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MATSCI 302
April 9, 2008
pn junctions
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Email him if
you are an offcampus student.
Reading: Chapter 5 from Streetman’s text
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View Full Document Review of notation
i
E
T
k
E
E
i
o
B
i
F
e
n
n
)
(

=
F
E
C
E
V
E
)
ln(
i
o
B
i
F
n
n
T
k
E
E
=

D
i
o
D
o
N
n
p
N
n
2
=
=
T
k
E
E
i
o
B
F
i
e
n
p
)
(

=
)
ln(
i
o
B
F
i
n
p
T
k
E
E
=

;
;
For an ntype doped material:
10
8
6
4
2
0
2
4
6
8
0.0
0.2
0.4
0.6
0.8
1.0
What happens when p and ntype semiconductors come
together?
Fp
E
Fn
E
ptype
ntype
1
FermiDirac
Distribution
)
(
E
f
T
k
E
E
B
F
e
E
f
)
(
1
1
)
(

+
=
The Fermi Level must be
constant at equilibrium.
If it weren’t, there would
be a flow of carriers.
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View Full Document A pn junction at equilibrium
o
qV
F
E
o
V
C
E
V
E
= contact potential
T
k
qV
n
p
p
n
B
o
e
p
p
n
n
=
=
)
ln(
)
ln(
)
ln(
)
ln(
)
ln(
)
(
)
(
2
n
p
p
n
i
p
n
o
i
p
i
n
o
Fp
ip
in
Fn
o
p
p
q
T
k
n
n
q
T
k
n
p
n
q
T
k
V
n
p
q
T
k
n
n
q
T
k
V
q
E
E
q
E
E
V
B
B
B
B
B
=
=
=
+
=

+

=
What is
?
o
V
E
in
E
ip
Another derivation of the contact potential
0
]
)
(
)
(
)
(
[
)
(
=

=
dx
x
dp
D
x
E
x
p
q
x
J
p
p
p
μ
T
k
q
D
dx
x
dp
x
p
x
E
D
B
p
p
=
=
)
(
)
(
1
)
(
dx
dV
x
E

=
)
(
(Potential energy of electron =
)
qV

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This note was uploaded on 12/01/2011 for the course MS&E 302 taught by Professor Mcghee during the Spring '08 term at Stanford.
 Spring '08
 McGhee

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