Chapter 3

Oxidation

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Chapter 3:
Oxidation

Thin films layers:

 Thermal oxides
 Dielectric layers
 Polycrystalline silicon
 Metal films

Schematic cross section of a metal-oxide-semiconductor field-effect transistor (MOSFET)

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 Topics:

 The thermal oxidation process used to form silicon dioxide (SiO2)

 Impurity redistribution during oxidation

 Material properties and thickness measurement techniques for

SiO2 films

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Chapter 3:
Oxidation

Oxidation:
Process by which a layer of silicon dioxide (SiO2) is grown on a silicon substrate.
Applied exclusively to Si, since GaAs, Ge, and other semiconductors don’t form native oxides.

Uses of Oxide Film:

 Device Protection and Isolation
 Surface Passivation
 Gate Oxide Dielectric
 Dopant Barrier (implant/diffusion mask)
 Dielectric Between Metal Layers

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Chapter 3:
Oxidation

Oxidiation methods:
 Thermal oxidation
 Electrochemical anodization
 Plasma –Enhanced Chemical Vapor Deposition (PECVD)

For gallium arsenide:

Thermal oxidation results in generally nonstoichiometric films.
The oxides provide poor electrical insulation and semiconductor surface protection.

We concentrate on the thermal oxidation of silicon

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Thermal SiO2 Properties

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Chapter 3:
Oxidation

Thermal oxidation Process

• Dry oxidation:
Si + O2 → SiO2 (better quality)

• Wet oxidation:
Si + 2H2O → SiO2 + 2H2 (faster growth rate)

Oxidation temperature 900°-1200 °C

Gas flow rate is about 1 liter/min.

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Chapter 3:
Oxidation Thermal oxidation Process

Schematic cross section of a resistance-heated oxidation furnace

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Chapter 3:
Oxidation Thermal oxidation Process

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Chapter 3:
Oxidation Thermal oxidation Process

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Chapter 3:
Oxidation Thermal oxidation Process

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Chapter 3:
Oxidation Thermal oxidation Process

Silicon oxide structure

Basic structural unit

of silicon dioxide

Amorphous silica density 2.21 g/cm3

Quartz density 2.65 g/cm3 13
Chapter 3:
Oxidation Thermal oxidation Process

Silicon Consumption

 During growth, 1 mole of SiO2 takes up more volume than 1 mole of Si.
 To grow an oxide layer of thickness d, a layer of Si of thickness 0.44d is consumed.
 The oxidizing species diffuse through the oxide to the Si surface and react.

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Chapter 3:
Oxidation Thermal oxidation Process
Calculation of SiO2 thickness
 The molecular weight of Si is 28.9 g/mol, and the density is 2.33 g/cm3
 The molecular weight of SiO2 is 60.08 g/mol and the density is 2.21 g/cm3

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 Thermal oxidation Process

Silicon Dioxide
56%
Level of original silicon layer
44%

Silicon

1 µm Si oxidized

2.27 µm SiO2

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Chapter 3:
Oxidation Thermal oxidation Process
Deal-Grove Model
• Three-step mechanism:
– Oxygen diffuses through the gas to the top of the wafer
– Oxygen diffuses through the oxide that has formed on the wafer to the Si
interface
– Oxygen reacts with silicon to form SiO2

• Limitations of the model:

– 1D model (planar substrates)
– Not accurate for heavily doped silicon
– Not accurate for thin oxides, < 20 - 25 nm

• Assumptions:
- Temperature: 700 - 1300 oC
- Pressure: 0.2 - 1.0 atm
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- SiO2 thickness: 0.03 - 2 µm
Chapter 3:
Oxidation Thermal oxidation Process

C0 = concentration of oxidizing Oxidant

Oxide Semiconductor
species at oxide surface (cm-3)
CS = concentration of oxidizing
species at Si surface (cm-3)

d = oxide thickness

F´s = fluxes (cm-2s-1)

Basic model for the thermal oxidation of silicon

At 1000 °C and a pressure of 1 atm, the concentration C0 is 5.2×1016 molecules/cm3

for dry oxygen and 3×1019 molecules/cm3 for water vapor
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Chapter 3:
Oxidation Thermal oxidation Process

dC D (C0  Cs )
F1  D 
dx x
F2  Cs
DC0
At steady-state F1  F2  F 
x  ( D / )

D = diffusion coefficient of oxidizing species

x = thickness of existing oxide layer

k = surface reaction rate constant

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Chapter 3:
Oxidation Thermal oxidation Process
Growth Rate

If: C1 = The number of molecules of oxidizing species/unit volume of the

oxide
= 2.2 × 1022 silicon dioxide molecules/cm-3 for O2
= 4.4 × 1022 silicon dioxide molecules/cm-3 for H2O

dx F DCo / C1
 
dt C1 x  ( D / )

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Chapter 3:
Oxidation Thermal oxidation Process

Solution:
• Initial condition: x(0) = d0

2 2D 2 DC0
x  x ( t  )
 C1

where:   ( d 02  2 Dd 0 /  )C1 / 2 DC0

which represents a time coordinate shift to take into account the initial oxide layer d 0

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Chapter 3:
Oxidation Thermal oxidation Process
For small values of t

for larger values of t

During the early stages of oxide growth

Surface reaction is the rate-limiting factor
Oxide thickness varies linearly with time

As the oxide layer becomes thicker

The oxidant must diffuse through the oxide layer

to react at the silicon-silicon dioxide interface

The reaction becomes diffusion limited

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Chapter 3:
Oxidation Thermal oxidation Process

Compact Form
x2 + Ax = B(t + t)

where: A = 2D/k
B = 2DC0/C1
d 02  Ad 0

B

Then: x = [Bt + 0.25A2 + do2 + Ado]0.5 – 0.5A

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Chapter 3:
Oxidation Thermal oxidation Process
Limiting Cases
A = 2D/k
𝑑𝑥 𝐵 B = 2DC0/C1
= Rate equation
𝑑 𝑡 2 𝑥+ 𝐴 B/A=kC0/C1

Short times (reaction rate-limited):(t+t) << A2/4B

(x<< A/2)

“Linear Regime”
B/A linear rate constant

Longer times (diffusion-limited): (t+t) >> A2/4B

(x >> A/2)

x2 = B(t + t) “Parabolic Regime”

B parabolic rate constant 24
Chapter 3:
Oxidation Thermal oxidation Process
Parameters affecting the thermal oxide thickness
The oxide growth rate depends on the:

I. Crystallographic orientation of the wafer (<100>, <111>, or <110>)

II. Oxidizing ambient (oxygen or steam)
III. Temperature
IV. Amount of impurities (i.e., B or P) in the wafer
V. Amount and kind of impurity in the oxidizer
VI. Pre-oxidation Si wafer surface cleanup
VII.Amount of stress in the oxide and in the Si wafer
VIII.Pressure
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Chapter 3:
Oxidation Thermal oxidation Process

• For wet oxidation, initial oxide thickness d0 is very small (or ≈ 0)

• For dry oxidation, extrapolated value of d0 at t = 0 is about 25 nm

• Thus, dry oxidation on bare silicon requires a value for t that can be
generated using this initial thickness

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Chapter 3:
Oxidation Thermal oxidation Process

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Chapter 3:
Oxidation Thermal oxidation Process

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Chapter 3:
Oxidation Thermal oxidation Process

Linear rate constant versus temperature Parabolic rate constant versus temperature

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Chapter 3:
Oxidation Thermal oxidation Process

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Chapter 3:
Oxidation Thermal oxidation Process
Example:
a. Calculate the oxide thickness from a wet oxidation done at 1100oC
for 1hr. Assume no initial oxide exists on the <100> wafer (do = 0).

Solution: x2 + Ax = B(t + ) with  = 0, x = [Bt + 0.25A2 + do2 + Ado]0.5 – 0.5A

B/A = 497 Å/min. and B = 87x104 Å2/min.  A = 1750.5 Å

Then x = [Bt + 0.25A2]0.5 – 0.5A = 6403 Å
b. Now assume we would like to do additional 180 min of dry
oxidation on this wafer at 900oC. Calculate the new oxide thickness.
Solution: Need initial time:  = (do2 + Ado )/B with do = 6403 Å
B/A = 2.08 Å/min and B = 5590 Å2/min.  A = 2687.5 Å
Then  = 10413 min. 31
Chapter 3:
Oxidation Thermal oxidation Process

The new thickness is: x = [B(t + ) + 0.25A2]0.5 – 0.5A  x = 6468Å.

So the additional thickness due to 3hrs of dry oxidation at 900oC is

6468-6403 = 65Å.

c. Assume we need a total of 7200Å of oxide. Calculate the oxidation

time needed if we were to do wet oxidation at 1000oC.

Solution:
do = 6468A, B = 520000 Å2/min., B/A = 111 A/min  A = 4685Å
Then :
7200 = [520000t + 0.25(4685)2 + (6468)2 + (4685)(6468)]0.5 – 4685/2
 t= 25.84 min.
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Chapter 3:
Oxidation Thermal oxidation Process

Example:
A silicon sample is oxidized in dry O2 at 1200 oC for one hour.
(a) What is the thickness of the oxide grown?

Solution:
From Table 3-2, for dry O2 @ 1200oC
A = 0.04 mm, B = 0.045 mm2/h, t = 0.027 h
Using these parameters, we obtain an oxide thickness of
x2 + 0.04x = 0.045(1+ 0.027)
x = 0.196 mm 33
Chapter 3:
Oxidation Thermal oxidation Process

(b) How much additional time is required to grow 0.1 mm more oxide
in wet O2 at 1200 oC?

Solution:  From Table 3-1, for wet O2 at 1200 oC

A = 0.05 mm, B = 0.72 mm2/h
d 02  Ad 0
Since d0 =0.196 mm from the 1st step,   0.067 h
B

The final desired thickness is x = d0 + 0.1 mm = 0.296 mm.

Using these parameters, we obtain an additional time t

using x2 + Ax = B(t + ) to be t = 0.076 h = 4.53 min
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Chapter 3:
Oxidation Thermal oxidation Process

Experimental results

Experimental results for silicon dioxide thickness as a function of reaction

time and temperature for two substrate orientations.

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Chapter 3:
Oxidation IMPURITY REDISTRIBUTION DURING OXIDATION

Impurity profile at the oxide interface

“Segregation coefficient”
• When two solids come together, an impurity in one will
redistribute until it reaches equilibrium.
• While the oxide is growing, Si is being consumed and the
impurities that are in Si must be redistributed.
• The manner in which this distribution occurs depends on
(i) segregation coefficient k of the impurity, (ii) diffusion
coefficient of the impurity in Si, and (iii) diffusion
coefficient of the impurity in SiO2.
equilibriu m concentrat ion of impurity in silicon
k
equilibriu m concentrat ion of impurity in SiO 2
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Chapter 3:
Oxidation IMPURITY REDISTRIBUTION DURING OXIDATION

Segregation in Si/SiO2
In general as oxidation proceeds four cases are possible:
1. The oxide takes up the impurity and the silicon surface is
depleted of impurities (k < 1). Slow diffusion of the impurity
through the silicon dioxide (fig a).

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Chapter 3:
Oxidation IMPURITY REDISTRIBUTION DURING OXIDATION

2. The oxide takes up the impurity and the silicon surface is

depleted of impurities (k < 1). Fast diffusion of the impurity
through the silicon dioxide (fig b).

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Chapter 3:
Oxidation IMPURITY REDISTRIBUTION DURING OXIDATION

3. The oxide rejects the impurity (k > 1).

If diffusion of the impurity through the silicon dioxide is relatively
slow, the impurity piles up near the silicon surface (fig c).

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Chapter 3:
Oxidation IMPURITY REDISTRIBUTION DURING OXIDATION

4. The oxide rejects the impurity (k > 1).

When diffusion through the silicon dioxide is rapid, so much impurity
may escape from the solid to the gaseous ambient that the overall
effect will be a depletion of the impurity (fig d).

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Chapter 3:
Oxidation IMPURITY REDISTRIBUTION DURING OXIDATION

Four different cases of impurity redistribution in silicon due to thermal oxidation

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Chapter 3:
Oxidation

Masking Properties of SiO2

Oxides as Dopant Masks
• SiO2 provides a selective mask against diffusion at high
temperatures.
• Oxides used for masking are ~ 0.5-1 mm thick.
Dopants Diffusion Constants at 1100 oC (cm2/s)
B 3.4 × 10-17 – 2.0 × 10-14
Ga 5.3 × 10-11
P 2.9 × 10-16 – 2.0 × 10-13
As 1.2 × 10-16 – 3.5 × 10-15
Sb 9.9 × 10-17
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Chapter 3:
Oxidation Masking Properties of SiO2

SiO2 Masks for B and P

Thickness of silicon dioxide needed to mask boron and phosphorus

diffusions as a function of diffusion time and temperature. 43
Chapter 3:
Oxidation

Oxide Quality
Dry vs. Wet Oxides

• Wet oxides are usually used for masking

• SiO2 growth rate is much higher when water is the oxidant.
• Dry oxidation results in a higher quality oxide that is denser
and has a higher breakdown voltage (5 – 10 MV/cm).
• Thin gate oxides in MOS devices are usually formed using
dry oxidation.

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Chapter 3:
Oxidation
Oxide Quality

Oxide Charge Locations

- Interface trapped charge (Qit): located at Si/SiO2 interface

- Fixed oxide charge (Qf): positive charge located within 3nm of Si/SiO2 interface
- Oxide trapped charges (Qot): associated with defects in the SiO2
- Mobile ionic charges (Qm): result from contamination from Na or other alkali ions
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Chapter 3:
Oxidation

Oxide Thickness Measurement

Color Chart
Thickness (mm) Color
0.07 Brown
0.31 Blue
0.39 Yellow
0.41 Light orange
0.47 Violet

 Not very accurate

 Colors repeat periodically at higher thicknesses
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Chapter 3:
Oxidation

Oxide Thickness Measurement

Profilometry

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Chapter 3:
Oxidation

Oxide Thickness Measurement

Polarization and Ellipsometry
• Polarization in electromagnetic waves, such as light, is specified by
the direction of the wave's electric field. All electromagnetic waves
propagating in free space or in a uniform material of infinite extent
have electric and magnetic fields perpendicular to the direction of
propagation. Conventionally, when considering polarization, the
electric field vector is described and the magnetic field is ignored
since it is perpendicular to the electric field. The direction of the
electric field oscillation in electromagnetic waves is not uniquely
determined by the direction of propagation. The term polarization thus
describes the possible orientations of the electric field in the plane
perpendicular to the wave's path.
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Chapter 3:
Oxidation

Oxide Thickness Measurement

Ellipsometry

• Polarization changes occur when

light is reflected from or transmitted
through a medium.

• Polarization changes are a function of optical properties, thickness, and

wavelength and angle of incidence of the light beam.
• Differences in polarization measured by an ellipsometer, and oxide
thickness can be calculated.

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