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Homework 8
Prob. 8.1
For an electron is localized in a finite quantum well with a homogeneous electric field
F
:
We will use the parameters from a quantum well photodiode implemented by the III-V materials
for the WKB estimate.
The potential well height is 0.3eV, the effective mass is
m*
= 0.067
m
0
and the quantum well is 10nm wide.
The kinetic energy is 0.026eV (for room temperature).
Estimate the electric field that will give the electron a life time of 1ns.
(10 pts)
Prob. 8.2
We will consider the energy quantization in a linear potential case (the parameters
correspond to the case of a MOSFET channel, as introduced in the class).
≥
<
∞
=
0
0
)
(
x
qFx
x
x
V
.
The exact ground state energy is:
3
/
1
2
2
2
1
2
338
.
2
=
m
F
q
E
m
.
You can use
m = 0.8m
0
and
F
= 3×10
5
V/cm (close to the field when impact ionization will
become large).
The ground state of the channel is typically called the first sub-band.
(a)

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