Mark Lundstrom
9/27/13
ECE656
Fall 2013
1
SOLUTIONS:
ECE 656 Homework (Week 6)
Mark Lundstrom
Purdue University
1)
In Lecture 14, we discussed M(E) for a 3D semiconductor with parabolic energy bands.
Answer the following two questions about a 3D semiconductor with nonparabolic
energy bands.
a)
Assume that the nonparabolicity can be described by
E
1
+
!
E
( )
=
!
2
k
2
2
m
*
0
( )
.
Derive an expression for the corresponding
M E
( )
.
b)
Using the following numbers for GaAs
m
*
0
( )
=
0.067
m
0
=
0.64
,
plot
M E
( )
from the bottom of the
!
valley to
E
=
0.3
eV comparing results from
the nonparabolic expression derived in part a) to the parabolic expression quoted
in the lecture.
Solutions:
a)
Begin with the definition:
M
3
D
E
( ) =
h
4
x
+
D
3
D
E
( )
(1)
x
+
=
1 2
( )
E
( )
(2)
Step 1: compute
D
3
D
E
( )
for nonparabolic bands
Step 2: compute
E
( )
for nonparabolic bands
Step 3: multiply the two to get the answer
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View Full DocumentMark Lundstrom
9/27/13
ECE656
Fall 2013
2
Step 1:
D
3
D
(
E
)
dE
=
N
3
D
k
( )
!
4
"
k
2
dk
=
1
4
3
4
k
2
dk
=
1
2
k
2
dk
(3)
E
1
+
!
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 Fall '14

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