5.32
Phosphorus atoms are to be diffused into a silicon wafer using both predeposition and drivein
heat
treatments; the background concentration of P in this silicon material is known to be 5
⋅
10
19
atoms/
m
3
.
The predeposition treatment is to be conducted at 950°C for 45 minutes; the surface concentration of P
is
to be maintained at a constant level of 1.5
⋅
10
26
atoms/m
3
. Drivein diffusion will be carried out at
1200°C for a period of 2.5 h. For the diffusion of P in Si, values of Q
d
and D
0
are 3.40 eV and 1.1
⋅
10
4
m
2
/s, respectively.
(a) Calculate the value of Q
0
.
(b) Determine the value of x
j
for the drivein diffusion treatment.
(c) Also for the drivein treatment, compute the position x at which the concentration of P atoms is
10
24
m
3
.
Solution
(a) For this portion of the problem we are asked to determine the value of
Q
0
. This is possible
using Equation 5.12. However, it is first necessary to determine the value of
D
for the predeposition
treatment [
D
p
at
T
p
= 950°C (1223 K)] using Equation 5.8. Thus
D
p
=
D
0
exp
!
Q
d
kT
p
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 Spring '11
 Gregory
 Atom, pH, Natural logarithm, Dd td, drivein treatment, Drivein diffusion wil, ivein heat treatments

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