Biomedical Engineering Reference
In-Depth Information
*
2
2
2
m a V Z
| |
2
2
κ a
+
(
ka
)
=
B is a normalization constant and a is the well half width. Note that the
values of m h and V z depend on whether the calculation is for an electron
or hole.
Figure 3.22 shows the infinite well wave function where
1 2
/
=
2
π
z
L
Ψ
cos
infinite
L
x
x
L x is the effective well width and depends on the particle type used in
equation.
Figure 3.23 shows both wave functions superimposed. In this figure, the
shaded region is the difference in area between the finite and infinite wave
functions. The area difference is expressed by the integral
) 2
Areadifference
=
Ψ
d
x
(3.36)
finite
infinite
−∞
(
2
2
=
Ψ
2
Ψ Ψ
+
Ψ
infinite d
)
x
finite
finite
finite
−∞
+
L
2
z
= −
2 2
Ψ Ψ
finite
infinite d x
L
2
z
FIGURE 3.22
Infinite well wave function.
- L eff
0
L eff
2
2
- L eff
L eff
2
0
2
FIGURE 3.23
Infinite and finite well wave functions.
- L
L
2
2
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