Biomedical Engineering Reference
In-Depth Information
Fig. 5.7
The top views of the plots of the highest five valence band states
H
1
,
H
2
,
H
3
,
H
4
,and
H
5
are shown for the SQD, QDM-3, and QDM-4 systems. The intensity of the colors indicates the
magnitude of the hole wave functions: the
red color
indicating the largest magnitude and the
light
blue color
indicating the smallest magnitude. The
dotted circles
are marked to guide the eye and
indicate the boundary of the QD bases
wave functions is oriented along the [ 110] directions. This
110
-symmetry is mainly
due to the strain and piezoelectric potentials that lowers the overall symmetry of
the QD system and favors this direction [
39
]. To verify the impact of the strain
and piezoelectricity, if we conduct a numerical experiment and switch off their
contributions in the electronic structure calculations, the TE
[
110
]
/TE
[
110
]
ratio for the
QDM-3 system decreases from 10.92 to 0.85 and it decreases from 10.73 to 3.2 for
the QDM-4 system. Similar distributions of the hole wave functions are observed
for bilayers [
5
] and a single QD layer with AR
[
]
0.25 [
33
].
The orientation of the hole wave functions determines the magnitude of the
TE
[
110
]
and TE
[
110
]
modes since the lowest electron wave function (see Fig.
5.4
)
is symmetrically distributed. All of the highest five hole wave functions are oriented
along the [ 110] direction in the case of the QDM-3 and QDM-4 systems. This results
in a strong reduction of the TE
[
110
]
mode due to considerably reduced electron-hole
wave function overlaps in this direction. The significant reduction in the TE
[
110
]
mode makes it to be even smaller than the magnitude of the TM
[
001
]
mode as can be
seen in Fig.
5.6
c,d. This change in the relative magnitudes of the TE
[
110
]
and TM
[
001
]
modes results in a flip of sign (
≥
) for the DOP
[
110
]
as indeed measured in the
experiments [
4
,
9
,
44
]. Hence we conclude that the isotropic polarization response
demonstrated by the experiment is a result of two factors: (i) increase in the TM
[
001
]
mode due to enhanced HH-LH intermixing and (ii) the reduction of the TE
[
110
]
mode due to the orientation of the holes along the [ 110] direction.
+
→−
