Biomedical Engineering Reference
In-Depth Information
where
m
e x
k
k
⊥
and
m
h z
⊥
are the effective masses of the electron and hole in the
z
direction
V
e
(
z
e
) and
V
h
(
z
h
) are the depths of the electron and hole QW potentials
F
⊥
is the electric field perpendicular to the MQWS layers
The effective masses for both of the discontinuity split ratios can be calcu-
lated as shown in Figure 3.20.
The kinetic energy operator for the interacting particles or exciton and
their reduced effective mass are
=
−
2
2
d
d
H
(3.17)
KE
eh
r
2
2
μ
r
*
*
*
m
m
m
m
e
h
μ =
*
+
e
h
with
m
e
*
and
m
h
*
being the effective masses of the electron and hole in the
plane parallel to the layers. There are the normal bulk effective masses. The
Coulomb potential energy due to the interaction of the electron and hole is
2
−
e
V
( ,
r z z
,
)
=
(3.18)
e h
−
e
h
2
2 1 2
)
/
ε
(|
z
−
z
|
+
r
e
h
3.11.2 Solution of the Exciton Energy
The next step to finding the energy levels is to compute the expectation value
of
H
. This gives us the energy of the exciton
E
ex
= 〈
Ψ
| |
H
Ψ
〉
(3.19)
or
E
=
E
+
E
+
E
ex
e
h
b
85:15
57:43
M
e*
0.0665 + 0.0835
x
0.0665 + 0.0835
x
M
h
*
-h
0.45 + 0.31
x
0.34 + 0.42
x
M
l
*
-h
0.088 + 0.049
x
0.094 + 0.043
x
V
e
(meV)
340
228
FIGURE 3.20
Effective mass calculation table.
V
h
(meV)
60
172
Search WWH ::
Custom Search