Biomedical Engineering Reference
In-Depth Information
and
0 indicates an ellipsoidal QD with its major axis aligned along the [110]
direction. For an ideal circular base QD,
η
<
1
.
1.0. Note that we do not alter the height
of the QD layers which is kept fixed at 4.0 nm, so the ellipsoidal-base QDs will have
slightly smaller volume when compared to the circular-base QD (see Fig.
5.1
fin
Ref. [
10
]).
Figure
5.8
b plots the values of the DOP
[
110
]
η
=
and DOP
[
as a function of the
110
]
elongation factor
η
.For
η
>
1
.
0, [110] elongation of the SQD increases the TE
[
110
]
mode and decreases the TE
mode. This can be understood as follows: the few top
most valence band states have dominant heavy hole (HH) character due to the strain-
induced large splitting between the HH and LH bands. These heavy hole states
are mainly comprised of
[
110
]
symmetry
w
ave functions, where
X
and
Y
are selected along the high symmetry [110] and [110] directions, respectively. The
lowest electron state (
E
1
) is mainly symmetric
|
X
and
|
Y
type wave function (as a good
approximation). The elongation of QD along, for example, the
X
-direction will have
negligible impact on the
|
S
|
S
type wave function, but it will increase (decrease)
|
X
2
(
|
Y
) component of the valence band states. Therefore, TE
X
∝
|
X
|
S
|
component
2
of the electron-holes transition will increase and TE
Y
∝
|
Y
|
S
|
component will
decrease. The opposite is true for
η
<
1.0, where the [110] (
Y
) elongation of the
2
).
The analysis of the calculated TM
[
001
]
component reveals that it also increases for
the elliptical QDs. The reason for this increase is twofold [
10
]: (i) the LH component
in the valence band states increases for the elliptical shapes of the QD and (ii) the
elongated shape of the QD layers modify the electron and hole wave functions,
thereby increasing their spatial overlap along the z-direction. The increase in the
TM mode and the decrease in the TE mode along the minor axis lead to a drastic
decrease in the values of the DOP
[
n
]
along the minor axis of the ellipsoidal SQD
as shown in Fig.
5.8
b. More interestingly, the values of the DOP along the major
axis of the ellipsoidal SQD also slightly decreases. This implies that the elliptical-
shape of the SQD, in general, improves the polarization response compared to the
circular-base. The largest dec
re
ase (
2
) and it decreases the TE
[
110
]
mode (
SQD increases TE
mode (
|
Y
|
S
|
|
X
|
S
|
[
110
]
23 %) in the value of the DOP
[
110
]
(from 97 to
74.5 %) is calculated for the [110] elongation (
≈
54).
In the previous section for the circular-base QDM-4, we have shown that
TM
[
001
]
>
η
=
0
.
TE
[
110
]
leading to DOP
[
110
]
<
0. However, a significant anisotropy
in the in-plane TE mode results in TE
[
110
]
>
TM
[
001
]
and DOP
[
110
]
>
0. Sim-
ilar anisotropies in the DOP
have been recently reported by Alonso-Alvarez
et al. [
47
] and Humlicek et al. [
48
]. Our multi-million atom simulations explain that
this large in-plane anisotropy (DOP
[
110
]
=
[
n
]
) is due to a strong confinement
of th
e
hole wave functions at the interfaces of the QDM-4 which tend to align along
the [110
DOP
[
110
]
]
-direction for the QDM-4 (see Fig.
5.7
), and thus significantly reduce the
TE
[
110
]
mode, on the other hand, does not observe any such
decrease. The small increase in the TM
[
001
]
mode due to the relaxation of the
biaxial strain, in particular around the center of the QDM-4, is also not sufficient to
overcome the TE
mode. The TE
[
110
]
mode and therefore the DOP
remains considerably larger
[
110
]
[
110
]
than zero.
