ECE 340
Homework IX
Fall 2003
Due: Wednesday, October 15, 2000
(20 points total)
1.
Consider the following Si p-n junctions operating at 300 K.
(a) Using Eq. (5-8), calculate the contact potential V
o
for N
a
= 5x10
14
and 10
19
/cm
3
, with N
d
= 10
14
, 10
15
,
10
16
, 10
17
, 10
18
, 10
19
/cm
3
in each case and plot V
o
vs. N
d
.
(b)
Plot the maximum electric field
E
o
vs. N
d
for the junctions described in (a). What levels of N
d
doping are required so
E
o
can exceed 10
5
V/cm when N
a
= 2x10
19
/cm
3
?
(c)
Plot the width of the depletion region
W
vs. N
d
for the junctions described in (a).
Solutions
The relevant equations used in part (a), (b), (c) are:
0
2
ln
a
d
i
N N
kT
V
q
n
=
,
0
0
0
2
d
n
a
d
a
d
qN x
qV
N N
N
N
ε
ε
⎛
⎞
Ε
= −
= −
⎜
⎟
+
⎝
⎠
,
0
2
1
1
a
d
V
W
q
N
N
ε
⎛
⎞
=
+
⎜
⎟
⎝
⎠
,
(a),
N
a
(cm
-3
)
14
5
10
×
14
5
10
×
14
5
10
×
14
5
10
×
14
5
10
×
14
5
10
×
N
d
(cm
-3
)
14
10
15
10
16
10
17
10
18
10
19
1 10
×
V
0
(volts)
0.498
0.557
0.617
0.677
0.736
0.796
N
a
(cm
-3
)
19
10
19
10
19
10
19
10
19
10
19
10
N
d
(cm
-3
)
14
10
15
10
16
10
17
10
18
10
19
1 10
×
V
0
(volts)
0.754
0.814
0.874
0.933
0.993
1.05

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