is shown in Appendix III. The Resistivity is the
corrected value, the Doping is calculated from Irvin's work,[7] SR is the
actual spreading resistance, UR is the uncorrected resistivity, and RC is
the radius of contact, RC = UR (2 x SR). Layers are separated by a blank
line. The output speed is limited by the Teletype printout rate of 10 char-
acters/sec. The computer has sufficient core storage for approximately 100
data points, in addition to the program itself.

5. Results and Summary

The accuracy of the corrected spreading resistance profile, and thus of

the CF calculations, can only be verified by comparing the results to those
of an independent measurement technique. For the conducting substrate
boundary condition, diode C-V profiling is an ideal method of directly mea-
suring the carrier concentration profile, however, it is limited in depth by
breakdown voltage. Two examples of this comparison are shown in figure 4.
Wafer A988-7 is relatively thin epi with a sharp interface. Wafer RL5-1 has
been heated at 1,200°C for 8 hours to produce a large amount of outdiffusion.
In both cases the two methods match well over the limited range of the C-V
profile.

For epitaxial layers grown on opposite type substrates, sheet resist-

ance may be easily measured by a four point probe. This sheet resistance can
also be calculated by SRPROF using a point by point summation of the calcu-
lated resistivity. In most cases that we measured this calculated sheet
resistance matches the measured value within + 10%, and in all cases within
+ 20%.

In conclusion, SRPROF is shown to be a fast, convenient, and accurate

method of reducing spreading resistance profile data, which is applicable to
epitaxial layers with either conducting or insulating substrates.

References

[1] R. Holm, "Electric Contacts Hand- [2] Solid State Measurements, Inc.,
book", Springer, Berlin (1967). Monroeville, Pennsylvania.
[3] P. A. Schumann and E. E. Gardner, [4] T. H. Yeh and K. H. Khokhani, J.
Jr., Solid St. Elec. 12, 371 Electrochem. Soc. 116, 1461
(1969). (1969).

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[5] S. M. Hu, Solid St. Elec. L5, 809 [6] F. M. Smits, Bell System Tech. J
(1972) . 37_, 711 (1958).
[7] J. C. Irvin, Bell System Tech. J.
4_1, 387 (1962) .

Appendix I

20.10 C SRPROF
20.11 E
20.12 T I!!;A "SLICE"P, "SF"SF, "ORNTIIOR," POINTS ON OXIDE"Z
20.14 T !!;S J=1;S LT=FLOG(10);D 27
20.16 A " THK"TK(J);I (TK(J))20.24,20.24;A "TYPE"T(J)
20.17 S J=J+1;G 20.16
20.24 T I I,"ENTER TAPE",!;S 1=1
20.25AR(I);I (9000-R(I))20.3;I (R(I)-.1)20.28
20.26 S 1=1+1
20.28 G 20.'25
20.30 S P=-1;S SP=-2
20.33 S P=P+1;S SP=SP+1;I (6000-R(P))20.42
20.34 I (FITR<R(P)/1000>-2)20.36,20.37
20.35 I (FITR<R(P)/1000>-4)20.37,20.38
20.36 S R(P)=FEXP<LT*(R(P)7500+2)>;G 20.33
20.37 S R(P)=FEXP<LT*(3000=R(P))/500>;G 20.33
20.38 S R(P)=FEXP<LT*(R(P)-1000)/500>;G 20.33
20.42 S SP=SP-Z;F I=l f SP;S R ( I ) = R ( I + Z )
20.44 A I I,"HOW MANY BAD POINTS?"P,!
20.45 S K=0;I (P-l)20.49
20.46 T I,"LIST I (FROM TRUE EDGE) AND R(I)",!
20.47 A III"I/"R(I)"R(I) , I
20.48 S K=K+1;I (K-P)20.47
20.49 D 24.5
20.52 S J=1;S NP(J)=FITR(TK(J)/SF)+1;S S=NP(J);S SH(J)=0
20.54 S I=S;D 21;S RJ(J)=UR
20.56 F I=1,NP(J);D 21;D 22;D 23;D 24
20.62 S J=J+1;T I;S SH(J)=0;I (TK(J)-.1)25.8
20.63 S NP(J)=FITR<(TK(J)-TK(J-1))/SF>
20.64 S M1=S+1;S M2=M1+NP(J)-1;S S=S+NP(J)
20.65 I (TK(J+1)-.1)20.69;D 20.54
20.67 F I=M1,M2;D 21;D 22;D 23;D 24
20.68 G 20.62
20.69 S RJ(J)=1E20;G 20.67

21.11 S D=SF*(I-1);I (SP-I)25.8;S K=FLOG(R(I)/1000)

21.13 I (T(J)-14)21.16,21.14,21.16
21.14 I (OR-111)21.22,21.32,21.22
21.16 I (OR-111)21.42,21.51.21.42
21.22 S UR=-.56655+1.0596*K+.01805*Kt2-.33462E-02*K+3
21.23 S UR=UR-.84064E-04*K+4;G 21.6
21.32 S UR=-.79246+.9936*K+.024673*K+2+.65968E-03*K+3
21.33 S UR=UR-.1731E-03*K+4-.39394E-04*Kt5;G 21.6
21.42 S UR=-.18876+1.0387*K+.059796*K+2+.27823E-02*Kt3
21.43 S UR=UR-.10481E-02*K*4-.14122E-03*K+5;G 21.6
21.51 I (R(I)-850)21.54
21.52 S UR=-.33364+2.2216*K-.70895*K+2+.12841*K+3
21.53 S UR=UR+.91035E-04*K+4-.13896E-02*K+5;G 21.6
21.54 S UR=-.57755+.71456*K-.037836*K-h2-.33079E-02*Kt3
21.60 S UR=FEXP(UR)

22.12 S RC+UR*1E04/(2*R(I));S X=TK(J)-D;S TR=X/RC

22.14 S XK=<RJ(J)+lE-07-UR>/<RJ(J)+UR>
22.16 I (TK(J+1)-.1)22.22
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22.18 I (T(J)-T(J+1))22.22,22.42
22.22 S K=1;I (TR-.1)22.92; I (TR-99)22.23;S XM=-.184;G 22.32
22.23 I ( T R - T O ( K ) ) 2 2 . 2 6 f 2 2 . 2 6 ; I (TO(K+1)-TR)22.26
22.24 S XM=IN(K+1)-(IN(K+1)-IN(K))*(TO(K+1)-TR)/(TO(K+1)-TO(K))
22.25 G 22.32
22.26 S K=K+1;G 2 2 . 2 3
22.32 S XX=TR*XM*FEXP<.2*FLOG(FABS(XK))>;S P=10*X/SF;S Z=l
22.33 I (23jZI-P)22.35;S Z=l.8923-.01528*P+1.0364E-04*P+2
22.34 S Z=Z-2.7879E-07*Pt3+1.895E-10*P+4
22.35 S CF=Z*(1+1.4*FEXP(XX));G 2 2 . 9 4
22.42 S K=1;I ( T R - . 1 ) 2 2 . 4 6 ; I ( T R - 9 9 ) 2 2 . 4 3 ; S XM=.48;G 2 2 . 4 8
22.43 I ( T R - T O ( K ) ) 2 2 . 4 6 , 2 2 . 4 6 ; I (TO(K+1)-TR)22.46
22.44 S XM=CD(K+1)-(CD(K+1)-CD(K))*(TO(K+1)-TR)/(TO(K+1)-TO(K))
22.45 G 22.48
22.46 S K=K+1;G 2 2 . 4 3
22.47 S XM=CD(1)
22.48 S CF=2-FEXP(-XM*XK/TR) ;I (CF-.01)22.92
22.52 S TP='(X+TK(J+1))/RC;I (TP-99) 22. 54;S TP=99
22.54 S TR=FSQT(UR/RJ(J))*FLOG(TP);I ( 4 . 6 - T R ) 2 2 . 6 2 ; S TR=FEXP(TR);S K=l
22.56 I (TR-TO(K))22.58,22.58;I (TO(K+1)-TR)22.58
22.57 D 2 2 . 2 4 ; G 22.65
22.58 S K=K+1;G 22.56
22.62 S XM=-.18
22.65 S XX=XM*TP*UR/RJ(J);I (-XX-100)22.68;S XX=-100
22.68 S CF=CF*(1+1.4*FEXP(XX));I (.1-CF)22.94
22.92 S CF=.09
22.94 S CR=UR/CF;I (1.5-1) 22.96;S LR=CR;R
22.96 S AV=(CR+LR)/2;S LR=CR;D 25

23.12 I (T(J)-14)23.2,23.3
23.20 I (CR-.926)23.22;S P=7.2E-17;S K=1;G 23.4
23.22 I (CR-.0324)23.23;S P=3.3E-11;S K=.65;G 23.4
23.23 I (CR-.00755)23.24;S P=1.47E-14;S K=.832;G 23.4
23.24 S P=4E-17;S K=.966;G 23.4
23.30 I (CR-1.43)23.32;S P=2E-16;S K=1;G 23.4
23.32 I (CR-.0847)23.33;S P=6.97E-14;S K=.837;G 23.4
23.33 I (CR-.00715)23.34;S P=6.93E-09;S K=.543;G 23.4
23.34 I (CR-.00128)23.35;S P=2E-l6;S K=.94;G 23.4
23.35 S P=1.43E-12;S K=.744
23.40 S NN=FEXP<FLOG(1/(P*CR))/K>

24.12 I (CF-.D24.2
24.14 T %4.02,D,%11.04,CR," "%3.03,NN,%7.04,CF,%9.03,R(i),%8.04,UR
24.15 T %6.03,RC,I;R
24.20 T %4.02,D," T/R TOO SMALL TO GET CF",%14.03,R(I),%8.04,UR
24.22 G 24.15
24.50 T :::," DEPTH RESISTIVITY DOPING CF SR";G 24.52
24.52 T " UR RC",!, "(MICR) (OHM-CM)";G 24.54
24.54 T " (CM-3) (OHMS) (OHM-CM) (MICR)",I 1;R
25.10 I (.1-CF)25.15;R
25.15 S SH(J)=SH(J)+SF*lE-04/AV;R
25.20 T !!;S Z=J-1;F P=1,Z;D 25.5
25.40 G 25.8
25.50 T "SHEET RES OF LAYER",%2,P," =",%7.02,1/SH(P)," OHM/SQ",!;R
25.80 T!,"END",!!;Q

27.12 FK=1,9;S TO(K)=K/10

27.14 FK=10,19;S TO(K)=K-9
27.16 STO(20)=20;S TO(21)=50;S TO(22)=100
27.20 SCD(1)=.063716;S CD(2)=.11739;S CD(3)=.162256;S CD(4)=.19951
27.22 SCD(5)=.23029;S CD(6)=.255749;S CD(7)=.27679;S CD(8)=.294377
27.24 SCD(9)=.309103;S CD(10)=.321649;S CD(11)=.383058
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27 26 S CD(12)=.404117;S CD(13)=.414196;S CD(14)=.419867
27 27 S CD(15)=.423970;S CD(16)=.427666;S CD(17)=.430601
27 28 S CD(18)=.433109;S CD(19)=.435383;S CD(20)=.443056
27 29 S CD(21)=.443031;S CD(22)=.478852
27,40 S IN(1)=34.3205;S IN(2)=13.5469;S IN(3)=7.5875;S IN(4)=4.9045
27 42 S IN(5)=3.42615;S IN(6)=2.5109;S IN(7)=1.8989;S IN(8)=1.46676
27.44 S IN(9)=1.146676;S IN(10)=.908661;S IN(ll)=.024871
27.46 S IN(12)=-.159883;S IN(13)=-.216875;S IN(14)=-.23553
27.47 S IN(15)=-.23995;S IN(16)=-.237247;S IN(17)=-.23304
27.48 S IN(18)=-.2267;S IN(19)=-.22073;S IN(20)=-.17056
27.49 S IN(21)=-.138155;S IN(22)=-.18421

Appendix II
Variable List
SF SCALE FACTOR (MICRONS/POINT)
OR ORIENTATION (111 OR 100)
TK (J) THICKNESS OF JTH LAYER
T (J) TYPE (N OR P) Of JTH LAYER
R (I) SPREADING RES (OHMS) OF ITH POINT
I POINT INDEX
J LAYER INDEX
SP TOTAL NUMBER OF POINTS
NP (J) NUMBER OF POINTS IN JTH LAYER
UR UNCORRECTED RESISTIVITY (OHM-CM)
CR CORRECTED RESISTIVITY
CF CORRECTION FACTOR
D DEPTH (MICRONS)
RC RADIUS OF CONTACT (MICRONS)

Comment Cards
20.20 Read Tape
20.29 Calculate true R (I)
20.40 Correct to bevel edge
20.43 Edit bad points
20.50 Do first layer
20.60 •* Do remaining layers
21.10 Calculate UR
21.20 N <100>
21.30 N <111>
21.40 P <100>
21.50 P <111>
22.10 Calculate CF
22.20 Insulating boundary
22.40 Conducting boundary
22.50 Correct for insulating boundary below cond layer
23.10 Calculate doping
25.05 Calculate sheet resistance
27.10 CF data matrix

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565-448 O -15 - 6
 Appendix III
SLICE:H40488 SF:.ll ORNT:100 POINTS ON OXIDE:4
THK:3.25 TYPE:N THK:250 TYPErN THK:0
ENTER TAPE
9999

HOW MANY BAD POINTS? :0

DEPTH RESISTIVITY DOPING CF SR UR RC

(MICR) (OHM-CM) (CM-3) (OHMS) (OHM-CM) (MICR)
0.00 0.4695 0.129E+17 0.6968 591.560 0.3271 2.765
0.11 0.4573 0.133E+17 0.6886 570.162 0.3149 2.761
0.22 0.4712 0.129E+17 0.6779 578.094 0.3194 2.763
0.33 0.4766 0.127E+17 0.6670 575.438 0.3179 2.762
0.44 0.4781 0.126E+17 0.6555 567.542 0.3134 2.761
0.55 0.4889 0.123E+17 0.6440 570.162 0.3149 2.761
0.66 0.4800 0.126E+17 0.6344 552.075 0.3045 2.758
0.77 0.4793 0.126E+17 0.6234 541.999 0.2988 2.756
0.88 0.4787 0.126E+17 0.6125 532.106 0.2932 2.755
0.99 0.4915 0.122E+17 0.5993 534.562 0.2946 2.755
1.10 0.4901 0.123E+17 0.5869 522.395 0.2876 2.753
1.21 0.4843 0.124E+17 0.5745 505.824 0.2782 2.750
1.32 0.4827 0.125E+17 0.6502 492.038 0.2704 2.748
1.43 0.4884 0.123E+17 0.5459 485.288 0.2666 2.747
1.54 0.4860 0.124E+17 0.5307 469.893 0.2579 2.744
1.65 0.4897 0.123E+17 0.5144 459.197 0.2519 2.743
1.76 0.4941 0.122E+17 0.4979 448.744 0.2460 2.741
1.87 0.5022 0.119E+17 0.4785 438.529 0.2403 2.740
1.98 0.4696 0.129E+17 0.4658 399.944 0.2187 2.734
2.09 0.4564 0.134E+17 0.4488 374.972 0.2049 2.732
2.20 0.3983 0.157E+17 0.4390 320.626 0.1749 2.727
2.31 0.3474 0.185E+17 0.4323 275.422 0.1502 2.726
2.42 0.3056 0.216E+17 0.4226 236.591 0.1292 2.730
2.53 0.2243 0.312E+17 0.4394 179.473 0.0986 2.746
2.64 0.1349 0.573E+17 0.4876 117.489 0.0658 2.799
2.75 0.0744 0.127E+18 0.5733 73.451 0.0427 2.904
2.86 0.0469 0.297E+18 0.6554 50.816 0.0308 3.027
2.97 0.0224 0.116E+19 0.7931 26.546 0.0178 3.352
3.08 0.0140 0.275E+19 0.8911 16.982 0.0125 3.681
3.19 0.0108 0.448E+19 1.0001 13.932 0.0108 3.861
3.30 0.0106 0.462E+19 1.0001 13.614 0.0106 3.884
3.41 0.0106 0.459E+19 1.0001 13.677 0.0106 3.879
3.52 0.0106 0.462E+19 1.0001 13.614 0.0106 3.884
3.63 0.0105 0.468E+19 1. 0001 13.490 0.0105 3.893
3.74 0.0106 0.462E+19 1.0001 13.614 0.0106 3.884
3.85 0.0106 0.459E+19 1.0001 13.677 0.0106 3.879

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Figure 1. Potential distribution due to equipotential probe on semi-infinite solid
of homogenous resistivity, p.

Figure 2. Spreading Resistance Correction Factors.

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 Figure 3. Flow Diagram of SRPROF,

Figure 4. Comparison of Spreading Resistance and Diode C-V profiles.

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Multilayer Analysis of Spreading

Resistance Measurements

Gregg A. Lee

Texas Instruments Incorporated

Dallas, Texas 75222

Spreading resistance measurements provide a highly flexible technique for the determination
of dopant profiles in semiconductors. However, because each measurement samples a greater
depth into the sample than the depth difference between successive measurements, the direct
conversion of resistivity readings to dopant concentration values will not yield a correct profile.

The technique discussed in this report analyzes direct spreading resistance readings to
deduce a "true" dopant profile. The model used is that of circular contacts to a laterally infinite
medium which is partitioned vertically into layers of homogeneous resistivity, each layer
corresponding to one spreading resistance measurement point. The analysis is performed by a
computer program. Some detail in the development of the program is discussed.

The results of this analysis technique compare favorably to profile results of other profiling
techniques such as capacitance voltage and incremental sheet resistance on profile types to which
they can be applied. The program execution time is usually fast enough that the computer charge
is less than the direct charge billed for making the spreading resistance measurements.

Key Words: Correction factors, computer modeling, dopant profiles, multilayer spreading
resistance model, resistivity, semiconductor dopant concentration, spreading resistance.

1. Introduction

Spreading resistance measurements provide a potentially powerful method for determining dopant concentration
profiles in semiconductor materials, because continuous profiles can be obtained over several orders of magnitude of
concentration change and across p-n junctions. The profiles are obtained by stepping the probe points down a bevel
lapped at a small angle to the original surface (fig. 1). Each measurement point is assumed to approximate a
measurement on a flat surface formed by removing all material from the sample above the depth of that point on the
bevel. By using small angles (17' to 5°) it is possible to obtain profiles in which consecutive points differ in depth by
less than 200 A l l ] 1 .

Unfortunately, the precision of the geometry is negated by the comparatively large volume in the material being
profiled which is sampled by the electrical measurement. This volume may extend one to several microns into the
material (which in shallow devices may involve orders of magnitude of resistivity change). As a result, the
characteristics at a given depth in the material being profiled affect not one, but several of the measurement points on
the bevel Thus, the direct result of spreading resistance measurements is somewhat like a profile of local averages,
rather thin of discrete point values. Figure 2 shows a hypothetical example of this effect. Concentration rather than
resistivity is plotted since this is the value of interest in process modeling and design.

The method described here, which is performed by a computer program, alleviates this problem by deducing the
"true" profile from spreading resistance data as originally recorded.
1
Figures in brackets indicate the literature references at the end of this paper.
75
 2. Theoretical Model

The theoretical model employed is similar to that utilized by several other authors[2,3,4]. The continuous
resistivity profile is approximated by a stack of layers, each of homogeneous resistivity, with thicknesses equal to the
spacing of the spreading resistance data. The potential distribution in this structure can be solved numerically and
employed to derive the actual profile from the originally measured values.

2a. One Probe Potential Distribution

The general solution of Laplace's equation in cylindrical coordinates (r, 6, z) for a circularly symmetric potential
such as that resulting from a single probe is:

where V is voltage and A and B are arbitrary functions of the integration variable X. This can be rewritten as:

where

and r0 is the effective radius of contact of the probe, which is assumed to be circular. In the case of a layered
structure, a separate voltage function, Vj, is defined for each layer, such that:

At this point boundary conditions are imposed which assume that current is flowing, which may be inconsistent
with Laplace's equation if charge accumulation exists. However, the expected error introduced is not large[5], and
the results of the method do agree with other profiling techniques.

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 The boundary conditions are these: (refer to fig. 3)

I. No current flows through the surface of the structure beyond the radius of the probe contact:

II. At each layer interface

a. V is continuous:

b. The current component perpendicular to the interface is continuous:

III. Two possible appropriate boundary conditions exist for the bottom layer. One assumes that the last
layer is semi-infinite and of homogeneous resistivity. The other assumes that a junction exists beneath
the last layer.

In the first case, the boundary condition is that

In the second case, no current crosses the junction:

When the expression for Vj(r,z) is substituted into these equations, they reduce to the following set of equations.
Note that 0} and «// j are functions of X only, as previously defined.

For the first case:

For the second case:

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Where

This gives 2N equations, which are sufficient for the solution of the N 6 's and N $ 's. An additional boundary
condition involving the current distribution under the probe contact has been used by some authors to resolve K in
equation 2.0[6] . However, because the final form of the current distribution will be affected by the second probe of
apparatus, in this treatment its resolution is deferred until after the potential distribution of the two probes in
combination is determined.

The solution of the system of equations derived above will be treated in detail in a later section. At this point
just note that only the solution of Vj, and thus 6 \ (since equation 2.1 shows that ty \ = 0 \) is necessary, since the
surface potential is the only potential encountered by the probe.

2b. Two Probe Potential Difference Measurement

The voltage measured by the spreading resistance apparatus is the potential drop between the two probe points.
This is derived from a superposition of the one probe solution for each of the two probes. For this solution point
contacts are assumed. This is not too unreasonable since the ratio of the probe spacing to the physical contact
diameter is 600 to 10, and that of the probe spacing to the effective electrical contact diameter 600 to 3.

The measured potential difference between the probes Vm, is

where Va and Vjj are the potentials at probe a and probe b.

Each potential consists of two components: the potential due to probe a and that due to probe b. Note that the
one probe solution coordinates of b relative to a and a relative to b are both (r = D, z = 0), where D is the probe
spacing. Their coordinates relative to themselves are of course (0,0). That is:

So

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 Noting from equation 2.1 that 6 j = \l> j, expressing Vj in the form derived in equation 2.0 yields:

where the 2 has been absorbed into K.

The method of performing this integration is discussed in Section 5.

2c. Resolution of the Proportionately Constant K.

The boundary condition imposed in order to resolve K is that the measured voltage on a semi-inifinite substrate
of ^homogeneous resistivity should equal the voltage measured on that same substrate covered by a finite kyer of
equal resistivity. That is, a two layer problem:

Surface

Two layer problem on semi-infinite medium.

In this case the boundary equations, in matrix form, are:

which solves to:

79
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 On a semi-infinite substrate the measured spreading resistance voltage would be:

The defined boundary condition is that

and

This expression could have been developed directly from the model of two discs on a semi-infinite medium. The
direct result of this development is:

However, it has been traditional to neglect the second term and write

The approach just shown was used primarily to employ standard formulations as much as possible for familiarity.

It is necessary to keep the sin~l (ro/D) term because the iterative technique (Section 3 a) employed in the
solution tends to reinforce this small error on successive iterations resulting in an error several times as large as that in
the initial approximation.

3. Solution Technique

Replacement of K in the expression for Vm yields:

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 Previous authors[2,3,4] have chosen to reorder this equation to:

and to define

Since po would be the correct resistivity if the measurement of Vm and I were taken on a semi-infinite sample of
homogeneous resistivity. (This is the usual calibration procedure for a spreading resistance probe.) In addition, the
bracketed factor is defined as a "correction factor", so that

and thus

As Hu has pointed out [4], this is not an entirely appropriate terminology since "correction factor" implies an
arbitrary adjustment on "fudge factor" rather than a logical data reduction scheme. However, in spite of the name,
the format is a convenient one and is used here.

3 a. Iterative Technique

The last equation can be reordered to

where C is a function of ro, d, and 6 \. 6 \ is itself a function of h j h2 ... h^ and pj P2 ... PN- In other words, the
equation for the "corrected" value of p \ is not explicit in that C is a function of p j. In general the integral factor of C
has no analytical solution, and thus the equation cannot be solved explicitly for p'\.

The approach to solving for p j taken here is to define po as an approximation of p j and to obtain successfully
better approximations of p\ from an iterative solution of 3.3. Since the calibrations obtained with the Texas
Instruments apparatus allow ro to be assumed constant, P 2 . . .PN an^ hi ...h^ do not vary throughout the
solution. Thus C may be treated as a function of p j only.

Simple Relaxation:

always converges, but often very slowly in terms of the number of repetitions required. In addition, the only available
convergence criterion is comparison of successive values of p\. The iteration is terminated when Ap/p falls below a
predefined limit. However, in some cases the convergence is so slow that Ap/p may reach .001 when p \ is still 10%
aways from the correct value.

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 A Newton-Raphson technique, which uses both the last value of p j and its derivative to compute a new p j,
converges 3 to 5 times as fast as relaxation, but suffers the same weakness of convergence criteria and may oscillate in
some cases, especially if the input data is not smooth, rather than converge. The relations used for iteration is:

where Cj = AC/Ap j from the previous iteration or from an extra (p\, C(p j,)) pair generated if Ap\ would be too
large.

Both relaxation and the Newton-Raphson method can be characterized as analytic techniques. Another
technique which can be employed is a pragmatic hunting method which converges about one-half as quickly as the
Newton-Raphson technique, but converges absolutely and to a known absolute accuracy. The technique is a familiar
one, and best described as "bracketing". If a criterion can be found to determine if the correct value of p \ lies
between two other values of p \, a search along the p j axis can be conducted using an arbitrary step size Ap until the
criterion is met. Once this has occurred, the correct value of p j is bracketed to a known accuracy. By splitting the
bracket and retesting either of the two new brackets created for the presence of the correct value the bracket size can
be reduced by one-half. Repeating the process results in a one digit accuracy improvement each 3.322 (=(log 2)~1)
iterations.

The correct value of p \ will have the following characteristics:

In other words, two relationships must be simultaneously satisfied:

The relationship of these two equations is depicted qualitatively in figure 4. Curve B is clearly a straight line. The
shape of curve A has been determined from numerical solutions of C (pj) and, except for local curvature reversals
associated with noisy data, the shape has been qualitatively the same for every case tested. Since the two curves cross
at the correct solution of p\, C^-CB W*U change sign at this point. This is the bracketing criterion discussed
previously. The initial search is always conducted upward to avoid the trivial solution at p j = 0. Figure 4 also
illustrates a hypothetical series of approximations toward the correct value of p j.

The program normally uses a combination of Newton-Raphson and relaxation techniques to achieve short
running time. However, bracketing is selected for use on profiles which are ill-suited to the Newton-Raphson analysis.

3b. Bootstrap Solution

An iterative solution is applied to only one layer at a time. The method for correcting the entire structure is a
bootstrap process proceeding from the deepest to shallowest layer. In other words, the deepest layer is corrected on
the basis of the semi-infinite substrate or a junction boundary condition. Then the next is corrected on the basis of
the corrected value of the bottom layer and boundary conditions, the next on the basis of these two corrected
values, etc. The shallower layers, of course, do not affect the layer being corrected since they were not present at the
point on the bevel
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 3c. Summary

The sections which follow represent the greatest practical difficulties in performing the solution. However, they
are in fact sub-procedures to the scheme just discussed. So before proceeding a more concise summary of the overall
method is in order:

Resistivity layers are corrected one at a time, proceeding from the bottom to the top of the layer structure using
the previously corrected layers in the solution of later ones. The corrected .resistivity value is obtained from the
iterative solution of the implicit equation:

In this equation, C (p j) represents the following numerical integration:

The values of 0i(X) in this integral are obtained from the numerical solution of 2N simultaneous equations
where N is the number of layers in the structure.

4. Numerical Integration of C

In Section 3 it was found that

This integration is performed numerically using Simpson's Rule, which can be applied successfully since all functions
in the integrand are quite smooth. Two problems in performing the integration exist, however. First, the upper
integration limit is not finite; some way of approximating the upper limit with some finite limit must be found. And
second, the integrand is a product of three factors whose characteristics, or at least those pertinent to numerical
integration, are quite different.

The first problem is solved by breaking the integral into two parts and evaluating them separately:

The first integral can be evaluated by usual numerical techniques, but the second integral still has an infinite upper
limit. If L is chosen large enough, however, 9 \ can be made arbitrarily close to zero. (See Section 6, fig. 6 and fig. 8).
In this situation, the second integral becomes

83
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which, in a reversal of the process used above, can be rewritten as

The first of these two integrals can be solved analytically. The second can be evaluated numerically to an
arbitrary accuracy. Because the integral from L to °° has been approximated by an integral which does not involve 0 \,
its value will be independent of the layer structure. Thus it can be stored as a constant, so long as r0 and D do not
change.

When all physical dimensions (h, ro, and D) are measured hi multiples of ro, a value of L = 50 is adequate to
justify the approximation just discussed. (ro and D in this case are on the order of 1 to 3 microns and 600 microns)

The second problem mentioned manifests itself chiefly as a conflict between the maximum value of X required
to drive 6 \ to 0 and the small value of AX required to adequately approximate the Bessel function. D in units of ro is
approximately 400. This means that a zero of Jo occurs for every change in X of approximately .008. Even the
questionable allowance of 5 points per zero would require 31,250 integration points to reach X = 50. Fortunately, Jo
decreases in magnitude with increasing argument value. As X increases, the value of (1-JO(XDJ)) becomes dominated
by the 1 allowing the size of the integration increment, AX, to be increased. However, near X = 0 the size of AX must
be greatly reduced to prevent truncation errors caused by the subtraction of JO(XD) from 1, inasmuch as JO(XD)
approaches 1 as X approaches 0. This rapidly diminishing number cannot simply be ignored (i.e. assumed to be zero)
because in some cases (1 + 20) rises as fast as (1-JO(XD)) falls. In the case of the first layer above a junction, (1 + 26)
may rise nine orders of magnitude as X decreases from 10~2 to 10~^, while the value of the entire integrand rises
1 order and then falls eight.

The solution to these problems lies in careful selection of integration increments and some adjustment during
execution. The necessary number of integration increments is between twenty-two and twenty-three thousand.

5. Solution of B\

Each layer requires 3 to 20 iterations for the solution of equation 3.3 to converge. Each iteration requires that
the integral in equation 3.1 be evaluated once. Finally, each evaluation of the integral requires that a value for 8 \ (X)
be determined at nearly 23,000 values of X. Thus it is quite important that a fast method of solution for the system of
equations 2.1 and 2.4 be used. The next sections describe this method.

5 a. Reduction from 2N to 2N-2 to Equations

The set of simultaneous equations is solved numerically, but before the solution is performed, it is possible to
analytically reduce the size of the coefficient matrix by two in each direction by eliminating two equations and two
variables. Equations 2.1-2.4a, restated in matrix form, are:

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where Ej= e ™jX Tne geometry is as in figure 3 with hjsj -* °°. The areas of the matrix not shown are entirely zeros.

The case shown is for the infinite substrate boundary condition (2.4a). For the junction boundary
condition (2.4b) the last row of the matrix would become:

with the junction at hw in figure 3.

In both cases </> \ and <//N> an(* the outside rows and columns of the coefficient matrix can be eliminated. Since
the first equation is 6 \ = ^ \ , the first two columns represent the same variable and so can be added and the top row
eliminated. For the infinite substrate case, ^N is zero and so can simply be removed, along with its coefficients, the
right most column. The junction case for ^N is similar to that for $ \. Since the last equation expresses #N as a
function of 6 N only, this expression can be substituted into the previous two equations and the last row and column
eliminated. The result for a semi-infinite substrate is

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For the junction case the last 2 rows become

The elimination of the two equations and variables just discussed does reduce the solution time somewhat, but
especially for large, N, not significantly. It does, however, put the matrix into a better format on which to perform a
diagonal solution algorithm.

5b. Matrix Solution

The high sparcity and regularity of the coefficient matrix make it possible to construct a "diagonal algorithm"
which solves ford, in onepass of an iterative calculation along the diagonal of the matrix. Its development is
straightforward from consideration of a Gauss reduction in which steps for which the result is known because of zeros
involved in the calculator are eliminated. The algorithm is constructed to end at0, rather than 0j>j, as would be
conventional for the matrix as it has been presented.

The matrix need not be stored as a 2N X 2N away, but can be compressed to 2N X 4. This saves considerable
storage and is convenient for programming the diagonal algorithm as well.

Finally, to repeat a point made earlier, no back substitution to solve 02, ^ 1> • • •> e N> ^N ** necessary since only
01 appears in the expression for V j.

5c. Intermediate Coefficient Storage

As mentioned previously, the only coefficients in the matrix which change between iterations are those which
involve pj. This fact, and the fact that the matrix can be solved in one pass, make it possible to save the values
generated by the reduction at the last step before it enters the final two rows, and restart at this point on subsequent
iterations. This reduces the number of operations required for the matrix solution to those required for the solution
of a 3 X 3 matrix on all but the first iteration. Of course a different set of coefficient values must be stored for each
value of X at which 0 j is evaluated. This is practical only if the number of X's is relatively small. This is the case as
explained in the next section.

5d. Approximation of 0 \ by Interpolation and Extrapolation

The greatest time savings in evaluating 0 \ is not in finding a fast way to solve for 0 \, but in avoiding the solutio
entirely. It is possible to compute values for 0 \ at a relatively small (typically about 50) number of values of X and
interpolate or extrapolate 0 j at other values. The importance of this fact is made clear by the fact that the integration
involves nearly 23,000 values of X.

Figures 5, 6, 7, and 8 illustrate the behavior of (1 + 20 j) for two different situations. Figures 5 and 7 show
original and corrected profiles for a steep gradient away from a junction, and for a steep epi interface. Figures 6 and 8
show the associated values of (1 + 20 ) vs X at various values of N.

The boundary condition in figure 5 is that of a junction at the bottom layer. The (2 + 20 j) function for this
type profile is fitted very well by a power law, at least in the region 0 < X < 2.

It can be demonstrated that for the junction boundary condition, as X -*• 0,0 j -* °°.

This would present a serious problem to numerical integration were it not for the fact that the entire integrand
converges to 0 at X = 0. If X is taken near enough to 0, the contribution of the the integrand at that point becomes
immaterial.

Values of (1 + 20 j) generated by a profile similar to figure 7 are best fitted by a parabola. The actual system
used is a fitted parabola to each set of three consecutive points, with overlaps averaged. The overlapping is done to
avoid problems at inflection points.
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 The criterion of "good fit" used in both cases is the agreement to .1% of the value of (1 + 20 j) computed
exactly and interpolated at the midpoint of two successive values of X to be used as a basis for interpolation. If
adequate agreement does not exist, the midpoint is incorporated as an exactly calculated point in addition to the two
original points, and the test performed again in each of the two new intervals.

For intermediate values of X, a parabola fit is used with either boundary condition. For large values of X, 1 + 20,
approaches 1 asymptomatically. B j can be approximated in this region by an extrapolation of an exponential fit to
two selected values of 0 j at relatively low values of X. This extrapolation is used to calculate a few point values of 0 j
and the rest are linearly interpolated between them. The purpose of this exercise is to avoid excessive time consuming
exponential calculations. (In no case, has the approximated value of 0 j in the "tail" region differed from an exact
value by an amount affecting the first three significant digits.)

6. Data Pre-Processing

When input data is not "smooth", the Multilayer Analysis may magnify input irregularities into the output
profile. Figure 9, the original and analyzed profile of an epi-substrate interface, is an example of this effect. The
output profile is quite irregular even though the input appears smooth to the eye. The effect occurs when layers
beneath the layer being corrected make a major contribution to the measured voltage. When this is true, the program
decides that minor variations in the measured voltage must be caused by major ones in the single surface layer since its
contribution to the total measured voltage is relatively small. In figure 9 this is particularly true since the surface
layer at the point where irregularity begins is underlain by layers of from one to three orders of magnitude higher
conductivity than the surface layer.

The problem is not in the program per se, but in the fact that the theoretical physical model used does not
consider the problem of noisy data and also in the fact that although the model is a reasonable approximation of a
smooth profile, it is a poor one for the derivative of the profile. The problem, then, cannot be solved by any change
to the analysis technique short of complete revision. It must be solved at the input data. This is reasonable anyway,
since one normally believes that the profile is really smooth and that variations of the type discussed here are indeed
noise.

Modifying the input data presents two problems. The first is to define criteria of "smoothness". The second is to
smooth the data while avoiding both the loss of information originally contained in the data and the introduction of
an arbitrary shape to the data profile from the smoothing technique.

The second problem may not be completely avoidable, and in any case cannot be measured quantitatively, so the
best approach is to do as little as possible and accept some irregularity in the output profile if it is not severe.

Since the problem arises from the poor model of the derivative supplied by a step function profile, the basic
criterion of smoothness is a locally monotonic set of first differences, which are the finite difference analog of the
first derivative. The first difference between two data points is:

(Voltage, V, is normally smoothed since this is the form of the raw data, but R or p could be smoothed as well.) No
consideration of A^, the depth change, is necessary, since it is constant. The second difference is defined as:

Notice that if the set of first differences varies monotonically, then all second differences have the same sign.

Since the first differences must be smooth, it is these values on which the smoothing routine operates. However,
data may be too noisy to allow this operation to be performed directly. The routine followed is this:
• The initial data values are smoothed.
• First differences are computed from the smoothed values.
• These first differences are smoothed.
• The final profile is recomputed based on the smoothed differences.
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565-448 0 - 7 5 - 7
The smoothing procedure referred to is as follows:
• A best fit parabola is generated for each set of five consecutive original points.
• The center point of the five is recomputed from the parabola.
This avoids imposing a functional shape because no two points are adjusted using the same parabola. It also avoids
displacing the profile because only initial data is used to generate the smoothed result. That is, the parabolas are fitted
only to initial values, not to the smoothed results for previously adjusted points.

Second order smoothing does occur, however, when the first differences computed from a smoothed data set are
themselves smoothed. When a smoothed data profile is recomputed from the smoothed differences, displacement of
the profile from its original envelope is avoided by allocating the change in the first difference equally to the positions
of the data points at each end of the interval. Expressed algebraically for a non-end point:

Thus, the resulting profile contains not the smoothed differences, but differences changed in the direction of the
smoothed values, but limited by the original data envelope.

Two tests of this technique are particularly important. First, does the profile drift from its original position?
And second, does originally smooth data remain smooth? Both can be tested by smoothing profiles generated from
various polynomial and transcendental functions whose values and first derivatives are continuous. These profiles are
by definition already smooth. It was found that after five iterations of smoothing previously smoothed output, the
maximum deviation at any data points was .055% from the original. The results of the first smoothing operation
deviated at most .049%. The deviations on subsequent iterations did trend further in the same direction as the first
iteration deviations. This and the fact that the greatest parts of the deviations appear on the first iteration suggest that
some arbitrary shaping occurs. However, it is small.

At this point, the smoothing program makes no judgment as to the adequacy of the smoothing. In fact, no firm
criteria have been developed. The program simply performs the smoothing routine and supplies the initial and
smoothed data along with first and second differences. Neither does it attempt to remove grossly erroneous data
values from the initial data before smoothing. Occasionally it does change the shape of the profile, but only at very
sharp peaks or bends. Obviously it is still necessary to screen the results of smoothing before using them.

As an example of the results of this data preprocessing, figure 6 was obtained from the data used in figure 9, but
after smoothing. The smoothing routine cannot handle really noisy data at all. The best procedure in this case is very
much as in the past. A best fit curve is drawn by eye and smooth data read from this curve for input to the analysis
program.

7. Results

The effect of this analysis on different profile types has been illustrated in figures 5 and 7, but these only verify
that the results are qualitative as expected. Some measure of quantitative accuracy can be obtained by comparison
of dopant profiles obtained from analyzed spreading resistance data and other profiling techniques. The techniques
used were junction and mercury probe capacitance-voltage measurements and in cremental sheet resistance. While
these techniques cannot be used on all types of profiles, they do have a known reliability for specific profile shapes.

The result of such comparisons is general agreement, but certain discrepancies exist. The first is illustrated in
figure 10, a comparison of analyzed and unanalyzed spreading resistance profiles and capacitance-voltage profiles of
an epi-substrate structure. The dip in the analyzed spreading resistance profile at the interface of the flat section of
the profile and the steeply rising section is a program artifact. Fortunately, it is one which is easily recognized by an
experienced user and thus need not be confusing. The absolute dimensions of the structure involved determined the
importance of this defect; the feature is quite prominent in figure 10, but not nearly so in figures 5 and 7, whose
absolute depth is greater.

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 The effect seems to arise from a discrepancy between the probe model and reality. Recall that the model used
for the probe contact was a single circle of uniform potential. However, optical microscopy and SEM of the probe tips
and the probe "prints" left on a sample reveal that the contact is actually composed of a large number of smaller
contacts over a generally circular area. Furthermore, when a calibration of spreading resistance versus resistivity is
attempted using the equation R = p/2ro, the value of ro obtained is significantly less than the radius of the probe
print [ 1 ]. Unfortunately, an analytical solution for a model more resembling the probe geometry has not been possible
because of the complex boundary conditions involved in a tight array of contacts, either in a density distribution or
some arbitrary pattern.

A simple "non-real" model can explain the value of ro obtained by the calibration. If the contact is viewed as
having a constant voltage, but a limited number of conducting areas in a uniform distribution so that the probability
that a contact touches a given point within the limits of the array is 8, then the development of the two probe
equation is nearly identical to that of the conducting disc model. The final form is

where rrj is the radius of the damaged area of the probe point, or the limit of the contact array. Since 8 is the
probability of contact to an arbitrary point, 5 = AC/AD, where AC is the total area of contact and Aj) is the area of
the region of the array of contacts, or the damaged area. Thus the ro measured in calibration is

This allows a solution for AC, but this is of little help since neither the density nor the size of the individual
contacts is revealed in the calibration procedure. Also, observation of probe point hardly suggests uniformity. This
model does help to confirm the conjecture that AC is less than ATJ, however.

The value of ro given by a R vs p calibration is usually called the "effective" radius, and is treated as though it
were the radius in a calibration for uniformly doped samples. This is reasonable since the lateral displacement between
the points of contact is small compared to the probe to probe distance.

Multilayer analysis, however, is concerned with the potential distribution immediately beneath the probe, so the
distribution near individual contacts is important. Figure 11 is a hypothetical representation of the real problem. In a
distributed contact array with individual contacts small enough for the potential distribution near each contact to
resemble that of an isolated small circular contact, the previously developed contact model indicates that the voltage
near the small contact will fall off more quickly than that near a large one.

The single contact probe model then may look too deep in calculating C, and for certain geometries it
"overcorrects"; thus, the dip. But the problem is more than one of depth alone; the shape of the potential under the
probe is also important. Simply reducing the value of ro does indeed remove the dip, but it also moves the rest of the
analyzed profile away from the capacitance-voltage data. Figure 12 repeats the C-V curve of figure 10, but with the
C-V data reduced to a smooth curve. The two analyzed spreading resistance curves are for r o = 1.556Mm, the value
given by calibration, and for ro = .5 MHI, the largest value which removes the dip. Intermediate values produce profiles
between the two shown.

A typical comparison of an incremental sheet resistance profile to an analyzed spreading resistance profile of a
shallow phosphorus diffusion is shown in figure 13. The results are in good agreement on the steeply inclined portion
of the profile, but they differ near the surface. It is not completely clear whether this is a program artifact or whether
it arises in the measurement technique since unexpected deviations of the original profile near the surface may occur
in all shapes of profile, as in figure 7. Reducing the value of ro for this type of profile produces no better correlation
and no improvement in the analyzed profile shape near the surface. Removing the coating used to enhance the quality
of the surface-to-bevel corner on the sample reduces the effect, but does not eliminate it.

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 Since the multilayer analysis is performed by a computer program, an important consideration is speed of
execution, which will significantly affect the practicality of the measurement by affecting cost. Figure 14 is a plot of
run time vs points in the profile. These are typical; noisy data and abrupt corners will increase the run time.

The analysis program cost is usually about one-half or less of the cost of the original data acquisition.

Conclusions

The multilayer analysis of spreading resistance data provides a significant improvement over directly calibrated
data when exact profile shape is of interest.

However, the analysis makes certain mistakes related to deficiencies in the probe contact model now used. These,
errors are easily recognized, but require that the analysis results be screened by someone familiar with the problem.

An improved contact model will be necessary to correct the problem. This is a logical next step to consider.

The cost of the analysis is reasonable for routine use.

Acknowledgements

The author wishes to thank Gordon Gumming for considerable discussion both on modeling and on
programming techniques, and Francois Padovani and Fred Voltmer for providing spreading resistance measurements.

References

[ 1 ] F. Voltmer, personal communication.

[2] P. A. Schumann, Jr., and E. E. Gardner, "Spreading Resistance Correction Factors," Solid-State Electronics,
Vol. 12, pp. 371-375(1969).

[3] T. H. Yeh and K. H. Khokhani, "Multilayer Theory of Correction Factors for Spreading Resistance
Measurements,"/. Electrochem. Soc. Electrochem. Tech., Vol. 116, No. 10 (1969).

[4] S. M. Hu, "Calculation of Spreading Resistance Correction Factors", Solid-State Electronics, Vol. 15, No. 7F,
pp. 809-817(1972).

[5] See also: P. A. Schumann, Jr. and E. E. Gardner, "Multilayer Potential Distribution," Technical Report 22,404,
IBM Components Div., East Fishkill.

[6] E. E. Gardner and P. A. Schumann, Jr., "Potential Distribution in Multi-Layered Structures," IBM Technical
Report 22, 191.

[7] H. Ruiz, "On the Calibration and Performance of a Spreading Resistance Probe," this publication.

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 Figure 1. Spreading Resistance Probe Geometry (Scale Distorted).

TRUE PROFILE

SPREADING RESISTANCE DATA

Figure 2. Hypothetical Concentration Profile and Resulting Spreading Resistance Readings if the Left is Nearer the
Top of the Bevel.

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 Figure 4. Qualitative Representation of
Bracketing Convergence Technique and a
Typical Set. of Consecutive Approximations
of p.

Figure 5. Original Data and Result of

Multilayer Analysis for Epi-DUF-Junction
Structure.

Figure 6. 1+26 versus X for Profile

Shown in Figure 5.

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 Figure 8. 1+20 versus X for Profile
Shown in Figure 7.
Figure 7. Original Data and Multilayer
Analysis Results for an Epi Layer on
Infinite Substrate Structure.

Figure 9. Result of Analysis of Data Figure 10. Comparison of Spreading Resis-

Without Preprocessing. tance and Capacitance-Voltage Profiles.
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Figure 11. Hypothetical Comparison of
Single and Multiple Contact Probe Voltage
Equipotentials Showing Deeper Penetration
of Single Probe Field Near the Surface.

Figure 12. Effect of Changing Effective

Radius of Contact, rQ, on the Analyzed
Spreading Resistance Profile.

Figure 14. Execution Time versus Number

of Layers in the Profile for Two General
Figure 13. Comparison of Analyzed Types of Profiles. Times Vary Consider-
ably Due to Noise and Shape of Individ-
Spreading Resistance and Incremental ual Profiles.
Sheet Resistance
Copyright Profiles.
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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

An Automated Spreading Resistance Test Facility

James C. White, Jr.

Western Electric Co., Inc,
555 Union Blvd.
Allentown, Pa. 18103

An automated spreading resistance test facility has been designed

and constructed at the Allentown Works of the Western Electric Co.
This system has been shown'to provide a rapid, semi-nondestructive,
and reproducible measurement of epitaxial layer resistivity which can
be used in a production environment. The system has the advantages
of operator independence, well protected probes, and four-inch capa-
bility. Surface or in-depth measurements can be performed with on-line
calculations of resistivity and impurity concentration. Cycle time is
less than five seconds per measurement and system reproducibility is +
1.30 (IS).

Key Words: Automated testing; epitaxial silicon; impurity concentration;

resistivity; semiconductor materials; silicon; spreading resistance.

1. Introduction

Probably the first question that comes to mind when the automation of a test facility
is proposed is "Why Automate?". The motives for automation range from a desire to remove
operator variability from a measurement to a need for rapid reproducible measurements. At
Western Electric - Allentown, the spreading resistance technique was investigated as a
tool to satisfy the need for a rapid, nondestructive method for measuring epitaxial layer
resistivity. A rapid technique was desirable for use for epitaxial reactor control. A
nondestructive technique was attractive for a measurement directly on product with minimal,
damage to the wafer.

2. Alternative Measurement Techniques

The most widely used measurement technique for determining epitaxial layer resistivity
is the four-point probe or control wafer technique (l)-*-« While this technique is rapid,
it is not directly applicable to a majority of the epitaxial material being processed
today. An isolating junction must exist between the epitaxial layer and the substrate.
Therefore, n/n+ and p/p+ structures are not directly measurable nor is the technique
easily applied to wafers with subdiffused patterns. -For these structures, substrates of
opposite conductivity type from the layer to be deposited are placed in the reactor and
layers deposited on these wafers are evaluated using a four-point probe. The assumption
is made that the growth conditions on these control wafers do not differ significantly
from those on the product wafers.
Other techniques such as diode voltage-capacitance and MOS voltage-capacitance (2) are
destructive and/or require extensive sample preparation prior to measurement.

Because the spreading resistance technique appeared to satisfy the requirements for
both a rapid and a semi-nondestructive measure of epitaxial layer.resistivity directly on
any type of structure, it was investigated as a possible tool for use in a production
environment.
1
Figures in parentheses indicate literature references at the end of this paper.
*J
 3. Why Automate?

A manual system was first constructed to determine the 'precision and to gain a work-
ing knowledge of the technique. The experience gained from use of this manual system
demonstrated that the technique had the resolution and precision required for an epitaxial
layer resistivity measurement. However, many of the advantages of the technique were lost
in the manual system.

To satisfy the requirement of rapid feedback for epitaxial reactor control, it was
felt necessary to provide for on-line calculation of resistivity and/or impurity
concentration incorporating the relevant calibration and correction factors. Because of
the importance of reproducible contacts between the probes and the wafer surface, it was
deemed imperative that lowering and loading of the probes, application of current, and
measurement of voltage all be done in a controlled manner with no operation interaction
if possible. Moreover, because of the ability of the spreading resistance technique to
detect small fluctuations in resistivity, several measurements on a wafer were desirable
to obtain an average resistivity. Based on these criteria, the decision was made to
automate the spreading resistance facility (Fig. l).

k. Automated Facility Description

A block diagram of the automated test system is shown in Figure 2. The heart of
the system is a Hewlett-Packard 21l6C digital computer with l6K words of memory and a
16 bit word. Control and timing of all measurement functions are handled via this
computer. The computer is programmed in BASIC. A conversational language was chosen in
lieu of machine language because of the versatility and programming ease offered by
conversational languages. Calibration curves, correction factors, sequencing, and other
variables are easily changed by anyone with a minimum of programming experience. The
constant current supply is marketed by COSAR and is continuously programmable over the
range of one nanoampere to one ampere with a compliance voltage of 50 volts.

The wafer stage is positioned by two 500 steps/revolution stepping motors driving
an X-Y movement with a twenty pitch lead screw. This provides 0.0001 inch resolution and
a total travel of four inches in both the X- and Y-directions.

The remainder of the electronics consists of a high impedance digital voltmeter, a

digital thermometer for temperature corrections if desired, and an X-Y recorder and a
Teletype for output of resistivity and/or impurity concentration.

The probing arrangement selected is manufactured by Jandel Engineering Limited

(Figure 3)• This probe consists of three tungsten carbide needles individually loaded by
gram gauges. These gauges are readily adjustable in the range of 0-100 grams. A
kinematic needle guidance system employing precision ruby ball guides and polished tungsten
carbide rods eliminates any sideplay of the needles and keeps friction to a minimum.
Because of the subsequent availability and industry acceptance of the Mazur two-probe
spreading resistance test system, the decision was made to convert the Western Electric
system for a two-probe measurement. The three probes have been maintained, however,
providing the versatility of performing a one-, two-, or three-probe measurement at will.
5. Measurement Sequence

The testing sequence begins with a series of questions to be answered by the system
operator. The conductivity types of the layer and the substrate, crystallographic
orientation, and thickness of the epitaxial layer are input via the Teletype. The wafer
is then automatically positioned under the probes and the measurement sequence begins.

To insure a reproducible contact between the probes and the wafer surface and to keep
wafer damage to a minimum, the probes are lowered to the wafer surface under their own
weight. The loading is then applied at a controlled rate through an air dashpot. No
current is forced until the probes are at rest on the wafer surface and are fully loaded.
This precaution is taken to protect the integrity of the probes and to further reduce wafer
damage.
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 The constant current supply is automatically ranged to produce a voltage at the probes
of "between five and fifty millivolts. At each measurement location, voltage measurements
are taken with current flowing in both the forward and reverse directions to minimize
erroneous measurements due to injection and electrical noise. For most samples, measure-
ments can then be performed with normal incident light. An added benefit of the forward-
reverse current pair is the capability of detecting the presence of p-n junctions from
large forward-reverse voltage differences.
From each resistance measurement, an uncorrected resistivity is calculated using
calibration curves developed from four-probe measurements on bulk polished wafers. This
result is then corrected for finite layer thickness using a routine similar to that
described by Dr. Bernard Morris (3) and the impurity concentration is calculated from a
piecewise-linear fit to Irvin's curves (4). If desired, on-line plotting of resistivity
or impurity concentration vs. wafer position is available.
For surface measurements, a series of measurements are taken in an X-pattern as shown
in Figure k. When all measurements on the wafer are complete, the wafer is returned to its
home position, well away from the probes. Radial resistivity gradient, average resistivity
and standard deviation for the wafer are output on the Teletype.
While the chief use of the automated spreading resistance system is for measuring
average surface resistivity, in-depth capability has also been provided. The surface
preparation for this method involves a rotary grooving technique which produces a
cylindrical groove in the wafer surface. This technique was chosen over angle-lapping
because of the sharp angle produced by the groover at the wafer surface and the subsequent
ease with which this edge can be aligned. An interference-contrast microscope mounted at
a known fixed distance from the probes is used for the alignment.
An initial dialogue similar to that for surface measurements is answered with the
additional input of groove width. The edge of the bevel is automatically aligned with the
probes and a series of measurements is taken. If small steps, less than 0.0005 inch, are
to be taken, a zig-zag motion is incorporated to prevent overlapping of damaged areas.
At each measurement location, the depth of the measurement is calculated, based on the
width of the groove and the lateral distance moved, and the resistivity is corrected for
this depth. As for surface measurements, output can be selected on the Teletype and/or
the on-line plotter.

6. Summary
The decision was made to develop an automated spreading resistance test system to
provide versatility not available in any other system. A system was developed which has
the reliability, versatility, and reproducibility necessary for daily use in a production
environment. The system has the advantages of operator independence, well protected
probes, and four-inch capability. Surface or in-depth measurements can be performed with
programmable cycle times, on-line calculations and corrections of resistivity and impurity
concentration, and on-line plotting of these corrected results. The system is able to
accomplish this with a total cycle time of only five seconds per measurement and has been
found to be reproducible to + 1«3$ (IS).

7« References
(1) W. J. Patrick, Solid State (3) B. E. Morris, Symposium on
Electronics 9, 203 (1966). Spreading Resistance Measurements
(197*0.
(2) W. C. Niehaus, W. VanGelder, T. D.
Jones, P. H. Langer, Silicon Device (4) J. C. Irvin, Bell System Tech. J.
Processing (National Bureau of Stand- iO., No. 2, §87-^10 (March 1962).
ards Special Publication 337), 256-72
(1970).
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 COSAI 501 H.P. 34801
CONSTANT CURRENT DIGITAL VOLTMETEI
SUPPLY
PROIE
DORIC CONTROL
H.P. 2116C
DIGITAL SLO-SYN
THERMOMETER DIGITAL COMPUTER
STEPPING
MOTORS
1
H.P. 7004R KSR-35 TTY
X-Y RECORDER

BLOCK DIAGRAM OF
AUTOMATED SPREADING
RESISTANCE TEST SYSTEM

FIGURE 2 BLOCK DIAGRAM OF AUTOMATED SYSTEM

FIGURE 1 AUTOMATED SPREADING

RESISTANCE TEST FACILITY

PROBE
GUIDANCE
SYSTEM RADIAL RESISTIVITY
MEASUREMENT LOCATIONS
FIGURE 3 PROBE GUIDANCE SYSTEM FIGURE 4 RADIAL RESISTIVITY MEASUREMENT LOCATIONS

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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Angle-Bevelling Silicon Epitaxial

Layers, Technique and Evaluation

P.J. Severin

Philips Research Laboratories

Eindhoven, Netherlands

The properties of a steel probe for a spreading-

resistance system are discussed stressing the effect of
micro- and macrocontacts. The need is explained for
producing small-angle bevels and a lapping jig for
making such bevels is described. With small-angle be-
vels the slice topography cannot be neglected and a
simple instrument is described by which the surface
topography of the whole slice can be recorded. By re-
cording the slice topography before and after bevelling
the local reduction of thickness by the bevelling pro-
cess is determined. This method can be used for angles
between 1/50O and 1/2OOO. It is indispensable for the
proper interpretation of spreading resistance measure-
ments on bevelled N on N junctions.

Keywords: bevel, interferometer, jig, microcontacts, silicon,

spreading resistance, steel probe, topography.

1. Introduction

For advanced applications of epitaxially grown structures the dope

concentration profile and the extent of the concentration gradient be-
tween substrate and epitaxial layer are of paramount importance. This is
of particular interest for thin layers, a few microns or less thick. The
capacitance-voltage technique £lj* is very well suited for study of the
charge carrier distribution up to a level of about 10^' cm"-, but for
study of the full interface properties surface probing techniques should
be used and therefore the interior should be exposed by bevelling the
slice. The method for surface probing is the spreading resistance tech-
nique, which is accepted now as a very powerful tool for investigating
epitaxially grown structures.
For obtaining a large resolving power with the bevel technique the
probe averagingdepth should be as small as possible. With the spreading
resistance probe used by us the horizontal averaging lengthis fairly
large, about 25 (jm. Therefore the bevel angle must be very small. This
implies, however, that for precise correlation between horizontal posi-
tion and depth below the original surface the departure from ideal flat-
ness of the slice is taken into account. In the next section the sprea-
ding resistance probe used in our laboratory for several years is dis-
cussed and a number of details essential for understanding the mode of
operation is presented. A polishing jig and a laser-operated interfero-
meter are described in the third section. Their use in producing the
bevel and for evaluating the local bevel angle, taking into account
any departure from perfect flatness of the slice, is explained in the

figures in brackets indicate the literature references at the end of this paper
99
fourth section. The method is illustrated with a fully worked-out example:
an N on N+ epitaxial layer is bevelled, evaluated and spreading-resis-
tance measured. The formalism for deducing the resistivity profile is
critically discussed in another contribution to this Symposium £2} .

2. The steel spreading resistance probe

The spreading resistance probe system now in use in our laboratory

£3,4,5] for several years is based on the use of a specially hardened
steel probe taken from a conventional Dumas four-point-probe head. This
probe is broken and sharpened until the untouched bottom of the tip is
about 25 \an across, which yields a mechanical contact diameter of about
15Mnu
Microscopic evidence proved conclusively that the bottom surface of
the probe is multi-tipped and that the mechanical contact to the silicon
is made up of a number of microcontacts. ¥ith high-power dark-field illu-
mination the most pronounced prints made by the microcontacts are visible
and with a chromic etch these prints stand out more clearly. With an in-
terference contrast microscope more details can be seen of the etched
print, but the size and depth of the microcontacts cannot be assessed and
must be less than 0. 1 jjm. With a scanning electron microscope the print
could not be found, because the minute damage due to the microcontacts
is more wide than it is deep. For a given probe the print pattern is
completely reproducible , and shown in figure 1.
It is well-known that below a circular metal contact to a semicon-
ductor of resistivity ^ the potential drops from the applied potential
V to about 0. 1 V at a depth of about twice the* radius. This holds for
each of the many microcontacts of radius a. At that level the equipoten-
tial lines are almost horizontal and the microcontacts cannot be dis-^
tinguished individually any more. This occurs at a depth which is very
shallow compared to the diameter 2A of the total contact area and there-
fore this new, deep, macrocontact is again subjected to the spreading
resistance phenomenon.
In this model the micro- and macrocontact resistance R S "I. and R S3.
can be considered acting in series. The currents through the microcon-
tacts are supposed to be independent and the series combination of the
macro- and microcontacts yields the equivalent circuit shown in figure 2
with

where n and.a are the number and average radius of the microcontacts. For
a steel probe total spreading resistance was found £3»^} to be propor-
tional to a over four decades, both for N- and P-type Si

where A represents the equivalent radius of the contact. A number of

authors have reported that for their, harder, probes

where k($) is a correction factor of order unity attributed to a variety

of causes, generally ^-dependent zero-bias-barrier resistance in series
to the true spreading resistance.
Although it appears possible to experimentally separate the two con-
tributions R and R . because they have widely different thermal time
constants, aifff non-l:nrea>ritie$ can readily be generated in the microcontacts,
we simply measure A and A and apply eqs (l) and (2).
The value of A is found from microscopic examination of the print
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and the value of the equivalent radius A is found from calibration
measurements. The latter depends weakly on the nature, surface texture
and preparation of the semiconductor. It is slightly different for each
probe and decreases slowly during a probe lifetime.
Normally a large contact resistance is undesired because it spoils
the proportionality to f of the spreading resistance in series, as shown
in eq. (3)- The resistance of the microcontacts shows a spreading resis-
tance controlled proportionality to $ and their contribution is welcomed
because of the ensuing small information collecting depth a. This will be
discussed below in connection with the resolving power.
It is an essential property of this type of steel probe that the mi-
crocontact distribution after a short formation process shows hardly any
alteration in many thousands of measurements on polished silicon. Evi-
dently the probe is loaded elastically only. ¥hen the probe is applied
to a lapped sample the distribution pattern of the microcontacts changes,
but the value of na remains very nearly the same. It is well-known from
mechanical and thermal contact studies and experiments in friction and
wear that any metal surface has protrusions. These are referred to as
asperities. The protrusions, often harder than the matrix material by
an order of magnitude, have been the subject of many controversial expe-
riments and speculative theories. Their nature and origin are problems
beyond the scope of this paper. The reproducibility of this steel probe
spreading resistance amounts to about 1$, as shown by some surface pro-
bing tracks, presented in figure 3«
Typical values of the various parameters for a load F = 15O gram on
polished N-type silicon are A =2.2 |jm, A = 12.5 V&t hence na = 2.7 \B&,
which with n « 10O yields a «s O.03 (Jm; also R ,/R **,*:>. Generally a small
contact radius is considered desirable for spreading resistance measure-
ments. However, with a steel probe the load cannot be reduced without
seriously degrading the performance of the spreading resistance probe.
The following experiments were done with the intention of shedding
some light on the dependence of A and A on the load F. The probe is
broken in order to expose a large number of asperities and sharpened
until the contact area left untouched is only slightly smaller than the
stable area found after plastic deformation with the lowest load used
in the experiment. Then with successively increased loads the probe is
applied on a lapped and subsequently on a polished surface. The values
of A* and A* on both types of surface and of A on the polished sur-
face are determined. On a lapped surface no prinx is visible so that A,
cannot be determined but at a given load must be between A— at the same
and the lower load. It turns out that A .. increases linearly with F, as
shown in figure 4, whereas the radius A is almost constant. Below a load
of 1OOg a very erratic signal was produced. Apparently the spreading re-
sistance on polished material can only be properly measured with a probe
which is on the verge of yielding. Above 10O g the probe is again load
ed up to the yield strength on polished material. The contact on lapped
material at low loads is determined by na only, but at about 1OO g the
influence of A is dominant. On lapped material not only the probe aspe-
rities, but also, probably even more important, the roughness of the
sample determines the microcontact contribution. Because the asperity
pattern is completely rearranged by application of the probe to lapped
material, the value of A determined by the asperities, does not show
a very systematic dependence on F.
In figure 5 the results of similar experiments with another probe
and sample are presented, the only difference being that the starting
probe radius A was about 10 (jm. Here the signal on polished material at
low loads was again very erratic, but A 1 again increases almost linear-
ly. As mentioned above, the experiments on polished silicon are influenced
by the measurements on lapped material in between. This procedure is ne-
cessary to keep an unfractured probe tip over so long a load range.
Over a shorter range the probe reshaping on lapped material is not needed
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 S3C 3feSt 2/3
and the curve labelled A is found. The slope, A «oF ' , is more or
less equal to the slope for* A and for A* above lOOPg. It is also clear
that the microcontact contribution plays an important role. It is inte-
resting to note that in figures k and 5 the three values of the equiva-
lent radius for polished slices are almost equal at 15O g. That is why
this is chosen as the working load.
As mentioned above,the double-stage probe structure has a bearing
on the resolving power of the spreading resistance probe. With surface
probing both the micro- and macrocontact stage average horizontally over
about 2A. A relatively large contribution R. . could be a drawback for
surface probing. When the horizontal resistivity distribution in a sili-
con slice is the desired information, this could be shielded by the va-
riations in a one micron thick top layer. However, it has been found that
spreading resistance tracks with pronounced maxima and minima do not
change when a one micron thick layer is removed. Hence although the mi-
crostage represents about three quarters of the total resistance, the
microcontacts penetrate any surface layer which may be different due to
circumstances beyond control. More important,surface probing of a thin
epitaxial layer can be done advantageously with an shallow stage which
contributes significantly to the total resistance. It ranks among the
most favourable properties of the steel probe that for the microcontact
stage which represents about three quarters of the spreading resistance,
any isotype thin layer can be considered as a sample of infinite thick-
ness. The thickness correction should be applied to the deep contribution
only, if necessary. For a heterotype structure the thickness correction
is a function of both the micro- and macrocontact contributions, as shown
elsewhere £ 2,5] . In general the thickness corrections have been calcula-
ted for an abruptly layered structure and evidently some doubt exists of
the value of d in a real structure. In case the shallow stage contribution
is sufficiently large, the improvement obtained by applying the more or
less accurate correction is good enough.
In summary, we use a probe which averages horizontally over a circle
about 2A <fc 25 pm across and in depth over a length of about 3a ^tO. 1 jjm.
For surface probing the small information sampling depth is a great asset.
For profiling averaging horizontally over 25 (jm is quite a nuisance
for, with a desired resolving power of O.05 (jm in depth, the angle should
be 1/5OO or more. We shall describe in the next section how bevels up to
1/20OO can be produced and evaluated.

3. The bevelling jig and the interferometer

Conventional angle-lapping jigs have been used before for bevel and
stain measurements at relatively large angles. The reliability of these
instruments is limited by mechanical tolerances. Here we first describe a
more stable and versatile tool, which matches well the interferometer to
be described later.
As shown in figure 6, the slice S to be bevelled is mounted on a pis-
ton A. It can slide without play in the holder B and can be fixed at any
height and position by screw C. This assembly rests on three balls on the
support ring D and can be moved with respect to the support by two screws
E. With one screw the assembly can be tilted about the axis between the
other screw and the third ball. In this way the angle between the axes of
B and D can be varied in a simple and precise way. The holder B and the
support D are held in position by three resilient clamps F. The jig rests
on a number of pieces of silicon G glued to the support D. Hence during
lapping and polishing no foreign particles are produced and because their
total surface area of about 1O cm is much larger than the area to be
bevelled the pressure and rates are constant during the process. The slice
is mounted on the piston A in a thick layer of beeswax by heating. When
it is allowed
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 The lapping and polishing is done on a machine on which the slice is
subjected to three different motions. For the lapping a slurry of water
and AlpOo is used. The subsequent polishing is done with diamond paste un-
til the roughness is reduced sufficiently to make the surface mirror-
like. At this stage the surface shows some pits and scratches due to deep
lapping damage, but usually the polishing process is not continued. It
has been found that there is about 2O$ difference in spreading resistance
between touched and non-touched parts. Because profiles are measured ge-
nerally on a logarithmic scale, this difference in calibration is unimpor-
tant. It can be reduced by chemtmechanical polishing.
A bevel of relatively steep slope and mirror surface quality can
easily be evaluated with an interference microscope. In order to obtain
a reliable value for the slope at least a dozen contour lines should be
visible, and it has been found that for steep angles up to, say, 1/200
reliable results can be obtained. However, for small angles the slice
turns out not to be flat enough to unambiguously define its slope with
respect to the reference flat. Moreover, the method is time consuming
and it is impossible to obtain an overall impression. In this section an
instrument of greater field of view is described with which the untouched
part of the surface of a bevelled slice can be seen and used as a hori-
zontal reference in determining the slope of the bevel.
The optical layout of this interferometric instrument, which is not
at all critical, is shown in figure 7» A HeNe laser (l) operating at
6328 A at about 2 mW power level provides an extremely monochromatic,
coherent, relatively intense and narrow light beam. The light is inci-
dent on a diffuser ( 3) » which serves as an intense and monochromatic
light source. Via a semi-reflecting mirror (5) the enlarged-diameter pa-
rallel beam is incident on the polished side of the silicon slice (7)
which is positioned face to face with a semi-reflecting optical flat (8),
about 1 cm thick. The fringe system arising from multiple interference
at the positions of appropriate slice-flat distance is imaged by a lens
(9) onto a screen, a television camera or a photographic camera (10). As
the light turns out to be still 'so coherent that speckles can be seen,
the diffuser (3) is mounted on a motor axis which revolves sufficiently
fast that they disappear. With the instrument shown in figure 7 the com-
plete topography of slice (7) with a diameter up to the diameter of the
parallel light beam is obtained in a single picture. Examples of such a
picture are given in figures 8 and 10 below. In these pictures the dis-
tance between two contour lines corresponds to a height difference equal
to /I/2 = O.316 (jm and the resolving power is about O.O6 (jm.

k. Evaluation of bevel angle

In general a slice is not flat and, although the bevel as produced

may be flat, local thickness of a bevelled epitaxial layer plotted vs
horizontal position may not be a straight line. Typical surface topographs
of silicon slices can be seen in figure 8. Usually the contour lines
show a maximum or a minimum, manifested by closed lines, and sometimes
saddle points . The radius of curvature of an extremum is roughly between
2 and 20m for 25O(jm thick slices. Hence the slope may change over 5 nun
by an angle 1/500. However, with the procedure to be described such va-
riations in slope do not present a real problem because the profiles of
both the original surface and the polished bevelled surface can be mea-
sured accurately. To produce a bevel the slice is mounted on the jig.of
|)Thisimpliesthatconcavity measured as a standard routine £6j a
commonly called bowing or dishing, does not adequately describe the
topography of silicon slices.

103
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565-448 O - 75 - 5
figure 6 and the mirror (8) of figure 7 is placed on top of the silicon
pieces G of the jig. Using the screws E the piston A is adjusted such that
on the television monitor a pattern arises with easily recognizable fea-
tures. This pattern is photographed. Then the desired angle is adjusted
with screws E and the piston is lowered until the slice touches the opti-
cal flat and is fixed again with screw C. After lapping and polishing
the slice is positioned again such that the pattern on the non-touched
part of the slice compares well to the photograph made earlier and photo-
graphed again.
In practice the procedure runs as follows. A mark, labelled A in the
inset of figure 9, is scratched on the slice. In order to see this mark
on the photograph a small rectangular patch of paper, noted B in figure 9»
is glued to the slice. The slice is adjusted to such an angle with the
optical flat that a number of closely spaced interference fringes perpen-
dicular to the patch is visible, and photographed (figure lOa). The slope
of the part to be bevelled may correspond to the desired angle, otherwise
the desired angle is adjusted, the patch of paper is removed and the slice
is bevelled. As before, a patch of paper is glued on the slice and the
slice is adjusted as well as possible in the same position as before bevel-
ling and photographed (figure 1Ob). Then, from the photographs the profiles
along the spreading resistance track to be made, are measured and plotted.
Of course it will not be possible to reproduce precisely the pattern on
the non-touched pait. This is shown clearly in figure 9» where curve A re-
presents the profile as measured on the original photograph. After bevel-
ling, the profile labelled B is measured, which is different from the ori-
ginal one, though the left-hand side non-touched parts should be identical.
This arises from the fact that the angles with respect to the optical flat
in the two cases were slightly different. This can be corrected by pivo-
ting curve B around the origin so that A and B are coincident. The diffe-
rence between curve A and the first part of curve B turns out to be, as
expected, a straight line, labelled C. Extrapolating this correction, due
to slightly different tilt of the slice, over the range where the slice
has been bevelled, the true surface profile curve A~ is obtained from the
measured curve B. The difference between curve A 1 and A?, plotted as a
curve labelled D, is the true depth below the original surface. Due to the
surface topography and the nature of the polishing process, there is no
linear relation between depth and horizontal position. Therefore some me-
thod to obtain a curve like curve D of figure 9 is definitely indispensa-
ble for precise and accurate work on spreading resistance profiles.

5. Discussion and conclusions

With a specially hardened steel probe spreading resistance measure-
ments can be done on chem-mechanically polished and epitaxially grown sur-
faces with a precision of about 1$. Because of the large contact area,
about 25 Min across, which cannot be made smaller, the slope of a bevel
should be 1/500 for a resolving power of about O.05 (Jm in depth. For such
slopes a procedure has been developed which takes into account the original
surface topography. In this way the horizontal and vertical scales are
correctly correlated. ¥hen the bevel is chem-mechanically polished the
spreading resistance can be measured with a precision also of about 1$.
The inference of the dopant atom distribution from the measured sprea-
ding resistance profile is obstructed by a number of serious difficulties,
which are itemized below.
1. The correction formulae which should be applied to the spreading resis-
tance measured on a layer of finite thickness have been critically dis-
cussed elsewhere £2] and the sensitivity of the solution to the boundary
conditions chosen makes the validity of these expressions dubious within
about 1O$.
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2. The transition of the layered structure is not abrup-t so that the
thickness, particularly of thin, layers or near the bevel edge, is not well
defined.
3. The measured data should be corrected for the proximity of the bevelled
layer edge, particularly in the case of steep bevels.
4. The charge carrier density n can be deduced from the resistivity g
only with the well-known curves, which are valid, however, only in uni-
form and neutral material; neither condition is satisfied, because mobile
charge carriers generate a space charge in any steep atom profile. More-
over the spreading resistance correction formulae have been derived using
Laplace's equation, implying the absence of space charge.
5. The space charge is perturbed due to the exposure on the bevel £ 2 J.
The micro- and macrocontact contributions should be distinguished care-
fully. A dominant macrocontact resistance, which is more common for small
than for large contact area probes, is more sensitive to corrections. A
large probe with dominant microcontact contribution hardly needs any
correction for finite thickness. Therefore the items 1 "to 3 do not apply
to our probe system. The problem of the necessary small-angle bevel where
the original surface topography is important for the correlation between
depth and horizontal scale, has been solved.

Acknowledgement

The assistance of Mr.G.Poodt and Mr.H. Bulle in the experimental work and
of Dr. J.D. Vasscher in carefully reviewing the manuscript is gratefully
acknowledged.
References
1. P.J. Severin and P. Poodt, J.Elec- 4. P.J. Severin, Silicon Device Pro-
trochem. Soc. 119 (1972) 1384. cessing, NBS Special Publ. 337
2. P.J. Severin, Proc. Symp. Sprea- (197O) 224.
ding Resistance Measurements, NBS, 5» P.J. Severin, Philips Res. Repts.
Gaithersburg, 197^. 26 (1971) 359.
3. P.J. Severin, Sol. St. Electr. 14 6. Monsanto Evaluation Standards,
(1971) 2^7. Monsanto Electronic Materials,
St. Peters, Missouri, 1973> no
16-ME-O05-0472.

Figure 1. The print of a steel probe

as seen with an interference contrast
microscope.

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 Figure 2. The equivalent circuit of
the spreading resistance probe contact
as measured with a specially hardened
steel probe. Rg^ is the microcontact
contribution of ohmic, low-resistance,
high-pressure contacts and diodic,
high-resistance, low-pressure contacts
which can be neglected. Rga is the
microcontact contribution acting in
series.

Figure 3. The reproducibility of the

steel probe system is demonstrated by
some tracks on an epitaxial layer (a),
an N substrate (b) and a longitudinal
section (c).

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 Figure 4. The effective radius on lapped A-^ and
on polished A£ material, the real radius A^ mea-
sured on polished material as functions of the
load F. The probe is applied to lapped and Figure 5. The same parameters as presented in
polished material alternately. figure 4, but with a larger starting real radius
A_. The effective radius A_ is measured on
polished material without interjacent lapped
material probing.

Figure 7. The layout of the interferometer with

the slice placed polished side up: laser (1),
mirror (5), di'ffuser (3), lenses (2, 4, 9), opti-
cal flat (8), slice (7), (television) camera (10).

Figure 6. Schematic view of the angle-polishing

jig. The slice S is waxed to the piston A,
which fits tightly into holder B and can be
clamped with screw C. With the screws E the
slice
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1 23:23:49 EST the support
D, whichbyrests: on pieces of silicon G.
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 Figure 8. Typical topographs of silicon slices. On the right-hand
side of the reference flat the aluminum support is visible, which
also reflects.

Figure 9. Profiles of the original surface (A), of the

bevelled surface (B) and the depth below the surface
(D). The auxiliary line (C) is the difference between
the left-hand sides of A and B. When the right-hand
side of B, is corrected by the difference C, the line
A2 is found. The difference between A and A- yields
curve D which represents the true depth below the orig-
Figure 10. Topograph of a slice adjusted before bevelling inal surface. In the inaet the scratch mark A, the patch
(a) and after bevelling (b). A small rectangular patch of of paper B and the spreading resistance track C are shown.
paper glued on the slice serves as a starting point for the
photographic analysis and spreading resistance measurements.
Figure 11. A spreading resistance track on an N on N bevelled
epitaxial layer, probed at 25 ym intervals. The slope at the
center of the profile can be evaluated from fig. 10 to be 1/720,

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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Spreading Resistance Measurements on Silicon

with Non-blocking Aluminum-Silicon Contacts

J. Krausse

Siemens AG, UB B GE 1
8 Miinchen 46, Frankfurter Ring 152
P.R. Germany

The paper concerns the measurement of resistivity fluc-

tuations in n-type silicon starting material in the resistivity
range from 1 to 1000 fi cm. The microscopic resistivity fluctua-
tions that are associated with the well-known striations re-
quire a measurement technique of high accuracy and high local
resolution. We chose the spreading resistance method. However,
in contrast to the conventional method, in which the metal
probe is pressed directly onto the silicon surface, we supply
the silicon slice with non-blocking aluminum-silicon contacts.
The radius of the contact area is exactly defined. Any contact
radius can be realized according to the resolution desired in
lateral direction and in depth. When the metal probe is applied
to the aluminum-silicon contact, the contact is not destroyed.
Thus it is possible to perform spreading resistance measure-
ments and four-point probe measurements along one and the
same measuring track and in this manner at the same time to
vary the local resolution. A comparison of both measurement
results will in particular yield information on the condi-
tions of the resistivity in axial direction of the slice.
Essential prerequisites for an absolute measurement are ful-
filled with the aluminum-silicon contact. However, the investi-
gations made up to now show that the resistivity calculated
from the spreading resistance is smaller than the one obtained
with the four-point probe measurement by approximately a factor
of 0.8.

Key words: Absolute measurements; aluminum-silicon contact;

resistivity inhomogeneities; spreading resistance; striations.

1. Introduction
The lateral and the axial distribution of the resistivity in star-
ting silicon is e.g. in several respects of importance for the electrical properties
of power devices. Since resistivity variations as low as 5 to 20$ can be distinctly
effective, it has to be the aim to measure such variations as exactly as possible.
The microscopic resistivity fluctuations associated with the well-known striations
are of the order of AQ £» + 10 to 20$ (see [l]-[4})and therefore require a measure-
ment method with high accuracy and high local resolution.

Figures in brackets indicate the literature references at the end of this paper.
109
 Our interest is concentrated mainly on n-doped silicon material with a resisti-
vity in the range of 10 to 1000 Qcra, as it is used for manufacturing power devices.
For the manufacture of devices silicon slices are processed that are cut perpendicular-
ly from rods grown in <1"M) -direction. We perform measurements of the resistivity
fluctuations on such slices.

2. The Conventional Spreading Resistance Method

The well-known method of MAZUR and DICKEY [5] presented itself as a suitable
measuring procedure. This procedure at present is an important method to determine
the doping distribution of diffusion profiles and multilayer structures. However, as
yet it is not clear if it is suitable for an exact quantitative measurement of the
relatively small resistivity variations in starting silicon. The reason lies in the
fact that the physical properties of the contact between metal probe and silicon
surface are hard to define. This manifests itself in the calibration factor k which
is rather obscure. For the spreading resistance R of a circular, two-dimensional
contact of radius a

holds. However, the conventional spreading resistance method yields a resistance R

for which one can write

The factor k contains the whole problematic nature of the conventional

spreading resistance method. It depends on several details of the handling of the
metal point as well as on the properties of the bulk and the surface both of the
silicon to be measured and of the metal point. KRAMER and VAN RUYVEN [6] published
a compilation of k-factors that were measured in different laboratories, figure 1.
Note that the k-values scatter by approximately a factor of 10. In addition, in the
range of high resistivity that is of interest to us, the k-factor always depends
strongly on the resistivity of the silicon material, k decreases with increasing
resistivity. According to eq (2) this means that Rc depends less than proportionally
on Q . This in turn means an increase in the inaccuracy of the measurement for a
AQ -determination.

5. The Non-blocking Aluminum-Silicon Contact

In contrast to the conventional spreading resistance method, in which the probe
is pressed directly onto the silicon surface, we supply the surface with non-blocking
aluminum-silicon contacts. In [4] and [10] we have already described the reasons that
led us to take this step, as well as the structure and the preparation of the
aluminum-silicon contact.
A cross-section of the structure of an aluminum-silicon contact as we use it
presently is drawn in figure 2. Etching the polished cross-sections makes visible
the phosphorus diffused n-region. The etch patterns obtained in this way confirm the
well-known observation that the underdiffusion amounts to about 2/3 of the penetra-
tion depth b of the phosphorus. The radius of the contact is thus given by

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 In order to measure the spreading resistance, a metal probe is applied onto the
aluminum of the contact. The resistance Rc of the contact is obtained from a current-
voltage measurement between the probe and the back surface of the slice which is
diffused and contacted across the entire area. Normally we operate with a constant
de-current of 10 uA. The polarity is always "probe plus". The thickness d of the
silicon slices is normally approximately 500 urn. As the penetration depth b of the
phosphorus diffusion we choose for routine measurements b «* 6 to 12 urn, in contrast
to our first investigations [4»10] .By this means an ohmic behavior of the current-
voltage characteristic could be obtained over a wide voltage range. Figure 3a gives
two typical examples of characteristics that were measured on silicon of very
different resistivity. (This result and all the following ones were obtained for
a temperature of 23°C). Here, as in the following, Qs indicates the resistivity
that was calculated according to eq (5) from the contact resistance of the aluminum-
silicon contact (see section 5)» Even for the case of the high-resistivity silicon
the characteristic shows ohmic behavior in the wide voltage range between approxi-
mately 30 mV (aMkT/e) to 1V (a#40kT/e). For the polarity "probe plus", the ohmic
behavior continues even up to voltages of approximately 20V, while for the polarity
"probe minus", an overproportional increase of the current is observed with rising
voltage.
It should be mentioned here already that four-point probe measurements, for
which four probes are lowered onto four adjacent aluminum-silicon contacts, show
a purely ohmic behavior independent of the current direction (see figure 3fc* Q4
indicates the resistivity measured by the four-point probe measurement). Here again
we would like to emphasize the wide voltage range in which Ohm's law holds even
for the case of the high-resistivity silicon. In contrast to a conventional four-
point probe measurement, the characteristic shows ohmic behavior into the range
of 1V.
We see two essential advantages in the aluminum-silicon contact:
a) The possibility to vary the local resolution (by a variation of the radius a;
by a combination of spreading resistance measurement and four-point probe
measurement).
b) The aluminum-silicon contact constitutes a spreading resistance contact with
clearly defined reproducible properties that are homogeneous across the contact
area and across the area of the wafer. Essential conditions for an absolute
measurement of the spreading resistance are fulfilled.
In the following two sections we will discuss these two topics in detail.

4. Local Resolution
The volume in the silicon that is covered by the spreading resistance measure-
ment is approximately a hemisphere with a radius 3& (approximately 80$ of the
spreading resistance is concentrated in this volume). In contrast to the conventional
spreading resistance method, the radius a of an aluminum-silicon contact is
clearly defined. Since any contact radius larger than 2 urn can be realized
technically, the local resolution in axial and lateral direction can be varied in
the desired way by a proper adjustment of the contact radius.
A typical example for an experimental realization is shown in figure 4* Results
of spreading resistance measurements are plotted here that were measured along two
parallel tracks of aluminum-silicon contacts. The distance between tracks was 180 urn,
the distance between aluminum-silicon contacts 60 urn. The tracks ran from wafer rim
to wafer rim through the center of the wafer. The measurement curves are inter-
rupted every 2 mm over a distance of 200 urn. This representation should indicate
that the sequence of aluminum-silicon contacts had gaps every 2 mm of 200 urn length,
for technical reasons during the preparation of the structure. In the figures the
resistivity Qs(x) at the location x is plotted, normalized to the mean value of all
measurement points along the track. The way the value of Q$(x) *s calculated from
the spreading resistance will be treated in detail in section 5 (see eq (5) )•
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 The two contact tracks differ only in the radius a of the aluminum-silicon
contacts. By means of a very shallow phosphorus diffusion (b = 0.7 urn), it was pos-
sible to obtain aluminum-silicon contacts with a very small radius. The measuring
track of figure 4a consisted of such contacts with a radius a = 3*0 urn. In contrast,
the aluminum-silicon contacts of the track of figure 4b had a radius of 16.5 urn.
Thus, while in figure 4a a depth of about 9 urn was resolved, in figure 4b the wafer
was covered to a depth of approximately 50 urn.
Qualitatively, one can recognize the same macroscopic resistivity profile for
both tracks. However, quantitatively, in the case of figure 4b the decrease of the
resistivity in the center is larger by about 50$ than in figure 4a. This comparison
shows the inhomogeneous resistivity distribution in axial direction. This is in
accord with observations made by VOSS of the infrared breakdown radiation from
diodes which were prepared from silicon wafers cut from the silicon rod parallel
to the pulling direction [11] .
While in figure 4a microscopic resistivity variations were observed in the
center of the wafer, figure 4b shows a quite undisturbed, continous resistivity
profile in this area. Obviously, the resistivity variations in figure 4a are very
inhomogeneous in axial direction and were therefore averaged out in figure 4^-
In contrast to this, the quite strong microscopic resistivity variations out-
side the center of the wafer change only slightly in the transition from figure 4a
to figure 4b. This is demonstrated further in the section figure 4c where both
measurement curves are plotted together. (The separation of the two curves on
the left side of the figure is caused by the different macroscopic resistivity
profile which is superimposed over the microscopic variations. This also reflects
the different depth resolution of the two measurements). The investigations in
[10] suggest that here we are dealing with resistivity variations associated with
the well-known striations.
The example chosen in figure 4 demonstrates that no essential information is
lost for the manufacturer of power devices with the relatively large contact radius.
This statement could be verified for various rods and led us to normally use contact
radii of a a* 10 to 20 urn for routine measurements. The advantages are:
a) We can diffuse phosphorus with deep penetration (ba*6 to 12 urn). Thereby the
current-voltage characteristic obtains an ohmic behavior over a wide range
(see figure 3a).
b) An exact determination of the radius a is necessary for an absolute measurement
of the spreading resistance (see section 5)» The accuracy of the measurement
becomes better with increasing radius.
In order to save measuring time and in order to ensure a proper handling of the
measurement apparatus for routine measurements, we furthermore normally use
structures in which the aluminum-silicon contacts have a distance of 200 urn.
For a routine measurement of a silicon slice we provide the entire surface of
the slice with aluminum-silicon contacts in a square grid arrangement. The distance
between contacts is 200 urn in x-direction as well as in y-direction. The arrangement
permits a measurement along two tracks that are perpendicular to each other and run
through the center of the slice, see figure 5« The flat is already ground into the
rod to indicate the position of the wafers in the rod.
Since the aluminum-silicon contact is not destroyed by the application of the
metal probe, one and the same contact can be measured several times. Hence, it is
possible to start out with a spreading resistance measurement along a track, then
remove the counter electrode of the wafer and repeat the measurement along the same
track using four probes as a four-point probe measurement. Here the probes are
arranged in the direction of the track . Since the distance between probes is 200 urn,

2
Investigations of this aspect showed that in this arrangement the lateral resolution
is better than when the probes are applied perpendicular to the track.
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now the resolution in lateral and axial direction is distinctly reduced. The silicon
wafer is certainly covered into a depth of at least 200 urn. In the following two
examples (figures 6 and ?5) we will show that by a comparison between spreading
resistance measurement and four-point probe measurement valuable information on
the axial resistivity distribution can likewise be gained. In the upper part of the
figures in each case spreading resistance results are depicted, in the lower part
the four-point probe results.
In figure 6 a high-resistivity silicon wafer was measured. As an unusual
feature it can be seen that for the spreading resistance measurement in y-direction
the resistance increases from rim to rim by about a factor of three. In the case
of the four-point probe measurement the increase of the resistivity is significantly
less. The comparison shows that the resistivity increase measured with the spreading
resistance method cannot be homogeneous in axial direction, since it would have to
be noticeable to the same quantitative degree with the four-point probe measurement.
Figure 7 depicts results taken from a silicon wafer in which the resistivity
variations associated with striations are very distinct. The figure can be considered
as a typical example for a strong resistivity dip outside the center of the wafer.
The corresponding four-point probe measurement, in comparison, yields only a very
slight indication of the dip. The comparison of both results leads to the conclusion
that the resistivity dip is highly localized in axial direction even more than in
lateral direction.

5. Absolute Measurement
For the calculation of the spreading resistance of an aluminum-silicon contact,
we approximate the geometrical shape of the sn-n junction in figure 2 by a semi-
ellipsoid with radius a of the circular base and height b. Then the spreading
resistance is given by

According to eq (?) the radius a can be calculated from the diameter <J) of the SiOp-
window and the penetration depth of the phosphorus diffusion.
From experience with the conventional spreading resistance method, we know
that we cannot equate the contact resistance RC of an aluminum-silicon contact and
the spreading resistance Rs from the start. We therefore write in formal analogy
to eq (4)

Here Qg is the resistivity as calculated from the measurement of the contact resis-
tance. This measured value is plotted in figures 4» 6, 7 and 8. Only in the case
that the resistance Rc of an aluminum-silicon contact is determined solely by the
spreading resistance, i.e., if

As to the calculation of Qs see section 5» especially eq (5).

For the calculation of eq (4) based on eq (53*>) and (54) of [12] the author wishes
to thank E. Spenke. For the limit of b « 0 one obtains the well-known relation of
eq (1) for a circular two-dimensional contact, for b = a the relation R =Q/2Tiaof
a semispherical contact.
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holds, the calculated Qs -value equals the actual resistivity Q of the material.
In order to check if the assumption in eq (6) holds true, a second method is
required that also permits an absolute measurement of the resistivity. For this
purpose the four-point probe measurement with aluminum-silicon contacts presented
itself, as was treated already in section 4*
The exact theory of the four-point probe measurement requires that the contact
radius a of the aluminum-silicon contacts and the phosphorus penetration depth b be
small as compared to the probe distance s of 200 urn. This was not fulfilled. Thus,
we first of all had to make sure that the finite dimensions of the aluminum-silicon
contact do not distort the four-point probe measurement. For this check one takes
advantage of the fact, that the distance between the probes, s, can be varied very
easily, e.g., by just using every second (s » 400 urn) or every third (s = 600 urn)
aluminum-silicon contact for the four-point probe measurement. In this fashion,
four-point probe measurements could be performed with greatly varying distances
between probes. The probe distance s and the thickness d of the investigated
wafers5 were varied in the range
s * 200 to 3000 um
d » 150 to 2000 um
d/s = 0.2 to 10.
Here, a was never larger than 20 um. The Q, -values were calculated according to
SMITS [14] for d/s < 1.4 and according to VALDES [15] for d/s > 1.4. Within the
measuring accuracy of + 2$ no influence was noticed of the distance between probes
on the Q^ -value. In addition, in deviation from the normal case by feeding the
current into the two inner probes and measuring the voltage at the two outer ones,
we were able to verify that the Q. -value is independent of such exchange of probes.
Similar results had already been obtained by SEVERIN [16] when investigating
his unconventional four-point probe method, in which mercury is used as a contact.
In this case, too, the diameter of the mercury contact was already of the order
of the probe distance.
In order to check the assumption in eq (6), spreading resistance measurements
and four-point probe measurements (s = 200 um) were performed in x- and y-direction
(figure 5)» the latter measurements after the bottom diffused layer was removed.
The spreading resistance measurements were evaluated according to eq (5). For both
tracks (i.e. for approximately 2 • 150 measurement points) the average values Qs
and Q, were calculated and compared with each other.
Typical results that so far were confirmed quantitatively by all our measure-
ments are shown in figure 9» Plotted are the results obtained from 33 silicon
slices. The slices were taken from three different silicon rods that differed as
far as their average resistivity and their microscopic resistivity variations were
concerned:
group 1: 11 wafers in the range Q4 « 20? Qcm + 16$.
"Short wave-length" microscopic resistivity variations with small
"amplitude". Figure 6 shows the measured resistivity distribution of one
of these slices. (The slant of the curve measured in y-direction is not
typical, though).

Included in these investigations was neutron activated silicon with very

homogeneous resistivity [13] which will be treated in connection with figures 8
and 9.

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group 2: 12 wafers in the range Q4 » 39-1 Qcm + 4$.
"Long wave-length" microscopic resistivity variations of large "amplitude",
Figure 7 shows the measured resistivity distribution of one of these
slices. (The resistivity dip in x-direction is not typical, though).

group 3: 10 wafers in the range Q^ = 3.19 ftcm + 2.5$.

Neutron activated silicon [13]* no microscopic resistivity variations.
Figure 8 shows the measured resistivity distribution of one of these
slices".

Since the spreading resistance measurement reaches into a much lower depth of
the silicon wafer than the four-point probe measurement, the values (5g and Q^ do
not correspond to the same volume in the specimen. Hence, it is not surprising that
values Qs/Q^ smaller than one are measured. However, it has to be noted that the
relation §c/§4 is always smaller than one. On the average it is approximately 0.8.
This result cannot be explained by the differing local resolution of the two
methods, especially since it was also obtained with the homogeneous silicon of
group 3.

Analogous to the conventional spreading resistance method we are forced to

introduce a calibration factor

for the aluminum-silicon contact in eq (5):

Naturally, this step rests on the assumption that principally §" = ^ holds true and
that there can be no doubt as to the accuracy of the four-point probe measurement.

The k-values of figure 9 were plotted in figure 1. It should be noted that

MAZTJR and DICKEY [5] and KRAMER and VAN RUYVEN [6] also measure k-values smaller
than one, although only in the high resistivity part of their measurements range.
If one takes into account that the k-value is determined by many factors (descrip-
tion of the sn-n junction by a semi-ellipsoid, which holds only approximately; the
approximation: underdiffusion * 2/3 « b; the measurement of the penetration depth
of the phosphorus, b, and the diameter <J> ; current-volt age measurement etc.), a
deviation of the k-values from the theoretical value of k » 1 by 20$ is basically
not surprising. However, it is disturbing that k is always smaller than one by
approximately 20$. This points to a systematical error.

We could not determine unequivocally whether the two Qs -dips measured with the
spreading resistance method in y-direction had to be considered as properties of
the material or whether they rather were pure measurement errors.

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 For this reason we varied drastically the experimental conditions:
a) a from 2.5 to 50 um "I where the distance between two contacts and the
b) d from 150 to 2000 um J thickness of the wafer were always larger than 10a.
(figure 9 also comprises two different values of a and in the case of the
homogeneous silicon also different values of d).
c) b from 0.7 to 12_um
d) measurements of DC and ^ on wafers that were cut along the <111) -direction
from a rod pulled*in that direction'.
e) measurements of Qc and D/ on contacts without metallization. The metal point
was applied direct ly__onto the phosphorus diffused silicon.
f) ac-measurements of Qs. The frequency was approximately 150 Hz.
In none of these cases was there a noteworthy influence on the k-values. The k-values
were always scattered statistically around ka*0.8.

The term "statistically" applies here only with restrictions. Unfortunately, at

the time of these investigations silicon with homogeneous resistivity was not yet
available to us. Since the local resolution of the two measurement methods was dif-
ferent, we would have had to investigate a large number of wafers in order to arrive
at a statistical interpretation. It would have been too time-consuming. Therefore,
in some cases only four silicon slices were measured with one experimental condi-
tion varied. We can thus not claim true "statistics". It is only recently that in
the neutron activated silicon we have a material with homogeneous resistivity. The
investigations are to be repeated with this material. Surely, results with still
higher certainty will be obtained with respect to the k-value.

6. Final Remarks

A disadvantage of the aluminum-silicon contact consists in the time-consuming

and costly processing steps needed for the preparation of the contacts. As far as
simplicity is concerned, the conventional spreading resistance method in many cases
would be better suited, since it requires only a simple surface treatment of the
silicon slice. Therefore, it is now our aim to help answer the technically inter-
esting question whether the conventional spreading resistance method permits
measurement of relatively small resistivity variations in starting silicon with
satisfactory accuracy. Ve intend to perform measurements of comparison between
the conventional spreading resistance method and our method of measurements with
aluminum-silicon contacts. The measurements are to be performed on the same wafer
on adjacent tracks. In order to arrive at a result as general as possible, we have
sent silicon wafers of groups 1 , 2 and J in figure 9 after they were measured by us
to a number of laboratories. These laboratories are concerned with the conventional
spreading resistance method and will use it to measure our silicon wafers.

7. Acknowledgements

The author would like to thank J. Burtscher for helpful discussions. He also
would like to thank G. Schuh for supplying the wafers with aluminum-silicon contacts
and H. Vindisch for taking the measurements.

'In contrast to the investigations of GARDNER et al. [7] (see figure 1) and
MURRMANIT, SEDLAK [17] , with aluminum-silicon contacts there is no indication of a
dependence of the k-factor on crystal orientation.
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 8. References
[l] Muhlbauer, A., Kappelmeyer, R., and [10] Burtscher, J., Krausse, J., and
Keiner, P., Widerstandsfeinstreifung Voss, P., Inhomogeneities of the
in tiegelgezogenen Si-Kristallen, resistivity in silicon: two diagnos-
Z. Naturforsch. 20a 1089 (1965). tic techniques, Semiconductor Silicon
[2] Mazur, R.G., Resistivity inhomoge- (Ed. by H.R. Huff and R.R; Burgess),
neities in silicon crystals, J. p. 581, The Electrochem. Soc. (1973).
Electrochem. Soc. 114 255 (196?).
[3] Krausse, J., Widerstandsschwankungen [11] Toss, P., private communication
in Siliziumkristallen, paper presen- [12] Ollendorff, P., Grundlagen der Erd-
ted at the 2. DFG-Kolloquium in schlufi- und Erdungsfragen, Berlin,
Burghausen (1970). Verlag von J. Springer (1928).
[4] Burtacher, J., Dorendorf, H.W., and [13] Schnoller, M., Breakdown behavior of
Krausse, J., Electrical measurement rectifiers and thyristors made from
of resistivity fluctuations associa- striation-free silicon, IEEE Trans.
ted with striations in silicon crys- Electron. Dev., to be published.
tals, IEEE Trans. Electron. Dev. [14] Smits, P.M., Measurement of sheet
ED-20 702 (1973). resistivities with the four-point
[5] Mazur, R.G., and Dickey, D.H., A probe, Bell Syst. Techn. J. 711
spreading resistance technique for (1958).
resistivity measurements on silicon, [15] Taldes, L., Resistivity Measurements
J. Electrochem. Soc. 115 255 (1966). on germanium for transistors, Proc.
[6] Kramer, P., and van Ruyven, L.J., IRE 42. 420 (1954).
The influence of temperature on [16] Severin, P.J., private communication,
spreading resistance measurement, to be published.
Solid-St. Electron. J£ 757 (1972). [17] Murrmann, H., and Sedlak, P., Sprea-
[7] Gardner, E.E., Schumann, P.A., and ding resistance correction factors
Gorey, E.F., Measurement techniques for {111} and {100} surfaces,
for thin films, p.258, Electrochem. published in this volume.
Soc. (1967).
[Q] Pinchon, P., private communication
to P. Kramer and L.J. van Ruyven,
ref. {6].
[9] Keenan, W.A., Schumann, P.A.Jr.,
Tong, A.H., and Phillips, R.P.,
Ohmic contacts to semiconductors,
p. 263, Electrochem. Soc. (1969)«

Figure 1. The factor k as a function

of the resistivity for n-doped silicon
(see figure 2 in [6]). The bars
correspond to measurements on aluminum-
silicon contacts, figure 9.

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 Figure 2. Cross-section through a non-blocking aluminum-silicon contact.

Figure 3. U-I characteristic: a) spreading resistance measurement, a = 10 ym

(2.67ficm) or 12.5 ym (134flcm); b) four-point probe measurement, s = 200 ym.

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 Figure 4. Lateral resistivity fluc-
tuations along a diameter of a silicon
slice (average resistivity 55 ftcm)
a) a = 3.0ym (<J> = 5ym; b = 0.7um)
b) a = 16.5ym (<j> =32ym; b = 0.7um)
c) comparison of the two results in
a) and b) for the 0-6 mm positions

Figure 5. Arrangement of the aluminum

aluminum-silicon contacts for a
routine measurement.

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565-448 O - 75 - 9
Figure 6. Lateral resistivity fluctuations along two diameters of a silicon slice
(average resistivity 207 Item)
p : spreading resistance measurement, a - 12.5 ym
p^: four-point probe measurement, s « 200 ym.

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 Figure 7. Lateral resistivity fluctuations along two diameters of a silicon slice
(average resistivity 38.7 ftcm)
Pi*: four-point probe measurement, s • 200 um
p S : spreading resistance measurement, a = 10 ym

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 Figure 8 Lateral resistivity fluctuations
along two diameters of a neutron activated
silicon slice (average resistivity 3.17 ftcm)
p : Spreading resistance measurement, a «10ym.
p,: Four-point probe measurement, s - 200ym.

Figure 9. The factor k -p /p, of aluminum-

silicon contacts. Comparison of the absolute
values of p (spreading resistance measurement)
and of p, (tour point probe measurement)
group 1: a - 12.5 ym or 22.5 ym; <(>- 11.5 ym
or 32ym; b - lOym; d - SOOym.
group 2: a - lOym or 20ym; <(>= 10.5ym
or 31ym; b « 7ym; d* SOOym.
group 3: a - 10 m or 20 m; » 12 m
or 32 m; b » 6 m; d 200 m,100
group 3: a » lOym or 20ym; iji* 12ym or 32ym;
b - 6ym; d =<200ym, lOOOym, 2000ym

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

The Preparation of Bevelled Surfaces for Spreading Resistance

Probing by Diamond Grinding and Laser Measurement of Bevel Angles

A. Mayer and S. Shwartzman

RCA Solid State Division
Somerville, N.J.

A rapid and reproducible method for preparing bevel-

led surfaces on silicon has been developed as a prelimin-
ary to spreading resistance probe measurement of doping
profiles or junction depth determination by staining.
Several chips can be bevelled simultaneously. The sample
is mounted on a carrier which is clamped on the tilting
table of a microtome. The tilt is adjusted until a laser
beam reflected from the surface to a calibrated wall
chart is deflected to the desired angle. The bevel is
then ground with a high-speed diamond wheel mounted on the
microtome, taking cuts of several micrometers at a time.
The bevel edge is clearly defined even for very shallow
angles. The angle is accurately measured with the same
laser.
Because the ground surface is highly reflective, in
contrast to a lapped surface, a good reading of very small
angles of less than 30 minutes can be obtained. Up to a
6 meter base line is used with a Imw He-Ne laser and the
reflection is visible in normal room light.
Factors entering into spreading resistance are dis-
cussed, such as mechanical damage incurred in bevelling,
probe impact damage, and surface cleanliness. Judged by
spreading resistance, the amount of damage incurred during
grinding is small and reproducible, provided care is taken
to maintain the spindle so that it runs without vibrating.

Key Words: Bevelling, diamond grinding, laser bevel

angle measurement, layer thickness determination, materials,
resistivity measurement, silicon doping profiles, spreading
resistance measurement, surface damage.

1. Introduction
Solid state device properties depend on the distribution of carriers
around p-n junctions. The bevel-and-stain method [1,2] in conjunction with
four point probe resistivity has been the most widely used procedure for this
purpose, but the spreading resistance probe (SRP) is gradually supplanting it.
The major reasons for the slowness of the introduction of SRP into de-
sign engineering and process control are (a) the slowness of sample prepar-
ation, (b) the slowness of obtaining the SRP readings, (c) the lack of infor-
mation about the effect of sample preparation on the precision of the resis-
tance readings, (d) the lack of standard samples of sufficient uniformity to
ensure that the choice of the area was not the main reason for an observed
change in the calibration graph and, by implication, the stability of the
probe including the contact points and internal electrical circuits. Only
123
recently has sufficient work been done in commercial SRP* design and in the
study of sample uniformity by Subcommittee 6 of the ASTM Committee F-l to
show that calibration graphs are reasonably stable and approximate straight
lines. The speed and reproducibility of sample preparation present a bottle-
neck inhibiting the use of the SRP as a production control tool.
The work reported here was undertaken to improve the rate of sample pre-
paration (bevelling) to provide a basis for mechanizing the procedure. High-
speed grinding offered a chance to achieve this goal and it also provided a
shiny bevelled surface which permitted the angle to be measured by optical
reflection; the normal method consists of lapping, (which leaves a matte sur-
face) and measuring the angle by depth of focus of a toolmakers microscope.
Precision equipment was developed which led to the establishment of
grinding at any desired angle as a routine method for breveiling samples and a
novel high-precision method for measuring bevel angles with a laser as part
the total mechanical package.
It is known that the measured spreading resistance is the sum of series
resistance terms and the spreading resistance [3,4]. It has also been ob-
served that surface preparation contributes to the observed value and its
stability on storage. In ordei to make the bevelling procedure useful for
production control it became necessary to provide some insight into the con-
tributing factors, such as the degree of mechanical damage of bevelling in
relation to that added by the impact of the probe points; the contribution
due to the multiple contact points on each probe and the reason for the in-
creased contact resistance when probes were used to measure only smooth sur-
faces. This report describes the development of the novel bevelling and
measuring system which resulted from these enquiries.

2. Surface Grinding Development

2.1 Consideration of Surface Damage
A survey of the literature on spreading resistance measurement indicates
that the method of surface preparation plays a major part in the reproduci-
bility of SRP readings.
Severin I5J. observed that the contact to silicon is multipoint. Gorey
et al., 16] deliberately prepared multipoint tips by sandblasting. The
makers of the SRP suggest that apparent high spreading resistance;^, readings
obtained on a standard sample can be brought back to normal by allowing the
points to irapact on a roughly lapped silicon surface, a procedure which is
called reconditioning. We agree with these observations and have also found
that continued operation of the probe tips on only chemically polished sur-
faces gradually leads to high Rg readings; and that these can then be made to
read the normal, lower value after reconditioning.
The high readings probably result from the multiple contact points
gradually wearing away on the smooth sample surface giving a smaller effec-
tive contact area and reconditioning then roughens the probe points again.
The rough appearance of a normal imprint of a probe point is shown in the
scanning electron micrograph, figure 1. This effect is different from the
observation that the RS of a lapped surface is greater than that of the pol-
ished surface of the same wafer. The reason for the latter effect is the
degree arid depth of damage incurred during sample preparation. That uncon-
trolled (impact) damage causes variable change in measured Rs can also be in-
ferred from the observation that the drop rate of the probe tip on the sili-
con surface has to be well controlled. This is illustrated in figure 2; here,
the probe tip was .allowed to impact repeatedly on the same area of a polished
wafer and this led to a rapid increase of the measured Rg with each extra
impact. It is similar to the observation that insufficient damping of the
probe descent leads to high RS readings. The effect of damage is most pro-
nounced on highly doped silicon and disappears in the 10-100 ohm-cm range and
*We use a Model ASR-100 made by Solids State Measurements, Inc.
Murrayville, Pa.
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may even reverse at higher resistivities. This effect is discussed in more
detail and quantitatively later on.
Similar conclusions about damage were reached by Gupta et al.[7] who mea-
sured the Rs of lapped samples after progressive removal of damage by etching
with hydrogen chloride, and also by Chu and Ray [8] who worked on germanium.
2.2 Grinding Machine
The importance of the above observations in the choice of a grinding
machine for preparing bevels becomes clear when it is considered that vib-
ration of the spindle is likely to cause uncontrolled damage. The best
machines tried so far are an air-driven, pressure-mist lubricated spindle*
which has been in operation on a daily basis for a year and a similar, but
belt-driven one for 4 months. Most of the data reported here were obtained
with the former. It is being operated on 25 and 40 psi air pressure at
speeds of 30,000-60,000 rpm. The main problems.in the installation were
mounting the spindle rigidly on a level platform and the balancing and dress-
ing of the V O.D. diamond cup wheel** to reduce vibration. Periodic re-
dressing with an alumina or carbide stone is necessary to maintain reproduci-
bility. Cutting is performed with air or oil cooling and an "elephant trunk"
is used to exhaust the small amount of dust and mist generated. As can be
seen from the photograph, figure 3a and the schematic, figure 3b the spindle
is mounted on a microtome bed***; this has a ratchet feed capable of lifting
the specimen in 1 to 25ym increments per stroke. The specimen is mounted
rigidly with wax**** on a steel block which is indexed so that it can be lined
up in the microtome clamp by means of a .5mm wide steel key.
2.3 Bevelling by Grinding
The microtome is supplied with a tilting table which can be set so that
the waxed specimen is level with the sliding plane. It is then a simple mat-
ter to tilt the specimen to subtend the desired angle to the sliding plane
and to measure this angle by means of a Helium-Neon laser mounted parallel
with the spindle. After setting the tilt the grinder is started and allowed
to take a 3-5ym cut per stroke. Each stroke takes less than 4 seconds so
that even a 100pm thick layer can be sectioned in less than 2 minutes.
Finishing strokes of l-2ym at a time help to produce a finish with minimal
damage on the bevelled surface. For examining very thin payers we routinely
bevel at a 34 minute angle to obtain a tangent of about 6.01 or a magnifica-
tion factor of 100, while a 0.2 tangent (^11 degrees) is used to obtain com-
plete cross-sections of wafers or for thick epitaxial layers. Table I can be
used as a guide for selecting bevel angles and step length in relation to
layer thickness.

Table I. Guide to Bevel Angles & Step Length in Relation to Layer

Thickness. To obtain the true thickness multiply the SRP
step by the tangent.
Layer Thickness
ym up to 3 2-15 10-60 50-150
mil up to .12 .1-.6 .4-2.5 2-6
SRP step,ym 5 10 10 10
tan a .008-.012 .018-.025 .08-.12 .2-.4
approx. a h° 1° 6° 11°
H.P.Smith, Assoc., Cheshire, Conn; AVON spindle
Sample Marshall Labs.,Lyndhurst,N.J.; 100 concentration,9ym diamond,
plastic bonded cup wheel.
Reichert Sliding "Om E" microtome.
sticky wax, Corning Rubber Co., N.Y.
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 2.4 Surface Cleaning

When a suitable bevel has been ground, the block is transferred to the
SRP, the surface is wiped with a Q-tip moistened with solvent* and air dried
before measuring the Rg. This treatment removes oil mist and debris from the
surface. In contrast to surfaces which have been prepared by lapping or chem-
ical-mechanical polishing which is usually carried out with water based
slurries, we have found that the surfaces prepared by dry grinding and sol-
vent cleaning are stable. They show no significant drift upon standing in
laboratory air, and give reproducible RS when a fresh surface is prepared by
grinding as shown by the following example: The surface of a test wafer
having n- and p- type epitaxial layers was measured regularly each morning,
then reground, cleaned and its Rs re-read each day for about a month. The
longest time between regrinding was 68 hours, the shortest 30 minutes. The
mean resistivity recorded was 17.57ft-cm on the p-type layer, with a standard
deviation, SD,of 4%. The n-type layer measured 13.3£I-cm with a 6% SD. It
should be noted that these figures include errors due to the true differences
in resistivity of the sample as more of the sample was ground away.
The probable reason for this stability of the surface is that the
freshly exposed silicon sees only the relatively dry room air. It is be-
lieved that surface charge effects are often due to charge separation and mi-
gration of impurities ionized in the presence of the highly hydrated silicon
oxide film that forms when silicon is abraded under water. Similar stability
could be achieved on surfaces prepared with aqueous media by baking them at
150°C for about 15 minutes. The suggested new method of surface preparation
is simple and provides the basis for routine process control because of its
relative insensitivity to what would normally be regarded as a very crude sur-
face treatment. An illustration of the effect of impurities when samples are
prepared by wet-lapping with, silicon carbide is given in figure 4. Here,
the surface was just rinsed in water after lapping, air dried and the RS
measured, then the sample was cleaned with hot ammonia-hydrogen peroxide
(SC-1) solution and dried at 150°C for 15 minutes before remeasuring. Note
that the apparent noise as well as the average level of the Rs value has
changed significantly. When this series of experiments was repeated with
the above sample the freon-solvent cleaning and drying step consistently pro-
duced less noisy readings than the aqueous treatments. The absolute level of
the RS varied by more than 10%.
2.5 Standard Sample Preparation
It became clear in the course of this work that the reproducibility of
Rs on lapped surfaces, and later also on mechanical-chemically prepared sur-
faces required standardization of the cleaning and drying procedure. It was
noted when this was done that the day-to-day reproducibility of the Rs still
showed variations which were traced to the fixturing used in the lapping or
polishing process; the pressure applied during the operation could vary con-
siderably and give rise to various degrees of surface damage. Bevelling with
an aqueous silica gel slurry on a glass or Lucite plate was also found to be
a process difficult to control routinely so as to guarantee the same level of
residual damage. This may have been the main reason for the changes in the
slope of the calibration graphs prepared daily when the SRP was first intro-
duced into service. Kim, et al.l9] also found that surfaces prepared with
0.03 to lOym alumina gave Rs readings which were too noisy to resolve re-
sistivity striations.
When the grinding procedure was introduced as a routine process the cal-
ibration graphs remained constant over long periods (months) and also be-
came straight'lines when plotted as logarithms of RS against resistivity, as
shown in figure 5. This graph was constructed from 18 samples of (111) and 7
samples of (100) oriented silicon, which had been selected for being reason-
ably homogeneous, a very difficult task for the high resistivity range.
There is no significant difference statistically, when both the (111) and
(100) or only the CHI) samples are plotted. This is in contrast to private
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126
information indicating that some workers find that the n-type and some that
the p-type curves for (111) and (100) are significantly different. Much of
this sort of discrepancy is. probably due to bulk resistivity measurement
problems. The next point of interest is the marked difference between chemi-
cally polished and ground surfaces: note that the surface damage due to
grinding affects the n- and p-type highly doped samples in a similar manner
and very markedly and that the effect almost disappears at high resistivities.
We have no reliable samples for a good comparison in the greater than lOOft-cm
range. Perhaps this effect is due to the introduction of crystal defects
which change the effective carrier mobility, i.e., the trapping cross-section
for large carrier densities is greater than for the low carrier densities.
2.6 Factors Affecting Reproducibility
The confidence placed in any measurement procedure rests on the ability
to calibrate the instrument so that this calibration can be reproduced over
long periods of time. Our data suggest that the following factors enter
into this: grinding and impact damage, condition of the SRP points, and
standard sample uniformity.
The grinding process appears to introduce somewhat less damage than lap-
ping, and is more reproducible on a routine, long term basis. The major
problems are vibration in the spindle due to bearing wear, a loose clamp or
support block, or a grinding wheel which requires dressing. A good mainten-
ance schedule is essential. A daily check is easily made with a low resisti-
vity sample by observing the height of the step in the Rs readings between
the chemically polished and the ground surface as indicated in figure 6. In
the range 10^0 to lO^ carriers per cc a chemically polished surface gives
the lowest spreading resistance. Even with the greatest care in adjusting
the descent rate on our probe the surface is damaged. As can be seen in
figure 2, repeated impact on the same point causes drastic changes in the
apparent resistivity. Slight changes in the descent rate can change the de-
gree of damage and the observed R g . This is most obvious with low resistivity
samples, for example a O.Ollfi-cra n-type polished sample which was measured
repeatedly over a 6 week period, often two and three times a day gave a Rs
between 14 and 24 ohm, the average was 19.8 ohm and the SD was 12.4%; the
maximum fluctuation during a day was 9 % . To evaluate the variation in Rs
due to variation in grinding these figures were compared with Rs readings of
the same sample after bevelling. The calibration graph covering the range
1020 to 1014 carriers per cc shown in figure 5 is based on the statistical
average of samples read at least 10 times. It indicates a difference of 14
ohm between polished and ground surfaces of the test sample while the average
difference observed was 12 ohm with a SD of 11.8%. No difference was ob-
served between samples which had been freshly ground and ones which had been
held for 16 hours after bevelling. The SD in a similar test for a Ifi-cm n-
type sample (R s -10^ ohm) was 5 . 4 % and for a p-type, 20ft-cm sample (Rs^lO^
ohm) it.was 10.8%.
The data suggest that the variation in grinding damage contributes
slightly less to the total noise than the variation in impact damage. The
main practical benefit of this test is that it provides a ready means of
monitoring the impact damage, by routinely checking the RS of a low resis-
tivity standard sample having a damage-free, preferably an epitaxial, sur-
face. We can then set a limit to the value that is acceptable, and take
appropriate action if it is too high - adjust the impact height or recondi-
tion the points on a lapped surface.
If we read the Rs on a freshly bevelled portion of the same sample we
can again set a limit to the step height we wish to tolerate. If the ob-
served value is greater, re-balancing the grinder will usually obviate the
fault. It has already been noted that silicon reference samples prepared
from bulk crystal more often than not exhibit considerable resistivity
variation across the diameter. These gradients or striations are known to
reflect the crystallization phenomena of the solid-liquid interface, vari-
ations of byan
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uncommon. We have
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to 100pm thick layers on high resistivity opposite type substrates.
Spreading resistance measurements made on these epi layers show less than a
10% variation in Rs values over the surface of a 50mm diameter wafer and sug-
gest that this is probably the best method for the preparation of standard
samples for the calibration of the spreading resistance probe. These layers
can be measured by the four-point probe technique in conjunction with a
thickness measurement and the only uncertainty then lies in the calculation
oftthe integrated resistivity over the thickness and the p-n junction correc-
tion for the built-in field when the two kinds of measurements,-four-point
probe and spreading resistance- are compared. Subcommittee 6 of the ASTM
Committee F-l on Electronic Materials is working on this approach to
standardization.
The work mentioned above on the evaluation of impact and mechanical dam-
age required a large number of repetitive readings to be made by several
operators. It became apparent that once the initial shyness of a new operator
faced with a complex looking apparatus had worn o f f , no problems arose in the
rapid acquisition of the necessary skill for bevelling, determination of the
bevel angle and SRP readings.
In normal day-to-day practice we find grinding to give us satisfactory
RS data in terms of process control. In addition it is rapid and lends it-
self to the preparation of multiple samples and to mechanization.

3. Angle Measurement by Laser Reflection

3.1 Choice of Method
Process control requires the routine measurement of the width of sub-
surface layers. In order to convert the track marks of the SRP to width
measurement it is necessary to know the bevel angle precisely. The suggested
procedure for the ASR-100 probe is to use the calibrated toolmaker's micro-
scope as a depth gage; the precision of the tangent measurement depends on the
ease of focusing at the start of the bevel and at some known distance along
the bevel; this procedure is time consuming and requires well trained per-
sonnel for reliable output. A somewhat improved measurement of the angle, in
common use at RCA, depends on reflection of a collimated light beam from the
top surface and from the bevel,.followed by measurement of the displacement
of the two rays at a distance of about 50cm. This method cannot be applied
to lapped samples because the surface is not sufficiently reflective but
ground bevels do give reasonable reflections. However, to measure small
angles accurately a much longer pathlength is necessary and then the light
intensity is insufficient.
3.2 Use of Laser
We have successfully substituted a He-Ne laser for the collimated light
beam. A Imw He-Ne laser* is mounted on the microtome used for grinding the
bevels and serves in the first instance to adjust the tilt of the stage to
obtain any desired bevel angle, and after the bevel has been ground it is
used to measure the tangent of the angle precisely, without having to handle
the sample further. It obviates the need for lapping blocks with different,
precisely machined angles, it has great flexibility in permitting angles
from 20 degrees to less than 30 minutes i.e. angles with tangents of 0.2 to
0.01 to be selected and measured accurately, giving a range of multiplicat-
tion factors from 3 to 100. The arrangement for measuring the tilt of the
sample before grinding and the finished angle after grinding are shown in
the photographs figure 8a.andl>. The laser beam which has a diameter of
0.8mm is allowed to impinge on the top surface of a sample waxed to the pre-
aligned and levelled carrier block. The tilting stage is then adjusted so
that the reflected beam is deflected to the desired angle, a, or rather
* RCA Model L15404 and Exciter Model L15427A.
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to the desired tangent of a. This is determined by the distance between the
initial reflection of the level sample, and the new position Y (after tilting)
divided by twice the optical pathlength ABC between the sample and the scale:
tan o=XY/2 &T5£
It is essential to ensure that the laser beam is at near normal incidence
to minimize errors in calculating the tangent of the angle. After grinding
the bevel, its angle is measured precisely using the same laser and the same
optics. This time two reflected beams are visible one from the sample sur-
face and one from the bevel. The sequence of operations is shown in figure
8a,b,c»d.
The longer the baseline ABC between sample and scale, the more precise
is the reading of the beam separation. We have used a 6m baseline to measure
angles smaller than 20 minutes. In the existing permanent apparatus .a 1.8m
baseline is used which gives a 36mm separation of the reflected beams from a
34 minute angle with a tangent of 0.01 (corresponding to a magnification of
100). The laser beam we use has a nominal diameter of 0.8mm and a divergence
of 1 mrad. Surface scattering causes the reflected spot to widen to about
5mm in practice, as compared to a calculated 2.6mm. With silica gel polished
bevels the reflection tends to be more diffuse or elongated, especially with
small angles, due to some edge rounding. Excessive periodic vibration in the
spindle can produce deep ridges which cause a diffraction pattern to form and
this makes it difficult to detect the center of the reflection. Figure 9
shows photomicrographs of bevels obtained with a well balanced wheel.
4. Comparison and Reproducibility of Bevel Angle Measurements
The reproducibility of the laser measurement was determined by 10 repeat
tests by each of two operators who measured the bevel angle on one piece of
silicon'over a 5mm bevel length over a period of days. The average was a
tangent of .0533 with a SD of 1*25%. The measurements were also compared
with the depth of focus technique suggested by the SRP manufacturer and with
tracing the profile of the angle using a calibrated surface profilometer* as
shown in Table II.

Table II. Comparison of tangent measurements of the bevel angle. Each

figure consisted of 6 ridings taken by two operators over
a one month period..
Laser Profilometer Depth of Focus
Average .0073 .0075 ~~ "" .0087
Spread ± .0008 .0059 .002
Average .0143 .0153 .0155
Spread ± .0009 .0014 .0010
Average .104 .105 .100
Spread .001 .002 .004
The depth of focus is not only the most tedious but also gives the
least reproducible results, and the laser method is the most convenient and
agrees well with the profilometer procedure.
In conclusion we can say that the combination of laser angle measurement
and SRP track distance measurement produced values for the thickness of epi-
taxial layers which were in excellent agreement with infrared interfero-
metric methods, and that the procedure is well suited for routine process
control and engineering design work.

Summary
High speed grinding has been shown to be a useful method for the prepar-
ation of bevels prior to spreading resistance profiling of silicon samples.
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 The main advantages of the new procedure are its speed, convenience ,
cleanliness and accuracy. Multiple samples can be bevelled and their angles
determined rapidly on one block which is designed to fit directly onto the
SRP. Simply wiping the surface with solvent is sufficient to get reproducible
surface conditions. This method reduces the variability of Rs readings by
suppressing surface hydration and charge separation from impurity ions. By
combining the grinder with a laser it is easy to select the desired angle and
to measure it precisely without removing the samples from the apparatus. Also,
a wide range of angles can be selected so that full cross-sections of 150ym
thick wafers are as readily made as very shallow bevels of less than 30 min-
utes to measure thin layers with equal ease. In addition, the bevel edge is
readily visible and sharp. It should be noted that the bevel preparation by
grinding is a useful technique on its own because the ground surface is shiny
and can be stained by the methods used on polished samples.
An examination of the factors which contribute to the total resistance
measured by the spreading resistance probe indicate that damage due to the
method of surface preparation can be separated from damage caused by the im-
pact of the probe points provided homogeneous standard samples are available.
The SR difference between the damage-free and the bevelled surface is a good
guide to set up procedures which ensure that the grinder and the probe are
kept in good operation condition in routine use. Lastly, we have found that
the operation is readily learned and is relatively insensitive to operator
experience.

6. Acknowledgements

We are happy to record that Paul Delpriore's anjd Eric Cave's help, ideas
and encouragement, and Bernice Upton's devoted detailed work have contributed
greatly to the success of this project.

7. References

[1] "Test for Thickness of Epitaxial [6] Gorey, E.F., Schneider, C.P. and
or Diffused Layers in Silicon by Poponiak, M.R., J. Electrochem
Angle Lapping and Staining Techni- Soc., 117, 721, 1970
que", ASTM Method F 110-72, 1972
Annual Book of ASTM Standards, [7] Gupta, D.C., Chan, J.Y. and
Part 8, p American Society for Wang, P., Rev. Sci. Instr., 41,
Testing Material Philadelphia. 1681, 1970.
[2] Bond, W.L. and Smits, F.M., [8] Chu, T.L. and Ray, R.L., Solid
Bell System Technical Journal,35 State Tech., 14_, 37, 1971.
1209, 1956.
[9] Kim, K.M., Kumagawa,
[3] Mazur, R.G. and Dickey, F.J., J. Lichtensteiger, M., Mugai, A. and
Electrochem, So., 113, 255, 196 Martin, E., Annual Reports 1972-73,
Research in Materials,
[4] Gupta, D.C. ibid., 116, 670, 197 Massachusetts Institute of
Technology, p. 299.
[5] Severin, P.J., Solid State Elec-
tronics, 14, 247, 1971

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 Figure 1. Scanning electron micrograph of a
spreading resistance probe impact area on silicon.
Magnification 10,000 X; 70° specimen tilt.

AB - SURffcCE TRACE, EACH POINT 10/im MOTION

B-MOTION ARRESTED.
BC - NET INCREASE IN RESISTANCE DUE TO
PROPAGATION OF DAMAGE .

Figure 2. Change
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rights reserved);from
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the same place on the
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 Figure 3a. Grinding spindle positioned
over silicon sample.

Figure 3b. Photograph of grinding assembly consisting of a

microtome (x), a high speed grinding spindle (y) and a
mounting block and hold, fixture (z).

Figure 4. The Effect of Surface Preparation on

Spreading Resistance Profiles.

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 Figure 5. Spreading Resistance vs. Resistivity.

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Figure 6a. Spreading resistance
profiles of polished surface and
ground bevel of 0.11 ohm-cm n-type
silicon. Left, before dressing the
grinding wheel. Right, after dressing
the wheel.

Figure 6b. Spreading resistance

profile of polished surface and
ground bevel of 23 ohm-cm p-type
silicon.

Figure
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 Figure 8b. Select the desired tangent & adjust beam ABC, by
tilting the holding fixture, to point y on the wall chart.
Figure 8a. Adjust the holding fixture so that the reflected The distance XY»2 • (ABXX tan X). Lock the holding fixture
laser beam ABC coincides with point x on the wall chart. and grind the bevel. 'Example: If the actual distance from
the sample is 150cm and the angle desired is approximately
5°, then XY-2 (150cm) (.1) XY-30cm; .1- tan of'5° A31.

Figure 8d. Read the distance between the two spots (X and Z)
Figure 8c. Readjust the holding fixture so that ABC is moved on the wall chart and calculate the exact tangent. Example:
back
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Jan 1 23:23:49 tan OFOCY/ZABC tan a^SOcm/SOOcm-O.l.
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 Figure 9. Photomicrographs of 38* and 6°, ground bevels.

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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Spreading Resistance Correction Factors

for (111) and (100) Surfaces

H. Murrmann and F. Sedlak

Siemens AG, ¥erk Halbleiter
Muni ch, Ge rmany

The effective contact radius for spreading resistance

measurements on Si has been evaluated by comparision of
S.R. for epitaxial layers limited by a pn-junction or by
a v/ell conducting buried layer for different crystal orien-
tation. The contact radius on (100) surfaces showed to be
greater by a factor of 1,26 than for a (111) plane. Further-
more measurements were made on samples for both (100) and
(111) orientation in the resistivity range of 0,01 to SOttcm
with n and p-type doping. Data for spreading resistance and
resulting from the predetermined contact radius for the re-
sistivity dependent correction factor are given.

Key words: Contact radius, correction factors, silicon,

spreading resistance, surface orientation.

1. Introduction
The spreading resistance underneath a flat circular contact (radius a)
on a semiconductor (resistivity f) can be expressed in the form

In this formula the first term ?/4a represents the spreading resi-
stance (S. R.) of an ohmic contact on top of a semi-infinite medium of
metal with resistivity ? (figure 1). If energy barriers have to be consi-
dered between the contact and the medium (as is the case for most contacts
between metal and semiconductor) a generally 9-dependent factor k($) des-
cribes this effect. If furthermore the resistivity of the sample is non-
uniform, the distribution of the electric field t will be influenced,
giving rise to a correction term k (t) dependent on the 5-distribution
in the vicinity of the contact.
When applying the spreading resistance technique to quantitative
measurements on semiconductors, both these corrections have to be taken
into account. This generally includes a calibration of fhe specific
equipment with samples of known uniform resistivity, in which case the
k (e)-correction can be neglected.
Curves of measured spreading resistance vs. resistivity for n- and
p-type silicon have been published for different probe tip material and
contact radius /~1/, /£/, /37» />4/.1From these graphs the $ -dependent
correction can be derived provided the contact radius is sufficiently
well known.
Figures in Brackets indicate the literature references at the end of this paper.
137
 Only very limited data exist for the influence of crystal orienta-
tion on the correction factor [2]. On the other hand there is strong expe-
rimental evidence, that differences exist between SR-measurements on
(111) and (100) surfaces.
Figure 2 shows plots of RS.R. for (111) and (100) samples. In this
case p-type Si-substrates (8 cm) were used with a buried layer diffusion
(As, Xj = 4,5/urn, R = 25#/a) and a n-type epitaxial layer (As, depi
= 2,5/um, $ - 0,8^2cm). Though the thickness and resistivity in both
samples are the same, the SR-values show considerable differences. As the
resistivity distribution in the first approximation can be assumed to be
identical, the reason for such discrepancies can only arise from diffe-
rences in k(S) or in the contact radius for the two surface orientation.
In the following investigations we tried to distinguish between these
two effects.

2. Determination of contact radius

2.1 Theoretical consideration
The question of what the effective contact radius will be, when a
probe with a spherical tip is pressed onto a flat surface is very diffi-
cult to answer. Several investigators have dealt with this problem consi-
dering more or less idealized contact areas /"1/» /V resulting from app-
lication of the Hertz formulas /"6/ as well as arrangements of multipoint
contacts /"57. Optical evaluation of the surface depression after removal
of the tip in general only gives on approximate, figure for the contact
area. We have decided to try an evaluation by S.R. measurements making
use of equation (1):
As stated above the S.R.-value for a given ? at the surface is dependent
on the field distribution . The potential and hence the factor k(O has
been calculated for the special arrangement of a layer 1 with resistivity
?1 on top of a layer 2 with ?2 respectively (figure 3).
Two configurations are of specific interest:
a) £ 0 =°°' This implies that an insulating boundary limits the region of
layer 1. Technologically this is realized by a pn-junction.
b) 9p = 0: Here the conductivity of layer 2 is assumed to be much greater
than in layer 1. This case can be approximated by an highly
doped underlay of the same conduction type.
In both.cases the field correction factor is only dependent on the ratio
of d/a '. In figure 3 the results of a calculation following Schumann
and Gardner Cl] are plotted as a= function of d/a. If we furthermore com-
pare two configurations with ?2 °°and ?2 = ° respectively but otherwise
identical ?- and d, the ratio of the corresponding spreading resistances
is merely given by k(oo)/k(0) independent of ? and barrier effects but
only dependent on the ratio of d/a (figure 4).

So we may derive from the S.R.-ratio a certain value of d/a from

figure 4 and, when the thickness of layer 1 is known, the effective con-
tact radius of our spreading resistance equipment can be found.

' There exists a slight dependence on the spacing between the probes used
for measurement, but this effect is neglible for our considerations.
138
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 2.2 Experimental
For the experiments Si-wafers (1,25H diam.) with (111) and (100)
orientation and both p-type material (842cm) were used. After a thermal
oxidation (1/urn SiO£) the oxide was removed from a half of each wafer and
a buried layer diffusion was carried out (Sb, 25P/O, x^ = 4,5/urn) while
the other half of each slice was masked by the oxide. Following complete
oxide-stripping, As-doped epilayers were deposited (1150°C, SiCl4) in
four different runs with projected thickness of 2, 3, 5 and 8/urn. The
epithickness was evaluated by both IR-reflection and stacking7faults above
the buried layer diffused halves. S.R. measurements were made with a Mazur
Automatic Spreading Resistance Probe (ASR-100) with two probes loaded with
a force F of either 20 g or 45 g each. The measurements were taken on the
unprepared Si-surface after epitaxy on the half above the buried layer
(denoted as RSR (0)) and on the other half, where the n-epilayer is iso-
lated from the adjacent substrate by a pn-junction (RSR (°°))« Table 1
shows data of some of the slices examined.

Wafer F == 20 g F = 45 g d
epi
Nr. by IR

2 12,0 1,55 8,7 0,98 2,10

4 11,3 1,50 7,5 0,83 2,02
6 5,95 1,26 5,4 0,88 2,95
7 6,40 1,75 5,6 1,03 3,02
12 5,80 2,40 5,0 1,6 5,36
14 2,55 1,53 2,08 1,07 7,85
15 3,35 1,97 2,70 1,35 8,16
01 10,5 0,84 - - 1,94
03 10,2 0,82 - - 2,02
07 5,2 0,98 4,72 0,58 3,12
08 5,8 0,92 5,3 0,54 2,98
09 3,75 1,41 3,28 0,97 5,92
012 3,40 1,26 2,97 0,84 5,68
016 2,52 1,35 2,12 0,94 8,72

Table 1: S.R. above a pn-junction (R(o°)) and buried layer

(R(0)) for different probe loading F
(ASR-100, 2 tungsten probes with spacing of 600 /urn,
measurement voltage 10 mV, resistivity of the '
epilayer 0,6 - 1,3 cm).

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 2.3 Results
From the ratio R(<»)/R(0) using figure 4 and the determined epithick-
ness, an effective contact radius Ca) was evaluated with the results shown
in table 2.
Table 2. Contact radius for different probe loadings and two orientations

F = 20 g F m 45 g a (45 *)
a (26 g)
a (H1)Z}um7 2,20 2,82 1,26

a (I00)^um7 2,90 3,45 1,25

Within an experimental error of ± 8 % the values of (a) showed no

dependence on the epithickness within the range examined, indicating that
the thickness effective for S.R..and the thickness deduced from IR-reflec-
tion is approximately the same '/.
According to an early study of Hertz f6J, the radius of the contact
area resulting from a spherical probe (radius A, modul of elasticity E-|)
elastically pressed onto a flat medium (elasticity modul £2) by a force F
is given by

If the S.R. -contact mainly follows the laws of elasticity, the ratio
of the effective radius for two loadings F1 and F2 is given (independently
on orientation) by

The result derived from the measurements show a very good agreement with
this simple theoretical model (table 2).

3. Measurement on (111) and (100)

3<1 Experimental
In order to compare different crystal planes of otherwise identical
material the following procedure for sample preparation was chosen: The
resistivity of a number of n and p-doped Si-slices (orientation (111),
thickness 200/urn) with homogenous doping was measured by conventional
4 point probing. From the middle part of each slice we subsequently cut
two samples of 4 x 4 mm2. Taking one sample of each slice we stacked them
together and mounted them on a fixture under a certain orientation (figu-
re 5).

The only difficulty showed up for depi less than 2/urn at (100) orien-
tation with 45 g loading, where obviously the pn-junction got leaky
giving rise to R(oo)-values lower than expected. The data for this
special case have not been considered in the evaluation for table 2.
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 Then the sample block was polished 1) in order to expose the desired
crystal plane as predetermined by the sample orientation and the angle on
the mounting fixture. By repeating this procedure we finally got two cali-
bration blocks, one with (111) and one with (100)-surfaces, each consisting
of 8 samples covering a range of 0,010 to 20 cm for n-type and 0,013 to
78 cm for p-type material^'. Then S.R.-measurements were made with the
two-probe arrangement of the ASR 100. The polishing procedure and measure-
ment was repeated a total of five times within three months.
3.2 Results
The S.R.-data as received from the calibration blocks is given in
figure 6. Each point is a mean value of the five different measurements.
From this we finally plotted in figure 7 the $-dependent correction factor
as a function of resistivity using the different contact radii for (111)
and (100) as determined in section 2 for 1ft cm n-material and assuming
these values to be valid for the whole resistivity range and p-type as
well.

4. Conclusions
From the data given in section 1 and from additional analysis of the
measured values we finally can summarize the following conclusions of our
examinations:
a) The effective contact radius of our probes is a factor of 1,26 greater
on a (100) than on a (111) surface (n-material).
b) The spreading resistance on a (111) surface is always greater than for
a (100) surface within the resistivity range of 0,01 to 20 cm. This
holds for n- as well as for p-type material. The difference is greatest
in the region of 1 Hem, where we find a factor of 2,1 (n) and 1,8 (p)
respectively.
c) This behaviour can partially be attributed to the difference in the
effective contact radius.
d) There remains at least in the 1&cm region a clear difference in the
resistivity dependent correction factor between (100) and (111).
e) The spread of the values from repeated measurements is much smaller
for (100) orientation than for (111)
We hope that these experimental investigation are of some use for
others dealing with S.R.-measurements and their theoretical explanation.

1'^ Polishing was done first with Linde A abrasive and a final finish with
Syton polish.
2\1
It was checked by X-ray measurement, that each sample surface had the
desired orientation within ± 2,5°-
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 5. References
/17 Mazur, R. G. and Dickey, D. H., A Spreading Resistance Technique
for Resistivity Measurements on Silicon, J. Electrochem. Soc.
113. 255 (1966).
/27 Gardner, E. E., Schumann, P. A. and Gorey, E. F., Measurement
techniques for thin films, p. 258, Electrochem. Soc. (1967).
f*s Keenan, ¥. A., Schumann, P. A., Tong, A. H. and Philips, R. P.,
Ohmic contacts to semiconductors, p. 263, Electrochem. Soc.
(1969).
C*J Kramer, P. and van Ruyven,L.J., The Influence of Temperature on
Spreading Resistance Measurements, Sol. State Electr. 15* 757
(1972).
{5J Severin, P.J. Measurement of Resistivity of Si by the Spreading
Resistance Method, Solid-State Electron. .14, 247 (1971).
£6J Hertz, H., (Jber die Bertihrung fester elastischer K5rper und tiber
die Harte. Ges. Werke, Bd. 1 (Leipzig 1895).
[1J Schumann, P. A. and Gardner, E. E., Application of Multilayer
Potential Distribution to Spreading Resistance Correction Factors,
J. Electroch. Soc. 116, 87 (1969).

Figure 1. Schematic for S.R. of a

circular contact area (radius a) on
a semi-infinite metal and a semicon-
ductor with inhomogenous resistivity.
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142
 Figure 2. SRM on n n+p structures
with (111) and (100) orientation but
with identical dopings.

Figure 3. Correction factor due to

distortion of the electric field i
by a two layer configuration. (Two
probe arrangement with a spacing of
0,6 mm).

Figure 4. Ratio of the field cor-

rection factor for a two layer
arrangement with P2 - °°. and P2 ~ 0
respectively (two probes with 0,6 mm
spacing).

143
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 Figure-5. Calibration block con-
sisting of several samples with
different resistivities and (111) or
(100) surface orientation.

Figure 6. Spreading resistance for

n and p-type material and for (111)
and (100) surface orientation. (ASR-
100, probe spacing 0,6 mm, two
tungsten probes (tip radius 25 ym)
with a load of 20 g each).

Figure 7. Resistivity dependent cor-

rection factor derived from figure 6
with values of contact radius from
table 2.

144
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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

On the Calibration and Performance of a

Spreading Resistance Probe

H. J. Ruiz and F. W. Voltmer

Texas Instruments Incorporated

Dallas, Texas 75222

In this paper, techniques are presented for material standards

selection for calibration purposes, materials and calibration block
preparation, and techniques for data collection and processing for
the spreading resistance probe. A description of the variation with
time of the calibration of a spreading resistance probe is presented.
Problems encountered with characterization of high resistivity p-type
silicon are discussed, and examples of the probe performance in the
characterization of germanium are also presented.

Key words: Automated resistivity measurements, calibration, german-

ium characterization, sample preparation, silicon characterization,
spreading resistance, surface effects.

1. In tr oduc t ion
Spreading resistance measurements [I]1 are currently being used throughout the semicon-
ductor industry to characterize semiconductor materials in the bulk [2,3], in epitaxial,
diffused, and buried layers [1], and in some cases in finished devices [4]. The method con-
sists in measuring the total resistance of a metal-semiconductor point contact and relating
it through empirical calibrations of the bulk resistivity of the material.
Spreading resistance measurements today provide the most practical tool for character-
izing semiconductor materials, especially those involving n/n+ and p/p structures. The
spreading resistance, Rs, of a circular contact [5] of radius a on a material with resis-
tivity p is given by

However, it has been shown [1] that the exact relationship between spreading resistance and
material resistivity must be modified by an empirical factor K such that

where RC is the total electrical resistance between the metal probe and the silicon. De-
pending on the probe material used and the experimental conditions, several authors [6] have
shown marked variations in the behavior of K as a function of resistivity. Nevertheless,
all previous work seems to agree that the effective contact radius of the probe increases
towards low and high resistivity values for both n- and p-type silicon. In obtaining accu-
rate calibration data, the parameters of importance in achieving good accuracy and

1
Figures in brackets indicate the literature references at the end of this paper.
145
reproducibility are sample surface preparation, temperature control of the samples, a good
set of bulk material standards whose resistivity has been determined by a different method
such as the four-point probe, and properly conditioned probes. Careful selection of mate-
rial standards cannot be over-emphasized.

2. Equipment Description

2.1. Probes
Two different apparatuses were used in obtaining the data presented in this report.
One of the apparatuses was an in-house design with electrically activated mechanisms for
all moving parts. The probe tip material was an osmium-ruthenium alloy which has a 6 ym
tip radius and operated under a 20 gm load. The other spreading resistance probe had air-
accuated relays for all moving parts, an osmium-tungsten alloy probe tip with a 25 pm
radius, and operated under 40 gm loading. The probe assembly and the stepping motor were
obtained from Solid State Measurements, Incorporated.2

2.2. Electronics
Two probes make contact with the material surface to be characterized. The probe
spacing is 600 jam. The sample to be measured is generally electrically floating and the
probes are biased at +10 mV and -10 mV. By measuring the current flowing between the
probes, one calculates electronically the value of Rc, and a logarithmic amplifier provides
a signal proportional to the value of the spreading resistance. By adjusting the value of
RO, the bias resistance for zero current flow, one can cover values of spreading resistance
from 1 fl to 100 Mfl. The electronics are calibrated by shunting the probes with a 1% resis-
tor of the appropriate value, and adjusting the electronics so that the appropriate reading
is obtained. Shunting resistors from 1 n to 100 Mfl are available in the instrument. To
avoid the erratic behavior of rotary switches in the calibrate mode, push-button switches
are used to activate mercury-wetted relays. Thus, in the calibrate mode, one can for ex-
ample change the shunting resistor from 1 ft to 10 Kfl without having to go through the de-
cades in between.

2.3. Data Processing

The signal in millivolts which is proportional to the value of the spreading resis-
tance is digitized through a millivoltmeter, passed through an interface card, and fed into
an HP9810 minicomputer. The data can be on line converted to spreading resistance, resis-
tivity, carrier concentration, and plotted simultaneously on either a linear or logarithmic
scale. A program is also available for providing on line single layer correction factors
when characterizing single layer epitaxial or diffused films. The data obtained from the
minicomputer can be stored in magnetic tape, punched tape, or IBM cards for further pro-
cessing, as is the case when one performs multilayer analysis of the data.

3. Calibration Block Preparation

3.1. Material Standards Selection

Silicon wafers in the range .01 to 100 ft-cm were selected as potential material stan-
dards for calibration blocks. Using a 4-point probe for resistivity measurements, approxi-
mately 100 wafers were found in the desired resistivity range for both n- and p-type mate-
rial. Out of these wafers, ^20 were selected for each type as material standards for
calibration. The wafer selection was achieved through the following procedure:
(a) Each wafer was measured 10 consecutive times on 10 different occasions (a
total of 100 measurements) near the center of the wafer. For example, see
table 1.

2
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 (b) The measurements were corrected for temperature and thickness variations.
(c) Near the center of the slice, resistivity readings were made .5 mm apart,
and slices which exhibited more than 10% variation in the readings were
rejected as material standards. Spreading resistance measurements were
also used to determine which wafers had less than 10% microsegregation
of dopant.
(d) The resistivity value of the wafers chosen was the average of the 100
readings described in (a), and an attempt was made at obtaining a mini-
mum of 4 different material standards per decade in resistivity.

3.2. Materials Preparation

The wafers chosen were individually waxed down on microscope glass slides. Using a
diamond watering saw, .5 mm x 1.0 mm x 20 mm bars were cut out from each wafer as indicated
in figure 1. One bar from each of the wafers selected as material standards was waxed down
on a 0° stainless steel block which was threaded for mounting under the spreading resis-
tance probe. All of the bars were waxes down adjacent to each other and in order according
to resistivity to facilitate measurements to be made. Using a silicon carbide 1200 grit,
the samples were ground to the same thickness. Lustrox3 1000 was then used to chemically-
mechanically polish the samples until a scratch-free mirror-like surface was obtained.

Table 1. Example of Four Point Probe Readings Taken for

Material Standard Evaluation for Calibration Purposes
1 2 3 4 5 6 7 II 9 10

Sample 1 1.040 1.057 1.051 1.056 1.042 1.043 1.060 1.045 .043 .035
No. 2 1.030 .053 1.055 1.054 1.053 1.034 1.052 .051 .042 .035
11 3 .040 .059 1.059 1.062 1.051 1.044 1.051 .054 .052 .036
4 .040 .053 1.055 1.068 1.050 1.037 1.052 .042 .054 .043
N-Type 5 135 .060 1.051 1.065 1.051 1.037 1.056 .051 .040 .040
<111> 6 .050 .060 1.058 1.058 1.060 1.040 1.048 .048 .035 .034
7 .046 .055 1.067 1.050 1.051 1.046 1.059 .048 .042 .037
8 .050 .056 1.057 1.060 1.054 1.042 1.045 .050 .045 .043
9 .057 .062 1.054 1.049 1.055 1.039 1.049 .043 .048 1 04
10 1.055 .068 1.058 1.053 1.063 1.045 1.058 .051 .050 1.047

Average 1.0458 1.0583 1,0565 1.0575 1.053 1.0407 1.0530 1.0483 1.0451 1.0391
Average = 1.0497; Standard Deviation = .00695

4. Probe Calibration

4.1. Technique

4.1.1. Data Collection

The calibration block containing the prepared bars is mounted under the probe apparatus
for spreading resistance measurements. Twenty measurements, one every 20 ym, are made on
each one of the bars. The measurements are made automatically, the data is electronically
transferred on line to an HP9810 computer, and the computer computes the average value of
spreading resistance of each bar, and stores it along with the standard deviation of each
set of measurements. The process continues until all of the bars in the calibration block
have been read. The computer has stored the resistivity value of each one of the bars.

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 4.1.2. Data Processing

Once the measurements have been completed on the calibration bars, a linear least
square fit is performed on the logarithm of the spreading resistance and the logarithm of
the resistivity of each bar. A printout is obtained of the least square fit parameters of
the data and the correlation of the data points in relation to a linear fit. At the same
time, a plotter, on command from the HP9810 computer, plots the data points and the line
representing the linear fit of the points on log-log graph paper. An example of the type
of graphical display of the calibration data is shown in figures 2 and 3. Figure 2 corre-
sponds to calibration data on n-type material, and figure 3 corresponds to calibration data
on p-type material.

4.2. Calibration Parameters

The expression for spreading resistance is given by

Over the range of interest, let us neglect the dependence of the empirical factor K on the
resistivity of the material p. We thus have

where y is a constant. A linear fit through the calibration data points shown on figures
2 and 3 gives an equation of the form

where A is the slope of the line and B is its intercept (A and B will be called calibration
coefficients). For figure 2, the values of A and B are "1.025 and -3.466 respectively. In
figure 3, A and B are .989 and -2.99 respectively. From the calibration coefficients we
can compute the resistivity of material of spreading resistance Rs through

4.2.1. Variation of Calibration Coefficients with Time

Weekly during the past two years, we have performed calibration runs of the spreading
resistance probe using the same calibration block. Figure 4 shows the statistical distri-
bution obtained from the measurements made on each one of the different samples on the cali-
bration blocks. One should note that the standard deviation of the measurements becomes
larger with increasing resistivity, specially in p-type material. Figure 5 shows a plot of
A and B as a function of time for three sets of identical probes. The places where the
value of coefficient A took a sudden deviation appeared to correlate very well with that
point in time in which the probes became erratic with an increased amount of scatter. After
the probes were replaced, the behavior of the calibration coefficients was back to "normal."
The model proposed in equation (3) implies either a linear relationship between Rs and p or
a functional dependence of K on p. In the range over which our calibrations are made, it
is important to know whether or not the linear relationship holds. In equation (5), the
value of A determined over 100 calibration runs is such that A = 1.000 is within the a
limits of the frequency distribution of A. This implies that the linear model described in
equation (3) is valid. While we use the specific value of A as determined in the weekly
calibration1 runs for determining sample resistivity, it would be equally valid from a sta-
tistical point of view to set A equal to unity. However, our data definitely establish
that n- and p-type silicon behave differently. The difference in the value of B must be
due to a dependence of K on the semiconductor material, its orientation, and type. Figure
6 shows a variation of the calibration coefficients for different probe materials. Figure
5 corresponds to data taken with 25 ym radius probes made of osmium- tungsten alloy at 40
gms loading. Figure 6 corresponds to 6 ym radius probes made of osmium-ruthenium alloy with
20 gmsCopyright
loading. Figure
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coefficients A and B for both n- and p-type calibrations. Each set of probes that exhibited
a marked deviation in the calibration coefficients as shown in figure 5 was discarded. This
occurred after about 250,000 measurements.

4.2.2. Comparison of Two Probes

The performance of the two probes has been similar, except that the osmium-ruthenium
probe exhibits larger scatter in the high resistivity end, specially on p-type material.
Typical calibration factors for both probes are summarized below for p-type material.

6 vim Radius, 20 gms Load 25 ym Radius, 40 gms Load

Osmium-Ruthenium Probe Osmium-Tungsten Probe

A .992 .990
B -3.25 -2.950
% scatter at
70 cm p-type ^20% <5%

The range over which A varied for the osmium-tungsten probe was from .91 to 1.08. For
the osmium-ruthenium probe, the range of variation of A was from .90 to 1.07. The differ-
ence in B of the probes is indicative of the difference in the electrically active radius
of each probe.

5. Probe Performance

5.1. Characterization of N- and P-Type Silicon

In the resistivity range of .01 to 100 fl-ca, the performance of the probe was very
satisfactory on n-type material. Measurements obtained in this range were within 10% of
measurements obtained on the same material using other characterization technqiues [7],
i.e., C-V measurements, 4-point probe measurements, etc. Characterization of p-type mate-
rial had similar performance in the .01 to 10 ft-cm range. For resistivities larger than
10 Ji-cm however, the measurements were not as reproducible and were very sensitive to the
conditions of the sample surface. The empirical factor K in equation (2) has a different
value for p-type material than it does for n-type material. As can be seen from the cali-
bration plots of figures 2 and 3, the parameter K is more sensitive in the high resistivity
region of both n- and p-type calibrations.

5.2. Problems with High Resistivity P-Type Silicon

We have observed that surface preparation of the samples can contribute considerably
to error in the characterization of high resistivity p-type silicon. A mechanically
polished p-type high resistivity sample (^70 ft-cm) was used in the measurements to deter-
mine the effect of surface preparation on spreading resistance measurements. The sample
was first measured as received and the point is the first one on figure 8. The sample was
then placed in boiling water for the amounts of time indicated in figure 8. At the end of
each time cycle, the sample was allowed to dry in air and reach room temperature before mea-
surements were made. The bars in figure 8 indicate the range over which the data scattered.
It is important to note that neither an HF dip nor a boiling water bath affected the read-
ings obtained on a sandblasted piece of silicon from the same slice. This clearly indicates
that surface effects on a polished slice are a dominant factor in resistivity determination
of high resistivity p-type material. In an effort to determine if surface conduction was a
dominant factor in the phenomena, the following experiment was performed. A piece of the
slice being used in this experiment was sandblasted everywhere except for two circular areas
about 200 ym in diameter. The distance between the center of these areas was ^600 ym, the
probe separation. It was believed that microcracks introduced into the surface this way
would impede carrier motion along the surface. However, this did not occur and the be-
havior of this specially prepared sample was identical to that shown in figure 8. We also
had a Copyright
slice cleaved
by ASTMinInt'ltwo pieces
(all rights and placed
reserved); Fri Jan 1on the sample
23:23:49 EST 2016holder such that each probe
would Downloaded/printed
fall on a differentby piece. The two pieces were far apart physically so that the only
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current path was through the vacuum chuck. Again, the behavior was the same. In an attempt
to gain understanding of this phenomenon, the following experiment was also performed. A
high resistivity slice, p-type, was placed in an oxidizing ambient for various times. The
resistivity of the slice as determined by the spreading resistance probe was measured as a
function of oxide thickness and the results are shown in figure 9. The measurement accuracy
of oxide thickness below 50 A was questionable; however, the data point out an interesting
surface phenomena. At this point, the only conclusive statement we can make about our ob-
servations is that we are not dealing with a problem of surface conduction, but rather a
problem having to do with metal-semiconductor contacts which are markedly affected by sur-
face treatment or condition of the material. Again we must point out that we do not observe
this phenomena in n-type material up to VL50 fl-cm in resistivity. In performing our measure-
ments and calibration on p-type material higher than 10 ft-cm, we have had to re-polish the
calibration block previous to any characterization of freshly polished material.

6. Summary
Techniques have been presented for the calibration of spreading resistance apparatus
and the preparation of material standards for calibration purposes. It has been shown that
with proper care in the material standards selection and preparation, one should be able to
obtain an accuracy of 10% for measurements on both n- and p-type silicon in the range .01
to 100 fl-cm. However, for resistivities higher than 10 fl-cm, special attention must be paid
to surface treatment and condition of the samples to be measured. The relative accuracy of
the probe can be ^1%, as has been shown by shunting the probes with a resistor of value be-
tween 10 and 10 Kft, and observing that the variations in repeated measurements are ±.5%.
Potential problems have been outlined concerning the characterization of high resis-
tivity p-type silicon. It has also been shown that the performance of the probe on ger-
manium is comparable to its performance on silicon material.

7. References
[1] R. G. Mazur and D. H. Dickey, "A Spreading Resistance Technique for Resistivity Mea-
surements," J. Electrochem. Soc. 113 (1966) 255.
[2] F. W. Voltmer and H. J. Ruiz, "Use of the Spreading Resistance Probe for the Charac-
terization of Microsegregation in Silicon Crystals," 1974 Spreading Resistance Sym-
posium, Gaithersburg, Maryland.
[3] A. F. Witt, M. Lichtensteiger, and H. C. Gatos, "Experimental Approach to the Quanti-
tative Determination of Dopant Segregation During Crystal Growth on a Microscale," J.
Electrochem. Soc. 120 (1973) 1119.
[4] H. J. Ruiz and F. W. Voltmer, to be published.
[5] R. H. Holm, Electric Contacts, pp. 11-19, Springer, Berlin (1969).
[6] P. Kramer and L. J. Van Ruyven, "The Influence of Temperature on Spreading Resistance
Measurement," Solid State Electronics 15 (1972) 757.
[7] Gregg Lee, Walter Schroen, and F. W. Voltmer, "Comparison of the Spreading Resistance
Probe with Other Silicon Characterization Techniques," Spreading Resistance Symposium,
1974, Gaithersburg, Maryland.

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 Figure 1. Technique for Obtaining Calibration Bars from Material Standards.

Figure 2. #-Type Calibration Curve - Figure 3. P-Type Calibration Curve -

Spreading Resistance vs. Resistivity. Spreading Resistance vs. Resistivity.

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565-448 O - 75 - 11
 Figure 4. Statistical Distribution
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 Figure 5. Variation with Time of Calibration Coefficients A and B.
25 ym Osmium-Tungsten Probe, 40 gms. Loading.
Copyright by ASTM Int'l (all rights reserved); Fri Jan 1 23:23:49 EST 2016 Figure 6. Variation with Time of Calibration Coefficients
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 Figure 8. Effect of Surface Treatment on Spreading Resistance
Measurements of a 70 fl-cm P-Type Specimen.

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Figure 7. Frequency Distribution of Calibration Coefficients A and B.
 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Comparison of the Spreading Resistance Probe

with other Silicon Characterization Techniques

Walter H. Schroen, Gregg A. Lee, and Fred W. Voltmer

Semiconductor Research and Development Laboratories

Texas Instruments Incorporated
Dallas, Texas 75222

Range and precision of doping concentration data in silicon materials gained by the spreading resistance technique
are compared to values obtained by other characterization methods. They include junction and MOS capacitance-voltage
techniques, mercury probe, four-point probe, incremental sheet resistance technique, ion microprobe, and optical
methods. The comparison considers precision and resolution of each technique, range of silicon resistivities and layer
thicknesses, experimental effort, analytical interpretation, and time and cost of data acquistion and evaluation.
Examples are presented which demonstrate the range of applicability of each technique and how they can supplement
each other so that they cover the total doping range of silicon devices.

Key Words: automation; bevelling; comparison; four-point probe; incremental MOS capacitance-voltage;
incremental sheet resistance; infrared spectrometer; ion microprobe; junction capacitance-voltage; lap and stain; mercury
probe; Schottky capacitance-voltage; scanning Michelson interferometer; spreading resistance.

1. Introduction

The spreading resistance probe has recently been widely applied as a means of determining semiconductor
resistivity. Some uses to which it has been or may be put are shared with other measurement techniques. Thus it has
become pertinent to review the general capabilities of the spreading resistance probe and its alternatives and, where
possible, to make direct comparisons of the results of one or more techniques.

Spreading resistance is presently employed for three general purposes: production control, measurement of
resistivity laterally across a silicon slice, and measurement of dopant concentration versus depth into a sample. The key
advantage provided by spreading resistance for production control is its ability to probe small areas within an integrated
circuit to measure a local resistivity value. In this application reproducibility is extremely important. For scanning across
a silicon slice, the probe measurements must be not only reproducible but also of high precision and volume resolution
in order to detect micro-segregation or local oxygen content in crystals. The spreading resistance probe is the only tool
which has sufficient spatial resolution to perform this function. Other papers presented at this Symposium discuss the
application to production control and scanning measurements of the spreading resistance technique [1 to 6] *, thus this
paper is restricted to the comparison of techniques used to measure dopant concentration versus depth, commonly
called the dopant profile.

This comparision is performed with two questions in mind. First, for a given measurement, which is the best
technique to choose from a number of alternatives. Second, however, how may the capabilities of different techniques
be employed to supplement each other to provide a more complete or accurate measurement. A number of points of
comparison are pertinent; they are listed in figure 1. Precision and spatial resolution have already been mentioned above.
For the present purpose, the range of silicon resistivity and the range of layer thickness which can be resolved are also
important. Furthermore, it is useful to know whether or not the measurement process destroys the sample and to know
the degree of effort required to obtain the experimental data and then to analyze it. Last and by no means least, is the
cost of equipment required for the technique, the cost of making the measurement and of analyzing the data.

155
 A point worth mentioning is that the spreading resistance probe and many other techniques discussed here measure
electrically active dopants. For many investigations it is advantageous to supplement this capability with a technique
able to measure the total concentration, or active plus neutral dopants. The comparison of this paper will first be
concerned with techniques measuring only electrically active dopants; for the purpose of supplementing the spreading
resistance probe, it will then list brief ly the capability of total concentration techniques.

2. Capabilities and Limitation of the

Spreading Resistance Probe

The local impurity concentration T? is inferred from the local measured resistivity according to the expression

where the mobility, n, is inferred as a function of the carrier concentration n, and p-j is the measured local resistivity. In
the spreading resistance technique, the contact resistance of the small metal-semiconductor contact is determined and
related to the resistivity by the fundamental relation

where ro is the effective radius of the probe contact, determined by calibration with known resistivity standards. C is the
"correction factor" [7] which reduces the measured resistivity p -j to the true resistivity PQ.

The spreading resistance probe lends itself to automated operation, data acquisition and data evaluation. A
sophisticated probe is capable of operating as either a "one-point" or two-point probe. The descent rates on static
loading may be controlled independently for the two probes to ensure a constant and identical contact area for each
probe. The probes have* been calibrated for silicon, and the linear slope of unity, when spreading resistance is plotted
versus resistivity, verifies a constant contact area. A highly developed mechanical system allows stepping in 2.5, 5, 10,
25, 50, 100, and 250 nm steps automatically, through a 1-inch translation. Smaller steps can be taken, but the
mechanical damage to the silicon owing to probe impact would overlap, and it is still debated whether actual
measurement can be taken under these conditions. The entire mechanical control system is pneumatic, ensuring that
during electrical measurement of the resistivity, the system is otherwise in a quiescent state.

A constant 10 mV potential is applied to the probes after they contact the surface, and the current is measured
using a log converter which is linear over 8 decades. Standard resistors are used to calibrate the spreading resistance. The
calibration between spreading resistance and resistivity is obtained by measuring silicon samples of known resistivity and
from the resistivity and spreading resistance determining the contact area. The resistivity can be determined using either
a calibrated 4-point probe or by making Hall measurements. The precision of these calibrations depends on the
homogeneity of the reference sample, which can be determined by qualitative spreading resistance measurements.

3. Comparison of Profiling Techniques

in Reference to Sample Processing

Figure 2 lists five profiling techniques which are generally used for determining the concentration of electrically
active dopants: spreading resistance, incremental sheet resistance, incremental MOS capacitance-voltage, junction
capacitance-voltage, and MOS and Schottky contact capacitance-voltage. In addition to these techniques, the four-point
probe and lap and stain techniques are listed for supplying reference points. Sections of this paper discusses
supplementary techniques for determining active plus neutral dopants, namely the ion microprobe, several optical
methods, and the nuclear activation analysis.

A comparison and overlay of the most appropriate and accurate profiling techniques is presented in figures 3, 4,
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and 5. (see also [8]). The sequence of transistor processing steps is illustrated for typical impurity concentrations and
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depths. The superposition of the techniques is shown at decisive processing stages: in figure 3, after the diffusion of the
buried layer, in figure 4, after epitaxial deposition, and in figure 5, after base and emitter diffusions. The symbols
indicating the various techniques have not been selected as actual data points, but rather to indicate the qualitative
capabilities of the techniques. The connecting line has been added for clarity, but does not represent an actual
theoretical model.

The most versatile technique is the spreading resistance probe. It is shown qualitatively as "unconnected data," this
means the data as measured by the probe and translated into concentration values as though each measurement were
made on a homogeneous sample. By applying a multilayer model analysis these data points can be brought into close
agreement with theoretical predictions and also with other techniques such as the junction CV data [7,9]. The spreading
resistance probe can cover the widest range of doping concentrations, it can be used to measure both very shallow layers
and deep diffusions. It can probe close to pn-junctions and can measure both n- and p-type conducting material. It is the
only convenient technique to monitor buried layers and deep diffusions.

3.1. Incremental Sheet Resistance Technique

The incremental sheet resistance technique for determining concentration profiles had been used extensively in the
past several years [10] for the identification of control problems in the manufacture of shallow devices «1 jurn). The
method consists of measuring the sheet resistance after removing thin (about 200 A) layers of silicon by anodic
oxidation and stripping in HF. From the resistivity profile, a concentration profile is obtained by using suitable
conversion data, such as that of Irvin [11]. The incremental sheet resistance is an absolute technique since it compares
differences of resistivity data. It is the best technique known for measuring profiles in the high concentration regime and
in extremely shallow layers. It fails, however, to measure concentrations lower than 1 X 10^ carriers/cm^, so that it is
difficult to probe close to junctions. The primary drawback of the technique is the long period of time necessary to
perform the anodization and stripping experiments. An experienced technician may take at least one day to measure a
profile. The evaluation of the data can be automated, but little automation can be applied to the experiment itself.

3.2. Incremental MOS Capacitance-Voltage Technique

The relatively new incremental MOS CV technique [12] is capable of acquiring precise data in extremely thin
layers, such as ion implanted layers and bases of microwave transistors. The technique is best applicable at lower doping
concentrations, in particular concentrations where the incremental sheet resistance technique can no longer acquire data
(i.e., at concentrations lower than 10^ carriers/cm^). The incremental MOS CV technique removes thin layers of silicon
by the growth of anodic oxide. MOS CV measurements are made after each oxidation. The oxide is then removed, a new
oxide is grown and another MOS CV measurement is made. The process is repeated enough times to acquire data for a
complete profile. For each MOS CV curve the maximum width of the space charge layer Wm is determined and plotted
versus Xg, the total thickness of silicon removed. The impurity profile is found by calculating the curve Wm (Xs) for a
series of theoretical profiles. The profile whose Wm (Xs) curve matches the experimental curve, is taken as the correct
profile. The difficulty with this technique is its very time consuming experimental procedure, which is even slower than
the incremental sheet resistance technique, and the instability of the anodic oxide. It turns out that only for aluminum
metallization is the anodic oxide stable enough for precise capacitance measurements. Processes have unfortunately not
yet been developed to grow oxides stable enough for mercury probe contacts or gold bail bonds, either of which would
accelerate the data acquistion. Another requirement of the incremental MOS CV technique is an extensive analytical
computer program to convert the depletion region measurements for concentration data. This analytical technique is
particularly demanding when very steep profiles are considered, such as a three order of magnitude change in
concentration over a depth of .2 nm [12].

3.3. Junction Capacitance-Voltage Technique

The junction CV technique is one of the most effective methods of determining the concentration profile in
epitaxial material. An automated real-time system is shown in figure 6; it permits acquisition of CV data, transfer of the
data into a computer, evaluation of the data for the plot of doping concentration vs. geometrical distance, and output of
the data in printed form or by an x-y recorder. The expected profile as it relates to the cross sectional geometry of the
sample-under-test,
Copyright byisASTM
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 In addition to automated data taking, computer programs have been developed [13] which take into account
several corrections of the junction capacitance-voltage data. One correction is for the toroidal capacitance surroundinga
circular capacitor dot; the smaller the dot area relative to diffusion depth, the more important the contribution of this
toroidal capacitance. Another correction is the contribution of the capacitance caused by the space charge layer
penetration into the heavily doped side of the diffused junction. In figure 7 the two corrections are seen to pull the
profile in opposite directions and in this sense are compensating corrections. In the example shown, the importance of
the corrections is that the resistivity of the epitaxial material varies from 3.1 to 3.7 ohm cm (18% variation) and the
thickness of the epitaxial material varies from 5.0 to 6.1 jum at 10^ carriers/cm"^ concentration (20% variation).

For efficient process evaluation, electrical data acquisition and evaluation should be automated through the largest
extent reasonable. Not only does automation save time, it also reduces the involvement of human operators and
simplifies data retrieval. An example of an automated data reduction scheme is shown in the lower part of figure 6.
Another more general example is given in figure 8. A coupler system connects standard laboratory instrumentation with
a programmable calculator and allows data output on paper tape; an x-y recorder displays the evaluated measurements.

3.4. Mercury Probe and Schottky Capacitance-Voltage Technique

A modification of the junctions CV technique is the mercury probe or Schottky CV method. It employs a mercury
dot of precisely determined and reproducible area to contact silicon surfaces directly without the need of fabricating a
junction. Consequently, it lends itself for investigating unprocessed material (except for cleanups) with regard to doping
concentration and layer thickness. The method is thus nondestructive except for some possible but reversible mercury
contamination of the semiconductor surface. The relatively minor limitations of the mercury CV technique are: A
back-side contact is required for the slice; the sample should be flat to the order of the mercury contact area; and the
operation is limited to the breakdown voltage of the Schottky contact. The Schottky CV and the MOS CV techniques
are applicable only to thin or lightly doped epitaxial layers. When thick or heavily doped epitaxial layers have to be
measured, one has to resort to the junction CV technique where part of the layer is used up by the diffusion. It should
be stressed again that because of its nondestructive operation, the mercury contact or multiple mercury contacts lend
themself for automated real-time on-line production control.

3.5. Examples for Comparison of Techniques

Figure 9 shows an overlay of actual data points for spreading resistance measurements, junction capacitance-voltage
measurements, and mercury probe capacitance-voltage measurements. For the spreading resistance probe, both data "as
taken" and after multilayer analysis are shown. It can be seen that there is very good agreement for the surface value of
the concentration for all three techniques after the spreading resistance data has been analyzed. The profile then
proceeds to show the epitaxial concentration and the interface of the epitaxial layer and the diffusion of the buried
layer (see figure 7). There is also very good agreement between the three techniques for the definition of the epitaxial
thickness and the slope of the buried layer. The dip of the concentration displayed by the analyzed spreading resistance
data is an artifact of the multilayer analysis and is discussed in other papers at this Symposium [7,9]. In brief, the dip is
caused by an overreaction of the multilayer analysis to this steep increase of concentration under the epitaxial layer. In
addition, the multilayer analysis assumes that a circular contact is made between the probe and the silicon while in
reality there are many microcontacts in an array. Since it is an artifact, this dip can be disregarded.

Figures 10 and 11 illustrate the outstanding capabilities of the incremental sheet resistance for determining profiles
in very shallow layers. This technique has been used in the past few years as a tool for ion implantation investigations
and the development of models for doping profiles. Figure 10 shows the capabilities of the incremental sheet resistance
technique for ion implant boron modeling. A dense array of data points can be acquired in very shallow layers and at
relatively high concentrations. The data points fit very well the model predictions developed by Prince and
Schwettman [14]. The technique has successfully identified small discrepancies between theory and experiments, such
as indicated in figure 10 for the conditions of 1000°C annealing temperature at 30 minutes steam oxidation and the
choice of the segregation coefficient k = 10. On the other hand, figure 10 clearly exhibits the limitations of the
incremental sheet resistance technique. Carrier concentrations smaller than about 2-1017 cm~3 cannot be resolved. The
technique is therefore not able to probe close to p-n junctions.
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 Figure 11 demonstrates the capabilities and limitations of the incremtnal sheet resistance probe for implanted
arsenic and comparison with As implant models. The probe is able to detect the arsenic tail observed in ion implanted
arsenic layers and the relative immobility of this tail with annealing times and temperatures. As stated earlier, the
incremental sheet resistance technique detects only the electrically active dopants. There is, therefore, a discrepancy
between the theoretical model, which accounts for the total amount of dopants, and the electrically active part of it.
Models are presently being developed [15,9] to account for the percentage of electrical activation in implanted arsenic.

It is important that the spreading resistance values are "corrected" by the multilayer analysis [7] before they are
compared to incremental sheet resistance data. Figure 12 underlines dramatically the shift of the original data points
(crosses) towards the corrected values (diamonds and squares). There is good agreement between incremental sheet
resistance and spreading resistance values after multilayer analysis has been applied to the spreading resistance data.
Right under the surface, however, the spreading resistance technique (diamonds in figure 12) seems to suggest a
significant decrease in the phosphorus concentration. The probable origin of this drop is an effective reduction in carrier
concentration caused by the formation of a depletion region under the surface generated by the deposition of the
protective silicon nitride film. As figure 12 shows, the depletion region is partially reversed and eliminated
(square-shaped data points), when the silicon nitride film is removed. Consequently, this doping dip can be disregarded
as an artifact.

4. Small Angle Bevels for Spreading Resistance Probe

Figure 13 demonstrates the importance of the protective silicon nitride layer mentioned above. It is mandatory for
the extremely shallow bevels of angles of 0.3 degrees or less to have a very well defined edge between the original silicon
surface and the slope of the bevel. It has been found that unprotected silicon slices, or silicon oxide-covered slices, may
give rounded interface edges. Silicon nitride covered samples, on the other hand, turned out to result in very
well-defined sample slope edges when the films exhibited the correct hardness achieved by the right composition
between silicon nitride and silicon. Only with this well defined edge is it possible to probe very close to the surface, and
thus to measure the very high concentration parts of the doping layers.

5. Techniques for Acquisition for Singular Data Points

Figures 3 and 4 mention two techniques which can supply singular data points for material characterization: The
four point probe and the lap-and-stain technique.

5.1. Four-Point Probe

The four-point probe measures the average resistivity or net impurity concentration of substrates or diffused layers.
It has been employed as an indispensable material characterization tool for many years. Only recently have test
equipment, specimen preparation, measurement procedure, evaluation, and precision been subject to detailed
investigation with regard to reproducibiltty, and has a concise description of the standard method for measuring
resistivity of silicon slices with a collinear 4-probe-array been published by the ASTM [16]. The four-point probe
determines average resistivities from current and voltage measurements. The evaluation assumes layers whose lateral
dimensions are large and whose thickness is small in comparison to the spacing of the probes. For typical probe spacings,
this condition is amply met by diffused layers and also by 1 to 3 inch diameter wafers. If either the wafer thickness or
the lateral dimension of the semiconductor sample is comparable to the probe spacing, correction factors must be
applied [17].

5.2. Angle Lap and Stain Technique

It is the junction between opposite conductivity types where the angle and stain technique delivers an important
data point on the concentration profile for material evaluation. Lap-and-stain is destructive. The semiconductor sample,
whether large or small, is affixed to a rigid support, whose surface angle (i.e., perpendicular to its long axis) may lie in
the range from 90
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use of a precision collar. Using the silicon nitride overcoat shown in figure 13, the integrity of the bevel-surface interface
can be preserved. After obtaining a fresh, scratch-free polished surface at some specified angle which will reveal
diffusion, ion implantation, epitaxial or even damaged layers, the. sample is subjected to a combination of illumination
and chemical (usually acidic) etchants which will sharply distinguish such subsurface qualities as junction dep
concentration changes (in like-type material), shapes of penetration areas, and anomalous defects such as spikes, pipes,
or induced damage.

6. Techniques for Determination of Concentration

of Active Plus Neutral Dopants

6.1. Ion Microprobe

The ion microprobe is able to determine the profiles of diffused or ion implanted layers even for two-component
interactive situations. Figure 14 gives an example of boron and arsenic implanted layers which show a significant effect
on the boron distribution after the arsenic implant, the so-called base retardation. The ion microprobe is an important
analysis tool to acquire data for developing two-component interactive doping models [18], and for determining the
factor of electrical activation of dopants during annealing or diffusion heat treatments. The ion microprobe is
destructive.

6.2. Optical Methods

Two nondestructive techniques to measure the thickness of silicon epitaxial material are the dispersive infrared
spectrometer and the scanning Michelson interferometer. The IR interferometry, using the reflection inteference
spectrum obtained on an IR spectrometer, has been reviewed recently by Sever in [19] and has been exploited
extensively during the past decade. A standardized procedure based on IR interference has been adopted by ASTM.

Even though IR interferometer measurements have contributed considerably to simplify the measurement of
epitaxial films, in particular when based on a computerized system, the problem of mechanical wear resulting from
repeated cycling of the scanning mechanism in an IR spectrometer, remains. An automated scanning Michelson
interferometer has been developed [20], based on computer handling of the required Fourier analysis. Since no
restrictive slit mechanism is required and a reasonably wide angular aperture can be used without impairing performance,
the radiation throughput of the system is quite large. All wavelengths are viewed simultaneously by the detector, and in
a detector noise-limited system, this multiplexing of the spectrum will especially improve the signal/noise ratio. The
complete system for the measurement of epitaxial layer thickness utilizing the scanning Michelson interferometer is in
routine use for volume slice evaluation.

It should be kept in mind, however, that IR measurements are employed for epi films on buried layers of the same
conductivity type, and the value measured is somewhat within the high concentration side of the interface profile (see
figure 4, arrow "Reflected I R") since it is there that the absorption and reflection take place. IR measurements cannot
read epitaxial layers on opposite conductivity type because there is no absorption in the depletion region.

7. Conclusions and Recommendations

When compared with other resistivity profiling techniques, the spreading resistance probe has been shown to be the
most versatile. Its precision approaches that of incremental sheet resistance for shallow layers, yet can provide entire
doping profiles. It is rapid, and is easily adapted to automation. No special processing is required, other than angle
lapping, and therefore does not suffer from profile changes owing to oxidation or junction formation as in the C-V
techniques. Spreading resistance profiles can be obtained from finished devices as well.

There are, however, several areas where care must be taken in making spreading resistance measurements. Samples
must be carefully and reproducibly prepared and the probe tips must be adequately conditioned. Adequate standards
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 Several explicit recommendations for further work include extremely shallow angle sample preparation, i.e. less
than 15', definition of procedures for reproducible surface preparation, establishment of calibration procedures as being
defined by ASTM to provide multi-laboratdry precision development of on-line multi-layer correction factors for
complex profile evaluation, and reduction of probe spacing to 25 nm for probing smaller bars.

8. References

[1] White, J., An automated spreading resistance [10] Donovan, R. P., and Evans, R. A., Incremental
test facility, NBS/ASTM Symp. on Spreading sheet resistance technique for determining
Resistance Measurements, Gaithersburg, Md., diffusion profiles, Silicon Device Processing, ed.
June 1974. by Ch. P. Marsden (NBS Spacial Publ. 337,
Washington, D.C., 1970), 123-131.
[2] Ruiz, H., and Voltmer, F. W., On the calibration
and performance of a spreading resistance probe, [11] Irvin, J. C., Resistivity of bulk silicon and of
NBS/ASTM Symp. on Spreading Resistance diffused layers in silicon, Bell Syst. Techn. J. 41,
Measurements, Gaithersburg, Md., June 1974. 387-410(1962).

[3] Goldsmith, N., Experimental investigation of [12] Kronquist, R. L, Soula, J. P., and Brilman, M.
two probe spreading 'resistance correction E., Diffusion profile measurements in the base
factors for diffused layers, NBS/ASTM Symp. of a microwave transistor, Solid-State El., 16,
on Spreading Resistance Measurements, 1159-1171 (1973).
Gaithersburg, Md., June 1974.
[13] Buehler, M. G., Peripheral and diffused layer
[4] Edwards, J., Spreading resistance and MOS C-V effects on doping profiles, IEEE Trans. Electron
radial resistivity profiles of silicon wafers — a Devices, ED-19, 1171-1178 (1972).
direct comparison, NBS/ASTM Symp. on
Spreading Resistance Measurements, [14] Prince, J. L., and Schwettman, F. N., Diffusion
Gaithersburg, Md., June 1974. of boron from implanted sources under
oxidizing conditions, J. Electrochem. Soc. 121,
[5] Voltmer, F., Bulk microsegregation in silicon, 705-710(1974).
NBS/ASTM Symp. on Spreading Resistance
Measurements, Gaithersburg, Md., June 1974. [15] Shah, P. L, to be published.

[6] Vieweg-Gutberlet, F., Investigation of local [16] 7577 Annual Book of ASTM Standard,
oxygen distribution in silicon by means of (American Society for Testing and Materials;
spreading resistance, NBS/ASTM Symp. on Philadelphia, 1971), Part 8, 697-711.
Spreading Resistance Measurements,
Gaithersburg, Md., June 1974. [17] Smith, F. M., Measurement of sheet resistivities
with the four-point probe, Bell System Tech. J.
[7] Lee, G. A., Rapid multilayer correction factors, 37,711-718(1958).
NBS/ASTM Symp. on Spreading Resistance
Measurements, Gaithersburg, Md., June 1974. [18] Fair, R. B., Quantitative theory of retarded base
diffusion in silicon npn structures with arsenic
[8] Schroen, W., The impact of process control on emitters, J. Appl. Phys. 44, 283-291 (1973).
parameter stability — a review, Semiconductor
Silicon 1973, ed. by H. R. Huff and [19] Severin, P. J., On the infrared thickness
R. R. Burgess, (Electrochem. Soc., Princeton, measurements of epitaxially grown silicon
New Jersey, 1973), pp. 738-758. layers, J. Appl. Optics 9, 2381-2387 (1970).

[9] Schroen, W., Application of the spreading [20] Cox, P. F., and Stalder, A. F., A Fourier
resistance technique to silicon characterization transform method for measurement of epitaxial
for process and device modeling, NBS/ASTM layer thickness, J. Electrochem. Soc. 120,
Symp. on Spreading
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 COMPARISON OF TECHNIQUES
FOR SILICON DOPANT PROFILING
HOW DO THE CHARACTERIZATION TECHNIQUES COMPARE?
HOW CAN THE TECHNIQUES SUPPLEMENT EACH OTHER?
Figure 1. Comparison of Techniques
PRECISION for Silicon Dopant Profiling
RESOLUTION
RANGE OF SILICON RESISTIVITIES
RANGE OF LAYER THICKNESS
SAMPLE CONSERVATION
EXPERIMENTAL EFFORT
ANALYTICAL INTERPRETATION
EQUIPMENT COST
TIME AND COST OF DATA ACQUISITION AND EVALUATION

SILICON CHARACTERIZATION TECHNIQUES

CONCENTRATION OF ELECTRICALLY ACTIVE DOPANTS

SPREADING RESISTANCE
INCREMENTAL SHEET RESISTANCE
INCREMENTAL MOS CAPACITANCE/VOLTAGE
JUNCTION CAPACITANCE/VOLTAGE
MOS AND SCHOTTKY CONTACT CAPACITANCE /VOLT AGE
FOUR POINT PROBE
Figure 2. Silicon Characterization Techniques
LAP AND STAIN

CONCENTRATION OF ACTIVE PLUS NEUTRAL DOPANTS

ION MICROPROBE
OPTICAL METHODS
NUCLEAR ACTIVATION

Figure 3. Profile in Techniques Processing Steps — DUF Through Emitter Diffusion

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162
Figure 4. Profiling Techniques. Processing Steps - Dotted Line: After DUF, Solid Line: After Epitaxial Deposition

Figure 5. Profiling Techniques. Processing Steps - Dotted Line: After Epitaxial Deposition, Solid Line: After Base
and Emitter
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 Figure 6. Epitaxial Layer Impurity Profiles Using the Diode Capacitance-Voltage (C-V) Method

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 Figure 8. Multifunction, Interactive Data Aquisition
and Evaluation Facility

Figure 9. Multilayer Analysis Verification

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165
 Figure 10. Predicted and Experimental
Boron Profiles for 30 Min Steam Oxidation

Figure 11. Ion-Implanted Arsenic Profile,

Model and Experimental Data

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Figure 12. Multilayer Analysis Verification

Figure 13. Well Defined Shallow Angle Lap

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 Figure 14. Ion Microprobe for I on-Implanted Boron and Arsenic

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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Preparation of a Lightly Loaded, Close-Spaced

Spreading Resistance Probe and its Application
to the Measurement of Doping Profiles in Silicon

J.L. Deines, E.F. Gorey, A.E. Michel, and M.R. Poponiak

IBM System Products Division, East Fishkill
Facility, Hopewell Junction, New York 12533

A commercially available spreading resistance probe,

the ASR-100, was modified to operate with lighter probe
loading and smaller probe spacing. The advantages of
device structure profiling, increased resolution, and
reduction in the "correction factor" in the converted
impurity concentration profile are realizable with
smaller probe spacing. The effect of the probe
modifications on sample profiles and profile quality
is discussed for thin epitaxial layers, bipolar tran-
sistor structures, and ion-implanted layers. Sample
preparation, as influenced by the beveling technique,
is also shown to have an effect on profile quality.
A novel method for precise measurement of very small
bevel angles is described.

Key words: Bevel angle measurement; correction factor; epitaxial

layer; impurity concentration; ion-implanted layer; neutron activ-
ation; probe loading; probe spacing; spreading resistance

1. Introduction
The trend toward development of high density integrated circuits
has heightened existing problems in device characterization. Thin
epitaxial layers, ion-implanted layers and micron-size devices require
accurate and precise measurement of electrical and physical parameters.
The spreading resistance technique has been shown to be an effective
measurement tool [1-6].* The commercial availability of an automatic
spreading resistance probe the ASR-100 [7],has made production control
realizable by decreasing the time required for a measurement and
decreasing operator measurement error. The existence of an automatic
probe provides the potential for measurement standardization, which
is highly desirable as the need for accuracy and precision increases.
This paper describes efforts to improve the spreading resistance
measurement, determine optimum sample preparation procedures, and
optimize the capability of the commercial probe. Accordingly, a
beveling procedure employing diamond paste and water was used to
significantly decrease data scatter by yielding smooth, beveled
surfaces and sharp bevel angles. Probe spacing was reduced to 25 urn,
permitting device profiling, greater profile resolution, and a reduction
in correction factor used for computer correction of spreading resistance
profiles. Probe loading was decreased to minimize probe penetration,

*Figures in brackets indicate the literature references at the end of

this paper.
169
adding a high degree of sensitivity. A technique for more accurate measure-
ment of the very shallow bevel angles required for thin layer resolution is
presented as an inexpensive addition to the spreading resistance probe. The
effect of these probe modifications is shown in example profiles. Correlation
of spreading resistance profiles of ion-implanted layers with neutron
activation analysis demonstrates the accuracy and validity of the measurements.
The correction program for spreading resistance profiles will not be discussed
here except to say that it was an APL program developed by S.M. Hu [8]
utilizing the multilayer approximation of Schumann and Gardner [9] for a
circular contact to compute the resistivity profile and the Irvin's [10] curves
to convert to concentration.

2. Probe Codification
2.1 Probe Spacing
The ASR-100 Automatic Spreading Resistance Probe provides the semi-
conductor industry with a machine capable of a high degree of reproducibility
and accuracy in measurements. Installation of the ASR-100 was followed by a
period of experimentation to determine the ability of the machine and to
ascertain and implement modifications for improvement. Among the first points
considered was a modification of the detachable probe mount to permit close
probe spacing. Schumann, et.al., [11] described the benefits of using a close
probe spacing of the order of 12 urn. Close probe spacing permits the profiling
and measurement of very small regions on device wafers. In addition, the close-
spaced probe arrangement requires a smaller correction factor when converting
the raw spreading resistance vs. depth profile to an impurity concentration
vs. depth profile. The as-delivered ASR-100 permitted varied probe spacing
down to 635 jim. Shorting due to the geometry of the probe mount prevented
closer spacing. A simple redesign of the probe mount permitted probe spacings
of 50 to 75 urn without shorting or probe tip modification. Grinding of the
tungsten carbide probe tips to a chisel-like geometry permitted 10 urn spacing.
The development of the close-spaced probe is illustrated in figure 1.
The effect of probe spacing on a sample with a thin (~.6 urn) ion-implanted
layer is shown in figure 2. In this case, probe spacing was varied from 20
to 606 urn. The large changes in the uncorrected profiles dramatize the effect
of close-probe spacing. Note that the uncorrected profile at 20 urn spacing
is closest to the corrected profiles and that the neutron activation profile
compares reasonably well with the corrected profile at 20 urn spacing. The
large probe spacing appears to accentuate deficiencies in the correction
theory, resulting in inadequately corrected profiles.
Figure 3 shows the effect of probe spacing on raw spreading resistance
profiles obtained in laboratory room light and shielded from room light.
There is no observable difference between the close-spaced profiles.
Although junction depth is not affected by probe spacing, the photovoltage
at the junction is affected by probe spacing and lighting conditions.
Significantly more photovoltage is developed for wide-spaced probes than
for close-spaced probes. This effect can be used to advantage; wide spacing
and room light can make junction determination easier.
The obvious advantage of close-spaced probes, the ability to profile
very small areas, is shown in figure 4. Three corrected profiles of an
epitaxial layer over arsenic and boron diffused areas and a non-diffused
area are shown. The width of the diffused pattern was 5.0 mil. All three
profiles were obtained on a single bevel in the key area between the devices
measuring 20 mils. Probe spacing in this case was 30 urn.

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 2.2 Probe Loading
Loading on the probe tips can affect profile quality, machine integrity,
and profile reproducibility [12] . Light loading has an obvious advantage in
minimizing probe penetration that can distort or result in inaccurate profiles.
Beyond this, excessive loading can change the probe calibration. This can be
seen if the condition of the probe tips is described. The probe tip is not a
sphere or single point of contact. Rather, it contains a number of sharp,
small tips which are necessary to penetrate native oxide and insure reasonable
metal-silicon contact. Reduction in probe loading reduces the force with
which the probe impacts the silicon, decreasing the chance of changing this
multi-tip configuration and consequently the probe calibration. Light
loading can reduce probe wear, offering longer probe tip life. It can be
inferred that light probe loading and close probe spacing are features with a
high degree of interdependence. Probe loading was changed by adjusting the
position of the probe arm weights. The load was measured by counterbalancing
against known weights.
The effect of probe loading on an N-type epitaxial layer over an N
substrate is shown in figure 5. The 40 gram load profile indicates a 0.25 urn
shift in the apparent junction depth as compared to the 10 gram load profile.
In addition, all the uncorrected data points indicate a higher impurity
concentration in the 40 gram profile than the 10 gram profile. This discrep-
ancy in the uncorrected data and the junction depth is due to probe penetration
or "punch-through." The probe tip in the heavier load case penetrates the
silicon and the measurement is influenced by the higher concentration layers
below the beveled surface. A larger correction factor compensates for the
larger effective radius of contact seen by the probe tip yielding corrected
profiles at very nearly the same concentration level. The lightly loaded
probe produces less penetration, requires less of a correction factor, and
introduces minimal error in the junction depth determination. It is possible
in certain simple structures, such as shown here, to compensate the
concentration levels for excessive probe loading and punch-through via the
correction scheme. The effect of punch-through on very thin layers, however,
can result in gross error in the resolution of the junction depth and profile
shape. The effect of a 0.25 urn shift in X. for a 0.3 or 0.5 um layer would
be disastrous. -*
The effect of probe penetration on a complicated structure is shown in
figure 6, where the sample was P-type epitaxy over a diffused P-type region
in an N substrate. The uncorrected and corrected reference profiles of the
10 gram load are given in figure 6a and for the 40 gram load in figure 6b.
The surface intercept at 10 grams is 2.9 x 10 At/cc and at 40 grams is
8.3 x 10 . Note also the trend of higher impurity concentration in the
epitaxy and the lower peak height in the 40 gram profile. The 40 gram
profile shows higher epi concentration and lower peak height due to punch-
through, its effect on the radius of contact, and influence by the buried
layers. For this case the correction program is unable to yield an
adequately corrected profile.
Calibration curves are influenced by probe loading. The calibration
and sample profiles should be done at the identical probe load. Differences
in calibration due to probe loading for P and N-type (100) are shown in
figure 7. The 40 gram load calibration is shifted downwards from the 10 gram
calibration by a factor of approximately two in both the N and P standards.
Figure 8 goes further in showing differences in calibration resulting from
crystal orientation. The P-type (100) and (111) calibration curves were
found to be virtually identical for the different probe loadings. There were
differences in the N (100) and N (111) calibration for both probe loadings.
The 40 gram load appears to mask the differences below 0.4 ohm-cm. At 10 gram
loading the differences in the curves are evident throughout the range
measured.
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 3. Sample Preparation for Spreading Resistance
3.1 Beveling
a. Surface Preparation
Spreading resistance is an extremely useful and sensitive tool for
determining impurity concentration profiles, junction depth, etc. Its
sensitivity makes sample preparation an extremely important step in the
measurement process. Rounded bevels make the determination of the bevel
edge and zero depth measurement difficult. Excessively rough bevels can
cause significant scatter in the data, which is amplified when corrected.
The abrasive beveling medium most used in spreading resistance measure-
ments has probably been 0.3 urn Al^O- in water. Care in the beveling pro-
cedure can result in fine, uniforinly abraded surfaces. Scratches or other
imperfections and irregularities in the beveled surface can cause appreciable
scatter in obtained data, particularly on profiles requiring high resolution.
Figure 9a gives the raw spreading resistance vs. depth profile of an N
epitaxial layer over an N substrate which was beveled by lapping with 0.-3 urn
AloO, in water on a frosted glass plate. The sample had been mounted with
glycol-phalate on a bevel block for lapping and transferred to the special
mandrel for mounting on the spreading resistance probe. Scatter in the data
is evident in this high resolution profile of 2 log cycles. The sample was
rebeveled with water on a frosted glass plate which had been prepared by
working with a silicon slug and 0.25 urn diamond paste. The excess paste was
removed and the imbedded grit with water was used for beveling. The
resultant bevel edge was sharp, the bevel quite smooth, and scatter in the
data was significantly reduced as shown in figure 9b.
b. Bevel Angle Measurement
Shallow bevel angles in the order of 30 minutes or less are necessary
for satisfactory investigation of thin structures. Of critical importance
to such shallow bevel profiles is the bevel angle measurement. The
goniometer is not accurate enough to resolve these shallow angles. Tong,
et.al.,[13] introduced the Small Angle Measurement (SAM) apparatus as a means
of measuring shallow bevel angles with far greater precision than the
goniometer. Beyond this, certain modifications in the SAM technique have
been made to permit small angle measurements on any laboratory microscope [14]
Use of the ASR-100 microscope and rotatable stage facilitates the MSAM
(Microscope SAM) measurement and completely eliminates the need for the
specially constructed SAM apparatus. Measurement of the bevel angle at the
location where the profile was taken is now insured, thus increasing the
accuracy of the depth measurement.
The MSAM apparatus is shown in figure 10. The ASR-100 rotatable stage
and sample mounting block can substitute for the base plate and protractor
assembly. A thin wire of diameter s_ is inserted within the barrel assembly
of the 3X measuring objective or any long working distance lens. During
normal microscope use, the wire and the wire image projected below are not
visible because the lens has a short depth of field. In angle measurement
use, the beveled sample actually yields two images of the wire, one reflected
off each of the flat and beveled surfaces. An angle measurement is made by
focusing on the images of the wire. Rotation of the sample causes a rotation
of the images, each rotating about its own axis. The images are aligned by
rotating the microscope stage until the side of one image barely touches the
opposite side of the other image. At this point an angle reference reading,
al, is recorded as in figure 11. The stage is rotated until the images cross
over each other as in figures 12 and 13 and are aligned edge to edge on the
side opposite from that used for the reference reading, as shown in figure 14.
A second angle reading, a2, is made here. The total angular rotation, a, is
calculated,
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172
 where d is

the distance from the wire to the sample bevel edge (0.805" in this case) and
s is the width of the wire, 0.0153".
MSAM data on several shallow angle beveled samples is compared with
interferometer and SAM data in table 1. The MSAM data is an average of ten
measurements taken over a period of ten days.

Table 1. Comparison of Shallow Bevel Measurement Techniques

Sample Interferometer SAM MSAM* Ave 0 MSAM Ave % Dev
1 16.2' 16.2' 16.3' 1.4%
2 22.7' 23.3' 23.1' 1.6%
3 52.0' 52.0' 51.6" 0.5%

s • 0.0069 inches
d - 1.049 inches

The addition of a second wire parallel to, and a known distance from,
the single wire gives an effective increase in s_, enabling a wider range of
angles to be measured with a single objective lens attachment.

4. Summary
Modification of a commercial spreading resistance probe to operate with
small probe spacing and light probe loading has resulted in more accurate
profiles requiring less correction than wide, heavy probes. The sensitivity
of the probe has been increased and beveling procedures improved to reduce
data scatter. Shallow bevel angle measurement has been shown to be accurate,
quick, and inexpensive.

5. Acknowledgement
The authors would like to express their appreciation to Dr. S. M. Hu for
his comments and suggestions on spreading resistance correction and Dr. R. H.
Kastl for the neutron activation analysis.

6. References
[1] R.G. Mazur and D.H. Dickey, [5] R.G. Mazur, ibid, 114, 255 (1967).
J. Electrochem. Soc., 113,
255 (1966). [6] D.C. Gupta, J.Y. Chan, and P.
Wang, ibid, 116, 301c (1969).
[2] E.E. Gardner, P.A. Schumann, Jr.,
and E.F. Gorey, Electrochem. Soc. [7] Reference Manual and Operating
Symposia Proceedings "Measurement Instructions for the ASR-100
Techniques for Thin Films," Automatic Spreading Resistance
April 1967. Probe, Solid State Measurements,
Inc., 1971.
[3] D.C. Gupta, ibid, 116, 670 (1969),
[8] S.M. Hu, Solid State Electronics
[4] C.K. Chu, ibid, 115, 192c (1968). 15, 809 (1972).
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[9] P.A. Schumann, Jr., and [12] P.A. Schumann, Jr., J.M. Adley,
E.E. Gardner, J. Electrochem. M.R. Poponiak, C.P. Schneider
Soc., 116, 87 (1969). and A.H. Tong, J. Electrochem.
Soc., 116, 150c (1969).
[10] J.C. Irvin, Bell Syst. Tech. J.,
41_, 387 (1962). [13] A.H. Tong, E.F. Gorey and
C.P. Schneider, Rev. of Sci.
[11] P.A. Schumann, Jr., E.F. Gorey Instruments, 43, 320 (1972).
and C.P. Schneider, "Small
Spaced Spreading Resistance [14] J.L. Deines, E.F. Gorey and
Probe," Solid State Tech. M.R. Poponiak, IBM Tech.
(1972). Disclosure Bulletin, 15, #10,
"Measurement of Small~AYigles
with a Microscope, " (1973).

Figure 1 Close spacing

probe tip modifications.

Figure 2 Effects of probe spacing

on spreading resistance profiles of
thin structures as compared with
neutronactivation analysis.

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 Figure 3 The effects of ambient
light and probe spacing on
spreading resistance profiles.

Figure 4 Corrected spreading resistance profiles

of small device structures. Probe spacing 30 urn.

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Figure 5 Probe penetration effects Figure 6 Probe penetration effects
as a function of probe loading on a as a function of probe loading on a
simple N/N+ structure. complicated P-/P+/N- structure.

Figure 7 Calibration curves of (100)

orientation P and N-type silicon at 10
and 40 grains loading.

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Figure 8 Effects of probe loading on
(100) and (111) calibration curves.

Figure 9a Spreading resistance profile

utilizing 0.3 umAl^O, in water on a
frosted glass.

Figure 9b Spreading resistance profile

utilizing only water on a glass frosted
with 0.25 um diamond.

Figure 10 Microscope small angle

measurement assembly (MSAM).

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 Figure 11 Photograph taken with MSAM system
showing double images (1 & 2) of wire. Images
are positioned edge to edge at this orientation
of sample stage: 91°. This is the starting point
of specimen bevel angle measurement. By a second
exposure, image (b-b?) of sample's bevel surface
is also shown. NOTE: microscope focal point must
be changed between these exposures.

Figure 12 Double exposure photograph of wire

images (1 & 2) and sample's bevel surface.
Sample stage orientation is 72°. Dark band is
overlap of wire images.

Figure 13 Double exposure photograph of wire

images and sample's bevel surface. Sample stage
orientation is 54.5°; wire images (dark band)
have crossed over each other.

Figure 14 Double exposure photograph of wire

images and sample's bevel surface. Images have
completely crossed and are positioned edge to
edge. This is the final step of measurement.
Orientation is 44°. Total a = 1/2 x 47° =23.5°.
Specimen bevel angle = 69.5' where s = 0.0153 in.
and d - 0.0805 in.

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

A Direct Comparison of Spreading Resistance and

MOS-CV Measurements of Radial Resistivity
Inhomogeneities on PICTUREPHONE® Wafers

J. R. Edwards and H. E. Nigh

Bell Laboratories
555 Union Boulevard
Allentown, Pa. 18103

Small scale (~ 50 Mjn) radial impurity concentration

inhomogeneities in silicon wafers have been measured
using both the MOS-CV method and the spreading resistance
technique. The MOS-CV measurements were made using photo-
lithographically defined 50 |j,m square capacitors placed
on 75 M,m centers and the spreading resistance measure-
ments were made using a model 100 ASR probe on the same
wafers after removal of the MOS capacitors.
A direct comparison between these methods is pre-
sented for three specific types of (111) oriented silicon
wafers with an impurity concentration range between 5 and
10 x 10-^/cm3. in addition, a photograph showing the
direct effect of radial resistivity variations on the
dark field coring of a PICTUREPHONE® target is included.

Key words: Dark field coring; MOS-CV techniques;

PICTUREPHONE®; radial resistivity inhomogeneities;
silicon resistivity; spreading resistance techniques.

1. Introduction
In this paper we report the direct measurement of small scale (~ 50
radial resistivity inhomogeneities in silicon crystals using the MOS-CV
method. In addition, spreading resistance measurements using the ASR-100
spreading resistance probe were done on the same wafers which allows a
direct comparison between MOS-CV and spreading resistance measurements. In
the past, the spreading resistance probe technique has been used by several
experimentalists to measure small-scale radial resistivity inhomogeneities
in silicon crystals [1,2]1. Since this technique is empirical, reliable
calibration is necessary. Most investigators use four point probe measure-
ments for calibration, but the four point probe does not give adequate
calibration for the small spatial resolution desired in studying the radial
inhomogeneities in PICTUREPHONE® target material or in IC's. In particular,
we will demonstrate that the video shading which occurs in the dark field
display of silicon PICTUREPHONE® targets can be caused by substrate

Figures in brackets indicate the literabure references at the end of this

paper.
179
resistivity variations in the target material as small as 10$ over a distance
of 0.01 inches [3].

2. Experimental Procedure and Discussion of Methods Used

Although spreading resistance measurements can be made over a wide
impurity concentration range (lC>l^/cm3 to IC^O/cnP), precise measurements
are more difficult for the low range. Fortunately this range is particular-
ly well suited for the MOS-CV method [3,4] and is also the impurity con-
centration used for PICTUREPHONE® target material. As a consequence, the
wafers used in this study were (111) oriented n-type silicon wafers with an
impurity concentration 5 to 10 x lOl^/cnP (10-5 Q-cm resistivity). Both
float-zone refined and Czochralski pulled wafers were used.
The silicon wafers were chemically etched to remove saw damage and one
side was polished using Syton polishing compound. An 1100°C thermal oxide
of 1500-1800A was grown on the wafers after suitable chemical cleaning. The
MOS capacitors were made by vacuum depositing aluminum and subsequently
photolithographically defining 50 (j,m square pads on 75 M-m centers. This
choice of MOS pad size allows approximately 270 measurements on the diagonal
of the 0.850 inch diameter wafer used for PICTUREPHONE® targets. After the
MOS measurements were made, the aluminum and the SiOg were chemically re-
moved to prepare the wafer for spreading resistance measurements. Thus,
both types of measurements could be made without any heat treatment altering
the radial resistivity profile.
The C-V measurements were made at 1 MHz using a Boonton Model 71-AR
capacitance meter. The choice of thermal oxide resulted in capacitance
values approximately 1/2 pfd or less which allows full use of the 1 pfd
range. The analogue output from the capacitance meter was recorded to 3
significant digits using a DVM and the data reduction was done by computer.
Since the MOS-CV method averages the impurity doping over a region about
1 |j,m below the surface, there are two different methods which can be used
to evaluate the impurity concentration for absolute calibration of the
spreading resistance probe. In the first method, only two measurements are
necessary for the max-min high frequency technique [3]: oxide thickness,
and the accumulation - Inversion capacitance ratio. This means that
absolute values of capacitance are not necessary, which in turn eliminates
absolute capacitance calibration. Only the linearity of the analogue output
of the capacitance meter is 'necessary. Because the thermal oxide is uniform
to ± 30JI, only a single oxide measurement by a U-V Spectrophotometer is.
necessary to obtain the oxide thickness. Since the MOS-CV method uses only
known constants and measured parameters, it is estimated that the precision
with this method is ± 2$ and the absolute value of the impurity concentra-
tion calculated is 10$. This precision clearly allows determination of
impurity concentration inhomogeneitles across a slice which vary ± 10$ over
a distance of 50 p,m. The second method of MOS-CV evaluation uses the change
of capacitance in the depletion region with respect to the applied voltage
in order to calculate the doping as a function of the depth. For this
measurement, the absolute value of the capacitance and the differential
change of voltage are needed'in addition to the oxide thickness. The pre-
cision of this method is estimated to be ± 5$ with an accuracy of 15$.
Since the MOS-CV measurement techniques complement each other, a high
degree of precision with a spatial resolution of approximately 25 jj, is
assured.
When the spreading resistance probe is calibrated relative to the MOS-
CV measurements, a precision of ± 3$ is possible for the spreading resistance
measurements using the ASR-100 spreading resistance probe on chem-etched,
Syton polished silicon wafers. In comparison, we observed that the precision
and reproducxibility for the probe is only ± 20$ to 30$ on a mechanically
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 Using the wafers calibrated by the MOS-CV, it was found that additional
Syton polishing allowed the sample to be reused as a standard. This is
important when considering day-to-day calibration of the spreading resistance
probe. Several other factors were observed which affect the precision of the
spreading resistance technique, the primary one being the probe wear. It was
found that a 5$ deviation from the control measurements indicated excessive
probe wear. This usually occurred after about ten thousand measurements on
a Syton polished surface. The prdbes could be regenerated by using the probes
on a mechanically lapped silicon wafer for a few hundred measurement cycles.

3. Experimental Comparison
The ASR-100 spreading resistance probe was operated in the two probe
mode with the probes spaced about 40 mils apart. The actual values of
resistivity measured at 100 p,m increments are plotted in figures 1-3 for a
typical float zone refined wafer, a typical Czochralski pulled wafer and a
specially prepared Czochralski wafer. The next three figures show the re-
sistivity data converted to impurity concentration using the MOS measurements
as calibration points. This change was done to enable a direct comparison to
the MOS-CV impurity concentration data shown in figures 7-9. Both typical
wafers show dark field coring and also clearly demonstrate variations of
impurity concentration greater than ± 10$. Routine four point probe measure-
ments would not reveal these inhomogeneities, but both spreading resistance
and MOS-CV do allow a direct measurement. As a direct example of the effect
of resistivity inhomogeneities, figure 10 shows a silicon PICTUREPHONE®
target made from a wafer whose radial resistivity profile had been measured.
Note the dark field coring corresponding to the resistivity variations of
± 10$ for this Czochralski wafer.
In conclusion, it has been shown that the spreading resistance probe can
measure the radial resistivity profile of a wafer to a precision of ± 3$ for
a properly prepared wafer. This has been verified using MOS-CV measurements,
and the effect on dark field coring has been demonstrated by an actual target
photograph.

4. References
[1] Mazur, R. G., J. Electrochem. [3] Grove, A. S., Snow, E. H.,
Soc. Vol. 114, No. 3, March Deal, B. E., and Sah, C. T.,
1967, P. 255. Jap. 3S, 2458 (1964).
[2] Gupta, D. C., Chan, J. Y., and [4] Kennedy, D. P., Murley, P. C.,
Wang, P., J. Electrochem. Soc., and Kleinfelder, W., IBM J.
Vol. 117, No. 12, December 1970, Res. Dev. (1968) p. 399.
p. 1611.

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 Figure 1. Spreading resistance measurements for the
typical float zone refined wafer. Notice the large Figure 2. Spreading resistance measurements for
short-range fluctuations on both sides. typical Czochralski wafer. Notice the characteristic
core in the center.

Figure 3. Spreading resistance measurements for Figure 4. Spreading resistance impurity concentration
special
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.small fluctuations
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 Figure 5. Spreading resistance impurity profile for Figure 6. Spreading resistance impurity profile for
measurements of figure 2. This profile can now be uniform wafer whose resistance measurements are
directly compared with figure 8. shown in figure 3.

Figure 7. MOS-CV impurity concentration for the Figure 8. MOS-CV impurity concentration for the
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23:23:49 ESTwafer.
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Figure 9. MOS-CV impurity concentration for the specially prepared Czochralski
pulled wafer.

Figure 10. Picture showing dark field coring pattern for a PICTUREPHONE target
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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Investigations on Local Oxygen

Distribution in Silicon Single
Crystals by Means of Spreading
Resistance Technique

Fritz G. Vieweg-Gutberlet

Wacker-Chemitronic GmbH.
Physical Laboratory
D-8263 Burghausen, West Germany

By means of spreading resistance measurements subsequent

to heat-treatments at approx. 450°C and 1100°C alternatively
the local distribution of oxygen in the donor state in Silicon
single crystals was examined. Oxygen striations have not been
found which is in correspondence to a distribution coefficient
of ko = 1.25 i 0.17 for oxygen in Silicon. The radial distri-
bution of oxygen in the donor state is more or less uniform
except for an edge area of about 1.5 nun where the oxygen content
seems to be considerably lower. A very strong relationship
between electrically activated oxygen (donor state) and swirls
was found: in regions containing swirls a smaller amount of
oxygen was activated to the donor state. This result fits
De Rock's model describing swirls as consisting of vacancy-
OXYGEN-clusters.

Key words: Oxygen in Silicon, Silicon single crystals,

spreading resistance measurements, swirls.

1. Introduction

More or less knowledge exists about the local oxygen distribution in Silicon
single crystals. In connection with swirls the question arises if swirls may be
related to oxygen striations. The experiments carried out in the past either by
infrared transmission or by resistivity measurements have been handicapped by a very
poor local resolution. We selected the spreading resistance probe to continue the
electrical measurements from the past with the best resolution one can obtain up to
now.

It is well known that oxygen in Silicon may be changed from the electrically
neutral (interstitial) into a donor state by a heat-treatment at 450°C. It is also
well known that oxygen may be removed from the donor state by a heat-treatment at
higher temperatures and "crash cooling" of the sample, fy

1
Figures in brackets indicate the literature references at the.end of this paper

185
 The change between the electrically neutral and the donor state with respect
to the heat-treatment is detectable by resistivity measurements. In our experiments
we employed the spreading resistance probe for the resistivity measurements in order
to get highest local resolution.

Under the assumption that oxygen in Silicon does not change its local position
by diffusion during a heat-treatment at J100°C for approx. 90 minutes and for very
small differences in concentration, the local distribution of oxygen in form of
striations must be detectable by a change of the magnitude of the striations with
respect to the heat-treatment.

2. Procedure

A large number of samples of Silicon single crystals zone floated as well as

crucible pulled was taken. The following procedure was applied to the samples:

The as grown sample was polished and measured

by spreading resistance.

The sample was heat-treated at 1100 C (open air)

for 90 minutes. Within a few minutes the sample
was brought to room temperature ("crash cooling")
to avoid any activation of the donor state of
oxygen due to the 450°C temperature range.
After relapping the surface the sample was polished
and measured by spreading resistance.

The sample was then heat-treated at 1100 C

(open air) for 90 minutes and very slowly cooled
down to room temperature so that the sample was kept
for approx. 1 hour in the temperature range of
approx. 450°C. That means that oxygen will be
activated from the neutral to the donor state. After
relapping the sample was polished and measured by
spreading resistance.

Relapping of the sample after the heat-treatment was found to be necessary due
to the formation of a surface layer by the heat-treatment which is quite uniform in
resistivity. After removing this layer by lapping off a few micrometers the bulk
resistivity characteristic was found.

The spreading resistance measurements subsequent to the heat-treatment or on

the as grown material were taken in the same trace as correctly as possible. The
obtained spreading resistance profiles have been compared qualitatively by super-
imposing one over the other. A quantitative evaluation was done by converting the
spreading resistance readings into values of carrier concentration and comparing the
values obtained by crash cooling and 450°C treatment respectively.

The difference " A " (cm""-') between the values obtained by heat-treating the
sample for a long time at 450°C and the so called "crash cooling" is related to
donors generated by converting oxygen from the neutral into the donor state.

3. Results

In all our experiments we could not find any indication for oxygen striations.
The result is the same in cross section and longitudinal section for zone-floated
as well as for crucible pulled Silicon. This can be explained by the results of
Yatsurugi et al. who claim from their experiments that the distribution coefficient
of oxygen is k = 1.25 ± 0.1? [Q
186
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 For crucible pulled Silicon the radial distribution of the activated oxygen
was found to be more or less uniform except for an edge area of approx. 1.5 mm.
This is in agreement with Graff's results obtained by IR absorption at 9/um wave-
length [3] .

The average change of carrier concentration due to the oxygen activation

(donor state) at 450°C is quite different for zone floated and crucible pulled
Silicon crystals. This is related to the different oxygen content in these crystals.
In most of the zone floated crystals no change in carrier concentration was
observable. For crucible pulled crystals having an oxygen content of about 1
atoms cm"' (IR absorption £4] £53 ) the average change in carrier concentration
was approx. 10*-* cm~"-5 which corresponds to the results obtained by Fuller and Logan
£l] for a heat-treatment at 450°C for approx. 1 hour. In this case the change in
carrier concentration in the edge area (which is near to the skin of the as grown
crystal) is approx. 10*3 cm" .

Plotting the calculated values of donor generation (" A ", cm ) in radial and
axial direction of the crystal sample under test some areas have been found where
the donor generation was much lower with respect to the other parts of the crystal.
The distance between those regions of lower donor generation gave us the impression
that these areas might be related to swirls. Therefore the samples have been etched
for swirls applying Chromium Acid etch f6J . A comparison between areas of a lower
donor generation obtained by spreading resistance measurement with areas showing
swirls after etching gave a 100^ correlation for swirls and areas of lower donor
generation. The correlation is of such a quality that substructures in the density
of shallow etch pits in the swirl bands correspond to substructures in the spreading
resistance curves,

4. Discussion of the Results

With respect to the literature there is no doubt that additional donors

generated by a heat-treatment at 450°C are related to oxygen. Therefore the local
distribution of the additional donors is related to the local distribution of
activated oxygen atoms. Two effects obtained by our measurements must be discussed:

4.1. The Edge Area

In an area of approx. 1.5 mm from the.skin of the crystal a much lower amount
of activated oxygen exists. Therefore we assume that the oxygen content is lower than
in the entire crystal which is in agreement with Graff's results £3] .•
This may be due to out-diffusion of oxygen or Si-0x -formation on the Silicon surface
or evaporation of oxygen from the melt in the miniscus area near to the liquidus
solidus interface. Indications are that all of these effects work together.

4.2. Swirls

In the swirl bands oxygen is bound to the swirl forming complexes in such a
form that the single oxygen atom cannot be activated to the donor state. That means
that in the swirls oxygen is still there but will not be activated by 450°C heat-
treatment. This is in agreement with De Kock's model describing the swirl forming
complexes as VACANCY-OXYGEN-CLUSTERS.

This also explains some of the difficulties in the comparison of the 9/um
IR absorption coefficient with chemically obtained oxygen contents because Oxygen
bound to the swirlforming complexes does not show the 9/um -resonance.

187

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 On the other hand our results may explain what the reason for the swirl
formation is: We found that oxygen is incorporated to the Silicon crystal in a
uniform distribution. With respect to the rotation rate and the growth speed the
crystal will he supersaturated by vacancies in form of spiral bands. This
nonuniformity of vacancy supersaturation generates the nonuniform arrangement of
vacancy oxygen clusters WHICH IS SWIRL.

A discussion of this mechanism will appear in a later publication.

Acknowledgement

I am greatly indebted to my coworkers P. Siegesleitner (spreading resistance

measurements) and Mrs. A. Mayer (sample preparation and the heat-treatment
experiments).

I also have to express my thanks to my colleagues at Wacker-Chemitronic for

providing me with samples and for critical discussion of the results.

This work was supported by the German Federal Ministry of Research and
Technology, contract Nos. NT 381 and NT 506.

5. References

Fl] Fuller and Logan

J. Appl. Phys. 28 (195?) M ASTM, F 121-70 T
Annual Book of Standards,
p.142? part 8 (1973).
The American Soc. for Testing
£2] Yatsurugi, Akiyama, Endo and and Materials
Nozaki
J. Electrochem. Soc. 120 (1973) [>] Kaiser and Keck
p. 975 J. Appl. Phys. 28 (1957)
p. 882
[3] Graff, Grallath, Ades, Goldbach
and Tblg
Solid State Electr. 16 (1973) M Method of Test for the Detection
of Swirls and Striations in
p. 887 Chemically Polished Silicon Wafers,
ASTM Standard, to be published.

Fig.l Location of the Spreading Resistance Trace (trace A) of the measurements

reported in this paper.
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 Fig. 2 Spreading Resistance Profiles of Trace A (fig. 1)
Profile "a": 1100°C, 90 minutes, "crash cooling"
Profile "b": 1100°C, 90 minutes, slow cooling (approx. 1 hr. for 450°C)

Fig. 3 Difference "A" (donors cm ) calculated by deducting carrier concentration

obtained from profile "a" from carrier concentration of profile "b" of Fig. 2.

189
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 _3
Fig. 4 Comparison of "A" (donors cm ) profile of figure 3 with the swirl-pattern
obtained by etching the sample. The two horizontal lines in the photograph indicate
the spreading resistance probe traces.

Fig.5 The Radial Profile of donors generated at 450°C equivalent to the oxygen
distribution. Note the edge area of approx. 1.5 mm. and the swirl bands marked "s"

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Use of the Spreading Resistance Probe for the

Characterization of Microsegregation
in Silicon Crystals

F. W. Voltmer and H. J. Ruiz

Texas Instruments Incorporated

Dallas, Texas 75222

A technique for using the spreading resistance probe to quantitatively characterize

microsegregation in single crystal silicon is presented. For the first time, the use of Fourier
Transformations of the resistivity is developed to provide accurate quantitative information as to
the periodicity and amplitude of the various components giving rise to the resistivity variations. It
is demonstrated that the probe is reproducible and is capable of measuring fluctuations in
resistivity to ± 1 percent, which is well below the normally observed microsegregation. Examples
of the use of the technique are given by characterizing microsegregation in two Czochralski
grown crystals and one modified float zone crystal. The periodicity of the principle resistivity
fluctuation of the Czochralski grown crystals is evaluated by Fourier transform analysis and
agrees well with the anticipated fluctuations in impurity incorporation based on growth
parameters.

Keywords: crystal growth; Czochralski-, Fourier transform; .microsegregation; resistivity

characterization; silicon; Spreading resistance.

1. Introduction

The growth of doped single silicon from the melt or by the floating zone technique results in periodic variations
in impurity incorporation, the magnitude and frequency being determined by the impurity species and growth
conditions. Recently, the spreading resistance probe has been used to qualitatively characterize the fluctuations. [ 1 ] 1
In this paper, a technique is presented for the first time, to use the spreading resistance probe in conjunction with
Fourier transform analysis to quantitatively characterize the impurity microsegregation.

2. Experimental Technique

2.1. Crystal Growth

A number of 2000 gm, 2" diameter phosphorus doped (nominally 0.8 ohm-cm) silicon crystals were grown by
the Czochralski technique under various growth conditions (viz. crucible and seed spin, pull rate and thermal
environment) for characterization of microsegregation of the dopant impurity. Material was pulled from melts heated
by radio frequency induction and by radiant heat from resistance heaters. The Czochralski crystals were principally
grown in the <111> direction, although crystals were also grown oriented along the <100> and (115) directions.
Phosphorus was chosen as the dopant impurity because of its relatively low effective segregation coefficient (.45)
compared with boron and therefore its enhanced microsegregation. In addition, a crystal was grown by the modified
floating zone technique for comparison. The growth conditions included variation in pull rate from 2.75 to
16.9 cm/hr and seed rotation rates from 1 rpm to 75 rpm. The crucible was counterotated at 10 rpm for the most of
the crystals.
1
Figures in brackets indicate the literature reference at the end of this paper.
191
 2.2. Sample Preparation

The crystals as grown were approximately 12 inches long and 2 inches in diameter. Axial slabs 1/2 inch long
were cut from the crystal at one inch intervals for axial microsegregation characterization of spreading resistance, and
for interface delineation by etching. The configuration and location of the slabs are depicted in figure 1. Slabs were
taken at intervals to determine the influence of fraction solidified on the microsegregation. In order to allow for single
point spreading resistance measurements, the slabs were chemically-mechanically polished on one side and a gold
ohmic contact formed on the other side. The backside gold contacts were flash evaporated directly on the cleaned
back surface. The contact resistance of the gold-silicon interface was negligible when compared with the spreading
resistance contact.

2.3. Spreading Resistance Measurements — The Apparatus

Single point spreading resistance measurements using a modified Solid State Measurements2 mechanical probe
station and TI control system and electronics (figure 2) were made on samples from various positions along each of
the crystals.

The probe tips were Tungsten-Osmium with a probe radius of 25 Mm and a loading of 40 gms. The value of
spreading resistance measured is electronically fed to a minicomputer which is used for on line conversion of
spreading resistance to either resistivity or carrier concentration.

The sample is mounted on a copper vacuum chuck which is electrically isolated from any equipment. This allows
us to use the vacuum chuck as part of the current path when making single probe measurements.

2.4. Spreading Resistance Measurements — The Technique

The spreading resistance measurements were made on samples approximately 2" X 1/2" X 1/16" cut from the
crystal as shown in figure 3 so that the axial resistivity could be profiled. The sample was placed on the spreading
resistance probe chuck with the gold side down and held fast with a vacuum. The probe chuck was electrically
isolated and allowed a return current path for the probe bias.

A diagram of the locations of the measurements on the sample are also shown in figure 3 along with the interface
demarcation. Because the solid-liquid interface in crystal growth is usually curved, single point probe measurements
were made to optimize the spatial resolution. Use of two probes would have resulted in measurements which gave the
average resistivity of the regions being sampled by the two probes. Alignment of the probes collinear with the growth
direction is critical to insure accurate determination of the spatial frequency. A misalignment would increase the
apparent periodicity of the striations. Accuracy of the alignment is estimated to be better than 0.2 degrees.

The measurement sampling frequency was chosen a lOjum/step. A sampling frequency of 5 /im/step was also
tried, but did not provide-any more information than the lOjum/step frequency which was finally chosen. The
distance over which measurements were taken ranged from 1.5 to 4.5 mm.

The measurements were done automatically at the rate of 10 measurements per minute. The data, either
measured spreading resistance or computed resistivity values, were stored on either magnetic or punched paper tape.
It was subsequently transcribed to data cards for processing on an IBM 360 using an FFT (Fast Fourier Transform)
program. The data were also plotted such that any abnormal points (such as those caused by dust, scratches, etc.)
could easily be corrected in the data card file before the FFT program was run.

2.5. Spreading Resistance Measurements — Reproducibility

In characterizing microsegregation using the spreading resistance probe, one is concerned with measuring small
fluctuations in the resistivity over small dimensions. To determine the instrument's capability, three experiments were
performed; the first to establish the variations inherent in the electronics of the apparatus; the second to establish the
variations inherent in the mechanics of the apparatus; and the third, to establish reproducibility.

The first of the experiments consisted of connecting a 1000 ohm resistor across the probe input to the log
detector and cycling through a series of pseudo-measurements. The results of this sequence of measurements are
2
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plotted in figure 4 as resistivity as though one were measuring a sample of uniform spreading resistance such that
2RS = 1000 ohms. Fluctuations in the converted resistance (i.e., resistivity) were thus due to instabilities in the
electronics of the log converter and the A/D converter. As is apparent, the resistivity variation is less than ±0.5%. This
is more than an order of magnitude better than the resistivity variations due to microsegregation which are typically
measured.

The second experiment was to measure the resistivity variations on a uniform surface diffusion in order to
determine if the resistivity variations measured in the virgin material were due to impurity variations or mechanical
instability of the probes. It was assumed that the diffusion surface concentration was relatively constant. The
diffusion was adjusted such that the resistivity after diffusion was approximately 0.1 ohm-cm on a 10.0 ohm-cm
substrate. The results, again plotted as resistivity, are given in figure 5. The results are only slightly more than ±0.5%
indicating the stability of the mechanical system. These measurements constitute a worst-case situation, and the probe
stability is likely to be even better.

The third concern is the reproducibility of measurements of microsegregation where the resistivity fluctuations
are on the order of 10%. Two sets of resistivity measurement were made adjacent to one another, and the resultant
resistivity profiles are shown in figure 6. The reproducibility is apparent; only the absolute values are different owing
to the slight lateral displacement of the probes for the two measurements.

The results of these three experiments indicate that the probe as configured is adequate to characterize
microsegregation in bulk silicon in a reproducible manner.

3. Analytical Technique

Earlier attempts to describe the microsegregation of dopant impurities in semiconductors on solidification have
been largely qualitative. Determining the frequency distribution has resulted from counting striations or resistivity
variations in plotted data. For very periodic functions, with a single dominant frequency, this technique yields
reasonable results. In crystal growth, however, there are often a number of parameters, both thermal and mechanical,
which influence the impurity incorporation. Each of these parameters is likely to have a different frequency and
hence the impurity distribution may be a composite of a number of frequencies. In order to grow crystal with
uniform resistivity distribution, it is necessary to identify the source of the various resistivity fluctuations and this
requires analysis of the composite resistivity profile. The technique presented in this paper for determining the
relative strength and the periodicity of the various components of the resistivity fluctuations is Fourier Transform
analysis.

The axial resistivity profile constitutes a complex spatially periodic function p(x). The fundamental frequency
components making up this function are derived from the temporally periodic conditions during growth. The
temporal spectrum of the resistivity is thus obtained from

The function p(co) is complex and the spectrum is evaluated from

where p*(u>) is the complex conjugate of p(co).

The actual integration was performed numerically using FFT algorithm on an IBM 360 computer.

The non-zero average resistivity and the gradual change in the average resistivity owing to normal segregation give
rise to a large spectral peak at zero frequency (i.e., the transform of a constant is a zero frequency component to the
spectrum). This peak complicates the evaluation of the spectrum. In order to minimize the problem, a linear least
square fit to the resistivity was obtained and subtracted on a point-wide basis to eliminate all ramp and square wave
components of the function. Thus the actual resistivity function which is transformed is p'(x) = p(x) — p(x) wher
p(x) isCopyright
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 4. Results

In this section, representative results of measurements made on several single crystals of silicon are presented.
The resistivity plots and transformed resistivity spectra are given for data taken on three crystals grown under varying
conditions. Two of the crystals were grown by the Czochralski technique and the third by a modified float zone
technique. In figure 7, the actual resistivity profile is shown for measurements made at the center and edge of one of
the crystals. This crystal was pulled at 13.7 cm/hr, with the seed rotated at 35 rpm and the crucible counter-rotated at
10 rpm. The sample was taken at g = 0.6, where g is the molten fraction remaining at the time of solidification.[2]
The transform of the edge resistivity modified by subtracting the average as derived from a linear least square fit is
given in figure 8. The obvious spectral line at 58.8 jum agrees well with the observed frequency on the resistivity plot,
while the resistivity fluctuations corresponding to the 2000 Aim peak are not as readily apparent. In this case, the
58.8 jum periodicity can be accounted for by the growth of crystal during one revolution to within 10%. This value is
arrived at by determining the length of crystal grown in one revolution, i.e., periodicity = (seed pull rate ± crucible lift
rate) •=- (seed spin ± crucible spin). The peak at 2000/im corresponds to approximately one minute of growth which is
very near the thermal time constant of the crystal puller.

The resistivity measurements made on the second crystal, pulled at 11.0 cm/hr and with a seed rotation of 1 rpm
and a crucible counter-rotated at 1 rpm is presented in figure 9. The sample is taken at g = 0.6. The transform of this
spectrum is shown in figure 10. Here again there is an obvious spectral line, however, at a wavelength of 875 Aim,
although the low frequency peak 2000 nm is not present. The peak at 875 Aim agrees within experimental accuracy to
the calculated growth of the crystal in one revolution, viz 914 pim.

The resistivity profile of a modified float-zone grown crystal, as distinct of the Czochralski grown crystals
described above, is shown in figure 11. The growth conditions for this crystal were pull rate, 15 cm/hr; pull spin,
20 rpm. The transform of the resistivity spectrum is given in figure 12.

5. Conclusions

It has been shown that the spreading resistance probe can be used to quantify the resistivity microsegregation in
silicon crystals. Instrument noise is shown to be less than ±0.5% and measurement reproducibility has been
demonstrated. An analytical technique is described which allows calculation of the fundamental frequencies which
contribute to the microsegregation. The results allow identification of those mechanisms which are dominant during
crystal growth in determining impurity incorporation, and determination of the relative strengths of those
mechanisms. A subsequent publication will discuss the results from a crystal growth point of view.

6. Acknowledgments

The authors wish to acknowledge the assistance of Roy O. Byrd in making the spreading resistance
measurements.

7. References

[ 1 ] Witt, A. F., M. Lichtensteiger, and H. C. Gatos, "Experimental Approach to the Quantative Determination of
Dopant Segregation During Crystal Growth on a Microscale: Ga Dope Ge, J. Electrochemical Society 120 1119
(1973).

[ 2] See for example Pfann, W. G., Zone Melting, John Wiley & Sons, Inc., New York 1958.

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 Figure 1. The configuration and location of slabs cut
from the crystal for spreading resistance characterization.

Figure 2. Photograph of spreading

resistance apparatus.

Figure 3. Drawing of silicon sample showing

location of probing and interface demarcation.

195
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 Figure 4. Variation in instrument output for 1000 ohm
constant impedance across input to electronics. (See text)

Figure 5. Variations in surface

resistivity of a uniform diffusion.

Figure 6. Reproducibility of microsegregation

measurements determined by measuring resistivity
in two adjacent regions.

196

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 Figure 7. Axial resistivity of sample 73-042-10 measured at edge and center. (See text for growth conditions)

Figure 8. Transform of edge resistivity shown in Figure 7.

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 Figure 9. Axial resistivity of sample 73-049-6 measured at center. (See text for growth conditions)

Figure 10. Transform of edge resistivity shown in Figure 9.

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 Figure 11. Axial resistivity profile of modified float zone crystal. (See text for growth conditions)

Figure 12. Transform of resistivity of float zone crystal.

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565-448 O - 75 - 14
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 JNAJ.IONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Effects of Oxygen and Gold on Silicon Power Devices

Jacques Assour

RCA Solid State Division

Somerville, New Jersey 08876

Several important features that make the two-probes spreading

resistance technique a unique process control tool for designing and
manufacturing silicon power devices are elucidated in terms of the effects
of electrically active oxygen and gold centers on the characteristics of
transistors, thyristors, and rectifiers. The effectiveness of the spreading
resistance technique is compared to other commonly practiced techniques
for the investigation of diffusion mechanisms of oxygen in homotaxial
transistors and of gold in fast switching rectifiers and thyristors.

Key Words: gold in silicon, oxygen in silicon.

1. Introduction

The internal structures of silicon power rectifiers, transistors, and thyristors are
characterized by multiple diffused and/or epitaxially grown junctions ranging in depth from
10 to 125 microns with doping concentrations varying from 1Q13 to 10^1 A/cm^. The control
of diffusion and epitaxial processes used in designing and manufacturing these power devices
has relied mainly on two commonly practiced techniques. The first is angle lapping and
staining (1) to detect the presence and to determine the depth of a single junction or
multiple junctions. The second is the measurement of sheet resistance by the four-probe
method, which is used in conjunction with the staining technique to determine average
resistivities and surface concentrations of diffused and epitaxial layers. The intent is
not to discuss the reliability of each technique in terms of accuracy and reproducibility ,
but rather to review their limitations as process control tools in a present day manufac-
turing environment.

The results of studies based on spreading resistance measurements have shown that the
limitations of the staining and sheet resistance techniques reviewed below can be satis-
factorily resolved by the two-probe spreading resistance (SR) technique. In this paper,
the unique features of the SR technique that aided the investigation of the effects of
oxygen and gold centers on the internal structure and electrical characteristics of power
devices are discussed.

2. Limitations of the Staining and Sheet Resistance Techniques

The limitations of angle lapping, staining, and four-probe sheet resistance measurements
currently experienced in a manufacturing environment are noted in Table I. It is no surprise
that angle lapping and staining is operator-dependent, since this technique is considered by
many as something of an art, and since it is greatly dependent on the topography of the lap-
ped surface, chemical reaction of the staining solution, and relative doping concentrations
of the adjacent layers. The factors influencing the accurate delineation of n/n+ and p/p+
diffused layers are complex and little understood. Therefore, the delineation of multiple
diffused or epitaxially grown layers in power devices is often fortuitous. The staining
technique is also time consuming in terms of measuring junction depth and recording data
for permanent reference.

Figures in brackets indicate the literature references at the end of this paper.

201
 Because of analytical boundary problems, the sheet resistance technique is not readily
applicable to multiple layer structures, and consequently, special test samples of controlled
geometry are required so that consecutive diffusions or epitaxial growth process can be
monitored. This technique also inherently requires samples with areas 10 times larger than
the spacings of the probes in order to reduce the influence of geometrical correction factors.
Therefore, this technique cannot be used to study manufacturing problems in single, practica,l
power devices. The sheet resistance technique provides average values for a given volume
and is incapable of detecting microhonhomogenities. Therefore, it is incompatible with con-
trol requirements of current, sophisticated device designs. It is needless to add that the
above technique is cost prohibitive for diffusion profile studies in a manufacturing environ-
ment.

3. Calibration of the Spreading Resistance Probe

The spreading resistance probe used at RCA as a process control instrument has been
purchased commercially from Solid State Measurements. To date, over 400,000 points have
been recorded with excellent reproducibility and minimum maintenance. Since the calibration
of the SR probe is essential for accurate and reproducible data, the following procedure was
adopted to calibrate the instrument. Several n- and p-type silicon wafers ranging in resis-
tivity from 0.001 to 1000 ohm-cm were first profiled in bulk form by the SR probe for homo-
geneity. The resistivity of each wafer was then measured by the four-probe technique following
ASTM Standard F84-72. The homogeneous n-type and p-type calibration samples were then lapped
with an alumina abrasive, AO #305, and profiled by the SR probe. Using the SR and resistivity
data, a least-square straight line was calculate^ to fit the data. The resulting calibration
curves relating the measured spreading resistance with resistivity data for n-type and p-type
samples are shown in Fig. 1. The reproducibility and accuracy of these calibration curves
has been found excellent.

Other surface finishing methods based on mechanical and chemical polishing of the cali-
bration samples were also investigated. Although polished surfaces reduced the noise level
of the recorded data, these surfaces were found extremely sensitive to ambients and probe
pressure, thus resulting in nonreproducible calibration curves.

4. SR Profiles of Multiple Layer Structures

Figs. 2 and 3 show that the limitations of the staining and sheet resistance techniques
experienced in a manufacturing environment can be resolved by means of SR profiles. The SR
profile of a multiple epitaxial layer structure used in the manufacture of high voltage tran-
sistors is shown in Fig. 2. This structure consists of three epitaxial n/v/7r layers grown
consecutively on an n+ substrate. This single profile yields complete and accurate data on
the width and resistivity of each epitaxial layer, including the resistivity of the starting
n+ substrate. Clear delineation of the n/n+ and V/TT interfaces and the non-uniformities in
the resistivity of the v layer can be uniquely achieved with the SR probe. Without the SR
technique, angle lapping, staining, and sheet resistance measurements of two p-type control
samples would be needed to evaluate the n and v layers; the same techniques would have to
be applied to the epitaxial structure to evaluate the IT layer. No information would be
available on the uniformity of the grown layers and on out-diffusion and auto-doping effects
at the various interfaces. The data available from the SR profiles of epitaxial structures,
when properly corrected for p-n junction effects, allow the accurate calculation of the
breakdown voltages(2).

The second SR profile shown in Fig. 3, is that of an asymmetrical thyristor structure

profiled through the Tl surface. This device consists of four layers diffused into a homo-
geneous n-type silicon region. It is sufficient to say that a detailed evaluation of the
width and doping concentrations of all the active layers would have been a horrendous task
by any known characterization technique other than the spreading resistance technique.-
The next two discussions on the effects of oxygen and gold centers on power devices
can only be investigated with the spreading resistance technique because of its unique
ability to detect, peproducibly, micrononhomogeneities in complex diffused structures.
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 5. Effects of Oxygen on NPN Homotaxial Transistors

A cross section of an NPN homotaxial transistor is shown in Fig. 4. This device is

fabricated by simultaneous diffusion of an n-type impurity from each side of a homogeneously
doped p-type base. A mesa is etched on one side of the wafer to define the emitter and ex-
pose the base region for metal contacts. The starting p-type wafer is Czochralski grown,
boron doped silicon crystal. Inherent to their growth process, these crystals contain rela-
tively high concentrations of oxygen atoms, approaching lO^B A/cm^. It has been shown(3)
that under certain heat treatment cycles, the oxygen atoms form donor centers which greatly
affect the resistivity and lifetime of Czochralski grown n-type and p-type crystals.. The
influence of oxygen donor centers on the resistivity of one sample from a p-type crystal
after heat treatment at 450°C for one hour in an H2 ambient is shown in Fig. 5. An SR profile
in the radial direction of a 2-inch diameter wafer shows an initial resistivity of about 11
ohm-cm. Infrared measurements performed on this wafer revealed a strong peak at 9 micrometers,
which is characteristic of oxygen absorption. A concentration of approximately 4xlQl7 A/cm^
oxygen was determined from the absorption peak. After heat treatment, the SR profile in the
same radial direction reveals several resistivity peaks with values exceeding 2000 ohm-cm.
The resistivity upgrading is the result of oxygen donor formation whose detailed mechanism
is not known, but it has been found(3) to be dependent on the parameters of crystal growth,
such as heating or cooling rate, rotation rate, gaseous ambient, and crystal diameter. There-
fore, as far as wafer processing is concerned, the device manufacturer is completely at the
mercy of the impurities that the crystal grower has incorporated into the material. For
oxygen, in particular, there is no way to remove what has been grown in. Consequently,
unpredictable non-uniform concentrations of oxygen donor centers can form in both the radial
and axial directions of p-type wafers. The spatial distribution and magnitude of the high
resisitivity peaks shown in Fig. 5 were found by SR profiles to vary in wafers sliced from
the same crystal.

The influence of resistivity upgrading on the structure of NPN homotaxial transistors

fabricated with Czochralski crystals containing high oxygen concentrations is dramatically
illustrated in Figs. 6 and 7. Fig. 6 shows the doping profiles determined from SR profiles
of an NPN homotaxial transistor before and after heat treatment at 450°C for one hour. The
doping profile measured from the emitter surface clearly delineates the base width and doping
concentration, the emitter base, and base collector junctions. After heat treatment, however,
the p-base has converted to an n-type region with no apparent junctions. Similarly, in Fig. 7
the doping profile measured from the base contact surface clearly delineates the width of the
base region width and the base collector junction. After heat treatment, the p-base has
converted to n-type and, consequently, the junction appears displaced at the new p+/n boundary.

Similar profiles have been measured for several NPN transistor chips located in different
areas of a processed wafer. The rate of resistivity upgrading and conversion of the p-base
region from p-type to n-type resistivity varied with time and is assumed here to be dependent
on the relative concentration of oxygen donor centers across the wafer as shown in Fig. 5.
This phenomenon is shown in Fig. 8 for a transistor heated to 450°C. The SR profiles measured
from the emitter suriace have been superimposed to illustrate the rate of resistivity upgrading
and final conversion as a function of time in hours. In this sample, total conversion of the
base region from p-type to n-type silicon occurred after seven hours. It has also been
reported(3) that these oxygen donor centers can be neutralized by heating the crystal to
elevated temperatures. This phenomenon has been confirmed in several bulk wafers and processed
devices. In fact, the sample shown in Fig. 8 was heated to 1000°C for 60 hours to obtain the
SR profile shown before heat treatment.

Changes in the electrical characteristics of NPN homotaxial transistors with the type of
resistivity changes explained above may be summarized as follows; all of these changes lead
to yield rejects.

(1) Uniform resistivity upgrading in a device together with narrowing

of the base region results in breakdown from premature punchthrough.

(2) Localized resistivity upgrading in the base region results in

high leakage currents, IECO
(3) Conversion in the base region from p-type and n-type resistivity
results
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 (4) In all cases, transistors with high donor center concentrations
exhibit very low current gains as a result of poor minority carrier
lifetime in the base region. This result is also true in narrow base
transistors and has been substantiated for transistors heat treated
at 1000°C to neutralize the oxygen donor centers. In other words,
oxygen complexes precipitated in the base region can act as effective
recombination centers for electrons.

A closing note on this topic is the fact that NPN transistors fabricated with epitaxially
grown p-type bases with structures identical to those of the NPN homotaxial transistors
exhibit none of the oxygen phenomena discussed above.

6. Effects of Gold Doping in Power Devices

Gold is widely used to control the lifetime of minority carriers during the fabrication
of fast switching power devices. Despite extensive studies(4) of the characteristics of
gold doped silicon, there remain significant gaps in the understanding of the properties of
gold doped silicon. These gaps, or problems, have left the industry without a complete model
for gold diffusion into silicon. As a result, in a manufacturing environment, control of
gold diffusion is empirical and often elusive. Examples of the unsolved problems are the
accumulation of electrically active gold centers near the surfaces of silicon wafers, the
diffusion mechanism of gold through heavily doped n and p regions, and the lack of correla-
tion between the total gold concentration and resistivity upgrading of n-type and p-type
silicon.

A typical example of gold accumulation near the surfaces of wafers of finite practical
thickness is shown in Fig. 9. These are SR profiles of a gold doped n-type wafer for various
diffusion times. The wafer has one mechanically polished surface and one lapped surface (12
micrometers alumina). An oxide layer 1 micrometer thick was grown on both surfaces and then
removed from the polished surface only. A 50& gold layer was evaporated on the polished sur-
face. The wafer was divided into several samples which were diffused at 870°C for various
times in an argon ambient. The initial and final resistivity values in the bulk are noted
in Fig. 9 for reference. The SR profiles show evidence of the accumulation of gold centers
near both surfaces even though one surface was masked by a thick oxide layer. The region of
accumulation extends about 60 micrometers from each surface after 1 hour diffusion and de-
creases to about 20 micrometers after 4 hours. Excessive gold accumulation near surfaces has
been observed(4), and the degree of accumulation, in homogeneous bulk wafers, has been found
to vary slightly with surface and heat treatment of the samples. The diffusion mechanism
responsible for the accumulation of gold has been explained(5) theoretically and shown to be
related to vacancy generation in the bulk of silicon wafers. The difficulty with applying
this model for production processes, however, is that it is nearly impossible to predict the
concentration of defects and the accurate generation rate of vacancies in wafers that have
undergone various diffusion, oxidation, and cooling treatments.

In practical devices, the degree of gold accumulation near the surfaces is further com-
plicated by the differences in gold solubility in heavily doped layers. Gold appears to be
more soluble in phosphorous doped regions as compared to boron doped regions. This property
is illustrated in Figs. 10 and 11. Fig. 10 shows the SR profiles of p+/n and n+/n junctions
fabricated in the same wafer before and after gold doping. The resistivity upgrading in the
n region adjacent to the p+ junction is much higher than that in the neighboring n+ junction
This result is indicative of a difference in the concentration of electrically active gold
centers diffused into the respective n regions. In other words, heavily doped phosphorous
regions appear to getter gold atoms more effectively than boron doped regions. It is inte-
resting to note that regardless of the diffusion mechanisms occurring at the p+/n and n+/n
junctions, gold accumulation near the far surface is evident.

The above phenomenon is also illustrated in Fig. 11 for the case of a gold doped thyris-
tor structure. The SR profile measured from the Tl surface is shown for the structure both
before and after gold doping. In this example, gold has been diffused separately from the
Tl surface and from the T2 surface. The resistivity upgrading in the n region when gold is
diffused from the T2 surface is much higher and more uniform when compared to the Tl surface.
The differences in the Tl and T2 SR profiles are interpreted as resulting from differences
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in gold solubility and diffusion mechanisms in the n+ and p+ layers.

Although gold is used primarily to control the lifetime of minority carriers, its
complex diffusion mechanism through heavily doped regions of power devices influences other
important electrical parameters. In rectifiers, for example, excessive gold concentration
in the n region of p"*~/n/n+ structures causes increases in the forward voltage drop at nomi-
nal current rating, and extremely short recovery time; the latter causes "ringing" in typical
switching circuits. On the other hand, lower gold concentration causes yield depression be-
cause of long recovery times. In the case of gold doped thyristors, gold accumulation near
surfaces can cause a significant decrease in the lifetime of minority carriers injected from
the cathode into the p base; this results in higher gate currents and di/dt power dissipation
during turn-on conditions. Secondly, excessive gold concentration in the n region, even if
distributed uniformly, causes unpredictable, high resistivity upgrading which leads to pre-
mature bulk punchthrough breakdown. Thirdly, the forward voltage drop of thyristors in the
on-state is also influenced by gold doping, which greatly decreases the diffusion length of
minority in the n region.

7. Summary

The advantages and uniqueness of the two-probe spreading resistance technique as a

process control tool for designing and manufacturing silicon power devices have been compared
to other commonly practiced methods. The spatial resolving power of the SR method has been
used to elucidate the effects of electrically active oxygen and gold centers on the electri-
cal structure and performance of transistors, thyristors, and rectifiers. It is shown that
for NPN homotaxial transistors fabricated from Czochralski grown crystals, oxygen donor
centers in the base produced by low temperature heat treatment upgrade the resistivity of
that region or completely convert the base to n-type. Moreover, the diffusion properties of
gold atoms and their selective accumulation near the surfaces of finite, practical structures
are illustrated with spreading resistance profiles.

8. References

(1) Research Triangle Institute, Integrated (2) R. A. Sunshine and J. M.-Assour, Avalanche
Silicon Device Technology Volume IV.... Breakdown Voltage of Multiple Epitaxial
Diffusion by A. M. Smith, ASD-TDR-63-316, pn Junctions, Solid State Electronics,
Volume IV, Contract No. AF33(657)-10340, 16, 459-466 (1973).
Durham, North Carolina, February (1964).

(3) Fuller, C. S. and Logan, R. A., Effect (4) An excellent bibliography of the litera-
of Heat Treatment Upon the Electrical ture on the properties of gold-doped
Properties of Silicon Crystals, J. Applied silicon has been published by W. R. Thurber
Physics 28, 1427 (1957). and W. M. Bullis, Resistivity and Carrier
Lifetime in Gold-doped Silicon, National
Bureau of Standards, Washington, D.C.
AFCRL-72-0076 (1971).

(5) F. A. Huntley and A. F. W. Willoughby,

The Diffusion of Gold in Thin Silicon
Slices. Solid State Electronics, 13,
1231-1240 (1970).

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 TABL.E I
LIMITATIONS OF ANGLE-LAPPING AND STAINING TECHNIQUE
1. OPERATOR DEPENDENT
2. UNRELIABLE FOR n/n+ AND p/p+ DIFFUSED JUNCTIONS
3. TIME CONSUMING
LIMITATIONS OF FOUR-PROBE SHEET RESISTANCE TECHNIQUE
1. UNAPPLICABLE TO MULTIPLE DIFFUSED AND
EPITAXIAL STRUCTURES
2. REQUIRES LARGE-AREA SAMPLES
3. PROVIDES AVERAGE VALUES OF A GIVEN VOLUME
4. COST PROHIBITIVE FOR DIFFUSION-PROFILE STUDIES

Figure 1. Spreading resistance cali-

bration curves for n-type and p-type
silicon.

Figure 2. Spreading resistance pro-

file of a multiple epitaxial layer
structure.

Figure 3. Spreading resistance pro-

file of an asymmetrical thyristor
structure.

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 Figure 4. Cross-section of an NPN
homotaxial transistor.

Figure 5. A radial SR profile of a

Czochralski grown, boron doped silicon
wafer before and after treatment at
450° C for one hour in an H2 ambient.

Figure 6. Doping profiles of an NPN homo- Figure 7. Doping profiles of an NPN homo-
taxial transistor before and after heat taxial transistor before and after heat
treatment at 450°C for one hour. Profiles treatment at 450°C for one hour. Profiles
measured from the emitter contact region. measured from the base contact region.

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 Figure 9. SR profiles of gold doped silicon
as a function of gold diffusion time.

Figure 8. SR profiles of an NPN homotaxial

transistor as a function of heat treatment.

Figure 10. SR profiles of gold doped rec- Figure 11. SR profiles of a gold doped
tifier structures.
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2016 structure.
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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium.
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

The Evaluation of Thin Silicon Layers

by Spreading Resistance Measurementsl

Gilbert A. Gruber
Solid State Measurements, Inc., Monroeville, Pennsylvania
and Robert F. Pfeifer
NCR Microelectronics Division, Miamisburg, Ohio

The spreading resistance measurement technique is the only one

capable of providing precise thickness measurements and detailed
concentration profiles on any type of active device layer or structure
formed in silicon on a routine basis. The methods employed in the
evaluation of thin layer structures of the type used for microwave
devices is discussed and the application of these methods to thin
NN*, P+NN4" and P*li silicon structures formed by combinations of
diffusion, epitaxy and ion implantation is illustrated.
Key words: Diffusion; epitaxy; ion implantation; microwave devices;
profiling; spreading resistance; thin silicon layers.

1. Introduction
Important criteria for the successful operation of a silicon high frequency device
are layer thickness and impurity concentration profile of the device. One of the major
problems of process control in the development and production of this type device is
evaluation of these two important parameters. Techniques such as infrared interference
spectroscopy, angle lap and stain, anodic oxidation with differential four point probe
measurements and various capacitance-voltage techniques, however, yield only limited
information on micrometer and submicrometer thick structures or are extremely time
consuming. Only one method available today can provide precise thickness measurements
and detailed concentration profiles on any type of active device layer or structure
formed in silicon on a routine basis, i.e., the automatic spreading resistance measure-
ment.
The purpose of this paper is to illustrate the application of the spreading resis-
tance technique to routine evaluation of thin NN4", P^NN* and P*N silicon structures
formed by combinations of diffusion, epitaxy and ion implantation.

2. Measurement Procedure
The apparatus used for the measurements of spreading resistance for this study was
a Model ASR-100 Mazur Automatic Spreading Resistance System (1) » ^. This system is
shown schematically in Figure 1 and features a two point probing arrangement with an
1
Work was done at Westinghouse Research Laboratories, Pittsburgh, Pennsylvania 15235
2
Solid State Measurements, Inc., Monroeville, Pennsylvania 151^
3
Figures in parenthesis indicate the literature references at the end of this paper

209
X-Y plotter and a digital acquisition system for computer processing. The "conditioned"
probe tips used for this study were each loaded to twenty grams and were spaced one-hundred
micrometers apart.
Calibration of the instrument is done by periodic measurement of a specially prepared
calibration block made up of a number of individual silicon samples of known resistivities.
The calibration samples were initially measured using a four-point probe to determine the
average resistivity of each. It was also found desirable to measure these standard samples
with the automatic spreading resistance probe in a radial fashion in order to determine
their doping uniformity since the accuracy and reliability of the measured sample resistiv-
ities is obviously no better than the calibration data to which the sample is compared.
The surfaces of the calibration samples were prepared by chem-mechanically polishing
with an alkaline colloidal silica solution on a plastic plate. A -typical calibration curve
resulting from measurement of standards prepared in this way is shown in Figure 2.
The samples to be measured are prepared by.scribing, breaking and then mounting on a
bevelled polishing jig. A bevel is then chem-mechanically polished down through the layers
to be measured. Surfaces prepared in this way are both smooth with no rounded edges and
are damage free. They therefore meet the most important criteria necessary for reliable
spreading resistance measurements, i.e. reproducibility.
After polishing, the sample was mounted on the mechanical subsystem of the probe, the
bevel edge aligned with the probes and the precise bevel angle measured with the micro-
scope. The measurement cycle was begun and the spreading resistance plotted as a function
of position on the bevel edge. This position on the bevel is related to the actual thick-
ness of the layer by:

where T is the layer thickness in micrometers, N is the number of spreading resistance

points in the layer and S is the incremental step size in micrometers. For angles less
than approximately 15° then:

therefore, since the tangent is measured directly, a convenient working equation is:

A typical example of a profile of the kind obtained is shown in Figure 3« This is an exam-
ple of a thin multiple epitaxial structure measured with S « 2.5 micrometers per step and
a tanGL - .020, therefore, each step across the bevel represents a 500A increment in the
thickness of the layer.
Once a sample is measured and a plot is obtained, the real advantage of this technique
can be seen. The plot represents a map of the entire electrical structure obtained by the
various processing techniques employed. These "raw data" plots of spreading resistance as
a function of position on the bevel surface can be used as process monitors without further
processing of the data. When necessary, however, these data can be converted to resistiv-
ities, by comparison with the calibration curve described above, and impurity concentra-
tions by using the mobility data of Sze and Irvin (2).

3. Corrections for Insulating and Conducting Boundaries

Considerations of the geometric aspects of this measurement require correction to the
value Copyright
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two extreme cases of an insulating or a conducting boundary (3, **-, 5)» For this study the
correction for the presence of an insulating boundary (a P-N junction) described by Dickey
(4) and Mazur (5) was used. In this method the working equation for the correction of
resistivity in the proximity of an insulating boundary is:

Where Rm is the measured spreading resistance, Pcorr. is the corrected resistivity of a

sample at a particular point, "a" is the metal-semiconductor contact radius (3 x 10"^ cm.),
"p" is the number of probes used in the measurement, kGO) is a measure of the "zero bias
barrier resistance" (4) of the point being measured and "C" is the geometrical correction
factor for an insulating boundary. The parameter k is a function of the resistivity and
can be determined by solving this equation for kCO) using the calibration data and the, fact
that C » 1 in the absence of an insulating boundary. To apply this correction, an itera-
tive procedure is used. First, the resistivity, 0, corresponding to the measured resis-
tance, Rm (assuming C - 1 and choosing a value for k^O) corresponding to that resistivity)
is found. Then a value of C is calculated from the equations of Dickey (*0 given below:

"D" is the lateral spacing between a pair of spreading resistance probes (.01 cm in this
work) and "t" is the thickness of the layer below the spreading resistance probes in1 centi-
meters. From this data a value for 0Corr. is calculated. Then a new value for kfyO ) is
determined for this new value of p. A few iterations are usually all that are necessary to
bring the corrected resistivity value to within five percent of the previous value in the
iteration procedure.
This correction is based on geometric considerations of the spreading resistance mea-
surement. The following assumptions are made: 1. a perfectly circular contact of radius,
"a", 2. a perfectly insulating boundary, 3- a relatively uniform layer, 4. no edge effects
due to the pinching of the field as the probe approaches the edges of the sample and 5» an
accurate measure of the thickness at which the junction occurs. These assumptions do not
hold in all cases and are invalid in the vicinity of a junction. This procedure has the
advantage, however, of being easy to apply and gives results that compare favorably with
measurements made by other techniques (6, 7)»
The correction used for a conducting boundary is based on the work of Brooks and
Mattes (8). Since nearly all of the conducting boundary corrections are made to measure-
ments of lightly doped silicon layers on a heavily doped layer, e.g., an N-type epitaxial
layer on an M*" (N icP-9/cm.-') substrate, the substrate may be assumed to be a perfect con-
ductor. A copy of the relevant correction curve is shown in Figure 4. Here the ratio of
the corrected spreading resistance value Rcorr. "to the measured spreading resistance Rm is
plotted as a function of the thickness of the silicon above the conducting layer for a con-
tact radius of 3 x 10"^ cm.

^. Results and Discussion

The example in Figure 3 above, is a "raw data" spreading resistance plot of a thin P*N
epitaxial structure deposited at a pyrometer temperature of 1050°C. from a silane source on
an N* substrate (9). From this profile it can be seen that the spreading resistance in-
creases from the surface (the extreme left hand side of the plot) to the P-N junction (the
maximum spreading resistance value). The spreading resistance of the N-type layer appears
relatively uniform before dropping off to the substrate value. When these data are corrected
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for the presence of the P-N junction and for the conducting NN4" interface, the plot of con-
centration vs. thickness shown in Figure 6 is obtained. Three rather interesting effects,
not apparent in the "raw data" plot, can be seen. First, the impurity concentration of the
P4" region of the curve is uniform from the surface to the P-N junction. Secondly, a dip in
the concentration occurs at the N-N4" interface and third, a steeper N to N4" transition gra-
dient is seen at the N-N4" interface. Note again that none 4of these three effects is ap-
parent from the uncorrected "raw data" plot. The uniform P " layer is typical for this type
of epitaxial growth and is expected. The "dip" in the impurity concentration at the N-tr
interface, however, is in contradiction to the normal case where the transition from a
heavily doped substrate to lightly doped epitaxial layer occurs in a gradual fashion from
one concentration to the other. We believe the cause of this particular phenomenon is that
the N-type epitaxial deposition was purposely done in two steps in order to obtain the
steeper N to N+ transition gradient also observed. The first part of the layer was grown
with no dopant gas being injected into the reactor and so was doped only by the transported
and evaporated dopants from the 4substrates. After this initial growth which is designed to
increase the abruptness of the N " to N-type transition, phosphine is injected into the gas
stream to dope the remainder of the layer to the proper impurity level. This belief is
supported by the series of profiles shown in Figure 6 which are results obtained by varying
the length of deposition time for the initial or undoped layer. This study was done using
silicon tetrachloride but other experiments indicate that the same relative result is ob-
tained for the silane system. These are raw data plots and as such have not been corrected
for the presence of a conducting boundary as in the computer curve above, but the same
effect is shown. Curve A shows the effect of a zero time delay between silicon source gas
injection and dopant gas injection; and Curves B through D show the effects of delay times
of 1, 2 and 5 minutes respectively. As can be seen from the peak in Curve D, a higher re-
sistance layer is formed at the N-N4" interface the longer the delay time. This peak in the
resistance is equivalent to a dip in the impurity concentration. The choice of proper de-
lay time to give the sharpest N+ to N transition without forming this high resistance
layer, which would distort the electric field in this region, depends on the purity level
of the silicon source material and the backround purity in the epitaxial reactor.
The profiles shown in Figures 7 and 8 are the raw data plots of spreading resistance
and corrected impurity concentration as a function of layer thickness, respectively, for a
P* layer diffused into an N-type epitaxial layer grown on an N* substrate. In Figure 8 the
gradual change in the concentration of the P+ layer and the change in slope at approximate-
ly the midpoint of the layer which are not apparent in the "raw data" plot are typical for
a boron diffusion done in two steps - a predeposition and a drive-in. Because each of
these steps was done under different source conditions, i.e^ the predeposition from an in-
finite source and the drive-in from a limited source, the resulting profile is that of a
double diffusion as shown. It is also noteworthy that the impurity concentration in the N
region of this structure does not decrease as the N^N interface is approached and that the
N4" to N resistivity transition occurs over a wider region than seen in the previous ex-
ample. Both of these effects are probably the result of the higher temperature used
throughout the growth of this layer, compared to that of the previous example, and the
subsequent diffusion of impurities from the substrate into the epitaxial layer during both
the epitaxial deposition and the P-type layer diffusion.
The next example illustrating the use of the spreading resistance technique for pro-
filing thin layers is that of a silicon P-N junction structure prepared by ion implanta-
tion followed by an anneal to eliminate damage. This structure,,is shown in Figures 9 and
10. The ion implantation was done at a B+ dose of 6 x ICr^/cm. The most interesting
feature to be seen from these profiles is the region of higher impurity concentration be-
tween the surface and P-N junction. Although this type of profile is not normal in the
case of junctions formed either epitaxially or by diffusion, it is typical of junctions
formed by ion implantation (10). The position of the peak of this impurity profile and
the shape of the profile depends on the energy of bombardment and the crystallographic
orientation of the silicon crystal during bombardment.

5« Conclusion
The automatic spreading resistance probe, by providing detailed evaluation of thick-
ness and impurity concentration in thin layered structures has been shown to be unique in
its ability
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 General process features such as epitaxial resistivity uniformity and profile repro-
ducibility can be monitored on a routine basis by use of the raw data spreading resis-
tance profiles. In addition, computer processed resistivity or concentration profiles may
be obtained from the spreading resistance profiles to be used by the device designer for
material evaluation and product improvement.

6. References
(1) R. G. Mazur and D. H. Dickey, J. (5) R. G. Mazur, "Spreading Resistance Re-
Electrochem. Soc., 113f 255 (1966). sistivity Measurements on Silicon Con-
(2) S. M. Sze and J. C. Irvin, Solid State taining P-N Junctions", Extended Abs.
Electronics, 11, 599 (1968). of the Electronics Div.f Electrochem.
(3) E. E. Gardner, P. A. Schumann, Jr. and Soc.. Vol. 15, Abs. No. !#»•, (196
E. F. Gorey, Measurement Techniques for (6) R. N. Ghoshtagore, Phys. Rev. B, .
Thin Films. Bertram Schwartz and Newton 389 (1971).
Schwartz eds.. The Electrochemical (7) R. N. Ghoshtagore, ibid. 2, 397 (1971).
Society (196?) p. 258. (8) R. D. Brooks and H. G. Mattes, Bell
(**•) D. H. Dickey, "Diffusion Profiles Using System Tech. Jour. £0, (1971).
a Spreading Resistance Probe", Extended (9) T. L. Chu and G. A. Gruber, J. Electro-
Abs. of the Electronics Div., Electro- chem. Soc., nft, 522, (1967).
chem. Soc.. Vol. 12, 151 (196371 (10) J. F. Gibbons, Proc. IEEE, ^6, 295,
(1968).

Figure 1. Diagram of ASR-100 Automatic Spreading

Resistance System.

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 Figure 2. P and N-type Calibration Curves for a
Polished Surface, Probe Spacing: 100 Micro-
meters, Probe Load: 20g.

Figure 3. P+N Double Epitaxial Layer on an N

Substrate - Spreading Resistance vs. Position
on Bevelled Surface.

Figure 4. Conducting Boundary Correction Curve-

Ratio of Corrected Resistance to Measured Resis-
tance vs. Thickness.

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 Figure 5. P+N Double Epitaxial Layer on an N+
Substrate-Impurity Concentration vs. Thickness.

Figure 6. Effect of Time Delayed Dopant In-

jection on the Interface Between an N Substrate
and an N-type Epitaxial Layer.

Figure 7. Boron Diffusion into an N-type Epi-

taxial Layer on an N Substrate-Spreading Re-
sistance vs. Position on Bevelled Surface.

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565-448 0 - 7 5 - 1 5
 Figure 8. Boron Diffusion into an N-type Epi-
taxial Layer on an N+ Substrate-Impurity con-
centration vs. Thickness.

Figure 9. Boron Ion Implantation into an N-type

Substrate-Spreading Resistance vs. Position on
Bevelled Surface.

Figure 10. Boron Ion Implantation into an N-type

Substrate-Impurity Concentration vs. Thickness.

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Evaluation of the Effective

Epilayer Thickness by Spreading
Resistance Measurement

H. Murrmann and F. Sedlak

Siemens AG, Werk Halbleiter
Munich, Germany

Two types of double layer structure which

are dealt with in the multi layer theory have
been examined:
1. a top layer is insulated against a bottom
layer (i.e. pn-junction, R(o°)).
2. a top layer is shorted by a bottom layer
(i.e. n+-buried layer, R(0)).
In both arrangements the Spreading Resistance
depends strongly on layer thickness d and on
the radius a of contact area. Knowing the ef-
fective radius the epilayer thickness can easily
be evaluated from Spreading Resistance Measure-
ment and making use of the function R(°°) - f (£)•
This method is nondestructive and less time con-
suming than other common methods. A simple test
pattern is proposed for evaluating the thickness
on wafers in process. A comparison between this
method and an IR-reflexion method (Digilab FTG 12)
showed that both are in very good agreement in
thickness range of 2 6/urn.

Key words: Epilayer thickness, silicon,

spreading resistance, test pattern.

1. Introduction
Exact knowledge of the thickness of epitaxial layers is very impor-
tant in integrated circuit technology. The methods commonly used to deter-
mine thickness are:
angle lapping and HF-staining
stacking fault measurement
IR-reflexion measurement after epitaxial deposition
base breakdown voltage measurement during
IC-processing.
Lapping and staining is both destructive and time consuming. Evalua-
ting stacking fault depth is very inaccurate for thin epilayers. The IR-
reflexion method requires heavily doped buried layers with concentrations
exceeding 5 . 10^9 cm"'. Also using antimony as the buried layer dopant
to reduce autodoping and out diffusion effects this concentration limit

217
may cause problems for successful application of IR-reflexion method. In
addition there is often a need to measure the epilayer thickness on wafers
being processed in order to optimize and control the deposition process
and to characterize the wafers themselves. Based on previous investigations
/1/*we propose the Spreading Resistance Measurement I SRM) as a means to
evaluate epilayer thickness.

2. Method of Evaluation
We have examined two types of double layer structure which are dealt
with in the multi-layer-theory /2/:
1. a top layer is insulated against a bottom layer (i.e. pn-junction,
R(°°)).
2. a top layer is shorted by a bottom layer (i.e. n+-buried layer,
R(0)).
In both arrangements the SR depends strongly on layer thickness and
on the radius of contact area. In addition the ratio R(«>)/R(0)=k(<»)/k(0)
is a unique function of the ratio of the epilayer thickness and contact
radius and there is no dependence on resistivity and barrier effects at
the probes. In this way we were able to determine the effective radius
of the probe by SRM on wafers with known epilayer thickness for different
surface orientations and probe loads /1/J Knowing the effective radius,
the epilayer thickness can easily be evaluated from SRM of R(o°) and R(0)
and making use of the function R(<»)/R(0) = k(°°)/k(0) = f (d/a) in figure 1
and 2.

3. Accuracy of the Method

The graph in figure 2 shows the strong dependence of the function
R(OO)/R(O) = f(d/a) for d/a< 5. For larger values the curve will approach
1 asymptotically and the method becomes insensitive. To determine the
expected accuracy of the method within the region of interest we made
estimations using the error formula

and applying it to figure 2 with

The result is shown in figure 3. The total errorl\d in thickness in

the range d = 2 4/urn was less than 0,3/um. In this thickness region
the method will be a very useful tool for controlling the epilayer depo-
sition process.
It is worth noting that generally the buried layer maximum concen-
tration will not be located at the same point at which the epilayer starts
growing. The difference between the two depends on the buried layer and
epilayer deposition process. Therefore each evalution is strictly bound to a
specific set of process conditions and because of the semi-empiric nature
of the evaluation method the SR probe has to be calibrated for each speci-
fic process. In addition there should be calibration standard wafers with
known epilayer thickness which serve as check routines and as samples for
upper and lower tolerance limits.

figures in brackets indicate the literature references at the end of this paper.
218
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 4. Experimental Results
In order to test the possibility of applying this SRM method a compa-
rison was made with the IR-reflexion method. P-type wafers with (100) sur-
face orientation were oxidized and from one half of each wafer the oxide
was etched off. Then a buried layer diffusion was carried out (R=25*2/o,
Xj = 4,5/urn) and all the oxide was etched off. N-epilayers of different
thickness were deposited in the range of d = 2 10/urn /1/. Finally
thickness was evaluated by SRM on the wafer halves wi£h and without buried
layer using the graph of figure 2 with an effective contact radius of
a = 2,90/urn. Thicknesses were also measured using a Digilab FTG 12 IR-
equipmem;. The result of the comparison is shown in figure 4. The data
points are very close to a straight line with slope 45" passing through
zero. Within the thickness range 2 6/urn there is very good agreement
between the methods. However at about 10/um the deviation becomes larger
as is expected 1).

5. Proposed Test Pattern

The experiment in section 3 was carried out with wafers without pat-
terns. Now the question arises as to a suitable test pattern for the suc-
cesful evaluation of epilayer thickness on wafers in process. This test
pattern should consist of two areas which are separated by a straight
boundary. One area should have a buried layer underneath while the other
should be isolated by the substrate pn-junction. Test pattern dimensions
depend on the lateral influence of the field distortion by the low ohmic
buried layer. A theoretical evaluation is difficult but figure 5 shows
a practiced SRM made over the boundary between the two areas. A travel of
approximately 6QO/um is required to get out of the field distorted region.
Taking this effect into account we propose the test pattern shown in fi-
gure 5, with area 1,8 x 1,8 mm2 for a 0,6 mm probe spacing.

6. Conclusion
The SRM method proves to be a very useful tool for controlling the
epilayer thickness after the deposition process. It is nondestructive and
less time consuming than other common methods. Evaluation can be carried
out on wafers in process with a simple test pattern consisting of two areas
with and without buried layer underneath the epitaxial layer. A comparison
between this method and a IR-reflexion method (Digilab FTG 12) showed that
both are in very good agreement in thickness range of 2 6/urn.

7. References
/1/ Murrmann, H. and Sedlak, F., /2/ Schumann, P. A. and Gardner,
Spreading Resistance Correction E. E., Application of Multi-
Factors for (111) and (100) layer Potential Distribution
Surfaces Symposium on Spreading to Spreading Resistance Cor-
Resistance Measurement, rection Factors, J. Electro-
Gaithersburg, Maryland, 1974 chem. Soc. 116. 87, (1969)

1)
The error of the Digilab FTG 12 is ± 0,05/urn in the film thickness
range of 1,5 10/urn, provided there is'a sufficient high concentra-
tion in the buried layer.

219
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 Figure 1. Correction factor due to
distortion of the electric field by
a two layer configuration.

Figure 2. Ratio of the field cor-

rection factor for a two layer
arrangement with p
respectively (two probes with 0,6 mm
spacing).

Figure 3. Expected error Ad for

evaluation of epilayer thickness by
SRM [(a = 2,90 ym, Aa - 0,2 ym,
(R(«>)/R(0)) = 5%].

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Figure 4. Comparison of epilayer thickness measured by IR-reflexion and SRM.

Figure 5. SRM across boundary between area of R(0) and R(°°). (above). Dimensions
of the proposed test pattern (below) .

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

The Experimental Investigation of

Two-Point Spreading Resistance
Correction Factors for Diffused Layers

N. Goldsmith, R. V. D'Aiello and R. A. Sunshine

RCA Laboratories
Princeton, New Jersey 08540

Spreading resistance measurements have been made on a series

of erfc and Gaussian phosphorus diffusions into n and p-type
silicon. Conventional four point probe methods were used to obtain
values of sheet resistance and surface concentration. Comparison
between the two methods shows increasingly large disagreements as
the diffusion depth is decreased. The Dickey formula for accounting
for the presence of a junction is shown to work well for uniform (non-
diffused) samples but to fail to correct fully and properly for
diffusions less than- 20 um deep. Empiric curves for estimating
errors on lapped surfaces used in this study are given for a wide
variety of samples.

Key words: Correction factors; diffused layers; spreading resistance.

I. Introduction

The availability of commercial two-point spreading resistance probes is bringing a new

dimension to device fabrication, control, and analysis. With this tool, the internal de-
tails of devices having complicated doping profiles are reproducibly and rapidly revealed
to the device designer or engineer. However, as with any measurement technique, calibra-
tion and correction factors play an important role in the interpretation and usefulness of
the data.

In using the two-point probe spreading resistance method for analyzing diffused re-
gions in a semiconductor device, the Dickey [1]^ correction factor due to the junction prox-
imity is generally applied. However, Dickey's original formulation rests upon the assump-
tion that the semiconductor layer beneath the probes is of uniform resistivity. Indeed,
the early experimental work of Mazur and Dickey [2] showed this assumption to be quite use-
ful for uniform epitaxial layers and for very deep diffusions. In practice, this assumption
is violated in many devices and in particular, for shallow diffused layers where the resis-
tivity can vary by orders of magnitude over a distance of less than one effective probe
radius (^ 4 microns). This can result in serious errors in converting spreading resistance
data into a concentration profile, especially for devices having very shallow junctions and
narrow or partially "covered" internal layers. Inaccuracies can also result when device
parameters such as surface concentration, sheet resistance, and total charge are calculated
from measured spreading resistance profiles. A particular case of extreme importance is
the base region under the emitter in a bipolar transistor where the sheet resistance and
total charge are parameters which must be controlled.

In this paper we present an experimental study of the applicability of the spreading

resistance measurements to the case of diffused impurity profiles. We have evaluated a
series of diffusions of phosphorus and boron into silicon in which the surface concentration*

•^Figures in brackets indicate literature references at the end of this paper.

223
impurity distribution and junction depth were controlled variables. Both junction and non-
junction cases were examined for diffusion depths between 5 and 50 microns. Both four-point
sheet resistance and concentrations determined from Irvin's [3] curves are compared to the
corresponding values determined by an analysis of two-point spreading resistance measurements.
The effect of the Dickey correction factor is examined for a uniform sample and for the
diffused samples containing a junction. All of the work reported here is for lapped surfaces.
A block diagram summarizing our procedure is given in figure 1.

2. Experimental Procedure

2.1. Diffusions

In this section we discuss the methods used to prepare diffused samples having either
Gaussian or complementary error function distributions. The majority of the samples were
diffused using doped oxides [4] as the source. For samples in which a complementary error
function distribution was desired, the doped film was left on the sample for the full dif-
fusion time. For samples where Gaussian distributions were desired, the doped film was com-
pletely removed after an initial time at diffusion temperature. The sample was then coated
with an undoped film of deposited oxide and the impurities driven in by a second diffusion.
The second diffusion time was chosen to be at least 10 times longer than the first so as to
approach a Gaussian profile.

Doped oxides were selected since they are a clean and controllable impurity source
yielding reproducible surface concentrations below lo20Acm~3. The surface concentrations in
most of our experiments were kept below ^ 5 x 1Q19 A cm~3 to avoid anomalous diffusions
which can be caused by crystal damage due to excessively high impurity concentration [5,6],
Thus, with the use of doped oxides, following the procedure outlined above, one can expect
to obtain near theoretical complementary error or Gaussian profiles.

Doped oxide source films of one impurity type were deposited simultaneously on p- and
n-type wafers to obtain samples with the same surface concentration, both with and without a
junction. Although we prepared diffusions from both boron and phosphorus doped oxides, we
have restricted the discussion in this paper to the diffusions using phosphorus in order to
avoid possible problems associated with outdiffusion of boron at the oxide-silicon interface.

2.2. Measurements and Data Analysis

The diffused samples were measured using a four point probe to determine the sheet re-
sistance (appendix A-l). Sections from each wafer were then prepared for measurement by
the spreading resistance probe using the technique given in appendix A-2. The spreading re-
sistance measurements were collected in a manner suitable for analysis using an in-house
time-shared computer. By combining the junction depth measurement obtained from the spread-
ing resistance probe with the four point probe sheet resistance, the surface concentration
for the junction samples was calculated with the aid of Irvin's curves.

A computer program was written to perform all of the necessary calculations, including
those detailed in appendix B. The output of this program was arranged to give both tabular
listings of the calculated quantities and a graphic output on a Calcomp plotter.

3. Experimental Results

3.1. Test of Dickey Formulation

The first phase of our investigation was to experimentally verify the validity of the
commonly-used Dickey formulation for junction correction. Since this formulation was based
upon a uniformly-doped sample with a non-conducting boundary, we fabricated the sample shown
in the inset of Figure 2. One micron of oxide was thermally grown upon a uniform, n-type
silicon wafer. A poly-silicon "handle" 10 mils thick was grown on the Si02, and the sample
was flat lapped to reduce its thickness. Four point probe measurements of the sample com-
bined with the thickness obtained from spreading resistance measurements allowed us to cal-
culate the resistivity of the bulk sample. In carrying out the spreading resistance measure-
mentsCopyright
we madebycareful
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possible, when the points first contacted the oxide. This position of first contact was
assumed to correspond to the location of a p-n junction in the Dickey formulation. The nu-
merical procedure used to apply the Dickey correction is described in appendix B.2.1.

In figure 2 we show the Dickey-corrected and uncorrected impurity profiles for this
sample. As can be seen, the Dickey correction is very small at distances greater than
several probe radii from the nonconducting plane, but is very accurate for distances as close
as 0.3 pm, which corresponds to less than 1/10 of a probe radius. The average resistivity
determined from the two-point probe data agreed with that determined using the four-point
probe to within 2%.

3.2. Analysis of Diffused Samples

a. Dickey Corrections

Having experimentally verified the validity of the Dickey formula for uniform samples,
we attempted to apply it to samples with diffused junctions. Following the procedures out-
lined in Appendix B, we calculated sheet resistance for the diffused junction samples using
the Dickey corrected two point probe data. This calculated sheet resistance was then com-
pared with the value measured using the four point probe method. The results of this com-
parison are shown graphically in figure 3, where the ratio of the two point sheet resis-
tance to the four point sheet resistance is plotted vs. the junction depth for a variety of
samples. This plot shows that the sheet resistance calculated from Dickey corrected spread-
ing resistance measurements begins to deviate from the four point probe values for junction
depths less than 25 ym.

If the conversion from spreading resistance to corrected resistivity is properly done,

the sheet resistance calculated from two probe measurements should agree with that deter-
mined by four probe measurements regardless of the distribution of impurities within the
sample. Thus, even if our diffusion techniques failed to yield ideal distributions, the
failure to obtain the proper value of sheet resistance indicates that the Dickey procedure
does not correct properly for diffused samples.

Since, in a diffused sample, the conductivity is predominantcly determined by the

carrier density in the top-most portion of the diffusion the disagreement in the sheet re-
sistance for the shallow junction cases implies a large disagreement in the surface con-
centration. Figures 4a-4d are plots of the Dickey corrected concentration profiles for
samples with Gaussian diffusions of increasing junction depth. Superimposed on these curves
is a Gaussian distribution calculated using four-point data and Irvin's curves. Figures 5a-
5d are plots of similar profiles without any correction factors applied. As expected from
the values of sheet resistance, there is very poor agreement between the theoretical and
measured concentration profiles for shallow junction depths.

Furthermore, as Figure 5 indicates, the spreading resistance procedure underestimates

the concentration throughout the profile. The Dickey procedure corrects this data in such a
way as to provide the largest correction factor for the points closest to the junction. It
is clear from Figure 5a, for example, that the correction factor for a diffused sample should
be higher near the surface than the Dickey procedure provides.

b. Non-junction Samples

To determine to what extent the presence of a junction contributes to the errors found
in the samples just discussed, we analyzed the junctionless samples in the same manner as
described above. Plotted in figure 6a-6d are the impurity profiles determined from the two
point probe data for four such samples. These figures also have a superimposed Gaussian
distribution. The surface concentration for the Gaussian profile was chosen to be that cal-
culated from a simultaneously prepared junction sample. The departures from the theoretical
curve are similar to those found in the junction case. Changing from a Gaussian profile to
an error function complement profile introduces comparable errors, as shown in figures 7a
and.7b. These results indicate that the discrepancies found are not solely due to the
presence of a junction.

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 c. Comparison of Profiles

In an attempt to determine the range of errors associated with measurement of diffused

samples, we have plotted in Figure 8 the ratio of surface concentration calculated from four
point data to that calculated from two probe data vs. diffusion depth for a variety of
samples. The solid lines arbitrarily enclose the entire range of the data. It is clear that
the largest errors in surface concentration occur for the smallest diffusion depths. These
large errors are found not only at the surface but also over the whole profile as shown in
figures 9-12. No correction factors were applied to the data.

In Figures 9-12, to provide greater clarity, the distance scale has been normalized to
the diffusion depth. The results given in figures 9 and 10 are for n+ into p diffusions
while those of Figures 11 and 12 are for n+ into n-type substrates. The diffusion depth is
a parameter in all of these plots and is indicated in the figures. From figures 8-12 it is
apparent that the significant parameter in determining the error is the diffusion depth.
These graphs can be used to estimate the errors associated with the measurement of diffused
layers using a two point spreading resistance probe.

4. Discussion and Conclusions

In this paper we have demonstrated that the direct conversion of two point spreading
resistance data into concentration produces a very accurate representation of the impurity
profile for very deep diffusions (depths greater than 40 ym). However, when the same pro-
cedure is applied to diffusions shallower than 10 vim, very inaccurate results are obtained.
The inaccuracies result from the diffusion itself, rather than the presence of a junction,
since comparable errors were obtained for n+ diffusions into both n and p material. Al-
though the error is probably associated with the rapid variation of impurity concentration
over a depth comparable to a probe radius, we have found that the error is much more
strongly correlated with total diffusion depth than local gradient with a profile. The
errors grow extremely rapidly for diffusion depths comparable to, and less than, the
effective radius of the probe. Although we show that the Dickey correction procedure is
quite accurate for "step junctions" having uniform profiles, its application to diffused
samples results in a profile of the wrong shape. However, since the Dickey correction
factor increases rapidly as the junction depth decreases, its application to very shallow
junctions can produce results of the proper order of magnitude.

The data shown in figures 11 and 12 show that the maximum error occurs at a distance
roughly equivalent to a probe radius. Since there is no insulating boundary in these
samples, this effect can be interpreted as resulting from the presence of the high resis-
tivity substrate below the diffusion. In principle, a multi-layer correction scheme, such
as that described by Schuman and Gardner [9] can be used to correct the data. In practice,
this procedure requires an inordinate amount of computer time to be used on a routine basis.
Similar comments apply to the data shown in Figures 9 and 10, where there is a junction
present. As a practical matter, the degree of correction required for various types of
diffused samples can be estimated from figures 8-12.

It should be emphasized that the correction factor appears to be sensitive to the

manner of surface preparation. Based on a limited number of experiments, we have observed
that samples prepared by polishing, rather than by lapping, require less correction at the
surface.

5. References

[1] Dickey, D. A., "Diffusion Profile Studies [2] Mazur, R.G. and Mickey, D. A. "A Spread-
Using a Spreading Resistance Probe," ing Resistance Technique for Resistivity
Abs. No. 57, Paper presented at the Measurements on Silicon," J. Electrochem.
Pittsburgh Meeting of the Electrochem- Soc., 113 (3), 255 (1966).
ical Society, April 15-18, 1963; See
p. 151, Extended Abstracts of the
Electronics Division, Vol. 12, No. 1.

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226
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 [3] Irvin, J.C., "Resistivity of Bulk Silicon [7] Swartzendruber, L. J., "Correction
and of Diffused Layers in Silicon," Bell Factor Tables for Four Point Probe Resis-
System Technical Journal, j>6_ (2), 388 tivitiy Measurements on Thin Circular
(1962). Semiconductor Samples," Technical Note
199, NB.TNA, Nt'l Bureau of Standards,
[4] Barry, M. L. "Diffusion from Doped-Oxide April 15, 1964.
Sources," in Silicon Device Processing,
N.B.S. Special Publication 337m p. 175 [8] Caughey, D. E. and Thomas, R. E., "Carrier
(1970). Mobilities in Silicon Empirically Related
to Doping and Field," Proc. IEEE, p. 2192
[5] Tannenbaum, E., "Detailed Analysis of December 1967.
Thin Phosphorus-Diffused Layers in p-type
Silicon," Solid State Electronics ^, 123 [9] Schumann, P. A., Jr., and Gardner, E. E.,
(1961). "Application of Multilayer Potential
Distribution to Spreading Resistance
[6] Nicholas, K. H., "Studies of Anomalous Correction Factors," J. Electrochem Soc.
Diffusion of Impurities in Silicon," 116 (1), 87-91 (1969).
Solid State Electronics 9^, 35 (1966).

Appendix A - Measurement Procedures

A.I. Four Point Probe Measurements

Four point probe measurements were made using a Fell head. Probe spacing was measured
before the start of these experiments and was found to be 0.030". Voltage was read using a
Keithley 910B electrometer and current was supplied by a barrier driven source. Five readings
were taken on each sample in a region near the center of the sample-, and these were averaged
before applying the appropriate geometric correction factor [7].

A.2. Spreading Resistance Measurements

All spreading resistance measurements were taken using a Model ASR100 manufactured by
Solid State Measurements Corp. The samples were lapped on an angle block using 6 micron
garnet grit as recommended by the probe manufacturer. The angle of the lap was determined
by the use of the calibrated microscope mounted on the probe stage. Angles used ranged
from 1 to 12 degrees depending upon the junction depth. The instrument was calibrated using
uniform samples of known resistivity. This calibration is periodically checked to ensure
probe stability.

Appendix B - Data Acquisition and Analysis

B.I. Data-Acquisition

Because of the large number of calculations involved in a study of this type, the out-
put of the logarithmic amplifier was digitized using a 0-1.999V panel meter. The digital
output of this meter was transferred, by means of a locally designed and built parallel to
serial data decoder, to punched paper tape in a format suitable for use with an in-house
time-shared computer. At the start of each run the voltages corresponding to the fixed re-
sistors built into the equipment were recorded on the tape. A section of the analysis pro-
gram calculates the curve relating resistance to voltage so that problems of meter linearity
and long term electronic drift are eliminated. This program also contains a mathematical
representation of the measured spreading resistance vs. resistivity relationships for n- and
p-type material.

B.2. Numerical Formulation

B.2.1 Dickey correction

The Dickey correction factor for spreading resistance can be combined with the calibra-
tion data relating spreading resistance to resistivity to produce the following expression
for correcting the resistivity of a uniform layer in the presence of a junction.
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where
R(pO is the relation between spreading resistance and resistivity
R is the measured spreading resistance
sp
a = effective probe radius
D = spacing between the points
t = distance from the junction.

This trancendental equation is solved iteratively using a rapidly converging numerical

procedure.

B.2.2 Resistivity to Concentration Procedure

In order to convert from resistivity to concentration the following equations, modifi-

cations of those given by Caughy and Thomas [8], were used.

These formulations have been selected to provide agreement with Irvin's curves which were
used to analyze impurity profiles. A rapidly converging iteration procedure uses these re-
lationships to calculate a carrier density for a given resistivity. In every case where
average properties over a number of data points are required, the concentrations rather than
the resistivities are averaged.

B.2.3 Sheet Resistance

Sheet resistance from data point j to sheet resistance data point k (not crossing a
junction) is calculated using the formula

where p(i) is the calculated resistivity at data point i,

6 is the bevel angle
and s is the distance between measured points along the bevel,

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 DIFFUSIONS:
ERFC
GAUSSIAN

ASR-IOO
4-PT SPREADING
PROBE ANGLE
LAP RESISTANCE Figure 1: Flow Diagram for
MEAS.
PROBE Experimental Procedures

A/D CONV.
PAPER TAPE
TIME SHARING
COMPUTER IMPURITY DISTRIBUTIONS
PROGRAM
SHEET RESISTANCE

PLOTTER

Figure 2: Calculated impurity profile,

with and without Dickey correction, for a
uniform sample having an insulating boundary.

Figure 3: Ratio of sheet resistance calculated

from Dickey corrected two point probe data
to that measured using four point probe as
a function of junction depth.

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Figure 4: Theoretical and Dick, y corrected impurity profiles for Gaussian diffusions of
varying depths.
230 EST 2016
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 Figure 5: Theoretical and uncorrected impurity profiles for Gaussian diffusions of
varying depths.

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565-448 O - 75 - 16
Figure 6: Theoretical and calculated impurity profiles for Gaussian diffusions into bulk
wafers of the same conductivity type.
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 Figure 7: Theoretical and calculated impurity profiles for erfc diffusions into bulk
wafers of the same conductivity type.
Fig.9 Ratio of local concentration, cal-*
culated from four point probe data and
Irvin's curves, to that calculated from
uncorrected spreading resistance data as
a function of distance (normalized to
junction depth) for a series of Gaussian
diffusions with varying junction depths.
Fig.8 Ratio of Surface Concentration
derived from four point probe measurements
as a function of diffusion depth

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 Figure 10. Ratio of local concentration, calcu-
lated from four point probe data and Irvin's
curves, to that calculated from uncorrected
spreading resistance data as a function of dis-
tance (normalized to junction depth) for a series
of erfc diffusions with varying junction depths.

Figure 11. Ratio of local concentration, calcu-

lated from four point probe data and Irvin's
curves, to that calculated from uncorrected
spreading resistance data as a junction of dis-
tance (normalized to diffusion depth) for a
series of Gaussian diffusions with varying
diffusion depths.

Figure 12. Ratio of local concentration, calcu-

lated from four point probe data and Irvin's
curves, to that calculated from uncorrected
spreading resistance data as a function of dis-
tance (normalized to diffusion depth) for a
series of erfc diffusions with varying diffusion
depths.

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 NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Application of the Spreading Resistance Technique

to Silicon Characterization for Process and Device Modeling

Walter H. Schroen

Semiconductor Research and Development Laboratories

Texas Instruments Incorporated
Dallas, Texas 75222

In recent years, the interest in modeling of semiconductor processes and silicon device
parameters has intensified considerably. Precise knowledge of the doping distribution in the
semiconductor emerged as a key requirement for input and starting condition of many of
these models and for their verification. It turned out that the spreading resistance technique,
after careful probe calibration and multilayer data analysis, is able to supply some of the
required data better than any other characterization technique available. This paper
discusses these successful applications. On the other hand, this paper points out inherent
limitations of the spreading resistance technique with regard to resolution and precision, and
how this affects the verification of process and device models. Finally, the paper describes
ways to supplement the spreading resistance technique by other material characterization or
electrical techniques so that the combination of these methods is capable of generating the
required experimental data for the analytical models.

Key words: arsenic; boron; design; device modeling; doping distribution; phosphorus;
process control; process modeling; spreading resistance.

1. Introduction

Stimulated by the trend toward increased automation of circuit design and improved process control in silicon
device technology, new approaches and advances in modeling of processes, device and circuit parameters, and device
stability have been discussed in the literature [1-9] *. It has been recognized that many device parameters and their
stability are controlled by the distribution of the dopants in the semiconductor. The knowledge of details of this
distribution, such as variations of the concentration gradient with depth from the surface or with heat treatments
during processing, becomes increasingly important as device structures become smaller and shallower. Since the trend
in silicon device development is indeed in this direction — for reasons such as increased circuit speed, enhanced
packing density, and reduced fabrication cost — the detailed understanding and control of the doping profiles
becomes mandatory. In addition, analytical expressions or empirical data of the doping distribution form the
necessary inputs to device models.

This paper emphasizes the outstanding features of the spreading resistance technique as a tool for acquiring
precise doping distribution data. This data is needed both for inputs as initial condition of the doping models and for
verification of the models. Analytical expressions for describing doping profiles in silicon have been derived for the
case of semi-infinite medium, as well as infinite medium. For the semi-infinite medium, the situations of a limited

* Figures in brackets indicate the literature references at the end of this paper.

235
source, i.e., the drive-in from an initial condition (ion implantation and diffusion for base and emitter), and of an
infinite source, i.e., diffusion from a gaseous source or thick oxide have been treated. For an infinite medium, the
limited source situation, i.e., buried layer, is of particular interest. These doping distribution models comprise the
category "process modeling" in figure 1.

Process models and device characterization measurements, in turn, serve as inputs to "device models", see
figure 1. These models include diode models, intrinsic transistor models (forward active, dc, transient, etc.), and
actual transistor models (parasitics and geometry). The spreading resistance probe can supply precise input data
directly, or through process models. An example of direct device application for discrete diodes of small and large
geometries in epitaxial silicon was recently discussed by Morris [10].

The major part of this paper is devoted to applications of the spreading resistance technique to doping
concentration models. The examples are discussed in the sequence in which they appear in silicon device fabrication:
First, epitaxial layer growth and buried layer diffusions are described. Then, the formation of base and emitter is
illustrated. Finally, complete transistor profiles are presented. The examples demonstrate the capabilities and
limitations of the spreading resistance probe for modeling. Supplementary techniques are outlined briefly to indicate
ways of compensating for the limitations of the spreading resistance probe.

2. Application to Epitaxial Layers

and Deep Diffusions

Models for the doping distribution in epitaxial layers have to account for average doping, surface concentration,
and interface doping at substrate or buried layers. These models must therefore include not only doping redistribution
during epitaxial growth, but also diffusions during epitaxy of any doped layer generated before epitaxial deposition.

2.1. Epitaxy Models

Calculations for the epitaxial process describe the effects of up-diffusion and autodoping, which have been
investigated for a number of years [11-14] and reviewed by Grove [15]. Since some epitaxial layers are thick
(2 to 10 Mm), the spreading resistance technique is ideal for precise impurity distribution measurements over this wide
thickness range. Figure 2 represents an example [16] of an n-type epitaxial layer, 5 jum thick, deposited on a p-type
substrate of about equal carrier concentration. This substrate was measured to a depth of 15 jum for detection of
concentration irregularities. The data points represent analyzed spreading resistance measurements [17,18].

2.2. Buried-Laver Models

Buried-layer models describe limited-source diffusions in an infinite medium, with the boundary condition of
carrier conservation. The model has been established in strength for the case of linear diffusion constants [19,1], such
as antimony doping, using Green's functions technique. The distribution, C, as a function of depth, x, is initially

Its subsequent redistribution at a given temperature, T, follows the differential equation, with time scaled by the
diffusivity,

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The number of impurities has to be conserved, so that

The solution is given by the usual superposition expression

which can be calculated using standard numerical techniques.

For non-linear diffusion constants (such as arsenic doping) or field-aided effects different approaches have to
replace the linear model.

The spreading resistance probe proved to be the most suitable tool for acquiring the initial condition inputs, for
which only insufficient analytical expressions exist, as well as for verifying the buried-layer movements due to
diffusion. An example of an antimony buried-layer diffusion is given in figure 3. Although the buried layer had moved
only slightly during epitaxial deposition, an additional 45 minutes at the given processing temperature was enough
time to diffuse the buried layer all the way through the epitaxial layer. The data points in figure 3 are "as taken" by
the spreading resistance probe. Subsequent multilayer analysis will change the absolute values of the concentration,
but not the diffusion effect illustrated in figure 3.

The impurity distribution along the epitaxial layer/buried layer/substrate system displays two features perfectly
suited for investigations by the spreading resistance probe: deep penetration into the silicon slice, and a wide range of
doping concentrations. It seems justified, therefore, to illustrate this system by a few more detailed examples. They
will also offer an opportunity to point out some important features of the spreading resistance multilayer analysis,
which is indispensable for precise and reliable interpretation of raw spreading resistance data.

2.3. Multilayer Analysis

Figure 4 shows an n-type epitaxial layer of 2 jum thickness on an n-type buried layer almost 7 Aim thick, which is
diffused into a p-type substrate (beyond total depth of 9 Aim). The impurity concentration range covered by the
spreading resistance probe is more than four orders of magnitude. The crosses in figure 4 represent data as taken by
the spreading resistance probe, while the diamonds indicate the same points after mu Itilayer analysis. The
mathematical basis of the multilayer analysis [17] is discussed by Lee in another paper at this symposium [18]. In
essence, because each measurement samples a greater depth into the slice than the depth difference between
successive measurements, the direct conversion of resistance readings to dopant concentration values (crosses in
figure 4) will not yield a correct profile. The direct result of spreading resistance measurements is somewhat like a
profile of local averages rather than of discrete point values. The model used to arrive at the "true" doping profile
(diamonds in figure 4) starts with the assumption of one circular contact to a laterally infinite medium which is
partitioned vertically into layers of homogeneous resistivity, each layer corresponding to one spreading resistance
measurement point. The analysis consists of consecutive solutions of Laplace's equation for the potential distribution
generated by the circular contact on top of this stack of layers. The solution actually proceeds from the deepest of
the stack of layers, with known boundary conditions, back to the top layer. Since the spreading resistance probe
consists of two contacts, the two-probe solution is then obtained by superimposing two one-probe potential solutions
at a suitable distance. Techniques for the rapid solution of the simultaneous equations have been developed [18]
resulting in short enough execution time to allow economical routine use. The cost of the analysis is typically less
than the cost of the original measurement.

When input data is not smooth, the multilayer analysis may magnify input irregularities into the output profile.
Figure Copyright
4 gives anbyexample
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EST 2016 layer and the slope of the buried layer. The
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local concentration dip of the corrected data is an artifact of the analysis and can be disregarded. It occurs when
layers beneath layer being corrected make a major contribution to the measured voltage. Under this circumstance, the
program decides that minor variations in the measured voltage must be caused by major ones in the single layer under
test, since its contribution to the total measured voltage is relatively small. The program thus overcorrects. In figure 4
this is particularly true since the layer at the point where the irregularity begins is underlain by layers having one to
three orders of magnitude higher conductivity.

In addition to the question of smooth data, the shape of the potential distribution under the probe is also
important for analysis overcorrection. Real probe tips are not single circular contacts of uniform potential, but are
composed of a large number of smaller contacts over a generally circular area. Simply reducing the value of the
apparent tip radius to a more effective one does indeed remove the profile dip, but generates some side effects. An
exact analytical solution for a model of a real probe tip geometry is presently not available due to the complex
boundary conditions involved in a tight array of contacts.

The data in figures 2 and 4, and the following figures are analyzed data, thus representing "true" doping profiles.
Figure 5 gives another example of the epitaxial layer/buried layer/substrate system. The spreading resistance
technique was able to cover a wide range of depths (total of 18 jim) and concentrations (5 orders of magnitude) with
both n- and p-type silicon involved. The location of the junction at about 14.25 Mm depth can be clearly delineated.

3. Application to Doping of Shallow Layers

Recent advances in very small-angle beveling (< 0.3 degree) with precisely defined slope edges and scratch-free
surfaces [20] opened a new field for application of the spreading resistance probe: the shallow, doped regions of
emitter and base in bipolar transistors, and source, drain, and gate in MOS transistors. The data acquired by the
spreading resistance probe serve, similar to the applications described previously, as inputs to and as verification of the
doping distribution models.

3.1. Boron Distribution

Better understanding of the complex diffusion and redistribution processes in silicon and insulating layers has
made it evident that final doping distributions in silicon do not follow simple functional relationships. For instance,
dopant profiles were long thought of as characterized by a junction depth and sheet resistance. Consider the regime of
devices where both measurements are possible and even accurate. Simple functional forms for the profile
representation, namely Gaussian or complementary error function, were chosen and a preliminary device analysis
constructed accordingly. Figure 6 represents an actual deposition and drive-in for boron and a functional
approximation (Gaussian) with the same sheet resistance and junction depth. Sheet resistance of the Gaussian profiles
were calculated using accepted mobility-concentration relationships. Experimental values for sheet resistance are
accurate to ± 5%. Figure 6 indicates the problems which can arise because of segregation of the boron into the oxide.
For a bipolar base this can lead to an error of a factor of 2 in the base sheet under the emitter, and for MOS
technology one might find a surface inverted (weakly) when it was expected to be accumulated.

A realistic diffusion model, as the one developed by Prince [21] for ion-implanted boron under oxidizing
conditions, starts with an initial condition for the doping concentration, N(x,t)

given either by experimental data (e.g., gained by spreading resistance measurements) or theoretical expressions (LSS
range theory [22] for ion implantation). Defining the origin of the coordinate system at the Si-Si(>2 interface, the
diffusion of boron atoms is governed by

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where
D = boron diffusion coefficient in silicon
m = thickness of silicon consumed in growing unit thickness
of SiÜ2 (assumed to be o.44 in this instance)
x Q (t) = SÍÜ2 thickness
x = depth from Si/S¡02 interface into the silicon

Boundary conditions are

where
K = segregation coefficient of boron in the Si-SiC^ system.

The last boundary condition is derived from the requirement of conservation of boron atoms and under the
assumption that boron diffusion in the oxide ¡s slow relative to the oxidation rate dxQ/dt, which is true for steam
oxidation.

3.2. Arsenic Distribution

Comparing arsenic diffusion data with a Gaussian profile fit using sheet resistance and junction depth in an
analogous way to the boron data plotted in figure 6, would result in an even greater discrepancy due to the strongly
non-linear diffusion/annealing behavior of arsenic and its incomplete electrical activation at high concentrations. In
figure 7, the true arsenic profile is compared with a linear approximation (complementary error function) by
normalizing the concentration. The model and data apply to diffused arsenic. As can be seen, the experimental data
fall well into the range of a 10% variation of the ¡ntrinsic diffusion constant, D¡, for the non-linear model, but not at
all into the range of the erfc approximation. The non-linear model [1,23,24] incorporates the effects of an internal
electric field and the variation of equilibrium lattice vacancy concentration into the continuity equations. For
ion-implanted arsenic, Shah [25] employed field-aided diffusion, concentration enhancement due to enhanced
solubility of vacancies in heavily doped silicon, and electrical activation to formúlate a realistic relationship for the
diffusion coefficient D in the diffusion differential equation.

239
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565-448 O - 75 - 17
where
C+ = concentration of electrically active arsenic
nj = intrinsic carrier concentration (temperature dependent)
0 = fitting parameter for arsenic activation (temperature dependent)

As Shah has also pointed out, |3 can be chosen so that it fits the diffusion coefficient for boron previously used [1,21]
in the form

3.3. Phosphorus Distribution

The third species used for base and emitter formation is phosphorus. Figures 8 and 9 give examples of spreading
resistance data acquired in support of phosphorus distribution models. Figure 8 relates to diffused phosphorus,
figure 9 to ion-implanted phosphorus. The model of Tsai [26] assumes a moving boundary separating two distinct
phases, a constant concentration region and the transition region of the concentration profile. The phase boundary
reaction is the rate-limiting process and the phase boundary moves at a nearly constant rate. Subsequently,
Schwettmann and Kendall [27,28] have shown that the tail of the phosphorus profile is formed by enhanced
diffusion during low temperature heat treatments. The mechanism underlying this effect has been shown to be related
to the one forming the kink in the original unannealed layer. However, the detailed processes occurring in the high
concentration region are still not fully understood.

Figures 8 and 9 stress the capability of the spresding resistance probe for acquiring a dense array of data points
in layers less than 1 jum thick. As mentioned, this capability is based on the recent advances of fabricating very
shallow and well-defined angles [20]. It adds a new dimension to the investigation of emitter and base layers, since
the spreading resistance probe is applicable to both n- and p-type silicon, and since it can cover a very wide range of
doping concentrations, including steep doping gradients. A particularly important feature of the spreading resistance
probe is its ability to probe closer to a pn junction than any other characterization technique. Figures 8 and 9 also
compare spreading resistance data to measurements obtained by the incremental sheet resistance technique. There is
very good agreement after the spreading resistance data have been corrected by the multilayer analysis. This
agreement is significant since the incremental sheet resistance technique supplies absolute values by monitoring the
difference between data.

A comment may be added concerning the doping distribution in the silicon layer right under the surface.
Figures 8 and 9 show a discrepancy between spreading resistance and incremental sheet resistance data; the spreading
resistance values suggest a significant decrease in the phosphorus concentration close to the surface. The probable
origin of this drop is an effective reduction in carrier concentration caused by the formation of a depletion region
under the surface initiated by the deposition of the silicon nitride film; this film is needed for the precise definition of
the surface/bevel edge [20] during the small-angle lapping operation. As figure 8 shows, the depletion region is
partially reversed and eliminated (square-shaped data points), when the silicon nitride film is removed.

Profiles of implanted boron, arsenic and phosphorus, diffused to depths of 10jum, have been measured recently
[29] using the spreading resistance probe. The data confirmed diffusion calculations, and were in good agreement
with results of incremental sheet resistance measurements.

4. Application to Complete Transistor Profiles

An impressive summary of the capabilities of the spreading resistance probe as a tool for supplying doping
profile data for device modeling is the monitoring of a complete transistor profile. It demonstrates that the spreading
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resistance technique can measure different conductivity types, many orders of magnitude difference in doping
concentration, and shallow layers as well as considerable depth into the silicon slice. It also is a means of monitoring
junction depths, or profile parts in selected portions of the transistor, when their shifts as a function of continuing
time-temperature treatments are to be studied.

Figure 5 described the cross section of a silicon slice with the diffusion of an n-type buried layer up to the point
in time of deposition of an n-type epitaxial layer. The examples given in figures 10 through 13 depict and continue a
similar case history, namely an npn epitaxial test transistor with an experimental time-temperature sequence of the
diffusion processes. The major differences compared to figure 5 is that the remaining epitaxial layer is about 3 ^m
deep. Using a much finer depth scale than figure 5, figure 10 reproduces the concentration detail of the boron base
after completion of all temperature cycles except the emitter diffusion. The surface depletion due to boron
redistribution into the grown oxide is clearly visible. The same depth scale is used in figure 11 to measure the diffused
phosphorus emitter profile. The shoulder at intermediate concentrations is particularly prominent [27,28]. Figure 12
shows the very narrow boron region of the original base of figure 10 that remains after the emitter of figure 11 has
been predeposited and diffused. Figure 12 also emphasizes how close to pn junctions the spreading resistance probe is
able to measure.

Finally, figure 13 represents a composite of the measurements of the previous figures, resulting in a complete
transistor profile and illustrating the relative doping proportions. To avoid overcrowding only a few of the actual data
points have been plotted in figure 13. The connecting line has been added only for clarity and does not represent the
result of theoretical calculations. Cross sections like figure 13 are useful verifications of theoretical doping
distribution models, and they serve as inputs to device models concerned with the prediction of transistor
characteristics [3,30].

5. Conclusions and Recommendations

5.1. Capabilities of the Spreading Resistance Probe

for Modeling

This paper has pointed out the capabilities as well as the limitations of the spreading resistance probe for silicon
characterization needed for process and device modeling. The most significant capabilities include the doping
characterization of complete transistor profiles, covering the whole range from 10 to 10^ ' carriers/cm , the
measurement of layers from 0.2 Mm to greater than 20 /urn, and the determination of junctions between n-type and
p-type silicon. Consequently, the dopant distributions can be measured as a function of time and temperature
processing, and thus supply inputs, starting conditions, and verification of process and device models. Therefore, the
spreading resistance probe is an indispensable tool in support of epitaxy models, buried layer, base, and emitter
diffusion models, dopant deposition and redistribution models for both ion implantation and diffusion, and device
models as much as they are based on doping profile inputs. These capabilities are summarized in figure 14.

5.2. Limitations of the Spreading Resistance Probe

for Modeling

The limitations of the spreading resistance probe for its application to process and device modeling are the
possibly insufficient density of data points, and the restriction to electrically active dopants. The density
(number/depth) of the spreading resistance measurements is limited by the angle of the slice bevel (presently, smallest
angle routinely obtainable « 0.3 degrees), the probe tip diameter (presently, mechanical radius * 25 urn, electrical
radius « 1/im), and the minimum separation between tip placements (presently, no agreement on definition or
minimum). The limited measurement density is particularly aggravating when the doping profiles in extremely shallow
layers (< 0.2 Mm) or in very rapidly changing doping concentrations (> 3 orders of magnitude in 0.2 p.m) are to be
determined. High accuracy in these cases is required for some process models (e.g., doping profile shoulders [28]) and
device models (e.g., current gain hp^, injection efficiency, and cut-off frequency fj as a function of heavy doping of
the emitter-base profile [31 to 34]).
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 5.3. Recommendations for Improvements

More precise model predictions can be expected from improved inputs from the spreading resistance probe.
Consequently, efforts should be devoted to refine the angle-lap and surface-preparation techniques of the silicon
sample, to decrease the effective electrical tip diameter of the probe, and to minimize the distance between tip
placings for reproducible measurements. The multilayer correction factors should be extended to represent the
experimental situation of numerous micro-contacts forming the actual electrical tip geometry, and to accommodate
wider scattering of the data points.

5.4. Recommendations for Supplementary Techniques

In addition to improvements of the spreading resistance technique, it is recommended that the spreading
resistance probe be supplemented by the results of other and independent silicon profiling techniques. Most of these
techniques are compared to the spreading resistance probe in another paper at this symposium [20]. Figure 14 lists
three of these methods: incremental sheet resistance, incremental MOS capacitance/voltage, and Schottky contact.

The incremental sheet resistance technique for determining concentration profiles has been used extensively
during the past several years [35], especially for the identification of control problems in the manufacture of shallow
devices (< 1 //m). The method consists of measuring the sheet resistance after removing thin (« 200 A) layers of
silicon by anodic oxidation and stripping in HF. From the resistivity profile, a concentration profile is obtained by
using suitable conversion data, such as that of In/in [36]. The technique is suited for relatively high doping
concentrations (> 10l8/cm^).

The incremental MOS C-V technique [37] is best suited for low doping concentrations (< 10'°/cm^) and very
shallow devices. Thin layers of silicon are removed by the growth of an anodic oxide. MOS C-V measurements are
made after each oxidation. The oxide is then removed, a new oxide is grown and another MOS C-V measurement is
made. The process is repeated a number of times. For each MOS C-V curve the maximum width of the space charge
layer, Wm, is determined. An experimental plot is made of Wm versus Xs/ the total thickness of silicon removed. The
impurity profile is found by calculating the curve W m (X s ) for a series of theoretical profiles. The profile whose
W m (X s ) curve matches the experimental curve is taken as the correct profile.

The Schottky contact C-V technique [20] is best suited for lightly doped silicon, since it is limited to the
breakdown voltage of the Schottky contact. The depth resolution of its application is thus a function of the doping
concentration of the sample. This technique supplements the spreading resistance probe mainly for epitaxial silicon;
in addition, the low-concentration diffusion tails can be measured after the more highly doped layers have been
removed by anodization.

The three techniques described above measure the electrically active part of the dopants. For some models it is
desirable to know the sum of the electrically active and neutral dopants. This information can be supplied by
techniques such as the ion microprobe, nuclear activation analysis, and optical methods [20]. More detail about these
techniques can be found in the literature [1].

Experience has shown that the best way of acquiring the materials characterization needed for precise process
and device models is a combination of the spreading resistance probe and the incremental sheet resistance or the ion
microprobe techniques. This combination of methods is capable of generating reproducible, precise, and sufficient
data for the analytical models. In this context, it can be stated with confidence that the spreading resistance
technique will not only retain its place as an indispensable tool to acquire input and verification data for
semiconductor process and device models, but will increase its importance and flexibility, as experimental (bevel,
sample surface, probe tip) and analytical (multilayer analysis) methods are improved and standardized.

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 6. Acknowledgements

The author would like to thank Dr. F. W. Voltmer and Mr. R. Byrd for providing the spreading resistance
measurements, and Mr. G. A. Lee for supplying the multilayer analysis. The author is also indebted to Drs. P. L. Shah
and J. L. Prince for numerous discussions of doping distribution models.

7. References

[ 1 ] Schroen, W. H., The impact of process control on parameter processing, J. Electrochem. Soc., 121, 563-571 (1974).
stability — A review. Semiconductor Silicon 1973, ed. by
H. R. Huff and R. R. Burgess (Electrochem. Soc., Princeton, [15] Grove, A. S., Physics and Technology of Semiconductor
N.J., 1973), pp. 738-758. Devices (Wiley, New York, 1967) pp. 43-83.

[2] Jenkins, F. S.f Lane, E. R., Lattin, W. W., and Richardson, W. [16] DeVries, D. B., Lee, G. A., and Watelski, S., Integrated-circuit
S., MOS-Device modeling for computer implementation, process control and development, Techn. Report
IEEE Trans. Circ. Theory, CT-20, 649-658 (1973). AFAL-TR-73-268 (1973).

[3] Edwards, J. R. and Marr, G., Depletion-mode IGFET made [17] Hu, S. M., Calculation of spreading resistance correction
by deep ion implantation, IEEE Trans. Electron Devices, factors, Sol id-State El., 15, 809-817 (1972).
ED-20, 283-289 (1973).
[18] Lee, G. A., Rapid multilayer correction factors, ASTM/NBS
[4] Sigmon, T. W. and Swanson, R., MOS threshold shifting by Symp. on Spread. Resist. Meas., Gaithersburg, Md., June
ion implantation. Sol id-State El., 16, 1217-1232 (1973). 1974.

[5] Hachtel, G. D., Joy, R. C., and Cooley, J. W., A new efficient [19] Hu, S. M., Redistribution of diffused layers during epitaxy
one-dimensional analysis program for junction device and other process steps, J. Appl. Phys., 39, 3844-3849
modeling, Proc. IEEE, 60, 86-98 (1972). (1968).

[6] Kleppinger, D. D. and Lindholm, F. A., Impurity [20] Lee, G. A., Schroen, W. H., and Voltmer, F, W., Comparison
concentration dependent density of states and resulting of the spreading resistance probe with other silicon
Fermi level for silicon, Solid-State El., 14,407-416 (1971). characterization techniques, ASTM/NBS Symp. on Spread.
Resist. Meas., Gaithersburg, Md., June 1974.
[7] Poon, H. C., Modeling of bipolar transistor using integral
charge-control model with application to third-order [21] Prince, J. L. andSchwettmann, F. N., Diffusion of boron
distortion studies, IEEE Trans. Electron Devices, ED-19, from ion implanted sources and oxidizing conditions,
719-731 (1972). J. Electrochem. Soc., 121, 705-710 (1974).

[8] Whittier, R. J. and Tremere, D. A., Current gain and cutoff [22] Linhard, J., Scharff, M., and Schiott, H. E. Kgl. Danske
frequency falloff at high currents, IEEE Trans. Electron Videnskap Selskab, Mat.-Fys. Model, 33 14 (1963).
Devices, ED-16, 39-57 (1969).
[23] Hu, S. M. and Schmidt, S., Interactions in sequential
[9] Van Overstraeten, R., and Nuyts, W., Comparison of diffusion processes in semiconductors, J. Appl. Phys, 39,
theoretical and experimental values of the capacitance of 4272-4283 (1968).
diffused junctions, J. Appl. Phys., 43, 4040-4050 (1972).
[24] Fair, R. B. and Weber, G. R., Effect of complex formation on
[10] Morris, B., Some device applications of spreading resistance diffusion of arsenic in silicon, J. Appl. Phys., 44 273-279
measurements on epitaxial silicon, J. Electrochem. Soc., 121, (1973).
422-426(1974).
[25] Shah, P. L., to be published.
[11] Kahng, D., Thomas, C. O., and Manz, R. C., Epitaxial silicon
junctions, J. Electrochem. Soc., 110, 394-400 (1963). [26] Tsai, J. G., Shallow phosphorus diffusion profiles in silicon,
Proc. IEEE, 57, 1499-1506 (1969).
[12] Grossman, J. J., A kinetic theory for autodoping for vapor
phase epitaxial growth of germanium, J. Electrochem. Soc., [27] Schwettmann, F. N. and Kendall, D. L., Carrier profile
110,1065-1068(1963). change for phosphorus-diffused layers on low-temperature
heat treatment, Appl. Phys. Letters, 19, 218-220 (1971).
[13] Grove, A. S., Roder, A., and Sah, T. C., Impurity distribution
in epitaxial growth, J. Appl. Phys., 36, 802-810 (1965). [28] Schwettmann, F. N. and Kendall, D. L., On the nature of the
kink in the carrier profile for phosphorus diffused layers in
[14] Langer, P. H. and Goldstein, J. I., Impurity redistribution silicon, Appl. Phys. Letters, 21, 2-4 (1972).
during silicon epitaxial growth and semiconductor device
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243
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[29] Douglas, E. C. and Dingwall, A.G.F., Ion implantation for [34] DeMan, H. J., Mertens, R. P., and Van Overstraeten, R. J.,
threshold control in COSMOS circuits, IEEE Trans, on El. Influence of heavy doping effects on the f-j- prediction of
Dev., ED-21, 324-331 (1974). transistors, Electronic Letters, 10, (May 1974).

[30] DeMan, H. J., and Mertens, R., SITCAP - A simulator of [35] Donovan, R. P. and Evans, R. A., Incremental sheet
bipolar transistors for computer-aided circuit analysis resistance technique for determining diffusion profiles.
programs, 1973 IEEE Internal. Solid-State Cirucits Conf., Silicon Device Processing, ed. by Ch. P. Marsden (NBS
Feb. 15,1973. Special Publ. 337, Washington, D.C., 1970), 123-131.

[31] Mertens, R. P., DeMan, H. J., and Van Overstraeten, R. J., [36] Irvin, J. C., Resistivity of bulk silicon and of diffused layers
Calculation of the emitter efficiency of bipolar transistors, in silicon. Bell System Tech. J., 41, 387-410 (1962).
IEEE Trans, on El. Dev., ED-20, 772-778 (1973).
[37] Kronquist, R. L., Soula, J. P., and Brilman, M. E., Diffusion
[32] Van Overstraeten, R. J., DeMan, H. J., and Mertens, R. P., profile measurements in the base of a microwave transistor,
Transport equations in heavy doped silicon, IEEE Trans, on Solid-State El., 16, 1159-1171 (1973).
El. Dev., ED-20, 290-298 (1973).

[33] Mock, M. S., Transport equations in heavily doped silicon,

and the current gain of a bipolar transistor, Solid-State El.,
16,1251-1259(1973).

PROCESS MODELING

EPITAXIAL SILICON
BURIED LAYER DIFFUSION
ION IMPLANTATION AND DIFFUSION

DEVICE MODEL ING

DIODE MODELS
INTRINSICTRANSISTOR
ACTUAL TRANSISTOR

Figure 1. Spreading Resistance Technique Applied to Modeling

Figure 2. Epitaxy on Substrate

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 Figure 4. N Buried Layer Diffusion:
Figure 3. N Buried Layer Diffusion
Spreading Resistance Data with Multilayer Analysis

Figure 5. Epitaxy-Buried Layer-Substrate

Figure 6. Ion-Implanted Boron: Comparison

of Experimental Data [21] with Gaussian Model

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 Figure 8. Diffused Phosphorus: Comparison
of Spreading Resistance and Incremental Sheet Resistance Data
Figure 7. Arsenic Diffusion: Model and Experimental Data

Figure 9. Ion-Implanted Phosphorus:

Comparison of Spreading Resistance
and Incremental Sheet Resistance Data

Figure 10. Concentration in

Base Layer After All Temperature
Cycles Except Emitter Diffusion

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 Figure 11. Emitter Profile,
Without Base-

Figure 12. Base Profile

After Emitter Diffusion

Figure 13. Complete Profile

of Test Structure

Figure 14. Spreading Resistance Technique Applied to Modeling

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 This page intentionally left blank

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NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 400-10, Spreading Resistance Symposium,
Proceedings of a Symposium Held at NBS, Gaithersburg, Md., June 13-14, 1974.

Improved Surface Preparation

For Spreading Resistance Measurements
on p-type Silicon

J. R. Ehrstein

Institute for Applied Technology

National Bureau of Standards
Washington, D.C. 20234

The interpretation and the precision of spreading resistance

measurements have been seen to be strongly dependent on specimen
surface preparation. A bakeout at 150°C for 15 min. following
specimen surface preparation with any aqueous polishing solution
is considered here. It is shown both to improve the precision of
the basic calibration curve for spreading resistance measurements
and to significantly improve the correlation between resistivity
values derived from spreading resistance measurements on a variety
of specimens, and resistivity values derived from other measurement
techniques. No bakeout appears to be necessary if specimen surface
preparation is done with a non-aqueous polishing process.

Key words: Bevel polishing; p-type silicon; resistivity depth profiling;

resistivity radial profiling; semiconductors; spreading
resistance measurements; surface effects; surface preparation.

1. Introduction

Spreading resistance measurements, despite their high degree of spatial resolution

and versatility for measuring the dopant profile in multilayer semiconductor device
structures, are nevertheless subject to reduced sensitivity and even to misinterpretation
if the conditions of measurement are not properly defined and controlled. A recent change
in the surface preparation of silicon specimens prior to measurement was necessitated by
observation of apparent changes in the dopant density on the bevel polished surfaces of
bulk p-type specimens. The change in surface preparation, the addition of a thermal cycle,
or bakeout, 150°C for 15 min. was subsequently found to significantly improve measurement
results of three different types. The three measurement areas were 1) the construction of
a calibration curve from spreading resistance to resistivity for p-type silicon specimens,
2) radial resistivity profiling of silicon slices being inspected for use as four-probe
resistivity standards, 3) depth profiling of bevel polished specimens.

2. Observation of a Surface Effect

The existence of a surface related problem in spreading resistance measurements was

primarily noted as a result of an attempt to study redistribution of dopant atoms in
silicon resulting from thermal oxidation. For this study, because of the smallness of
the expected effect, it was necessary to run instrument electronics at nearly maximum gain:
full scale covered only 2 decades of measured spreading resistance as opposed to the
7 decadfe full scale normally used for profiling of device structures by spreading resistance,
All wafers in this study were approximately 10 fi-cm boron-doped silicon wafers which had
been sectioned by polishing with a silica gel polish at a small bevel angle with respect

249
to the top surface. The bevel sectioning was done to allow profiling of dopant distribution
in depth below the surface, as shown in figure 1. An apparent redistribution of dopant,
seen in the form of increased spreading resistance values, and hence of increased resistivity,
was observed both for wafers which had undergone thermal oxidation and for control wafers
which were merely polished wafers from the same starting batch. The effect was such that
even on the nonoxidized wafers the measured spreading resistance was higher on the freshly
polished beveled surface than on the original top surface by a factor greater than two.

It is to be noted that the nature of the bevel polishing procedure is such as to

remove material only from a section of the silicon chip at a small angle with respect to
the top surface. The rest of this original top surface, although it may be in contact
with the polishing solution, is not held under any load against the polishing plate, and
hence is protected from the effects of the polishing solution by the natural surface oxjde
of the silicon which remains intact. This surface oxide, generally of the order of 50 A
thickness is readily penetrated by the spreading resistance probes. If the bevel polishing
process were completely passive and simply removed silicon layers without leaving electri-
cally active residue or changing the nature the surface states of the silicon, it is
expected that the bevel polished and the top surfaces of the nonthermally oxidized chip
would have shown differences in spreading resistance of 10% or less. This small change
might be expected because of possible changes in contact shape from a slightly different
angle of the spreading resistance probe against the silicon surface, small possible changes
of resistivity in depth due to the original crystal growth, and possibly a very small
effect due to the native oxide on the original top surface.

3. Experimental Results

3.1 Early Surface Treatments

Since the shift in spreading resistance observed in probing across the bevel vertex
was much larger than expected as a result of all the component causes that had been
considered, it was judged that the polishing process used for beveling was not in fact
passive, but changed the electrical nature of the silicon surface. Subsequent similar
specimens, without thermal oxide, were bevel polished by the same polishing process and
were then variously bathed and swabbed in solutions of hydrofluoric acid, chromic acid,
ammonium hydroxide and ammonium hydroxide with hydrogen peroxide. Each of these chemical
treatments effected a change of the spreading resistance value of the bevel polished
surface from the value measured on the polished only surface, and all but the hydrofluoric
acid treatment left unaffected the spreading resistance value on the original top surfaces
of the chips which had been protected by the native oxide. However, in no case did one
of these chemical treatments bring reasonable agreement between the spreading resistance
value on the beveled surface and that on the original top surface. In fact, most of these
subsequent surface treatments caused increased measurement scatter as compared with the
polished only surfaces. Thermal cycling at 70 to 100°C under partial vacuum for 15 minutes,
subsequent to polishing also failed to change the measurement disparity between these two
exposed surfaces.

Comparison of these observations with those of members of various other laboratories

led to a recommendation1 for a bakeout at a minimum 150°C for 15 or more minutes subsequent
to polishing.

3.2 Bakeout of Bevel Polished Specimens

The recommended bakeout procedure was implemented on a series of bevel polished boron
doped silicon chips, each having nominal resistivity value of 10 fi«cm and having only an
ambient oxide layer prior to polishing. The effect of the bakeout procedure is shown in
figure 2 for chem-mechanical polishing using two different commercially available silica

^r. A. Mayer, RCA Laboratories (private communication)

250
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polishing compounds, both in strongly basic aqueous solutions, and the first of which was
the polishing compound used when the original surface preparation problem was noted during
the study of dopant redistribution. In both cases, the bevel polishing was done against
a sheet of methyl methacrylate. The specimens here were sections of a silicon wafer
actually measured at 11 fi-cm by the four-probe method (1)* and taken from a lot of wafers
for which capacitance-voltage measurements (2) and use of Irvin's curves (3) yielded
values of 10 to 12 ft-cm. The resistivity scales shown in figures 2 to 5 are derived from
a calibration curve which was generated from the spreading resistance values near the center
of silicon specimens whose resistivity values were carefully measured by the four-probe
method and which show a high degree of uniformity of radial resistivity. Spreading
resistance data for all parts of this work were taken at the same 2 decade/full scale gain-
setting at which the surface preparation problem was originally observed.

It should be noted that there is a shift in apparent resistivity across the bevel
vertex from the bevel polished to the original top surface of both unbaked chips. It should
also be noted that reasonable agreement with the four-probe and C-V values of resistivity is
not obtained on the freshly bevel polished surface, without the addition of the bakeout
cycle. This bakeout, however, succeeds in producing resistivity values from spreading
resistance which are within 10% of those from both other methods. A limit of about 5% on
the resolution of all data is imposed by the analog form in which data were acquired.

In order to investigate whether this shift in spreading resistance was a particular

result of silica polishing, further wafer sections were taken and were bevel polished
with a zirconium compound in an alkaline solution and with an alumina slurry in water,
the latter having a strictly mechanical polishing action. The results are shown in figure 3.
Because of the relatively large particle size in both these solutions it was not possible
to obtain a sharp bevel vertex. Consequently, polishing actually occurred for a small
distance onto the original top surface of the wafer section, which would normally go untouched.
This results in an increased value for spreading resistance for a distance on both sides of
the bevel vertex as seen in the figure. Again, the point to be noted is that freshly
polished surfaces yield spreading resistance, and their corresponding resistivity values
which are in marked disagreement with those obtained from the four-probe and C-V methods
whereas values obtained on specimens which have undergone the recommended bakeout are
in good agreement.

The cases of an etched surface and a surface mechanically polished in the only
non-aqueous based solution considered here are both shown in figure 4. Again, effects due
to the surface preparation are shown on both sides of the rounded bevel vertex because of
the inability to maintain sharp vertices with these processes. A. shift in measured spread-
ing resistance due to etching is seen which is also removed by thermal cycling. No measurable
shift is seen for the case of non-aqueous surface preparation. The exact mechanism is
unknown but the observations are in good agreement with the observations of Mayer and
Schwartzmann regarding the effects of aqueous preparations (4).

Two other specimen configurations were also tested for the presence of such an effect.
The first, a piece of p-type bulk silicon from the same batch used for previous measurements,
had a thermal oxide grown on the top surface before sectioning and bevel polishing. The
shape of the spreading resistance data (fig. 5) is of course influenced by the presence of
the oxide; however, again, agreement with four-probe resistivity values can only be obtained
by the addition of the bakeout subsequent to polishing. The second specimen configuration
was a chip with p epitaxy on a p+ substrate. The value of the epitaxial resistivity using
MOS C-V (5) measurements and Irvin's curves (3) was 12 fi«cm. This particular epitaxial
configuration was chosen siuce the effect of the high conductivity substrate, for data near
the epi-substrate interface, is in the opposite direction from that previously experienced
from the polishing process. Again, an artificial increase of measured spreading resistance
is seen for the epitaxial layer until the specimen has been baked-out, at which time
resistivity values within 10% of that obtained from MOS C-V measurements were achieved.

1
Figures in brackets indicate references at the end of this paper.
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 3.3 Effect on the Calibration Curve

The second area in which the thermal cycling of specimens was found to be of great
benefit was in the construction of the calibration curve itself. As reported elsewhere (6)
early calibration data for p-type specimens showed scatter of 50 to 80% in spreading
resistance values for specimens closely grouped in terms.of four-probe resistivity values,
lesser scatter being noted for n-type specimens. The observed scatter in data for p-type
silicon was particularly evident in the resistivity range from 1 to 100 ft-cm. Data from
a calibration on chem-mechanically polished p-type specimens, which had previously been
screened for radial resistivity uniformity of 10% or better, by use of spreading resistance
are shown in figure 6. The specimens used were chem-mechanically polished in an aqueous
solution against an artificial leather backing.

At first the data scatter seen in this figure may be judged to be insignificant
considering the total span and overall linearity of the data. However, our experience
indicates such a judgement to be optimistic, at least for high resolution applications,
because shifts of measured spreading resistance values, of the type already shown, while
strongly linked to the aqueous polishing medium, also appear to be linked to other
parameters of polishing such as composition of polishing substrate and rate of material
removal. This can be seen in figure 7 where the scatter of the data from figure 6 is
expanded by use of a reduced ordinate scale: ratio of measured spreading resistance to
four-probe resistivity; (also shown are data taken on the same specimens which had received
the bakeout after a fresh chem-mechanical polishing using a silica gel solution). It is to
be noted that there are both increases and decreases in measured spreading resistance,
rather random as a function of resistivity, resulting from the bakeout. This is particularly
to be noted for the three specimens with resistivity in the vicinity of 10 ft*cm where two of
the specimens show an increased spreading resistance after thermal treatment. This is
opposed to the strong decrease upon thermal treatment which was seen for all bevel polished
specimens, as discussed previously, which were chem-mechanically polished in the same
solution but using different loading and a different polishing substrate from the calibra-
tion specimens.

It is expected as a result of this variability in response to polishing without

subsequent bakeout, that a given specimen may not maintain a specific high or low bias
with respect to the line of regression. Therefore, for any highly accurate analysis where
the local calibration over a small range of resistivity values becomes important, large
scatter in the data about the local regression, particularly if not reproducible point
by point, may make interpretation of data erroneous. By contrast, it can be seen from
figure 7 that bakeout of the same calibration specimens after a fresh polishing results
in highly improved distribution of data about the line of regression.

3.4 Effect on Radial Resistivity Profiling

A third area of improved results due to the bakeout procedure lies in the area of
radial resistivity profiling. During the original examination of incoming material for
possible use as resistivity standards, now issued by NBS2 uniformity of radial resistivity
was a key acceptance parameter. It was a rather common experience, however, to find that
a slice from a crystal, particularly at the 10 ft«cm level, would yield resistivity profiles
radially uniform to within 5% by both four-probe measurements and combined photovoltage/
photocurrent measurements (7), while spreading resistance radial profiles showed as much
as 100% variation on the same diameter of the slice. Figure 8 shows a typical slice
profiled by spreading resistance both with and without a 150°C bakeout after polishing. The
sets of probe tracks were approximately along a diameter but were displaced laterally by
about 200 ym from each other. The measure of radial variation in the case of the baked-out
wafer is in quite good agreement with measurements on the same slice by both the four-probe
and photovoltage techniques.

Z
SRM 1520, Silicon Resistivity Standards; Office of Standard Reference Materials,
NBS, Washington, D.C. 20234
252

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 4. Summary

Although the mechanism for the surface effect is not understood, its inherent
association with aqueous based surface treatment is strongly indicated. Such effects may
be minimized by other variations in the polishing process such as loading, rate of
surface feed during polishing, or the nature of the polishing substrate, but bakeout
after polishing has been shown to remove such surface effects almost in their entirety.
It must be noted that the strength of the effect may well be related to conductivity
type and resistivity level; hence isolated experiments on a limited number of specimens
may be inadequate to characterize a particular polishing process for the full spectrum of
specimen types which may eventually be considered.

This research was supported by the Advanced Research Projects Agency of the
Department of Defense under ARPA Order No. 2397.

5. References

1. Standard Method for Measuring Resistivity of Silicon Slices with a Collinear Four-Probe
Array, ASTM Designation F-84, 1973 Annual Book of Standards, part 8, American Society
for Testing and Materials, November 1973.

2. Mattis, R. L., and Buehler, M. G., Semiconductor Measurement Technology: A Basic

Program for Calculating Dopant Density Profiles from Capacitance-Voltage Data,
NBS Special Publication 400-11 (in preparation).

3. Irvin, J. C., Bell System Tech. Journal 4d, No. 2, 387-410 (1962).

4. Mayer, A., and Schwartzman, S., this volume, pp. 123-137.

5. Lehovic, K., Solid State Electronics 11, 135-7, (1968).

6. Bullis, W. M., ed., Methods of Measurement for Semiconductor Materials, Process

Control, and Devices, Quarterly Report; April to June 1973; NBS Technical Note 806
(November 1973), pp. 9,10.

7. Blackburn, D. L., Schafft, H. A., and Swartzendruber, L. J., Journal of the

Electrochemical Society 119, No. 12, 1773-78 (1972).

253
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 Figure 2. Spreading resistance of nominal 10 ft-cm
Figure 1. Bevel polished chip being probed p-type beveled specimen for various polishes.
A. Silica gel solution
parallel to bevel vertex for depth profile.
B. Silica gel solution, followed by bakeout
C. Silica powder in potassium hydroxide solution
D. Silica powder in potassium hydroxide solution, followed by bakeout
Pointer arrow indicates position of bevel vertex

Figure 4. Spreading resistance of nominal 10 ft-cm

Figure 3. Spreading resistance of nominal 10 Q-cm p-type beveled specimen for various surface treatments.
p-type beveled specimen for various polishes.
A. CP, etched
A. Zirconium oxide solution
B. CP, etched, followed by bakeout
B. Zirconium oxide, followed by bakeout
C. Polished with alumina in glycerin and trichloroethylene
C. 0.3
Copyright ym alumina
by ASTM in water
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D. 0.3 ym alumina
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Pointer arrow indicates position of bevel vertex
Pointer
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Figure 5. Spreading resistance of other silicon specimens.
A. Thermally oxidized 10 fi-cm p-type, silica gel polished
B. Same specimen after bakeout Figure 6. Calibration curve .of spreading resistance
vs. four probe resistivity for silica gel polished
C. Nominal 10 fi-cm p epitaxy over p+ substrate, silica gel polished p-type specimens, no bakeout.
D. Same specimen after bakeout

Figure 8. Radial resistivity profile of a 10 fi-c

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Figure 7. Ratio of spreading resistance to four probe resistivity A. Silica gel polish only
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 DISCUSSION SESSIONS

The material In this section was taken from tape recordings of discussion periods which
were held at the conclusion of the Theory, Practice and Application Sessions with all the
speakers in the session forming a panel to respond to questions and comments. Such questions
as were asked directly after individual contributed papers, and their answers, are presented
in the appropriate discussion section. Since a list of all participants and their affiliations
is given at the outset, the respondents are inentified only by name in the discussions. Each
respondent was given the opportunity to review his comments prior to publication. Such changes
as were made were primarily grammatical or for clarification of intent. The content is substan-
tially unchanged. Editor's notes are also given where it is thought to benefit the discussion.

DISCUSSION SESSION PARTICIPANTS

R. P. Anand Carl A. Germane

Bell Telephone Laboratory Motorola Semiconductor Products Division
2525 North llth Street Box 241 P. 0. Box 2953, Mail Drop A-162
Reading, Pennsylvania 19604 Phoenix, Arizona 85036

Jacques Assour Gilbert A. Gruber

RCA SSD Solid State Measurements, Inc.
Somerville, New Jersey 08876 600 Seco Road
Monroeville, Pennsylvania 15146
Douglas A. Earth
Westinghouse Electric Corporation Norman Goldsmith
Defense and Electronics System Center RCA Corp. Labs
P. 0. Box 1521 MS 3525 Route 1
Baltimore, Maryland 21203 Princeton, New Jersey 08540

Dr. K. E. Benson Hans Mork Janus

Bell Telephone Laboratories Topsil A/S
555 Union Boulevard Lindervpvej, Frederikssund
Allentown, Pennsylvania 18103 Denmark DK-3600

David H. Dickey J. Korvemaker

Bell & Howell Bell Northern Research
Pasadena, California 91107 Department 8R81 - P. 0. Box 3511 Station C
Ottawa, Ontario, Canada KIY4H7
John R. Edwards
Bell Telephone Laboratories Dr. J. Krausse
555 Union Boulevard Siemens AG, LLBBGE1
Allentown, Pennsylvania 18103 Munich, Frankfurter Ring 152, F. R. Germany

J. R. Ehrstein Dr. Paul H. Langer

National Bureau of Standards Bell Telephone Laboratories
Washington, D. C. 20234 555 Union Boulevard
Allentown, Pennsylvania 18103
Stephen J. Fonash
Pennsylvania State University Alfred Mayer
231 B. Sackett Building RCA - Solid State
University Park, Pennsylvania 16802 Route 202
Somerville, New Jersey 08816
E. E. Gardner
IBM - SPD Robert G. Mazur
P. 0. Box A G37/B966 Solid State Measurements, Inc.
Essex Junction, Vermont 05452 600 Seco Road
Monroeville, Pennsylvania 15146
257
Bernard L. Morris Robert I. Scace
Bell Telephone Laboratories General Electric
555 Union Boulevard Electronics Park, EP7 Box 41
Allentown, Pennsylvania 18103 Syracuse, New York 13201

Dr. Helmuth Murrmann Dr. P. J. Severin

Siemens AG. WH MB EA 511 Philips Research Laboratories
Balanst. 73 Eindhover - Holland
Muenchen 80 West Germany
Stanley Shwartzman
Steve Mylroie RCA Solid State Division
Signetics Corporation Route #202
811 East Arques 9132 Somerville, New Jersey 08876
Sunnyvale, California 94986
Fritz G. Vieweg-Gutberlet
Pierre Pinchon Wacker-Chemitronic GMBH
RTC La Radiotechnique Complec P. 0. Box 1140
Code postale: boite postale 6025 - Burghausen, West Germany D-8263
14001 - CAEN CEDEX (FRANCE) 14001
Fred W. Voltmer
Michael Poponiak Texas Instruments, Inc.
IBM - East Fishkill P. 0. Box 5936 MS 144
Department 214, Building 300-94 Dallas, Texas 75222
Hopewell Junction, New York 12.533
James C. White, Jr.
Simon Prussin Western Electric
TRW Semiconductors 555 Union Boulevard
14520 Aviation Boulevard Allentown, Pennsylvania 18103
Los Angeles, California 90260
Don E. Williams
A. J. Robinson Bell Telephone Laboratories
IBM Reading, Pennsylvania 19604
9500 Godwin Drive
Manassas, Virginia 22110 Douglas Yoder
Delco Electronics, CMC
Dr. Walter H. Schroen P. 0. Box 1104, Plant 10, Room 328
Texas Instruments, Inc. Kokomo, Indiana 46068
P. 0. Box 5012, MS/72
Dallas, Texas 75222

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 1, THEORY SESSION
F. MAYER; I think the only speaker who addressed himself on theoretical grounds to the
difference between what should be observed on (111) versus (100) material is Steve Fonash.
I am interested to know what the other members of the panel expect from theoretical con-
siderations of an orientation dependence.

W. SCHROEN: The multilayer analysis is independent of crystalline orientation. It

considers only potential theory. However, I do not exclude that there could well be
influences of the crystalline orientation and a complete theory would include crystalline
orientation, stress effects, specific contact resistance, and other effects mentioned this
morning. The pure potential theory neglects all these.
R. MAZUR; I do not want to leave the question hanging with some of you who are not so
familiar with the question of crystallographic orientation but I have gone on record in the
past as indicating that I have never seen a significant orientation dependence. Now I get
disagreement there from all of IBM combined with all of Bell Labs and a few other places to
boot. I may have to retract on this statement in the future; that is possible. I have not
had the time to do extensive research with different orientation samples. Bernie Morris
did supply me with a couple of wafers about six months ago and I have not had a chance to
run them yet believe it or not. But the orientation dependence may, in many practical
cases, be so small as to be unobservable from a practical point of view. I see it as a
case of the jury still being out.
F. VIEWEG-GUTBERLET; We have had the same experience showing orientation dependence as
Bernie Morris, and this is based on over 100 measurements. We got the same curves as shown
this morning by Morris. We feel there is a dependence on orientation.
M. POPONIAK; In the last paper today [P-8], I will present some data showing the influence
of probe loading on the orientation or I should say the orientation effect due the probe
loading. We do see a difference and it is a function of probe loading. The lighter the
loading the more sensitive it is to the orientation effect.
F. VIEWEG-GUTBERLET: Does that mean that with constant probe loading you will get another
effect of impressions depending on the crystal orientation, i.e., if you set your probe
loading with respect to crystal orientation, you should not get a difference for (111) or
(100) material.

M. POPONIAK; What I am saying is that due to the atomic structure between (111) and (100)
and their mechanical properties, there is a critical level of stress from which we get
excessive fracturing, and that seems to be the problem.

K. BENSON: Steve Fonash this morning gave some numbers, about a factor of 10 I think for
p-type (100) versus (111) and I would like to hear from anybody here that has made a
calibration curve, does this number of a factor of 10 seem realistic?
S. FQNASH; I forgot to mention [T-l] the fact that the zero bias resistance also in the
contacts will depend on stress and I have a reference in my paper on that: Kramer and
van Reuyven did some experimental work on this and showed that the zero bias resistance of
the contacts does depend on stress also. I think this is rather well known but that is one
particular reference. There is another paper in which I made some comments on this which
appeared in Journal of Applied Physics in January of 1974. This effect also depends on
crystallographic orientation so you have an interplay of those two effects both of which
depend on crystallographic orientation. So regarding the factor of 10 which was brought
up first there is this interplay of two effects which may change the factor of 10. Sec-
ondly, it is based on data that were determined at lower stress levels and I do not think
the silicon is behaving elastically underneath these contacts and so I question the use of
that data. I am just trying to show the existence of an effect which I think we better
take a look at it.

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H. MURRMANN: We will present [P-5] in the afternoon experimental data showing a difference
between 100 and 111 material. We tried to split the data into mechanical phenomena including
the contact radius and other physical phenomena. I would like to reintroduce a p dependent
correction factor that Bob Mazur dropped some hours ago, [1-3] because I feel there is real
physical reason for it.
R. MAZUR; I would like to make a comment here, Dr. Murraann. I mentioned this to Bernie
Morris at the coffee break. I regret mentioning the K(p) factor in the way I did because
it was misleading. We did not really drop the physical model involved in that K(p)
function. I was referring to the fact that we had worked out a way to avoid using cumbersome
mathematics in making the corrections that get involved in having to plot an extra function:
K(p). You can treat it through the calibration data but the physical situation is still
the same and I would agree with you on that.
J. KORVEMAKER: I would like to know if any of you have any results on other materials than
silicon which has been discussed all morning.

R. MAZUR; There is data of course in the literature. I began making measurements on

germanium. There is also data in the literature on germanium from T. L. Chu. Not in the
scientific literature, but in Solid State Technology; that is a testimonial to the lack of
clout of spreading resistance measurements several years ago. Ting Chu was unable to get it
accepted by the prestigious journals, but it is good data and it is available in Solid
State Technology of several years ago, We at Westinghouse,years ago,did make spreading
resistance measurements on silicon carbide. There is a real question about spreading re-
sistance measurements on gallium arsenide. There are ways to do it; whether it is easy or
not may depend on a lot of things that would involve more discussion. That is about the
size of what I know about it.

K. BENSON; There is also Witt and Gatos' paper looking at inhomogeneities in indium anti-
monide crystals. I believe spreading resistance was quite easy to use because this mate-
rial was low resistivity.
B. MORRIS; I would say that probably in general as the band gap gets larger the measure-
ment is going to become more difficult as in the case of gallium arsenide where you have a
problem with four point probe measurements. From what I can see there should not be an
appreciable problem on materials whose band gaps are similar to silicon or perhaps a
little greater. If you can make four point probe measurements you should be able to make
spreading resistance measurements.
P. LANGER; I would like to find out what the panel thinks is the lower limit in terms of
the thickness to probe radius ratio to which one can extend the correction factor calcu-
lations on opposite conductivity type structures.

B. MORRIS; As I mentioned [T-5] we use a minimum value of 0.1 for t/a. This is somewhat
arbitrary. I would not say that this minimum value of t/a is all that good. I do not
know of any really good independent methods of experimentally verifying it. These methods
would be the only ones I would believe. I would not tend to believe any calculations that
close to the junction. Unfortunately the differential sheet resistance measurement has a
lot of problems that close to the junction. I would be very interested in finding another
method which would work in this region. The ion microprobe of course will go right
through the junction but then you have first of all the chemical analysis technique and,
instead of the net carrier concentration, you would have to subtract, say, the boron from
the phosphorus profile and those readings as absolute numbers are not terribly good with the
values that you usually get near a p/n junction for most microprobe analysis.

R. MAZUR: Paul should clarify whether he is asking the question of how close you can come
to a junction with a good corrected value or whether he is asking the question of how thin
a layer you can get a good corrected value on? That is: measurement on a beveled surface,
or on top of a thin surface. They are not the same question and it sounds to me that he
asked one question and Bernie answered another. On the subject of this layer measurement,
Gil Gruber's paper which comes up tomorrow, I believe, will carry good evidence of quite
reasonable results on certain sub-fractional micron layers in the range of 3,000 angstroms.
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N. GOLDSMITH: I would like to add a comment to that. In my paper [A-7] on the last day of
the session I will show an experimental model which you can use to test correction factors
very close to an insulating boundary.

E. GARDNER: I heard the Schumann and Gardner paper mentioned quite often this morning so I
think I should stand up at least and say hello. When Paul and I wrote the paper about 8
years ago we recognized a number of limitations in the spreading resistance technique and
we tried to identify a number of them in our paper. I think many people today are recog-
nizing those same limitations and going beyond our work and that was originally part of the
intention of the work, to interest people in developing correction factors for the spreading
resistance operation. It seems to me there are still a number of problems that have not
really been identified and one is that we, in our analysis, did a finite layer type of
structure in which we assumed a finite number of layers whether it was 2 or 40 and if we had
been smarter we thought that there should be some way you could do this, not on finite, but
on a continuous basis. That is problem #1. The second problem is one that people have
alluded to and that is that you do not have a single contact but you have many contacts and
how do you develop correction factors for many contacts? The third problem which is related
to this, is, how can one explain the spatial resolution that you get whenever you assume
that you have a 5 micron contact but you really show curves in which your resolution is 500
angstroms, or as some I saw this past week in which they were getting 50 angstroms resolution.
So those are some of the problems I think that still remain with spreading resistance.

B. MORRIS: I have an answer to the last comment on how you can get the resolution that we
do get. This is, I believe, due to the fact that instead of having one big flat contact for
which one could very nicely calculate a correction factor from theory, we have a large
number of small contacts, each of whose diameter is perhaps 1/10 micron, as opposed to 4 or
5 microns for the "flat" radius. Since the theory predicts a depth resolution of the order
of magnitude of your radius, this allows us to get this very fine resolution in depth, while
the effective radius of four microns is still the value that you get from the calibration
as defined by values you measure for p and R. Thus, on one hand the micro-contacts add
together so you can make real measurements, and on the other hand, you are also fortunate
in that, for fine resolution, you may take an average value of the depth, a weighted average
is more likely, and while this cannot be calculated it lets us make some very fine resolution
measurements. I would say that from measurements with the Mazur probe using 45 gram loading
that the physical penetration of the damage is approximately 1/10 of a micron. I cannot
measure any better than that and perhaps this is an absolute limit as to how fine you can
make the measurement.

J. ASSOUR; I have seen this morning several spreading resistance profiles through thin
epitaxial layers and nobody said how these were produced in terms of surface polishing or
lapping. I was wondering since we are worrying about correction factors and accuracy, how
reproducible are the results in terms of surface finishing?

W. SCHROEN; You will hear data this afternoon [P-6] on this very question of how to pre-
pare the sample surface and the probe tip, how reproducible the data are, and what we need
to do to get those very shallow bevels.

P. SEVERIN: May I comment on this question invoking the micro-contacts, which I talked about
in the Silicon Device Processing Symposium1 in 1970. With our steel probe the micro-
contact contribution, p/4na (where n is the number of contacts which act in parallel to
each other) acts in series with the term p/4A, where A is the total contact diameter. The
micro-contacts represent about 5 times as large a resistance in the series combination as
the large overall spreading resistance contact. In this case the resolving power of say
0.1 micron is easily explainable. That we have indeed these micro-contacts and that this
has nothing to do with contact resistance in the common physical sense is explained by the
fact that we find proportionality to p over 4 orders of magnitude which is a very unreal-
istic assumption for a contact resistance. Furthermore, micro-contacts are an extremely
interesting subject because there the mechanics and physics enter. Although the term micro-
cracking has been.used today several times, direct evidence has been given in Russian
literature2' 3' * that silicon behaves plastically at room temperature in a very shallow
top layer. The thickness of this top layer increases with the applied load. Indirect
evidence has been given earlier in various experiments of a different nature,5,6,7, .
I think that it is a pity that there are no people in this audience who have more experience
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on micromechanical properties. On a submicron scale you cannot just talk about the elastic
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 constant or hardness of silicon.
Ed. Note: In review of his comments, P. Severin supplied the following references.
T.Silicon Device Processing, NBS Spec. Pub. 337 (1970) 224.
2. V.P.Alekhin, O.V. Gusev, et al.-Sov. Phys. Dokl. 14, 894 (1970).
3. V.P. Alekhin, O.V. Gusov, et al. -Sov. Phys. Dokl. 14, 917 (1970).
4. V.J. Nitenko, M.M. Myshlyaev and V.G. Eremenko- Sov. Phys. Sol. St. 9_, 2047 (1968).
5. G.R. Booker and R. Stickler-Phil. Mag. 81, 859 (1963).
6. T.R. Wilshaw- J.Phys. D. 4_, 1567 (1971).
7. M. Renninger- J. Appl. Cryst. 5_, 163 (1972).
8. W. Ridner and J. Braun- J. Appl. Phys. 34, 1958 (1963).

R. MAZUR; I would like to answer - this is also to that last question. We cannot leave it
said that way. I mean that I cannot just sit here and leave it in the record that Mazur
did not say anything. Regarding the third part of Ed Gardner's comment I need to point out,
of course, to be consistent, that the very high spatial resolution can be explained in many
cases again because of the work function potential barrier which has a very, very shallow
penetration. It is restricted to the immediate surface material. The second part of the
question is that using what I call a conditioned probe, which you will remember I defined
as one which although made up of multi-contacts, will act as a single contact if you get the
little contacts close enough together and distribute them properly. I would refer anybody
to a paper by Greenwood (Brit. J. A. P., 1966) which lays this out in great detail. I have
pointed out in the past to many people that I think that when the questions come up about
spreading resistance resolution, people are often talking about spreading resistance mea-
surements with what I consider unconditioned contacts. If you damage the probes, you will
go on and get profiles and you will make measurements and you can even write papers but I
do not know that it is going to get anyone anywhere. So you have to be careful about
whether the original work and data that went into it was valid or not.

J. KORVEMAKER; I would like to ask Dr. Severin a question. In regard to the plastic be-
havior, is it similar to the behavior of glasses?

P. SEVERIN: We are talking about monocrystalline structures which are something quite
different from a glassy structure. I have given the reference of about 2 years ago about
this microplasticity at room temperature of silicon.
D. WILLIAMS; The question that keeps bothering me is that we have talked about accuracy say,
comparing spreading resistance to capacitance voltage, but I think in the latest report as
published by NBS1 they also say they have difficulty getting correlation between resistiv-
ities that are very close together and spreading resistance. If this is true, since you
have calibrated on a set of samples, what are you correcting when you get your profile.
Granted a profile may look very consistent but how valid is the calibration back to resis-
tivity?
1
Ed. Note: W. M. Bullis, Methods of Measurement for Semiconductor Materials, Process Con-
trol, and Devices, Quarterly Report; April to June 1973; NBS Technical Note 806 (November
1973), pp. 9, 10.
R. MAZUR: This is a point that should be kept in mind; i.e. that fussing with 2 or 3 or
even 5% on the thickness corrections and the other corrections may be senseless if the basic
calibration data limits you to ±10 or 15% accuracy. So you have to be practical. It is
quite possible still, even at this late date, to get hung up on the micromechanics of that
contact and fail to keep your eye on the main thing which is control of silicon processing,
if it has to be 100% empirical then that is the way it is going to have to be.

2, PRACTICE
N. GOLDSMITH; Jim White, I noticed in your program you require the orerator to input the thick-
ness. Don't you derive any thickness measurements from the spreading resistance data itself?

J. WHITE: Well, we use the test set for two functions; when making surface measurements,
of course, we cannot derive any thickness measurements. For depth dependent measurements
we could determine the thickness from the spreading resistance data but we do not use that
as an Copyright
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N. GOLDSMITH: That was my point.

F. VOLTMER: I wondered how you automatically align the probes at the bevel edge?

J. WHITE; We have an interference contrast microscope that is mounted a known fixed

lateral distance from the wafer stage. We align the bevel edge with the microscope cross
hair and we move laterally by the known distance to position the probes.

J. ASSOUR; I do not know if you said it or if I missed it. How do you measure the depth
again in the case of the groove? By staining technique?

J. WHITE; We measure the total width of the groove and from the width of the groove and
knowing the diameter of the grooving mandrel you can calculate the total depth and then
from each lateral distance you move you can calculate an incremental depth.

J. ASSOUR; I take it that the depth measured by the grooving method was proven by other
techniques?

J. WHITE: Yes.

J. KORVEMAKER: I noticed in all the talk about spreading resistance that you never said
anything about the quality of the silicon slice. In our company we have been looking at
slices, how much of the slice is really good and how much of the slice is not good. Does
this have any effect on the spreading resistance measurements?

F. VOLTMER: What do you mean by good?

J. KORVEMAKER; We have been doing x-ray analysis of the slice to get an overall view of
what part the slice would be suitable to get good devices from, and there is a fair amount
which is not suitable because there are impurities or strains or stresses. How do these
affect spreading resistance measurements? I think I have also seen this reported in the
Microelectronics and Reliability magazine that is from the United Kingdom. There is, I
would say, atleast 30 to 40% of a wafer as such is not useable.

M. POPONIAK: I would like to comment. I think in one of the references by D. Gupta of

Sylvania, he showed that higher dislocation areas of a slice gave him different spreading
resistance values if that is what you mean. Well^he has shown it. Jimmy Hu and I have
looked at a microscopic type effect. We looked at copper precipitates using the close
space probing and an infrared microscope so we were able to directly correlate spreading
resistance data as affected by a copper precipitate near the silicon surface and that was
published 2 years ago (Phys. Stab. Sol. 18, K5, 1973), so there is a sensitivity to this
type of a defect.

P. LANGER: I would like to ask some of the people who discussed other types of equipment
and modifications of the Mazur equipment what they have experienced in terms of precision
for two types of specimens. Let's say 1 Q-cm n-type and 1 ft*cm p-type specimens that are
uniform throughout. Let's go around the table for those people who have automatic probing
equipment and consider precision on a long term basis, say several months.

H. MURRMANN: As I pointed out, we have done these measurements on our calibration

blocks for (111) and (100) material. For (111) material we approximately get a reproduc-
ibility of ±13%. For the (100) surface the reproducibility of the measurements was re-
markably better, approximately 1/2 of this. The reason for that we really do not know.
It looks like the (111) surface is more sensitive either to surface contamination or con-
densation of humidity. In addition, there is some indication that the (111) samples are
more sensitive to the degree of misalignment between the exact (111) orientation and the
measured surface plane.

F. VOLTMER: Most of our calibration deals with the entire block which is 22 samples and we
do not very often compare an individual sample on that block. But from those times we have
done so, I feel that our reproducibility on a given sample is something like ±5% over a
long term. That is over a period of weeks. This must be qualified, however, since it
applies to calibration samples which are chosen to be as free as possible from microsegre-
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J. WHITE: We took an ion implanted slice which we had found to be rather uniform by making
repetitive probes across the diameter and got a short term reproducibility, say a one day
reproducibility, of maybe 10 different measurements, 5 mils apart, of ±1.3%. A long term
reproducibility would be around 5%.

P. SEVERIN; We use tf-type (111) silicon substrate slices for calibration, and since I
never have come across a substrate slice which has a resistivity uniformity better than 1
or 2 percent and since you cannot probe the same spot twice I think the reproducibility
should be determined as follows. When you measure a track and the next day make a track at
25 ym distance parallel to it, which is the most similar situation you can arrive at, then
you find the measured profiles are different by 1 or 2%. The main criterion however, by
which I think we should compare performances and quote precision is how much "grass" is to
be seen on a smooth spreading resistance curve. In our case this spurious signal amounts to
about 1%.

M. POPONIAK; All I have to say is that I agree with Severin. We have done some implanted
structures also and by independent measurements across the silicon wafer, say with resistor
type structures there were claims of 1% reproducibility or grading across the wafers and
what I saw with the probe is less than 2%. It becomes very hard to interpret data less than
2% so I am saying we are nearly at the limit either because of electronics or mechanical
stability of the probing system.

J. KORVEMAKER: I noticed that most of the panel speakers are of rather large multinational
companies and I wonder if they have any intercompany relations as far as how accurately they
can measure, or at different plants how accurately they compare, or is there just one
location where all these measurements are done.

F. VOLTMER; Within our plant we have two different probes in different buildings and we are
able to get within 10% reliability on those two probes measuring the same samples when they
are calibrated by the same procedure. So between two completely different kinds of probes
we can get within 10% on a given sample.

J. WHITE: At Western Electric - Allentown we have essentially two measurement systems also,
because there is a Mazur set in Bell Laboratories in the same building with us. I do not
have a number to compare the two probes but we use the same calibration samples. We are in
good agreement that way.

F. MAYER: The question was raised about intercompany comparison. We ran a pilot round
robin in Subcommittee 6 of ASTM. We prepared some 50 um thick epitaxial specimens, and
exchanged samples with 5 laboratories. Our first comparison indicated 6.7% difference
between the 5 labs which is not bad at all. We tracked across the surface on 2 and 3
decade paper and found less than 10% variation in uniformity across the sample. Each lab
used its own method of calibration and surface preparation.

P. PINCHON: I would like to stress one point about the measurement of a thin low resistivity
layer deposited on high resistivity material, because in that case the correction factor
acts in such a manner that you measure something controlled by sheet resistance. By ex-
periment it is nearly always the case that the spread in measurement is very much lower in
the case of low on high resistivity as compared with bulk material or high over low resis-
tivity material. So for the case of calibration, the reported stability of the probe on
ion implantation is something optimistic in my point of view.

R. ANAND: My question is concerned with the conditioning of the probes. Bob Mazur pointed
out that's one of the most important tricks of the trade, and I was wondering if people who
are using other than Mazur type probes, how do they condition their probes and make them
stable.

P. SEVERIN; We use steel probes and they are taken from a four-point probe, in general a
used one. In order to get a fine microcontact pattern the probe should be broken. Why are
the microcontacts there? They are there because there appears to be in steel little,
harder particles, therefore called asperities, which upon contact of a flat bottom surface
of such a needle with the flat surface of a silicon slice, act as protrusions. Under a
scanning electron microscope we found these protrusions to be very small,at most several
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tenths of a micron. But they are absolutely much harder than the steel and therefore the
steel acts as a softer matrix in which these asperities can move more or less elastically.
So the system is that you break the steel probe, and in some way that metallurgusts can
explain you expose a number of these asperities. Thereafter like a pencil you sharpen it
on a sharpening instrument so that the bottom remains untouched. You stop sharpening when
the bottom has almost the size which you think will be the final size and then you start
using it. At first the steel is too heavily loaded, and is plastically deformed until the
contact has expanded and become so wide that it is not anymore plastically deformed. Then
it remains just the same for say 10,000 or 20,000 measurements. Upon contact to the silicon
these asperities make very small, something like 0.1 or 0.05 micron, impressions which re-
main constant over the lifetime of the probe. When you use lapped silicon then you find
that a rearrangement of the asperity patterns takes place, but the microcontribution deter-
mined by (na) remains the same.

J. WHITE; We use tungsten-carbide probes and I have found that I am able to use a new
probe with no conditioning and get very reproducible results.

P. SEVERIN; What is the depth of the damage and do you think the damage does really mean
something to the result of the measurement? Tungsten carbide is harder than silicon and
the probe I am advocating is softer than silicon with only small protrusions which are
harder than silicon. In this way less damage is generated.

J. WHITE; I really do not have a number for the depth but when we compare our profiles
with profiles done on a Mazur set, they are similar. One thing you have to realize about
our system is that we do lower the probes on the surface unloaded. We load them only after
they come to rest on the surface so we probably get quite a bit less damage than a probe
that would come down on the surface completely loaded.

P. LANGER; Let me clarify that. I did work for Western Electric and helped in developing
their automatic spreading resistance probe. It is possible with that particular probing
arrangement to make indentations or to lower the probes to the surface and raise them under
100 grams apparent load such as to leave no visible marks. By no visible marks:you certainly
cannot see them under interference contrast,and even with oblique microscope lighting you
cannot find any tracks on the surface,so that this probing arrangement may yield a completely
different situation than lowering the probes under full load as is done with the Mazur probe.

P. SEVERIN: In order to increase the measurement cycle one could be tempted to increase the
landing velocity of the probe. It can be regulated from very small velocities up to about
6 mm/sec with the air escape valve. We have found that above 1 mm/sec the probe shows re-
bounding on a milisecond scale, actually losing contact and subsequently generating elastic
vibrations. It is an interesting observation that the correct spreading resistance value has
been reached at the first impact. We have found that a landing velocity of 1 mm/sec, where
no rebounds occur, and a measurement cycle of 5 measurements/min. produce most reliable
results.

A. ROBINSON: I address my question to Mike Poponiak. I noticed you showed a plot of con-
centration versus depth for the different probe pressures and there was difference in the
concentration peaks. Is that attributed to the difference in the probe pressures or is it
attributed to something else?

M. POPONIAK; Well there were two profiles I showed [P-8] and I think you are talking about
the high concentration regions, right? On 40 gram versus 10 gram. What I am saying why
there is an apparent difference is due to the inadequacy of the correction factor. They
should both be the same CQ. I am saying a 10 gram loading gives us a more accurate repre-
sentation of the CQ than a 40 gram loading.

A. ROBINSON; Is it determined by the monitor wafers that you use in your subcollector, or
in your diffusion? When you say that that is a more accurate representation of the CQ^is
that CQ the determined CQ that is seen on another monitor wafer and not by spreading resis-
tance?

M. POPONIAK; We have done independent correlation with neutron activation or differential

sheet conductance measurements. Independent techniques verify that the lower loading works
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better with our multilayer correction scheme. Excessive probe penetration at 40 gram
loading causes the inaccuracy.

C. GERMANO; I was wondering if any of the participants have noticed the effects of taking
small delta X increments where the damage left by the probe marks overlaps the previous
steps.

M. POPONIAK; This morning somebody showed data indicating repetitive measurements at the
same point and the spreading resistance increased dramatically. Well, in our close space
probing where we have done beveling on the probes we are able to achieve a lateral movement
of 2 1/2 microns without overlapping. Now a way to test this is to start with something
large: 10 micron steps across the surface, reduce it to 5 microns, reduce it to 2 1/2,
reduce it to 1. When you see an apparent shift to higher spreading resistance you know you
cannot go below that last delta X movement. Someone else said they had a 1/2 mil resolution
delta X. I am saying we can go 2 1/2 microns by preparing the probe points properly, without
overlapping.

P. SEVERIN; May I ask a question to Mr. Poponiak. One of the key questions that has come
here today is the potential distribution around the probe. For then we know whether there
is a contact resistance, either a physical contact resistance because of a barrier or a
contact resistance because of microcontact. You mentioned 15 microns as the distance
between the probes. Could you bring them still closer and then just find out what the key
problem is?

M. POPONIAK: It is very difficult, but so far we see no influence.

F. MAYER; In answer to your question we did check on the overlap question, if you have
probes that step on each other so to speak. With 2 1/2 micron steps, you see something
like a 10% increase in resistivity, with 5 micron steps it is hard to say whether there is
an effect: it is no more than 2 or 3%. With 10 micron steps you do not see any effect at
all. -
I am a little confused about your data, Fred Voltmer, on the interpretation of the con-
tact resistance that you showed. I think you showed a considerably increasing contact re-
sistance after you dipped in HF and as a function of boiling in water. Now on the next
slide you showed an oxide growth of up to 700 angstrom. Are you implying that in an hour's
boiling you grow 700 angstrom of oxide? Most people consider the maximum oxide growth in
boiling water to be about 30 or 40 angstroms. What is your interpretation of that value?

F. VOLTMER; What we did was to take a slice and dipped it in HF to ensure that there was
no oxide and when we did that we got a very high spreading resistance. We subsequently grew
an oxide in boiling water and measured the oxide thickness and the spreading resistance and
what we saw is a dramatic decrease in spreading resistance as the oxide thickness grew to
about 100 angstroms. It remained relatively constant then until we grew about 700 angstroms
of oxide at which point the spreading resistance got quite large indicating that we were not
penetrating the oxide. We grew the oxide for the thin layers of oxide we use boiling water,
for the thicker layers they were grown in a furnace tube.

F. VIEWEG-GUTBERLET: I think, Fred, I can now answer for this effect of dipping in HF. We
have the same experience measuring p-type polished wafers by four point probe and if you dip
the wafer into HF the resistivity increases by about a factor of 10 or more, and if you
store the wafer in a temperature of approximately 150° C or you boil the wafer in water,or
whatever you do,this increase of resistivity goes down by a time constant of approximately
40 minutes. You can do the same by lapping the wafer and if you lap the wafer partly and
you position your probe in the lapped area you can see the decrease of resistivity readings
versus time. Our explanation for that is: you have a fluoric layer on the surface, which
is strongly n-type, so you bind a part of the holes to that electron layer on the surface,
i.e. the negative active layer on the surface. This is related to fluoric ions on the sur-
face.

P. LANGER; Since we have gotten into the area of surface preparation I will just throw in
a few remarks and possibly Stan Shwartzman from RCA might want to comment on these. He has
the one technique that does not use a aqueous solution in his beveled sample preparation.

266 EST 2016

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What we have found when we went to a lighter loading probes was that you could affect
changes anywhere from 100 to 400% in the measured resistance on half ohm cm n-type by
heating for about 5 minutes at 180 - 190° C and then cooling the sample back down. These
changes have been stable right now up to 3 weeks. We have also found the same effect on
Bob Mazur's QTA, we were able to decrease the measured resistance by a factor of 2 by using
the same thermal cycle.

S. SHWARTZMANN; All of our samples including Bob Mazur's QTA remain stable after they are
swabbed with methylene chloride solution with our probes loaded to 45 grams. When specimens
are prepared in the presence of water the same degree of stability can be obtained by baking
them at 150° C.

P. LANGER; What I was saying was that since you are the only one that does not get tied up
with water during sample preparation you may not see this effect at all. I just wondered if
anybody else had seen this type of effect.

J. EHRSTEIN; I have just finished over the last month, following some very helpful sug-
gestions from Fred Mayer, measurements using a modified surface preparation procedure. I
hope to have something to say on it tomorrow in the fashion of a late newspaper. I think,
in terms of improvement, we have answered at least 3 problems which turned out to be re-
lated to surface preparation for the upper ranges of p-type material. I thought they were
separate problems, but they all seem to fall into consistent interpretation now, just be-
cause of a modified treatment, namely, the bake out procedure?150° C for 15 minutes or more
following an aqueous chem-mechanical polish. Probably this time-temperature cycle could
be made hotter and shorter, but we have not tried it. Let me wait until tomorrow to discuss
it further.

J. ASSOUR: Since our experience has been concentrated on deep diffusions for power devices,
we are not really relating to the thin layers most of you have been talking here. We did
look at polishing techniques versus lapping techniques. The lapping technique is what we
use constantly, but in terms of the polishing techniques that we tried on the same cali-
bration samples, and that means syton finish, or chemical polish, or other polishing tech-
nique, I must say that in these cases although we would reduce the noise level of our
spreading resistance readings we have not been able to reproduce our calibration curve in
terms of time stability; I mean that we can polish by syton or chemically, measure, and re-
peat the measurement two or three hours later and get different points due to drifting. In
other words, the ambients, dirt in the room,or humidity, or what have you, seem to influence
greatly the polished surface. Of course, since we have gone to the lap surfaces for the deep
diffusion structures that we are interested in, we really do not see these effects.

D. WILLIAMS: The TI paper that you had on the calibration and performance of the spreading
resistance probe, was that (111) material, syton polished?

F. VOLTMER; Yes, it was, it was all (111), but Lustrox polished.

D. WILLIAMS: In our case I used a least square linear regression. The numbers for the
slope for both n and p-types are almost the same. I compared the residual sum of squares
from the actual data to the fitted line and asked myself whether the slope was unity. With
95% confidence, both slopes included unity. Therefore as far as I can tell from the data
the slopes cannot be said to be different from unity. Do you use a slope of unity in your
work or do you use the exact value of slope as calculated from your least square regression
of the calibration data? I find it interesting that my calculated slope for n-type is
slightly larger than unity and for p-type it is slightly less than unity. This of course
would have implications for the simple linear model of the spreading resistance measurement.

F. VOLTMER; We use the actual values for slope and intercept from the least squares fit to
our calibration data for that particular week. For n-type, it is typically 1.03 and for p-
type it is 0.97. As I showed in my paper the long term distribution of the calculated
values for these slopes maintain values slightly higher than unity for n-type and lower than
unity for p-type. These values are obtained from a linear least squares fit of the data in
log-log coordinates, but of course a slope different from unity in these coordinates implies
a non-linear relation between spreading resistance and resistivity in the model used.
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D. WILLIAMS; Can you then determine resistivity values to better than 10%?

F. VOLTMER; Yes, I have the actual data for any given point in my calibration and the dis-
tance between that point and the spreading resistance value of the actual specimen of inter-
est allows me to determine its resistivity to better than 10%.

3, APPLICATIONS SECTION
P. IANGER; Fred Voltmer, you mentioned that you have multiple peaks related in some way to th«
the sum and difference of the rotation rates. Could you clarify that?

F. VOLTMER; Yes. For the multiple peaks, if you calculate the distance traveled for the
various rotation rates, for "example, just the crystal spin or just the crucible spin or the
sum of crucible spin and the crystal spin, you will get peaks where the periodicity of the
fluctuation corresponds to the growth for that time. So that it is not always so simple
that there is just one well defined frequency for the microsegregation, but sometimes there
are multiple frequencies, and they all can be related to mechanical conditions during the
growth of the crystal. It is not always.just a single frequency variation.

F. VIEWEG-GUTBERLET: Did you find for the distance between the peaks related to the ro-
tational striations that the equation d = F/W is satisfied where F is the relative pulling
rate and W is the rotation rate?

F. VOLTMER; Yes, in fact that was the point. The peaks in the resistivity translate to a
spacial frequency in the transform and that spacial frequency, i.e. the dominant frequency
is exactly that derived from the pull rate and the rotation frequency.

K. BENSON; Fred, have you been able to correlate the magnitude of the microinhomogeneity in
the radial direction versus the magnitude of microinhomogeneity in the longitudinal direction.

F. VOLTMER; Well, they should certainly correlate. We have not quantified it but the same
variations occur in both directions.

K. BENSON: Have you been able to correlate the magnitude of one versus the other?

F. VOLTMER; We have not yet done that. We will report on it when it is done.

B. MORRIS; If I am properly interpreting one of the last profiles shown.by Dr. Assour, more
gold was accumulating in the region of a p diffusion than that of an n , is that correct?

J. ASSOUR; No, more gold accumulates in the n region than the p+. The fact that the p+
junction seems to have been raised in resistivity is the fact that you have more gold that
accumulated right at the junction and in the n region.

F. VIEWEG-GUTBERLET; The explanation you derived from your results in oxygen distribution
may lead to the conclusion that oxygen is distributed nonuniformly into the crystal. But I
do disagree from our experiments and there may be an explanation that your experiments were
done with p-type material. That means that acceptors are distributed in the silicon crystal
nonuniformly in the form of striations. If you raise the level of oxygen related donors by
the heat treatment at 450° C, you will get compensation at some points and you will increase
the compensation rate so the residual resistivity will go up. But this is not due to non-
uniform oxygen distribution. It is more due to the nonuniform distribution of acceptors
that came out from our experiments when we tried to find out oxygen striations on p-type
material but this explanation gave a good agreement of the other measurements on n-type
material.

J. ASSOUR; According to your point of view I fail to explain the fact that infrared mea-
surements on wafers before heat treatment do show different oxygen concentrations across the
wafer..
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F. VIEWEG-GUTBERLET; This may be due to swirls because in crucible pulled material the
swirl complexes and distributed very nonuniformly.

K. BENSON: I did have one comment I would like to make to F. Vieweg-Gutberlet. You may
have only looked at one oxygen concentration. The problem with all techniques is dependence
on the concentration of oxygen in the crystal. If you look at an oxygen concentration of
1015 and then at one of 101' you may see completely different reactions. So whether you
have seen inhomogeneity or not, I think, depends on what the original oxygen concentration
was in the crystal.

F. MAYER: I would suggest that Ken's explanation may be close to the truth. I think the
question of time which it takes to develop oxygen donors during the heat treatment comes
into it. It takes a long time at 450° C to develop donor dependent resistivity changes
associated with striations. I suggest you might try to determine this experimentally.

B. SCACE: The papers were very .interesting, both Fritz's paper and the paper that was just
given, and we can get into an argument that would last for a week about what is going on
inside the silicon but the point is that we have an extremely powerful tool here now for
exploring just this kind of thing so let us not get off onto what is happening in the silicon.
Let us look at what is happening with the measurement.

$. PRUSSIN; We have been referring to the spreading resistance probe tests as being non-
destructive. However, there is no question in the earlier discussion that part of an
effective probe measurement is that it leaves a footprint, an area full of little cracks,
which act as very nice nucleation sites for dislocation generation if there is any kind of
thermal stress. I know that we have tried to remove generation of slip dislocations by the
means by which we prepared our wafers. We make sure that we have developed polishing tech-
niques that leave no mechanical damage and so forth and I know that a great many of the
studies that have been made in the past have shown a very direct correlation between the
presence of mechanical damage and slip associated with thermal shock. I am just wondering
has anyone looked into the spread of, or the generation of dislocations or slip from some
of these "nondestructive" spreading resistance probe measurements that we have made.

H. MURRMANN: We have not done it until now but we just started experiments and I personally
am not afraid of getting dangerous slip damage from that probe tip damaged region especially
for (100) material.

F. VIEWEG-GUTBERLET: In answer to the last question, you can see from the slides I showed
[A-2] we found spreading resistance traces after heat treatment, and again in the wafer when
we etched the wafer after repolishing them. So we have deep damage from the spreading resis-
tance probes and heat treatment at 1100° C.

H. MURRMANN: That is a question of the heat treatment you apply to the wafers, and what you
consider to be dangerous damage.

F. VIEWEG-GUTBERLET; May I ask a question of Dr. Murrmann? How does the accuracy of your
epi thickness measurement depend on the dopant distribution in your epi layer? Is it true
that the assumption is made that the epi layer is .uniform in resistivity?

H. MURRMANN: You are right, the method that we have proposed has to be calibrated for each
specific epitaxial process that you apply. For instance, you would get slight differences
between silicon tetrochloride epi and silane epi. In addition, the buried layer diffusion
process has some influence on this. But whenever you take a certain buried layer and epi-
taxial process you can well determine the effective epi layer thickness by this method. We
have checked it in addition by comparison with breakdown voltage measurements and these
values agreed very well too.

N. GOLDSMITH; The only region we have checked for thickness correlation between IR and
spreading resistance was a series of samples at around 100 micron epi thickness and here we
found that the error was really in point count: you have to choose where you place the
interface. For the samples I looked at we agreed to ±1 point count. For the step size and
angle we used this was ±1 micron out of 100. The accuracy is also limited by knowing where
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you start from which adds to the error of where you place the interface. Our interface
position is selected by our computer program which calculates the substrate resistivity and
then looks for the point where the substrate resistivity breaks and assigns that as the
thickness.

F. MAYER: I would like to add here that the subcommittee 6 of F-l has just undertaken the
evaluation of this method as a standard method and I think Fred Voltmer has volunteered to
draft it. Do you want to comment on this, Fred?

F. VOLTMER: Yes, I think that the thickness depends very much on the angle which you are
probing and the precision or the range of thicknesses you are looking at. For example, for
very shallow angles or very thin epitaxial layers the critical factors are quite often the
alignment of the probe and the precision with which you can form a bevel. We feel at XI
at least that when we are careful and when we are talking about lapping on 17 minute blocks
we can determine the thickness of an epitaxial layer, and that is a defined thickness, let
me point out, to about 400 angstroms. We define the thickness as the intercept of the
slope in the change in epitaxial resistivity with the extension of the substrate. When one
has p/n junctions it becomes quite a bit more difficult because there is quite often a
depletion region which makes it difficult to define exactly the point where the junction
occurs. For thicker epitaxial layers, it is a matter of how many steps you want to take
and how shallow a bevel you want to use for probing. In other words, if you have a thick
epitaxial layer and are willing to probe almost forever you can get these same kind of pre-
cisions. If you take larger steps the step size becomes a limitation on the precision.

G. GRUBER; Fred and I had a bit of discussion about this same thing at the committee meeting.
As he says the thickness measurement is dependent certainly on the ability to measure the angle
and also on the ability to determine the position of a p/n junction or what you would call
the interface between an n and n+ region. In most cases, I would say in the majority of
cases, the picking of the p/n junction is a matter of extrapolating the two sides of the
junction to the point of maximum inflection on the curve and calling this point the p/n
junction. If there is a broad high resistance region where the spreading resistance is off
scale then you do have a problem in choosing the junction. This however, is not the normal
case. For determining the thickness of a layer, such as an n/n+ or p/p+, most people do
exactly as Fred has said and pick the point where you get maximum inflection in the transition
region from n to n . In the normal situation we find that you can determine this thickness
to within several percent, or better.

W. SCHROEN; I would like to make a comment on epitaxial layer thickness and concentration.
We have seen data this morning which showed that there can be a distinct out diffusion from
the substrate at the interface of the substrate and the epi layer. The same sort of out
diffusion or autodoping can happen at the interface of the epi layer and the buried layer.
From a modeling standpoint this effect has been well explained by researchers at Fairchild
such as Grove and Deal and others. Now the question is how do we distinguish between this
experimental fact and the multilayer analysis which can pretend such an effect as we have
seen yesterday. The answer is that when there is a real out diffusion the original spreading
resistance data will show it. The original spreading resistance data can be corroborated
by the results of the C-V technique and thus distinguish a true out diffusion effect from
the artifact of the multilayer analysis.

$. PRUSSIN; The point was made that by using a very shallow bevels we can increase our
precision in measuring shallow diffusions or thin epi layers. By doing that we raise
another problem. That is the greater difficulty in determining where to start the probes
because the bevel's junction with top surface then becomes less sharp. I think that the end
of the layer is one of definition and is not really a problem, but I think there is a major
problem with exactly getting your probes to start at the surface-bevel intercept. I was
wondering whether there were some suggestions in terms of practical techniques which would
enable the operator to start more precisely at this junction.

F. VOLTMER; I would like to address that point. We have established a technique whereby
we grow a reactor deposited nitride on the surface of the slice as Walter Schroen pointed
out in one of the earlier talks. That nitride is hardness-adjusted to equal that of silicon
so that we can get a very distinct intercept between the lapped part and the nitride, so
distinct that it is quite apparent in the microscope. The subsequent probing across that
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shows then a very drastic change in the spreading resistance when you go off the nitride onto
the silicon layer and that then allows you to identify very precisely the position of the
beginning of the bevel. The problem is that if you are using, for example, the 17 minute
angle beveling block; a 5 micron error in the position of where you put the bevel will give
you a 500 angstroms error in depth and I feel that doing much better than that with the 5
micron probe point is quite difficult, but we use the nitride to define very precisely the
position at which the bevel occurs. This allows you to see if the bevel is straight, which
can be another source of error.

G. GRUBER; We have seen the same thing with an oxide layer on the surface. You can use the
same technique.

W. SCHROEN; In answer to your question, I feel as Fred Voltmer stated, that the intercept
of the bevel and the surface is no longer much of a problem. It is much more of a problem
to determine where the junction is with the substrate or with the buried layer, since we may
have to deal with the effects of out diffusion or the artifacts of the multilayer analysis.
However, anyone skilled in the art can extrapolate where the intersection of the epitaxial
layer and the substrate is. This extrapolation is usually precise enough, even for very
thin epi layers. I feel confident that we can determine the thickness of the epi layer at
the interface with the substrate.

S. PRUSSIN: One of the techniques that we have tried was to examine the bevel surface after
we completed the spreading resistance analysis and tried to find out where the first foot-
print appeared using interference microscopy. Possibly in this way one can determine very
accurately the relationship of the first footprint with the theoretical bevel-surface inter-
cept. What I want to know is whether techniques like this have been tried by anybody.

G. GRUBER: I would like to make the comment that we have been talking about very shallow
low angles for measuring very thin layers. We have found in some of the work that we have
done that you do not really have to go to as shallow an angle as you might expect to use for
a very thin layer. If you go to smaller increments, for example, across a less shallow
bevel, say 1 degree, many people worry about the overlap of the probe imprints and so forth.
We have been able to determine experimentally that even down to a 1 micron step increment
we have been able to repeat and reproduce the results without any problem due to overlap.

B. MORRIS; As to that, I would like to ask what surface preparation technique you use.

G. GRUBER; This is a Syton polished surface using a Plexiglas plate.

B. MORRIS; I have never found that to be true. I wish it were.

G. GRUBER; You have to be sure that when you calibrate, you use the same step increment
during the calibration as is used when running a specimen.

B. MORRIS; I still find that with less than 2 1/2 micron steps we have a very large signal
to noise degradation and the whole curve shifts. I have one other comment to make as to
the surface definition. We do an anodic oxidation, growing about 400 or 500 angstroms which
gives you a definite darkening of the surface. This involves no heat so you are not going
to change any of the profiles.

B. MAZUR; I have a comment on that, I have made this comment to a number of individuals
and perhaps should make it publicly to all, that the business of sample preparation and
particularly beveling with small anges is in part a matter of skill. At lunch, I pointed
out the similarity to the situation involved if someone buys a transmission electron micro-
scope and just goes in that afternoon and starts to prepare samples. There is a certain
amount of skill involved in the preparation of samples! The other point to this is that
basically what Gil Gruber has said has merits. What we are suggesting to you is that you
consider the possibility of actually being able to use one micron steps despite what Bernie
Morris said and thereby achieve greater precision in the measurement of thicknesses on such
layers. Along with that I will make a suggestion that I have made to a number of people
that I have talked to in the past and that is that the contacts we use are 5 - 6 microns
diameter and as someone pointed out when you are taking one micron steps and you go back to
look Copyright
at it afterwards you of course find it hard to see where that first one was because it
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is covered over by subsequent probe narks. I would like to suggest here that at the time
you begin the run you set up to center the first contact on the bevel edge and initially set
the probe to take a single measurement point. Then when it stops you shift the stage later-
ally by 5 - 10 microns and continue running. This causes a displacement of the rest of the
points in the run from the first point and allows you to go back later with an interference
microscope or a scanning electron microscope if you like and locate exactly where that first
point was relative to the bevel edge. Perhaps parenthetically, I guess, the point would
have to be made that the interference microscope is not going to do you much good beyond
about a quarter micron as far as determining where you are in depth.

M. POPONIAK: Just a comment on this overlapping. We have done a considerable amount of

study and it is a function of the actual resistivity. What I am saying is that there are
ranges of resistivity that you can apparently overlap and that is predominantly the high
concentration regions. As you go to lower concentration regions it is very sensitive to
this and you cannot overlap.

G. GRUBER; What do you mean by "you cannot overlap"?

M. POPONIAK; You get an increase in apparent spreading resistance, an error due to the
overlapping.

G. GRUBER: As I said, it is required that you calibrate using this same step increment as
when running the specimen. If you do this you can eliminate any effect of overlap.

M. POPONIAK: All right,that is your comment, but that has to be proven because now you are
trying to probe into a mechanical damage area, yet everybody is trying to get a good polish
to start with.

G. GRUBER; All I know is that I can use a step increment that results in overlap of suc-
cessive contacts and if I calibrate with that overlap I can get the same resistivity as for
the case where I have used a larger, nonoverlapping step increment for both calibration and
sampling.

D. DICKEY; I would like to comment on Goldsmith's paper. The errors that you found in your
diffused layers no doubt result from the fact that you do not have uniform resistivity in
those layers. The so called Dickey correction assumes that you have uniform resistivity
throughout the layer. That assumption is certainly not valid for shallow diffusions. This
points up the need for an improved correction scheme and that is the subject of my second
comment. The problem of correcting spreading resistance measurements in a layer having
depth dependent resistivity is something that needs working on. I indicated on my last
slide yesterday that the imaginary superposition of a number of layers of uniform resis-
tivity could be a useful approach. It occurred to be last night that that approach is really
just the spreading resistance equivalent of the incremental sheet resistivity experiment
that people have used for years with a four point probe. I suggest that you could derive
corrected spreading resistance measurements from an incremental approach using the same
mathematics that are used with incremental sheet resistivity. The calculations that would
be required would be rather trivial and I think it is a very logical thing to try.

N. GOLDSMITH; I will comment on your first point. In the interest of time I did not
choose to read our introduction which clearly said that your formula was derived from uniform
samples and was hardly expected to provide adequate corrections for a diffused layer.

W. SCHROEN: Let me question you with regard to your suggestion of another approach to cor-
rection factors. I did not fully understand your suggestion of using a procedure with over-
lapping steps in order to get to an analogous, situation of the four point probe. Would you
please repeat your suggestion?

D. DICKEY; I am just suggesting that you should go through the mathematics of using the
superposition principle and find out what the difference between successive spreading re-
sistance measurement should be at slightly different depths. The difference in the measured
resistance that you see at two microns down and at 2.1 microns down, for instance, should be
characteristic of the resistivity in that (1/10) micron increment just as it is in an in-
cremental sheet
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F. MAYER; Perhaps I could throw another question at you as it seems like an opportune
moment. Listening to what we had this morning there has been an excellent correlation
between patterns of resistivity established by other methods and by spreading resistance
measurements, which says that the spreading resistance probe has arrived as a tool that is
accepted. Not only is it accepted, by and large the data seem to fit the models we have of
production processes. Having gotten to this point I think it is pertinent to ask where we
go from here. Obviously we are moving into an era where we can begin to standardize
spreading resistance probe measurements and I think that is underway now. My opinion is
that we have not got the speed yet or the facility to use it as an on-line production control
instrument or even as a routine instrument in a development laboratory situation. It would
be interesting to hear what the panel and perhaps what Bob Mazur would have to say on this
subject.

W. SCHROEN; Your comment is well taken with regard to the actual probes. In addition, I
would like to suggest that'maybe the National Bureau of Standards should start to standardize
the multilayer analysis. This standardization should consider what needs to be done analyt-
ically, what are reasonable mathematical assumptions, what are reasonable calculation pro-
cedures, what are the best computer programs and so on to make sure that all users can uni-
formly use spreading resistance data.

G. GRUBER: I think it is obvious from this last day and a half that additional work is
necessary in the area of layer corrections, i.e. junction corrections and in technique. I
think also it is becoming obvious that the technique is becoming more accepted in the in-
dustry and that applications are being found almost every day, I think in a few years, when
we have the next seminar some of those seats that are empty will be filled.

K. BENSON: That was a nice leading question to ASTM Subcommittee 6 (of Committee F-l); I
made introductory remarks on it the other day. At present we have 3 documents in Subcommittee
6 on spreading resistance. One is how to make a surface measurement. We have another doc-
ument looking at how to make profile measurements and we have another document on using it
as a tool to determine thickness. The documents are in various states of preparation and we
have only been on this three or four years and every year we do make progress. If anybody
wants to speed this progress up I suggest that you be with us in Scottsdale, Arizona in
September and by that time we hope to have the first document (on surface measurement) well
underway so that the other two documents can be completed.

J. KORVEMAKER; I would like to add a question and remark to what Walter Schroen was saying
that NBS should get us some more idea about the method to follow; so I think what Jim
Ehrstein was doing in the last half hour of the lecture, in stating that there are certain
conditions you have to do to prepare to make the measurements more repeatable could be
applicable particularly when you go to a high resistivity area. I wonder if there is not
anything there but surface layers of moisture that will give you trouble. I personally
always had great trouble to measure pico-amps without having some trouble with moisture.
Are the methods that we use for measuring really repeatable and does everyone use the same
methods? I do not think so.

J. EHRSTEIN: I do not know exactly how to respond. I can say simply that the work I re-
ported on this morning was only a beginning of what we intend to do. The difficulty
is that in terms of any of us with the Bureau of Standards or probably with any government
agency trying to assess what problem areas need and deserve attention, none of us are really
trying to make work. We do need an accurate assessment of what problem areas still remain.

J. ASSOUR; Now listening here, I really cannot help to feel my frustrations a few years
ago when we first were introduced to the spreading resistance probe and the first question
that came to us is how do you calibrate the probe, and everybody said you use the four probe
sheet resistance method according to the NBS or the ASTM standards; and naively I said, after
working 10 years with silicon, what calibration sample should I use? I have a wafer here and
I measure 10 ft*cm on my instrument. How do I know it is 10 ft*cm material? Well that is when
I think I called Jim and other people and I asked how do I get my hands on something that I
can call 10 ft*cm material. But then I thought that for the many years I have been dealing
with silicon we have really never concerned ourselves with this problem and everybody had his
own technique for determining his calibration samples. Accordingly, the semiconductor in-
dustry has progressed very nicely. If we have 10, 10.2, or 10.5 ft*cm does it make a
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difference? For the past two years a lot of papers have shown that the spreading resistance
technique at least can answer many, many questions that frustrated all of us and I hate to
see here that we should get hung up on details about the damage or the microcontact or what
have you. At the National Bureau of Standards here I would like to see very much not only
two samples of known resistivities (SRM 1520) that one can purchase for calibration but a
larger number of samples that cover the whole range of resistivity that the semiconductor
industry is actively pursuing.

H. JANUS: I would like to ask if anyone has measured bulk resistivity striations letting
the probe steps going down towards 0, do the striations peaks head toward infinity or is
there an upper limit?

F. VIEWEG-GUTBERLET: We did a lot of measurements especially to build up a spreading resis-

tance topograph of striations and we found that for the rotationals as well as what we call
growth striations, which are autofluctuations, we do not see an advantage to lower the step
width below 10 micrometers. But for very sharp profiles sometimes it seems to be better to
switch from the two point probe mode to the one probe mode.

J. EDWARDS; What we found when we were trying to get very good precision was that as we
changed from the 25 micron to the 10 micron step increment, the noise level increased and as
we went to the 5 micron step increment the noise level was greater than the resistivity
fluctuations which we were trying to measure.

D. YODER: We have on occasion found we do not know what the conductivity type of the top
layer is when probing devices or multilayer structures. I wonder if anyone has any idea of
how to determine this? Has anyone tried putting a thermal probe in the spreading resistance
probe or something of this order?

B. MAZUR: This is in answer to the previous question about conductivity type. Some years
ago I did make a thermo-electric probe that went on one of the early prototype spreading re-
sistance probes. You can do that; it works. We do not have anything like that commercially
available. Obviously with the ingenuity that has been displayed here in the last day and a
half, it really is not going to take a whole heck of a lot for people to wrap little pieces
of nichrome wire around one of those probes, and you can do this if you like. I assume that
the question was asked in reference to small areas because obviously if you have a large
area exposed on the top surface you could check it with a standard thermo-electric probe. I
would suggest the use of chemical stains in conjunction with spreading resistance. I would
definitely not go home and pitch out your staining stuff. We have been using the stains
consistently from the beginning of our measurements as a qualitative indicator of what is
going on overall. Remember that the spreading resistance measurement is a very high spatial
resolution measurement and if you evaluate a epitaxial layer, you may choose to do so at one
point rather than all over the wafer or all across the diameter and so you may get a very
detailed picture but it is a very detailed picture of a localized region. It takes only a
few seconds after having the sample profiled on the spreading resistance probe to stain it
and get an overall view of whether the junction is uniform and so on. You are not then de-
pending on the stain to indicate a p/n junction or anything. You can simply compare it
back to the spreading resistance profile and use it as an indicator of that point on the
spreading resistance profile where it: falls and see whether the layer is uniform and so on.
This was found to be quite useful in the power device area for looking at the effect of
rough surfaces on diffusions and the like.

F. VIEWEG-GUTBERLET; May I comment to that problem? As you remember the paper presented
this morning from RCA with respect to oxygen effects in silicon and silicon striations.
There is a great interest to get information if compensation occurs or if the conductivity
type changes within the limits of striations so the question is does the system you are
suggesting have the resolution to find out these changes in conductivity type or compensation?

M. POPONIAK; Years ago when we had a three point probe which in reality was a one point
probe, we reversed the current polarity. If you increase the current sufficiently to get
into a non ohmic region you can determine the type down a profile or across the surface by
observing the forward and reverse voltages. It is especially sensitive on high resistivity
material.
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R. MAZUR; I have comments on both those courses. As far as Fritz's problem goes I do not
have a quick answer for you on that. You would have to look at the specific situation to
see whether anything could be done. We have generally been able to tell a lot about con-
ductivity type from the appearance of the profiie; in conjunction with other knowledge that
is available such as the thermo-electric probe conductivity type of the top surface and
perhaps the substrate region (the regions that are accessible) and we have used that in con-
junction with the appearance of the profile and with staining techniques to keep track of
conductivity type. Your situation may be a way-out case that is hard to do much with. The
other suggestion that Mike was talking about I would caution you about doing that with the
existing spreading resistance probes that you are using for making measurements. When you
start passing large currents through them, you will be heating the material in the region of
the probe and I do not know what microcontacts there are there but things could change after-
wards. I am not speaking from experience, I have not tried to do that, but just be aware.

M. POPONIAK; Just on a comment to Bob's. In essence, you do not have to go up every high
current to look at a very small differential voltage difference between forward and reverse
current so we did not burn our probes out and we did not see deterioration in our older type
probes. As far as looking at the general profile from a spreading resistance and relating
it to a conductivity type if you recall that one slide I showed yesterday where within 10
mils I had three complete different profiles and by no means did the spreading resistance
indicate I had a p-type layer all the way up to the top of the epi over my p+ subcollector.
Only the stain showed that up, we did not type it conductivity wise. Right adjacent to that
was an epi over p-t adjacent to that was a resistor of the same epi but over an n subcol-
lector. Spreading resistance profiles can be very difficult to interpret as far as conduc-
tivity type is concerned.

R. MAZUR: I think Mike has very well made my earlier point about the valuable usage of the
stain in conjunction with spreading resistance profiles.

F. MAYER: I have one question that arose out of what Bob said. I would just like to poll
the panel quickly. There are two ways of doing this, one is constant current and one is
constant voltage. I think the majority of the people here are using constant voltage meth-
od. How many of you are using the one millivolt or the 10 millivolt respectively?
J. EHRSTEIN; NBS tends to run the 10 millivolt constant voltage mode;
F. VIEWEG-GUTBERLET: We use the 10 millivolt mode;
G. GRUBER; For higher conductivity material, the opamps in the instrumentation tend to
saturate at the 10 millivolt level so we tend to use the one millivolt range;
J. EDWARDS; For the work that I did we used the 10 millivolt range;
F. VOLTMER: We use principally 10 millivolts;
N. GOLDSMITH; All our work was at 10 millivolts;
H. MURRMANN: We too work with 10 millivolts;
J. ASSOUR: 10 millivolts.

3. MAZUR: We are just in the process of modifying our standard equipment to use 5 millivolts.
There is a reason for that. The operational amplifiers that are readily available and most
readily used have an output current capability of 5 milliamps. When you bias one ohm with
a 10 millivolt signal you have to draw 10 milliamps. The older discrete circuit operational
amplifiers that we used were very nice in going ahead and doing their bit even far beyond
the call of duty. Now those are no longer available and we are using integrated circuit
modules that are more tightly designed and will not perform anywhere beyond the specified
output current so we are in the process of shifting to a 5 mV bias. The one millivolt
arrangement is tricky because drift in the operational amplifiers is such that one or the
other of the operational amps may drift in such a direction as to have the offset voltage
slightly exceed one millivolt in the wrong direction and if so your log Resistance-ratio
unit will malfunction and the output will go off scale up or down. It would then need to
have the offset voltages on the operational amplifiers reset which is a relatively compli-
cated procedure. Anyway, we are switching to 5 millivolts. If you need a standard for the
future, I would suggest starting there.

H. JANUS; I have one thing that has been worrying me. That is when you talk about the
accuracy of the measurements at high resistivities, at 5,000 fl»cm you have one phosphorous
atom in one cubic micron. How can you talk about an accuracy of even 10%?
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J. ASSOUR: I guess I should answer this. At least with oxygen and gold you do upgrade the
resistivities. I will not even guess what the accuracy of this resistivity is. Usually
when we reach these kind of resistivity levels we try very hard to get down as fast as
possible or be out of business.

D. EARTH: I want to comment on the closely spaced probes and a question. We have done
profiling of thin, one micron and less, epi at one micron stepping distances with a shallow
bevel and we have been able to get,with careful surface preparation (a good plate and good
polish), good flat curves without a lot of noise. Going down to a half micron and quarter
micron steps is very bad. From a noise standpoint, I would consider one micron a lower
limit for the time being. Having been involved in ECL and high power microwave transistor
work where we have a thousand angstrom emitters and 1,000 to 2,000 angstrom base widths,
device performance tells us we are close to that, and we measured that with a spreading re-
sistance probe. I have a question. Have any of you gentlemen done any work on very shallow
layers, and I am talking on less than 4,000 angstroms' where all the correction factor curves
stop, and have you had any success at making those measurements accurately and do you think
the spreading" resistance technique will be applicable to layers this thin?

G. GRUBER; I have looked at some 0.2 and 0.3 micron layers but they were usually n on n
type with no junction involved. We have also looked at thin ion implants but I do not have
anything more to say about them.

M. POPONIAK: A comment about Westinghouse1s question. We have done very shallow implants
and they will be reported on and it looks very feasible.

B. MAZUR: In partial answer to that question and also in line with something that Fred
talked about before, obviously, the development of the spreading resistance technique is not
finished. I think it is clear always that anything can be improved. We certainly expect
to do some additional development work in the future. We also expect to be able to
take advantage of some of the genius at IBM and at various other places in order to obtain
technique improvements similar to the "bent" probes that we now supply to a lot of people.
These are a practical approximation to the IBM closely spaced probes as produced by Ed
Gorey. Perhaps in the future we can get closer to the spacing now used at IBM. Certainly
I think that you would all agree that there is no fundamental limitation in the use of 25
micron radius probes and certainly no fundamental limitation in the lighter load that we use
in normal measurements of 20 grams. Improvements in the mechanical parts, improvements in
the probe tips and vibration isolation and so forth may well may allow us to get down to
perhaps 1 micron diameter contacts. It should be interesting to see whether something like
that can be done and perhaps we could then get to a one-tenth micron capability of doing
profiles or something similar for thin layers. One last comment on this and then I will shut
up, Fred. This applies to the Westinghouse question; it also applies to the comments that
TI has made about the junction position, the lack of information about it and so on. You can,
of course, use the spreading resistance probe, for instance in the case of samples with base
widths of 2 tenths micron or something. Now, if the spreading resistance profiles in those
structures are not perfect, what else have you got? Or to put it another way, you can con-
trol the production of those base widths and the like with spreading resistance profiles
even if you cannot interpret the data to give you absolute impurity concentration profiles.
The same thing goes with respect to junction position location. I would be happier to see
raw data used more.

D. WILLIAMS: This afternoon I have heard at least two suggestions on where we go from here.
The first was that we take a simple empirical approach to the measurement. The other, proposed
by Dickey, was that we do some more studying of correction factors. It seems to me first of
all that spreading resistance is supposed to do something very rapidly, but cheap and dirty
to verify something else you have done. NBS, RCA and TI, at least during this meeting, have
claimed that there is a linear relationship between resistivity and spreading resistance. I
hope this is true because this implies that the measurement data checks with the simple
model. Now, if we were not interested in going to doping profiles then all you would have
to do is have N samples which you keep the same and as long as you get the same spreading
resistance reading then you do not have to worry about the resistivity of the material, you
just say that your spreading resistance probe at least on these samples are measuring the
same thing. Maybe these are some of the areas that could be investigated. I think that the
studyCopyright
of correction factors
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Jan 1 23:23:49 and make a nice mathematical study. What
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does it have to do with actually studying your manufacturing process, if I get a certain
spreading resistance characteristic and I know I can get good product on that material and I
do not if it is some other material, is this the original intention of spreading resistance
measurement?

N. GOLDSMITH: I would like to add comments to that. There are two aspects to using spreading
resistance for production control. In one case you are interested in reproducing something
and in our case, as Jacques Assour showed, we have a high resistivity n layer covered over
by a high resistivity p layer and we want to control that high resistivity n layer. Well
then we simply control on the height of the recorder pen. The higher it goes, the higher
the resistivity and you can sort by the height of the recorder pen without a calibration
graph. That is a practical application; it works and it is in production. However, as
Walter Schroen pointed out, there are times when you want to go beyond that. You want to
predict in advance from the starting material what devices you are going to make. At that
point you have to have quantification of the data and that is when you have to include cor-
rection factors. You also have to know what your calibration curve is and it has to be
transferable from laboratory to laboratory.

J. ASSOUR; It is true that with production processes you like control. Good or bad. Of
course, good control makes good devices, and when you have bad control you try to make it
better. On the other hand, there are still a lot of device characteristics that we do not
understand in solid state devices and there comes a time when you have the structure of the
device you would like to sit down and think about it and try to correlate it with the
physics and in this instance you must have some data that you can rely on in order to devel-
op design modeling.

S. MYLROIE; I think it was alluded to in some of the other answers that there are really
two areas we are talking about. One is the production control area where the raw data is
good enough for process control and maintaining a process. The other area where we need
the calibration and correction factors is that of closing the loop back to the device char-
acteristics, in order to work with the circuit designer and the device designer. Then when
they know the devices they want, through models we can develop and characterize the pro- .
cesses needed to generate these devices. For this type of work we need to be able to relate
to doping concentrations and the device physics and this area is where we need the accurate
correction factors.

D. WILLIAMS: I perfectly agree, I think that the correction factors are an interesting
study and should be done. That is my point. However, there appears to be many chances for
error in going from spreading resistance to doping profiles. If I have spreading resistance
values I hope by calibration curves to translate to resistivity values. From there I can
hopefully go to dopant values by using Irvin's curves. Now, many factors, as pointed out by
NBS and RCA, may cause problems such as surface preparation that gives a high resistivity,
or maybe you have a damaged surface, but you are also going through at least two translations
and a correction factor from a spreading resistance to a doping profile before you come up
with any answers. How many other factors there are, I do not know.

G. GRUBER: I would like to comment, I think the fact that this is an NBS and ASTM jointly
sponsored symposium goes a long way in saying that the real need in the industry is for
standardization of the spreading resistance technique, in fact for standardization of all
resistivity measurements. This whole week was interesting for me, it was the first time I
had been to an ASTM meeting and I would recommend it to everyone in the industry. It pointed
up to me the need for standards in things that I considered pretty well standardized already,
such as wafer thickness. I also sat in on a discussion of the inaccuracies of mobility mea-
surements and the effects on Irvin's curves. Coupled with this I think what we have learned
at this Symposium is the fact that the Spreading Resistance technique can be no better than
the standards on which it is based.

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 CONCLUDING REMARKS BY PAUL LANGER
I would like to make a very brief summary. We have heard 22 papers and some last minute re-
marks in the last couple of days and I think it points up the direction that spreading re-
sistance measurements will probably go in the next few years. There are two areas that
will probably get the bulk of the development effort. The first area is probably the de-
velopment of more reliable correction factors for all types of structure* specifically very
thin transition regions between either one type or the same type of dopant. I think there
is also a need not only to have very complex correction factor models but also a need for
fast and simple correction factor models so that one will be able to perform these calcu-
lations on a calculator or a mini computer. The second area is that of surface preparation
and it is still a big unknown. Most laboratories have standardized more or less on their
own type of sample preparation. Under those constraints good intralab precision has been
obtained but this high level of precision may degrade in interlab studies due to differences
in specimen preparation. So I think surface preparation will get some closer looks over the
next few years. On the positive side, it is very nice to see the wide acceptance that
spreading resistance has had in all areas of the semiconductor industry. Crystal growers
are using it, the people in epi and diffusion are using it, and people modeling devices are
using it. Spreading resistance seems to have come of age. It probably does not really have
as far to go as one would think from listening to some of the discussions.
I would like to reemphasize the role of ASTM and NBS in the measurements area. The
American Society for Testing and Materials is your organization as is the Bureau of Standards.
These organizations are here to do the work that people in the semiconductor industry are
interested in getting done. The Bureau of Standards does not go off on research projects
for the sake of research alone as neither does ASTM. It gets its inputs from the industry and
if you have a specific project you think really needs to be pursued or if you would like to
help out in pursuing some of the work being done on electrical measurements or other means
of characterization I suggest you attend the next meeting in Scottsdale. It is right after
Labor Day and I think it will be very beneficial since in obtaining intercompany standard-
ization one really needs to exchange material based on spreading resistance measurements.
Finally I would just again like to thank the members of the committee who acted as session
chairmen, Ken Benson and Bernie Morris of Bell Labs, Fred Mayer of RCA, Francois Padovani of
T. I. and Fritz Vieweg-Gutberlet of Wacker Chemitronic; and also to our arrangements man,
Jim Ehrstein from the Bureau of Standards. Thank you all for coming and hope to see you all
again soon.

278
 APPENDIX-BIBLIOGRAPHY

The bibliography which follows is intended for the convenience of users of this
volume. While not pretending to be an exhaustive list of titles on spreading resistance,
it is nevertheless judged to contain all the major references commonly cited by those
working on spreading resistance measurements. Entries are listed by year of publication
and within each year, by the alphabetic ordering of the primary author's name

1. Kennedy, D. P., Spreading Resistance in Cylindrical Semiconductor Devices, J. Appl.

Phys. 31 #8, 1490-7 (1960).
2. Dickey, D. H., Diffusion Profiles Using a Spreading Resistance Probe, Extended Ab-
stracts of the Electronics Division, The Electrochemical Society 12, No. 1, 151 (April
1963).

3. Mazur, R. G., Dickey, D. H., The Spreading Resistance Probe - A Semiconductor Resis-
tivity Measurement Technique Extended Abstracts of the Electronics Division, The
Electrochemical Society 12, No. 1, 148 (April 1963).

4. Greenwood, J. A., Constriction Resistance and the Real Area of Contact, Brit. J. Appl.
Phys. 17_, 1621-1632 (1966).

5. Mazur, R. G., Spreading Resistance Resistivity Measurements on Silicon Containing p-n

Junctions, Extended Abstracts of the Electronics Division, The Electrochemical Society
15_, No. 1, (1966).

6. Mazur, R. G., Dickey, D. H., A Spreading Resistance Technique for Resistivity Measure-
ments on Silicon, J. Electrochemical Society,!^, 255-259 (1966).
7. Dickens, L. E., Spreading Resistance As a Function of Frequency, IEEE Transactions on
Microwave Theory and Technique3 MTT-15 No. 2, 101-109 (1967).
8. Greenwood, J. A., The Area of Contact Between Rough Surfaces and Flats, Trans. ASME3
Ser. F_. 89_, 81-91 (1967).

9. Holm, R., Electric Contacts,, 4th ed. Springer-Verlag, New York, (1967).

10. Mazur, R. G., Resistivity Inhomogeneities in Silicon Crystals, J. Electrochem. Soc

114, 255-259 (1967).
11. Adley, J. M., Poponiak, M. R., Schneider, C. P., Schumann, P. J., Tong, A. H., The
Design of a Probe for the Measurement of the Spreading Resistance of Semiconductors,
Semiconductor Silicon 19693 The Electrochemical Society, 721-736 (1969).
12. Keenan, W. A., Schumann, P. A., Tong, A. H., Phillips, R. P., A Model for the Metal-
Semiconductor Contact in the Spreading Resistance Probe, Ohmic Contacts to Semicon-
ductors, The Electrochemical Socity, 263-276 (1969).
13. Rymaszewski, R., Relationship Between the Correction Factor of the Four-Point Probe
Value and the Selection of Potential and Current Electrodes, J. of Sci. Instr.3 Series
2 Vol. 2, 170-174 (1969).
14.. Schumann, P. A., Gardner, E. E., Spreading Resistance Correction Factors, Solid-
State Electronics 12_, 371-375 (1969).
15. Schumann, P. A., Gardner, E. E., Application of Multilayer Potential Distribution to
Spreading Resistance Correction Factors, J. Electrochemical Society 116, 87-91 (1969).
16. Gorey, E. F., Schneider, C. P., Poponiak, M. R., Preparation and Evaluation of
Spreading Resistance Probe Tip, J. Electrochemical Society 117, 721-724 (1970)
279
17. Gupta, D. C., Chan, J. Y, A Semiautomatic Spreading Resistance Probe, Rev. Sci
Instrtm. 41_, 176-179 (1970).

18. Gupta, D. C., Chan, J. Y., Wang, P., Effect of the Surface Quality on the Spreading
Resistance Probe Measurements, Rev. Sai. Instrum., 41, 1681-1682 (1970).
19. Hoppenbrouwers, A. M. H., Hooge, F. N., 1/f Noise of Spreading Resistances, Philips
Res. Rep. 25_, 69-80 (1970).
20. Mazur, R. G., Spreading Resistance Measurements on Buried Layers in Silicon Structures,
Silicon Device Processing: Gaithersburg, Maryland, NBS Special Publication 337, 24
255 (1970).

21. Yeh, T. H., Khokhani, K. H., Multilayer Theory of Correction Factors for Spreading
Resistance Measurements, J. Electrochemical Society 116, 1461-1464 (1969).
22. Yeh, T. H, Current Status of the Spreading Resistance Probe and Its Application
Silicon Device Processing: NBS Special Publication 337, 111-122 (1970).

23. Brooks, R. D., Mattes, H. G., Spreading Resistance Between Constant Potential Surfaces,
Bell System Tech. J. 50_, 775 (1971).
24. Chu, T. L., Ray, R. L., Resistivity Measurements on Germanium Crystals by the Spreadin
Resistance Technique, Solid-State Tech., 37-40 (September 1971).

25. Ting, Chung-Yu, Chen, C. Y., A Study of the Contacts of a Diffused Resistor, Solid-
State Electronics 14_, 433-38 (1971).
26. Hu, S. M., Calculation of Spreading Resistance Correction Factors, Solid-State Elec-
Eleatronics 15_, 809-817 (1972).
27. Severin, P. J., Measurement of the Resistivity and Thickness of a Heterotype Epitaxially
Grown Silicon Layer with the Spreading Resistance Method, Philips Res. Rep. 26, 359-372
(1971).'
28. Severin, P. J., Measurement of the Resistivity of Silicon by the Spreading Resistance
Method, Solid-State Electronics 14, 247-255 (1971).
29. Tong, A. H., Gorey, E. F., Schneider, C. P., Apparatus for the Measurement of Small
Angles, Rev. Sci. Instrum. 43. 320-325 (1972).
30. Kraner, P., Van Reuyven, L., The Influence of Temperature on Spreading Resistance
Measurement, Solid-State Electronics 15_, 757-766 (1972).

31. Schumann, P. A., Small Spaced Spreading Resistance Probe, Solid-State Tech., 50-54,
(March 1972).
32. Burtscher, J., Krausse, J., Voss, P., Inhomogeneities of the Resistivity in Silicon:
Two Diagnostic Techniques, Semiconductor Silicon 197 3> The Electrochemical Society3
581-589 (1973).
33. Burtscher, J., Dorendorf, H, W., Krausse, J., Electrical Measurement of Resistivity
Fluctuations Associated with Striations in Silicon Crystals, IEEE Trans, on Elec.
Dev. ED-20, No. 8, 702-708 (1973).
34. Hu, S., Poponiak, M. R., Copper Precipitation in Silicon-Observation of Electrical
Effect, Phys. Stat. Sol. (a) 18 no. 1, 5-8 (1973).
35. Witt, A. F., Lechtensteiger, M., Gatos, H. C., Experimental Approach to the Quanti-
tative Determination of Dopant Degregat on a Microscale, J. Electrochemical Society
120, 1119-1123 (1973).

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36. deKock, A. J. R., Severin, P. J., Roksnoer, P. J., On the Relation between Growth
Striations and Resistivity Variations in Silicon Crystals, Phys. Stat. Sol. 22a, 1
166 (1974).

37. Morris, B. L., Some Device Applications of Spreading Resistance Measurements on Epi-
taxial Silicon, J. Electrochemical Society 121, 422-426 (1974).

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NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession 3. Recipient's Accession No.
BIBLIOGRAPHIC DATA No.
SHEET NBS SP-400-10
4. TITLE AND SUBTITLE 5. Publication Date
Semiconductor Measurement Technology: SPREADING RESISTANCE December 1974
SYMPOSIUM 6. Performing Organization Code
PROCEEDINGS OF A SYMPOSIUM HELD AT NATIONAL BUREAU OF STANDARD 5
June 13-14, 1974
7. AUTHOR(S) 8. Performing Organ. Report No.
James R. Ehrstein, Editor
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. Project/Task/Work Unit No.

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 11. Contract/Grant No.
WASHINGTON, D.C. 20234

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 13. Type of Report & Period
Covered _,. _
Final June 13-
Committee F-l of the American Society for Testing and 14, 1974
Materials and The National Bureau of Standards 14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 2.00-word or /ess factual summary of most significant information. If document includes a significant
bibliography or literature survey, mention it here.)
This Proceedings contains the information presented at the Spreading Resistance
Symposium held at the National Bureau of Standards on June 13-14, 1974.
This Symposium covered the state of the art of the theory, practice and application
of the electrical spreading resistance measurement technique as applied to character-
ization of dopant density in semiconductor starting materials and semiconductor device
structures. In addition to the presented papers, the transcripts of the discussion
sessions which were held directly after the Theory, Practice and Applications sessions
are also included. These transcripts, which were reviewed by the respective respondents
for clarity, are essentially as presented at the Symposium.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper
name; separated by semicolons)
Dopant concentration, dopant profiles, metal-semiconductor contacts, resistivity,
semiconductor surface preparation, silicon, spreading resistance.
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 Announcement of New Publications on
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 3 T151 D O D S M S m 1

Spreading Resistance Symposium,

National Bureau of Standards,
1974./ Spreading Resistance Sym

DATE DUE

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