Biomedical Engineering Reference
In-Depth Information
The energy
W
1
is taken to be the lowest energy level of the particle with zero
field. This is simply
2
2
⎡
⎢
π
⎤
⎥
(3.26)
W
=
1
*
2
m L
⊥
x
The value
W
1
is also used to define the unit for the electric field
W
eL
2
F
=
1
x
The values of
Z
at the QW walls are
Z
±
=
Z
(
±
1
2
L
)
x
and therefore, using Equations 3.23 and 3.26
Z
±
becomes
1 3
/
⎡
⎤
−
π
Z
±
=
(
W
+
1
2
f
)
(3.27)
⎢
⎥
f
⎣
⎦
If we use the boundary conditions that ς(
Z
)
±
= 0 at the QW walls we find from
Equation 3.25 a resulting equation which completely determines the eigen
energy:
0
=
Ai Z Bi Z
(
)
(
)
−
Ai Z Bi Z
(
)
(
)
+
−
−
+
This equation is completely independent of well width and effective mass.
3.11.4 Determination of
E
B
The exciton-binding energy
E
B
can be rewritten in the following form
=
+
(3.28)
E
B
E
E
KE
pE
r
r
E
KE
r
is the kinetic energy of the relative electron-hole motion in the layer
plane. It is described by the following equation:
2
E
= 〈
∅
( )
r H
∅
( )
r
〉 =
(3.29)
KE
e h
−
KE
e h
−
r
r
eh
2
2
μλ
Search WWH ::
Custom Search