1
ECE 495N EXAM II:
Wednesday, Nov.5, 2008, ME118, 1130A-1220P
CLOSED BOOK
PRACTICE EXAM II
Problem 1
[p. 2, 3]
8 points
Problem 2
[p. 4, 5]
8 points
Problem 3
[p. 6, 7]
9 points
Total
25 points
Useful Relations: These will be provided in the exam.
1
(
)
Fermi function
1
exp(
) /
f E
E
kT
µ
=
+
−
1
exp( (
) /
)
Law of equilibrium
P
E
N
kT
Z
α
α
α
µ
=
−
−
[ ( )]
[
]exp(
.(
))
Bandstructure
nm
m
n
m
h k
H
ik
d
d
=
−
∑
(
)
(
( ))
Density of states
k
D E
E
k
δ
ε
=
−
∑
( )
(
)
(
( ))
Density of modes
x
k
v
k
M E
E
k
L
π
δ
ε
=
−
∑
Problem 1:
A channel has four energy levels all with the same energy
ε
, but the interaction
energy is so high that no more than one of these levels can be occupied at the same time.
What is the average number of electrons in the channel if it is in equilibrium with chemical

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