Question 1.
A semiconductor device made of silicon has, under thermal equilibrium, an Mshaped electric
field distribution as shown in the figure below.
E
/
E
max
1
0.5
0
a
/2
x
a
a

a
/2
a)
Find
N
d

N
a
between
x
= 
a
and
x
=
a
, as a function of
E
max
b)
Find the total potential across the semiconductor as a function of
E
max
with
a
= 0.1
m
c)
Find
E
max
and the builtin voltage
i
d)
Plot
N
d

N
a
for

a
x
a
and indicate numeric values. Specify whether the
different regions are
p
–type or
n
type.
a) From poisson’s one dimensional equation:
s
a
d
s
N
N
q
dx
d
)
(
E
From the diagram above, for
2
a
x
a
,
a
a
x
max
2
)
(
E
E
and
N
d

N
a
=
qa
s
max
2
E
Similarly, for
0
2
x
a
,
N
d

N
a
=
qa
s
max
E
for
2
0
a
x
,
N
d

N
a
=
;
max
qa
s
E
and for
a
x
a
2
,
N
d

N
a
=
qa
s
max
2
E
.
b) The potential equals:
dx
x
x
)
(
)
(
E
, resulting in:
4
5
)
(
0
max
E
a
x
total
.
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 '08
 staff
 Pn junction, depletion layer width, Na Nd, 293 Volt

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