Transcript Deal-Grove Model Predictions

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
Boron
B
PPhosphorus
11
1200 C
Mask thickness
(mm)
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.
– The measurement may be performed at multiple
angles of incidence to obtain a higher degree of
accuracy

One can get the index of refraction as a function
of wavelength as well as the extinction
coefficient
– 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
B C
n( )  A  2  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