ECE 440
Homework X
Spring 2008
Solution to be posted by Saturday, March 15, 2008
1.
An n
+
p Si junction with a long pregion has the following properties: N
a
=2x10
16
/cm
3
; µ
n
=
1000 cm
2
/Vs; µ
p
= 360 cm
2
/Vs;
τ
n
=1 µs. If we apply 0.65 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 p
side is in x>0.
Since this is a n
+
p junction, we can ignore the contribution of holes to the diffusion
current.
s
cm
u
q
kT
D
n
p
n
/
9
.
25
2
=
=
cm
D
L
p
n
p
n
p
n
00509
.
=
⋅
=
τ
3
2
250
,
11

=
=
cm
p
n
n
p
i
p
so
0.7263A/cm
1
e
n
L
D
q
0)
(x
J
J
kT
qV
p
p
n
p
n
p
diff
n
=

=
=
≈
.
On the p side, far from the junction, the contribution of diffusion current approaches
zero while the drift current due to holes is dominant. Since current must be
continuous along the xdirection we know the drift current far from the junction will
be equal to the diffusion current near the junction.
)
(
)
(
)
(
)
0
(
x
E
x
p
q
x
J
x
J
p
p
n
drift
p
p
diff
n
μ
=
∞
→
≈
=
cm
V
x
p
q
x
J
x
E
p
p
p
diff
n
/
6305
.
0
10
2
360
10
6
.
1
7263
.
0
)
(
)
0
(
)
(
16
19
=
⋅
⋅
⋅
⋅
=
=
=
⇒

μ
Once we have an equation for E(x) we can construct the band diagram.
Notice that
the electric field points in the same direction as the electric field in the depletion
region.
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 Spring '09
 Lie
 Quadratic equation, Pn junction

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