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Junction Diode

Characteristic s 65 At very low temperatures say 0 K, the ideal structure is achieved and the

semiconductorbe haves as an insulator, since no free carriers

of

electricity are available. However at

roomtemperature , some
of

he covalent bonds will be broken because

of

the thermal energy supplied tothe crystal, and conduction is made possible. An

electron which for the greater period

of

timeforms part
of

a covalent bond, is

shown as being dislodged and so free to wander in a randomfashion throughout the crystal.
1,2,3,

and 4, are Ge atoms with 4 valance electrons

(Fig.
o

0@
2.4).

These four valence electrons

of

each atom are shared by:

.

other atoms and so bounded by

covalent bonds, except for atom

;
:)'01'
I. The electron
of Ge

atom I is dislodged from its original

: 0.(

Ifr
.

Electron

position, because
of

he thermal energy and so the covalent bonds

o_

'.

..:.....
0

bonding the electron are broken. So this

electron is now a free

o

(J.:....:.

0'. : ..

__
0

electron to wander anywhere in the material ti

II

it collides with
o

@:

:Q)
some other atom. The absence
0

of

the electron in the covalent

..
: bond is

represented by a hole. This is the concept

of

hole. The: : energy required to break different

covalent bonds will be different.

.
So at a time at room temperature all

the covalent bonds are not

o

\:..)0

broken to create innumerable free electrons. Fig

2.4

Covalent bonds The energy

Eg

required to break such a covalent bond is

about 0.72 eV for Germanium and

1.1

eV for silicon (at roomtemperature ). A hole can serve as a carrier

of

electricity. Its significance lies in this characteristics.T he explanation is given below:When a

bond is incomplete so that hole exists, it is relatively easy for a valence electron

in a neighbouring atom to leave its covalent bond to fill this hole. An electron moving from a bond tofill

a hole leaves a hole in its initial position. Hence the hole effectively moves

in the directionopposite to that of the electron. Thus hole in

its new position may now be filled by an electronfrom another covalent bond and the hole will correspondingly

move one more step in the directionopposite to the motion

ofthe

electron. Here we have a mechanism for the conduction

of

electricitywhich does not involve free electrons.

Only the electrons are exchanging their position and thereby current is flowing. In

other words, the current is due to the holes moving in

the oppositedirection to that

of

electrons. To explain this further,2 3 4 5 6 789

10 (a)
0000000000
0000000000

(b) 2 3 4 5 6 7 8 9
10.

Fig. 2.5

Current flow by the movement of holes

In row (a) there are 10 ions

in Fig. 2.5. Except for 6, all the covalent bonds

of

the ions areintact. The ion

6 has a broken covalent bond

or

one
of

its valence electrons got dislodged. So

theempty place denotes a hole. Now imagine that an electron from ion 7 moves into the hole at ion

6. Then the configuration is as shown in row (b). Ion

6 in the row is completely filled. There is no

-broken covalent bond. But ion 7 has a vacancy now, since it has lost one
of

its valence electrons.

66
Electronic Devices and Circuits Effectively the hole has moved from ion 6 to ion

7. So the movement of holes is opposite to that

of

electrons. The hole behaves like a positive charge equal in magnitude to the electron charge.

In a pure semiconductor the number

of

holes is equal to the number of ree electrons.

Thermal agitation continues to produce new electron hole pairs

whereas

some other hole electronpairs disappear as a result

of

recombination.T his is analogous

to passengers travelling in a bus. Bus is the semiconducting material.Standin

g passenger are free electron. When a sitting passenger gets down, a hole is created. Thishole is filled by a free electron that

is a standing passenger. This process goes on as the bus ismoving from stage to stage.
If

there are many standing passengers, without any vacant seat, it is analogous to ntype

semiconductor. Ifthere are many seats vacant without any standing passengerit is like a p-type semiconductor.S

o the semiconductros are classified as :

n-type Sefiliconductor p-type Semiconductor

Free electron concentration

'n'

is greater thanhole concentration.

D

>

p.Hole concentration
'p'

is greater than free electronconcentr ation. p

>
D.

Instrinsic Semiconductor
D

=
p.

2.4 CONDUCTIVI TY

OF

AN INTRINSIC SEMICONDU CTOR When valence electrons are exchanging theIr

posItions, we say holes are moving. Current is contributed by these holes current is

nothing but rate

of

flow
of

charge. Holes are positivelycharge d. So hole

movement contributes for flow

of

current. Because
of

the positive chargemovement , the direction

of

hole current is same as that

of

conventional current. Suppose to startwith, there are many free electrons, and these wiIl be moving in

random directions. A current isconstituted by these electrons. So at any instant, the total current density

is summation
of

thecurrent densities due to holes and electrons. The charge

of

free electrons is negative and itsmobility is

J..ln.

The hole is

positive, and its mobility is

J..lp.

The charge
of

both holes and electronsare same

'e'.

A hole can move from one ion to the nearest where as an electron is

free to moveanywhere till it collides with another ion or free electron. Electrons and holes move in

oppositedirectio ns in an electric field E. Though they are

of

opposite sign, the current due to each ion is in

the same direction.Current Density, J

=

(JE J

=
(n

J..ln

+ pJ..lp)

x ex E

=
(J

x En

=
Magnitude
of

Free Electron Concentrationp

=
Magnitude
of

Hole Concentration
(J
=

Conductivity

n/
cm or Seimens
(J

=
(n
J..ln

P
J..lp)

neJ..ln + peJ..lp

A pure
or

intrinsic semiconductor is one in which n

p
=

nj

where n
l

is intrinsic concentration. In

a pure Germanium at room temperature, there is

about one holeelectron pair for every2

x

10
9

Germanium atoms. As the temperature

increases, covalent bonds are broken and so morefree electrons and holes are created. So n
l

increases, as the temperature increases, in accordancewith the relationship,

Junction Diode Characteristic s

3

n.'=
AxT2

e-EGo/2kT
I

EG

= Energy Gap in ev. e = Charge

of

an Electron
or

holeA = Constant for a semiconductor;fo r Ge A = 9.64

x

10
21

;for
Ge

EG

= 0.785 eV at 0 oK
forSi

EcJ= 1.21 eV at 0 oK
EG

at room temperature,for Ge = 0.72 eVfor Si= 1.1 e VT

=
Temperature

in 0 oK k = Boltzman s Constant.

67
..........
(2.12)

As n
l

increases with T, the conductivity also increases, with temperature for semiconductor.

In other words,

the resistivity decreases with temperature

for

semiconductor.
On the otherhand

resistance increases with temperature

for

metals.
This

is
because,

an increase

in temperature for metals results in greater thermal motion

of

ions and hence decrease

in the meanfree path

of

the free electrons. This results in decrease

of

the mobility
of

free electrons and sodecrease in conductivity or increase in

resistivity for metals.

2.5 DONOR
TYPE OR
n-

TYPE

SEMICONDU CTORS

Intrinsic or pure semiconductor is

of

no use since its conductivity is less and it can not be chargedmuch.

If

a pUie semiconductor is doped with impurity it becomes extrinsic.

Depending uponimpurity doped, the semiconductor may become

n-type, where electrons are the majority

carriersor donor type,

since it donates an electron. On the other hand
if

he majority carriers are

holes,it is p-type or acceptor type semiconductor,

because it accepts an electron to complete thebroken

covalent bond.Germanium atom with its electrons arranged in

shells will have configuration asIs2 2s2 2p2 3s23p6 3d

1o

4s24p2Ge is tetravalent (4).

'Ge'

becomes n-type
if

a pentavalent (5), impurity atoms such asPhosphorus (P), or Arsenic

are added to it.The impurity atoms have size

of

the same order as that

ofGe

atoms. Because
of

the energysupplied while doping, the impurity atom dislodges one from its normal position in

the crystallattices takes up that position. But since the concentration

of

impurity atoms is very small

(aboutI atom per million

ofGe

atoms), the impurity atom is surrounded by Ge atoms. The impurity atom

is pentavalent. That is, it has 5 electrons in the outermost orbit (5

valence electrons).
Now

4
of

these are shared by

Ge

atoms, surrounding the impurity atom and they form covalent bonds. Soone electron
of

the impurity atom is left free.

The energy required to dislodge this fifth electronfrom its parent impurity atom is very little
of

he order
of

0.01 eV to 0.05 eY. This free electron is in excess to the free electrons that

will be generated because

of

breaking
of

covalent bonds due tothermal agitation. Since

an excess electron is available for each impurity atom, or it can

denotean electron it is

called n-type, or donor type semiconductor.


\
.

68 Electronic
Devices

and Circuits

2.6
ACCEPTORTYP E OR

PTYPE

SEMICONDU CTORS
An

intrinsic semiconductor when doped with trivalent (3) impurity atoms like Boron, Gallium Indium,Aluminiu

m etc., becomes p-type or acceptor type.Because

of

the energy supplied while doping, the

impurity atom dislodges

ane

Ge atom fromthe crystal lattice. The doping level is low, i.e., there is

one impurity atom for one million Ge atoms,the impurity atom is surrounded by Ge atom.
Now

the three valence electrons

of

impurity atomare shared by 3 atoms.

The

fourth Ge atom has no electron to

share with the impurity atom. Sothe covalent bond is not filled or a hole exists. The impurity atom

tries to steal one electron fromthe neighboring

Ge

atoms and it does so when sufficient energy is supplied

to

it. So hole moves.There will be a natural tendency in the crystal to form 4 covalent bonds. The

impurity atom (andnot

just

3) since all the other Ge atoms have 4 covalent bonds and the structure
ofGe

semiconductor is crystalline and symmetrical. The energy required for the impurity atom to steal one Ge electron

is 0.0 I e V to 0.08 e Y. This hole is in excess to the hole created by

thermal agitation. 2.7

IONIZATION ENERGY

Ifintrinsic semiconductor is doped with phosphorus,

it becomes n-type as Phosphorus is pentavalent.The 4 electrons in

the outer orbit

of

Phosphorus are shared by the 4 Germanium atoms and thefifth electron

of

Phosphorus

in the outer orbit is a free electron. But in order that this electron is

completely detached from the parent Phosphorus atom, some energy is

to be supplied. Thisenergy required to separate the fifth electron is called

Ionization Energy.
The value
of

ionizationenergy for Germanium is 0.012

eV, and in Silicon, it is 0.044 eY.

For different impurity materials,these values will be different, in

Silicon and Gennanium. As this energy is small, at room temperature,we assume that all the impurity

atoms are ionized. 2.8

HOLES

AND
ELECTRONS

In intrinsic semiconductors, n
=

p
= ni.

Or

the product n x p

ny. In

extrinsic semiconductorsa y n-type semiconductor practically the

electron concentration, 0
OJ.

As a result holes, minoritycarrier in n type, encounter with free

e l ~ ~ t m n s , . a J l ( i t h - i s p r o b a b i l i t

is much larger since n p.

Sowhen a hole encounter a freeelectrc)\:;, both electrons and holes recombine and the place
of

holeis occupied by the free electrons and this probability is much lager since 0
p.

The result is

thatboth free electron and hole are lost. So the hole density
'p'

decreases and also that

of

electron

density'
n'

but still 0
OJ.

This is also true in the case

of

p-type semiconductor p
OJ,

ndecreases in

acceptor type semiconductor, as a result

of

recombination,
'p'

also decreases butp

>>OJ.

It has been observed practically that the net concentration

of

the electrons and holesfollows the realtion n x p

n7.

This is an approximate formula but still valid. Though

'p'

decreases

in n-type semiconductor with recombination, '0' also decreases, but 0

OJ

and because
of

breaking
of

covalent bonds, more free electrons may be cr.eated :and

'0' increases.In the case of p-type semiconductor the concentration of acceptor atoms

Na

n
l.

Assumingthat all the acceptor atoms are ionized, each acceptor atom contribute at

least one hole. Sop

OJ.

Holes are the majority carriers and the electrons minority carriers. As p
OJ,

thecurrent is contributed almost all, by holes only and the current due to electrons is negligibly small.
If

impurities
of

both donor type and acceptor type are simultaneously doped in

intrinsicsemicond uctor, the net result will be, it can be either,prype or n-rype

depending upon their individualconcent ration. To give a specific example, suppose

donor atoms concentration is 100 n

l,

and acceptoratoms concentration in 10

nl"

Then
No
=

0.1 N
I.

The number
of

electrons combine contributed by

Junction Diode Characteristic s

69
ND

combine with number

of

holes contributed by Na. So the net free electrons will be equal to 0.9
No
=

90 Ni. Such a semiconductor,

can be regarded as n type semiconductor.

If
NA
=

ND

thesemiconductor remains intrinsic. 2.S.1

INTERSTITIAL ATOMS

Intrinsic
or

pure semiconductor
is

practically not available. While

doping a semiconductor withimpurities, pure Phosphorous, Arsenic, Boron

or

Aluminium may not be available.

These impuritiesthemsel ves will contain some impurities. Commonly found such undesirable impurities are Lithium,Zinc, Copper, Nickel

etc. Sometimes they also act as donor

or

ac:::eptor atoms.

Such atoms arecalled as

interstitial atoms,
except
Copper

and Nickle
other

impurities do not affect much. 2.S.2

EFFECTIVE MASS

When quantum mechanism is used to specify the motion

of

electrons
or

holes within a crystal,holes and electrons are treated as imaginary particles with effective masses
mp

and

mn

respectively.This
is

valid when the external applied field

is

smaller than the internal periodic

fields produced bythe lattice structure.Most metals and semiconductors are crystalline
in

structure, i.e., they consist

of

spacearray
of

atoms
in

a regular tetrahedral
or

any other fashion.

rile regular pattern of atomarrangemen t is called lattice.

In

the case
of

metals,
in

each crystal, the atoms are very close toeach other. So the valency electron

of

one atom are as much associated with the

other

atoms aswith the parent atom.

In

other

words, the valance electrons are loosely bound to the parent atomand the electrons
of

one atom are shared by

another

atom. So every such valenceelectron has almost zero affinity with any individual atom.

Such electrons are free to move withinthe body

of

the metal under the influence

of

applied electric field.

So conductivity of metals islarge.

On the other hand, for a semiconductor also, the valence electrons

of

one atom are shared by the other atoms. But

these binding forcesare very strong.

So the valence electrons are very much less mobile.Hence conductivity

is

less; As the temperature

is

increased, the covalentbonds binding the valance electrons are broken and electrons madefree to move, resulting

in electrical conduction.

Valence Electrons
are the
outer

most electrons orbiting

aroundthe nucleus.

.
\J
f\

.
.+4

..
ree electrons
are those valence electrons which are separatedfrom the parent atom.

Since the covalent bonds are broken. Germaniumhas 4 valence electrons.

Number

of

electrons

is

equal to number of

Fig
2.6

Covalent bonds
protons. The atom is neutral

when no electric field

is

applied.
In

theadjacent figure, the ion

is

having a charge

(circles) with 4 electrons around

it.

The covalentbonds are shown by I nes I nking one electron

of

one atom to the nucleus

of
other

atom (Fig. 2.6). 2.S.3

HOLES

AND
EXCESS ELECTRONS

When a covalent bond

is

broken due to thermal agitation, an electron

is

released and a hole iscreated in the structure

of

that particular atom. The electron so released

is

calledfree electron orexcess electron since it is

not

required to complete any covalent

bond

in its immediateneigh borhood.

Now

the ion which has lost electron will seek

another

new electron to fill the

EDC k Lal Kishore

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1.1 ELECTRON DYNAMICS 1.3 SIMPLE PROBLEMS INVOLVING ELECTRIC AND MAGNETIC FIELDS ONLY 1.4 PRINCIPLES OF CRT 1.5 DEFLECTION SENSITIVITY 1.6 APPLICATION OF CRO 2.1 REVIEW OF SEMICONDUCTOR PHYSICS 2.2 ENERGY BAND STRUCTURES 2.3 CONDUCTION IN SEMICONDUCTORS 2.4 CONDUCTIVITY OF AN INTRINSIC SEMICONDUCTOR

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