Environmental Engineering Reference
In-Depth Information
Figure 4.1 Schematic diagram the T-shaped quantumstructure.
propagating along the x direction as follows:
N ξ
[ A n e ik n ( x x ξ )
B n e ik n ( x x ξ ) ]
ψ ξ ( x , y )
η n ( y ),
=
+
(4.28)
n = 0
ξ
where x ξ is the reference coordinate in region
along the x axis,
η n ( y )representstheorthonormaltransversewavefunctionofmode
n inregion
, A n ,and B n areconstantstobedeterminedbymatching
the boundary conditions. When the stress-free boundary condition
( n ·∇ ψ = 0) is employed at the edges with n being the vector
perpendicular to the edge, the transverse function η n ( y )canbe
expressed by
ξ
2
/
W ξ cos( n
π
y
/
W ξ ),
if n
=
0
η n ( y ) =
1
0 .
(4.29)
/
=
W ξ ,
if n
ψ =
However, when the hard wall boundary condition (
0) is
employed at the edges, itshould beexpressed as
η n ( y )
2
0, (4.30)
which is similar to the case of the electron propagation. It is
worthnotingthatthestress-freeboundaryconditionoftheacoustic
phonon allows the propagation of an mode with
=
/
W ξ sin( n
π
y
/
W ξ ), if n
=
0 as one expect
for elastic waves, while the hard wall boundary condition does not.
Because of many similarities in the derived process for these two
ω =
 
Search WWH ::




Custom Search