Homework 10
Prob. 10.1
We will look at the density of states in a MOSFET inversion channel.
This can be
viewed as electrons being confined to a 3D box, but the gate direction (assigned as
z
here) has
much more confinement than the channel length and width direction.
Effectively, we can look at
the system as a quantum box of dimension (
a, b, c
), where
c << a, b
.
(a)
Write down the eigenfunctions and eigenenergy for this system.
Is there any difference
from Eq. (10.6) and (10.7)?
(5 pts)
(b)
Construct the 3D plot of (
k
x
, k
y
, k
z
) and the allowable points.
What is the influence from
the relation of
c << a, b
?
(5 pts)
(c)
The density of state will seem to have discontinuities at energies
2
2
2
=
c
n
m
E
z
nz
π
,
establish expressions for the DOS in the energy ranges
0 ≤ E ≤ E
1
, E
1
≤ E ≤ E
2
and E
nz
≤
E ≤ E
nz+1
.
(5 pts)
(d)
On the same figure of
g(E)
vs.
E
, plot DOS from (c) and the standard DOS for regular 3D
box of Eq. (10.33), i.e., without the constraint of
c << a, b
.
(10 pts)
Prob. 10.2
For a 3D particle in the potential of
(
29
2
2
0
2
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 '05
 TANG
 Gate, pts, quantum number nx

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