Callister - An introduction - 8th edition

140 • Chapter 5 / Diffusion
12.4 10 3 m 2 3.87 eV/atom
/s2 exp c
d
18.62 10 5 eV/atom # K211173 K2
5.73 10 20 m 2 /s
The value of Q 0 may be determined as follows:
(b) Computation of the junction depth requires that we use Equation 5.13.
However, before this is possible it is necessary to calculate D at the temperature
of the drive-in treatment [D d at 1100C (1373 K)]. Thus,
D d 12.4 10 3 m 2 /s2exp c
Now, from Equation 5.13,
Q 0 2C s B
D p t p
p
15.73 10 20 m 2 /s2130 min2160 s/min2
12213 10 26 atoms/m 3 2 B p
3.44 10 18 atoms/m 2
1.51 10 17 m 2 /s
Q 0
x j £ 14D d t d 2ln a
bd
C B 2pD d t d
•14211.51 10 17 m 2 /s217200 s2
3.87 eV/atom
18.62 10 5 eV/atom # K211373 K2
d
1/2
1/2
3.44 10 18 atoms/m 2
ln £
11 10 20 atoms/m 3 2 21p211.51 10 17 m 2 /s217200 s2 §
2.19 10 6 m 2.16m
(c) At x 1 m for the drive-in treatment, we compute the concentration of
B atoms using Equation 5.11 and values for Q 0 and D d determined previously
as follows:
C1x,t2 Q 0
x2
exp a
2pD d t 4D d t b
3.44 10 18 atoms/m 2
21p211.51 10 17 m 2 /s217200 s2 exp c 11 10 6 m2 2
14211.51 10 17 m 2 /s217200 s2 d
5.90 10 23 atoms/m 3
MATERIALS OF IMPORTANCE
Aluminum for Integrated Circuit Interconnects
Subsequent to the predeposition and drive-in
heat treatments just described, another important
step in the IC fabrication process is the
deposition of very thin and narrow conducting
circuit paths to facilitate the passage of current
from one device to another; these paths are called