1
Homework 7
EE 606
Spring 2004
1.
Solve problems 5.10, 5.11, and 6.8 from the textbook.
2.
Work out the following problem ……
Depletion Approximation vs. “Exact” Solution of the PN Junction
To analyze a semiconductor device, we must solve the continuity equations for electrons and
holes, the driftdiffusion equations, which describe how carriers move in response to an electric
field, along with Poisson’s equation because when they move, they change the electric field.
In
general, these equations are too complex to solve analytically (the equilibrium problem is solved
in problem 5.14), so we resort to approximations such as the wellknown and frequentlyused
depletion approximation.
The depletion approximation is extremely useful, when it is valid, so it
is important to understand its limitations.
In this exercise, you will compare the results of
depletion approximation analyses of PN junctions with the “exact” solution obtained by solving
the equations of state directly by numerical simulation using the computer program, ADEPT.
1)
A Si step junction maintained at room temperature under equilibrium conditions has a p
side doping density of
N
A
= 2 x 10
15
/cm
3
and an nside doping of
N
D
= 10
15
/cm
3
,
Use the
depletion approximation to compute:
(a)
V
bi
(b)
The depletion layer boundaries,
x
p
,
x
n
,
and the depletion width,
W
(c)
The electric field at
x
= 0
(d)
The electrostatic potential at
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 Spring '08
 Staff
 Pn junction, pn junction, depletion region, depletion approximation, depletion approximation result

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