
163Nanosensor Laboratory
regime). It is one among the best established, celebrated models in silicon
processing.
According to the Deal–Grove model, the thickness of thermal oxide is
expressed as
t
A t
A B
ox
=
⎛
⎝
⎜
⎞
⎠
⎟
+
+
−
⎧
⎨
⎪
⎩
⎪
⎫
⎬
⎪
⎭
⎪
2
1
4
1
2
τ
( )
(3.4)
where
B/A is linear rate constant
B is parabolic rate constant
τ denotes a shift in the time coordinate to account for the presence of the
initial oxide layer
Example 3.1
Wet oxidation of silicon is carried out at 1000°C. Given the follow-
ing values of parameters in the Deal–Grove model: A = 0.226 m,
B = 0.287 m
2
h
−1
, and τ = 0, nd the oxide thickness for growth times
t = 0.01 h and ...