Callister - An introduction - 8th edition

5.6 Diffusion in Semiconducting Materials • 137
Therefore
and thus
Using an interpolation technique as demonstrated in Example Problem 5.2 and
the data presented in Table 5.1,
The problem stipulates that x 0.75 mm 7.5 10 4 m. Therefore
This leads to
Dt 6.24 10 7 m 2
(5.10)
Furthermore, the diffusion coefficient depends on temperature according to
Equation 5.8; and, from Table 5.2 for the diffusion of carbon in -iron, D 0
2.3 10 5 m 2 /s and Q d 148,000 J/mol. Hence
Dt D 0 exp a Q d
RT b1t2 6.24 107 m 2
148,000 J/mol
12.3 10 5 m 2 /s2 exp c
18.31 J/mol #
d1t2 6.24 10 7 m 2
K21T2
and, solving for the time t,
C x C 0 0.60 0.20
C s C 0 1.00 0.20 1 erf a x
22Dt b
x
0.5 erf a
22Dt b
x
22Dt 0.4747
7.5 10 4 m
0.4747
22Dt
0.0271
t 1in s2
exp a 17,810
T
b
Thus, the required diffusion time may be computed for some specified temperature
(in K). The following table gives t values for four different temperatures
that lie within the range stipulated in the problem.
Temperature
Time
(C) s h
900 106,400 29.6
950 57,200 15.9
1000 32,300 9.0
1050 19,000 5.3
5.6 DIFFUSION IN SEMICONDUCTING MATERIALS
One technology that applies solid-state diffusion is the fabrication of semiconductor
integrated circuits (ICs) (Section 18.15). Each integrated circuit chip is a thin square
wafer having dimensions on the order of 6 mm by 6 mm by 0.4 mm; furthermore,