ECE 440
Homework
IX
Spring 2006
Due: Wednesday, March 08, 2006
1.
When a prolonged diffusion or a highenergy implantation is conducted to form a p/n
junction. The doping profile near the junction is usually graded, and the stepjunction
approach is no longer suitable to find the relationship between the width of the depletion
region and the contact potential. However, the underlying principle used to establish
equations 513 to 523 remains intact, and they can still be used to determine similar
equations for the graded junction.
Assume that the doping profile varies as N
a
N
d
=Gx where
G is 3x10
20
/cm
4
in a linear junction.
(a) Find and plot the electric field,
ε
(x),
for 
∞
<x<+
∞
.
(b) Determine the relationship between the width of the depletion region and contact
potential for the junction at equilibrium.
2.
An abrupt Si pn junction has the following properties at 300 K:
pside
n

s
i
d
e
A
=
1
0
4
cm
2
N
a
= 1x10
17
/cm
3
N
d
=
1x10
16
/cm
3
τ
n
=
1 μs
τ
p
= 10 μs
μ
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 Spring '11
 Leburton
 Pn junction, Si pn junction, cm /Vs

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