Biomedical Engineering Reference
In-Depth Information
QDM is relatively hard to determine and is strongly influenced by geometry of the
QDM, i.e., QD base diameter, QD height, QD layer separation, etc. Ultimately the
strain profile that controls the strength of the coupling between the QD layers inside
the QDM determines the position of the hole states inside the molecules.
This is also worth mentioning that due to the small inter-layer spacing (4.5 nm)
resulting in the strong coupling of the QD layers, the electron wave functions are
spread over all of the QD layers (see Fig.
5.4
). Therefore, despite the confinement
of the hole wave functions is atomic-like (confined in the individual QD layers), the
electron-hole wave function overlap remains strong. This is different from the case
of the QDMs with weakly coupled QD layers (large inter-layer separations) where
both the electron and the hole wave functions will be confined in the individual QD
layers and therefore the oscillator strength will be small due to the electron and hole
wave functions being in the different QD layers. We suggest that the QDMs with the
small inter-layer separations are better candidate for the tuning of the polarization
properties while maintaining relatively large oscillator strengths.
5.4
Polarization Properties
5.4.1
Enhanced HH/LH Intermixing Implies TM
[
001
]
Mode Increases
In a QD system, the HH states consist of contributions from
p
x
and
p
y
orbitals
and the LH states consist of contributions from
p
x
,
p
y
,and
p
z
orbitals. These
configurations imply that the TM mode (which couples along the
z
(growth)
direction) will only couple to the LH states. The large splitting (
152 meV) of
the HH-LH bands (see Fig.
5.3
a) resulting in a weak LH contribution in the SQD
system will result in very weak TM
[
001
]
mode for this system. Thus from Eq. (
5.2
),
the DOP will be close to 1.0 and the polarization response will be highly anisotropic.
As the size of the QDM increases, the larger intermixing of the HH and LH bands
(see Fig.
5.3
b-e) increases the LH contribution in the valence band states. This
will result in an increase of the TM
[
001
]
mode of the inter-band optical transitions
reducing the anisotropy in the DOP by bringing it closer to 0.
≈
5.4.2
Optical Intensity Functions, f
()
Figure
5.6
plots the optical intensity functions computed from our model as a
function of the optical wavelength for the four quantum dot systems under study:
SQD, QDM-2, QDM-3, and QDM-4. The calculation of the optical intensity
function is done as follows: first we calculate optical transition strengths by using
Fermi's golden rule for TE
[
110
]
,TE
[
110
]
,andTM
[
001
]
modes between the lowest
