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ECE 340
Homework IX
Spring 2004
Due: Friday, March 19, 2004
1. A n
+
p Si junction with a long pregion has the following properties: N
a
=1.5x10
16
/cm
3
; μ
n
= 1020 cm
2
/Vs; μ
p
= 380 cm
2
/Vs;
τ
n
=1 μs. If we apply 0.7 V forward bias to the junction at 300 K, what is the electric field in the pregion far from the junction?
Draw a band diagram in the pregion far from the junction assuming that the junction is at x=0 and the pside is in x>0.
Solutions:
2
43
1.5 10
i
p
p
n
nc
m
p
−
==
×
,
2
/
0.0259 1020
26.42
/
nn
Dk
T
q
c
m
s
µ
×
=
6
26.42 10
0.00514
n
L
cm
−
=×
=
since it’s an n
+
p Si junction,
/
19
0.7/0.0259
2
26.42
(
1) 1.6 10
15000 (
1)
6.74 /
0.00514
qV kT
n
p
n
D
Jq ne
e
A
c
m
L
−
=−
=
×
××
−
=
Far away from junction, the diffusion current goes to zero, the current composed of drift current:
()
(
0
)
drift
p
pa
Jx
J
q N
=∞ =
=
=
=
Ε
19
16
6.74
7.39 /
1.6 10
380 1.5 10
Vc
m
−
Ε=
=
×
×
, E is toward –x direction since p is on x>0
Band diagram:
2.
Consider the following Si pn junctions operating at 300 K.
(a) Using Eq. (58), calculate the contact potential V
o
for N
a
= 5x10
14
and 5x10
18
/cm
3
, with N
d
= 10
15
, 10
17
, 10
19
/cm
3
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