ECE 440
Homework VII Solutions
Spring 2008
1.
Consider a silicon sample at 300 K. Assume that the difference of hole concentration varies
linearly with distance. At x=0, the hole concentration is p(0). At x=10 μm, the hole concentration
is p(10 μm)= 5x10
14
/cm
3
. If the hole diffusion coefficient, assumed constant, is D
p
=14 cm
2
/sec,
determine the hole concentration at x=0 for the following two diffusion current densities: (a) the
diffusion current density at x=0 is found to be J
p
diff
= + 0.19 A/cm
2
and (b) J
p
diff
=  0.19 A/cm
2
.
The expression for the diffusion current is in 422b.
We can replace the derivative with the
slopes of the hole concentration.
0
f
0
f
p
diff
p
x
x
)
p(x
)
p(x
qD
J



=
Thus,
p
0
f
diff
p
f
0
qD
)
x
(x
J
)
p(x
)
p(x

+
=
(a)
3
14
19
3
14
10
85
.
5
)
14
)(
10
6
.
1
(
10
19
.
0
10
5
)
0
(



=
+
=
=
cm
x
x
x
x
x
p
(b)
3
14
19
3
14
10
15
.
4
)
14
)(
10
6
.
1
(
10
19
.
0
10
5
)
0
(



=

+
=
=
cm
x
x
x
x
x
p
2.
The donor profile of a silicon sample is shown below. Assume that the majority carrier
mobility can be obtained from Fig. 323 (or the enlarged graph potsed in the 440 wbsite), and
the sample is at thermal equilibrium at 300 K.
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 Spring '09
 Lie
 Magnetic Field, Electric charge, diffusion current densities

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