Transcript Chapter 6 OXIDATION

Models

The first major model is that of Deal and
Grove (1965)
 This
lead to the linear/parabolic model
 Note



 The
that this model cannot explain
the effect of oxidation of the diffusion rate
the oxidation of shaped surfaces
the oxidation of very thin oxides in mixed ambients
model is an excellent starting place for
the other more complicated models
CHEMICAL REACTIONS

Process for dry oxygen
Si + O2  SiO2

Process for water vapor
Si + 2H2O  SiO2 + 2H2
OXIDE GROWTH

Si is consumed as oxide grows and
oxide expands. The Si surface moves
into the wafer.
Original
surface
54%
46%
SiO2
Silicon
wafer
MODEL OF OXIDATION

Oxygen must reach silicon interface
 Simple
model assumes O2 diffuses through
SiO2
 Assumes no O2 accumulation in SiO2
 Assumes the rate of arrival of H2O or O2 at
the oxide surface is so fast that it can be
ignored
 Reaction
rate limited, not diffusion rate limited
Deal-Grove Model of Oxidation

Fick’s First Law of diffusion states that the
particle flow per unit area, J (particle flux), is
directly proportional to the concentration
gradient of the particle.

We assume that oxygen flux passing through the
oxide is constant everywhere.
F1  hG (CG  CS )

F1 is the flux, CG is the concentration in the gas
flow, CS is the concentration at the surface of the
wafer, and hG is the mass transfer coefficient
No
Silicon
dioxide
J
Silicon
N
Ni
SiO2
Si
Xo
Distance from surface, x
J   D( N O  N i ) / xO
F2  D(CO  Ci ) / xO
Deal-Grove Model of Oxidation

Assume the oxidation rate at Si-SiO2
interface is proportional to the O2 J  k N
s i
concentration:
F3  ksCi

Growth rate is given by the oxidizing flux
divided by the number of molecules, M, of
the oxidizing species that are incorporated
into a unit volume of the resulting oxide:
dx0
DN0
J


dt M M x0  D k s 
Deal-Grove Model of Oxidation

The boundary condition is
x0 t  0  xi

The solution of differential equation is
2
0
x
x0
t 

B B A
2D
2 DN o
A
B
ks
M
xi2
xi
 
B B A
Deal-Grove Model of Oxidation
xox : final oxide thickness
xi : initial oxide thickness
B/A : linear rate constant
B : parabolic rate constant
xi: thickness of initial oxide layer
: equivalent time required to grow initial oxide layer

There are two limiting cases:
 Very long oxidation times, t >> 
 xox2 =
Bt
 Oxide growth in this parabolic regime is
diffusion controlled.
 Very
short oxidation times, (t + ) << A2/4B
xox = B/A ( t +  )
 Oxide growth in this linear regime is reactionrate limited.

At short times, B/A is the linear rate constant
Process is controlled by the reaction at the Si surface
Temperature (0C)
1200
10.0
1100
1000 900
1.0
B/A
(mm/hr)
800
700
H2O (640 torr)
EA = 2.05 eV
0.1
(111) Si
(100) Si
0.01
Dry O2
EA = 2.0 eV
0.001
0.0001
0.6
0.7
0.8
1000/T (K-1)
0.9
1.0
1.1
At long times, B is the parabolic rate constant (xO2 a B)
Process is controlled by diffusion of O through oxide
Temperature (0C)
1200
1100
1000
900
800
1.0
H2O (640 torr)
EA=0.78eV
B(mm2/hr)
0.1
0.01
Dry O2
EA=1.23eV
0.001
0.6
0.7
0.8
0.9
-1
1000/T(K )
1.0
Deal-Grove Model Predictions

Once B and B/A are determined, we can predict
the thickness of the oxide versus time
Deal-Grove Model of Oxidation
Oxide as a Diffusion Barrier
Diffusion of As, B, P, and Sb are orders of
magnitude less in oxide than in silicon
 Oxide is excellent mask for high-temperature
diffusion of impurities

10
10
Mask thickness
(mm)
Boron
B
PPhosphorus
11
1200 C
1200 C
1100 C
0.1
0.1
1000 C
1100 C
900 C
1000 C
900 C
0.01
0.01
0.1
0.1
1.0
1.0
10
10
Diffusion time (hr)
100
100
Other Models
A variety of other models have been suggested,
primarily to correct the deficiencies of the Deal-Grove
model for thin oxides
 These include
 The Reisman power law model
 The Han and Helms model with parallel oxidation
paths
 The Ghez and van Meulen model to account for the
effect of oxygen pressure
 Some of these models do a much better job for thin
oxides
 None are widely accepted

Other Topics
Several topics other than the simple
planar growth of wet and dry oxide are
important
 These include

 Thin
oxide growth kinetics
 Dependence on oxygen pressure
 Dependence on crystal orientation
 Mixed ambient growth kinetics
 2D growth kinetics
Example: 2D Growth
Example: 2D Growth
Example: 2D Growth

There are several interesting observations
 There
is significant retardation of the oxide
growth in sharp corners
 The retardation is more pronounced for low
temperature oxidation than for high
temperature oxidation
 Interior (concave) corners show a more
pronounces retardation that exterior (convex)
corners
Example: 2D Growth
Example: 2D Growth



Several physical mechanisms are needed to understand
these results
1. Crystal orientation
2. Oxidant diffusion
3. Stress due to volume expansion
Kao et al suggested changes to the linear-parabolic
(Deal-Grove) model to correct for these effects
Most of these effects are built into the modeling
software such as SUPREM IV and ATHENA
Measurement Methods

The parameters of interest include
 Thickness
 Dielectric
constant and strength
 Index of refraction
 Defect density

There are three classes of measurement
 Physical
(usually destructive)
 Optical (usually nondestructive)
 Electrical (usually nondestructive)
Physical Measurements
Simple step height technique (DekTak)
 Etch away oxide with HF
 Use a small stylus to measure the resulting step
height
 The resolution is <10 nm
 More complex technique uses one or more of the SFM
concepts (AFM, MFM, etc)
 Technique has atomic resolution
 SEM or TEM (electron microscopy)
 All require sample preparation that makes the tests
destructive and not easy to use in production

Optical Measurements


Most optical techniques use the concept of measuring
reflected monochromatic light
 If monochromatic light of wavelength  shines on a
transparent film of thickness x0, some light is
reflected directly and some is reflected from the
wafer-film interface
 For some wavelengths, the light will be in phase and
for others it will be out of phase
 constructive and destructive interference
Minima and maxima of intensity are observed as  is
varied
Optical Techniques
Color Chart
http://www.htelabs.com/appnotes/sio2_colo
r_chart_thermal_silicon_dioxide.htm
Optical Measurements

Instrument from
Filmetrics
(http://www.filmetrics.com)
Optical Measurements

The positions of the minima and maxima
are given by
2n1 x0 cos 
min,max 
m
1  n0 sin  
  sin 

n
1


m=1,2,3… for maxima and ½,3/2,5/2,… for minima

This is called reflectometry and works well
for thicknesses over a few 10’s of nm
Optical Measurements


If one does not know n, or if the film is very thin, then
ellipsometry is better
When multiple wavelengths of light are used, the
instrument is known as a spectroscopic ellipsometer
Optical Measurements

Here, one uses polarized light.


One can get the index of refraction as a function
of wavelength as well as the extinction
coefficient


The measurement may be performed at multiple
angles of incidence to obtain a higher degree of
accuracy
Can be used to measure thickness to <1 nm
Fitting routines are necessary to take into
account rough interfaces between Si and SiO2
layers.
Cauchy Equation
n( )  A 
B

2

C

4
 ...
Sellmeier Equation
B3
B1
B2
n( )  1  2
 2
 2
 ...
  C1   C2   C3
2
2
2
http://en.wikipedia.org/wiki/Cauchy%27s_equation
Electrical Measurements


These measure properties that correlate directly to the
performance of the devices fabricated using the oxides
The dominant techniques is the C—V measurement

The basic structure for the measurement is the MOS capacitor
The usual combination is Si-SiO2-(Al or pSi)

Any conductor-dielectric-semiconductor can be used

MOS Capacitor
Al
+
tox
Si wafer
Al
V
-
http://www.mtmi.vu.lt/pfk/funkc_dariniai/transistor/mos_capacitors.htm
C-V Plot
http://ece-www.colorado.edu/~bart/book/book/chapter6/ch6_3.htm#fig6_3_5
C-V Plot

Differences between high frequency and
low frequency C-V data
 Doping
concentration in Si near Si-oxide
interface

Voltage shift proportional to charged
defects within oxide