  The demonstration of isotropic polarization response from semiconductor
quantum dots (QDs) is a crucial step towards the design of several
optoelectronic technologies. Among many parameters that impact the degree of
polarization (DOP) of a QD system, the shape asymmetry is a critical factor. We
perform multi-million-atom simulations to study the impact of the elliptical
shapes on the electronic and polarization properties of single and vertically
stacked InAs QDs. The comparison between a low aspect ratio (AR) and a high AR
QD reveals that the electronic and the polarization properties strongly depend
on the AR of the QD; the elongation of a tall QD allows tuning of the DOP over
a much wider range. We then extend our analysis to an experimentally reported
vertical stack of nine QDs (9-VSQDs) that has shown significant potential to
achieve isotropic polarization properties. We analyse the contribution from the
shape asymmetry in the large, experimentally measured, in-plane polarization
anisotropy. Our analysis shows that the orientation of the base elongation
controls the sign of the DOP; however the magnitude of the base elongation has
only a very little impact on the magnitude of the DOP. We further predict that
the elliptical shape of the 9-VSQDs can only tune either DOP[110] or DOP[-110]
for an isotropic response. Our model results, in agreement with the TEM
findings, suggest that the experimentally grown 9-VSQDs has either a
circular-base or a slightly [-110] elongated base. Overall the detailed
investigation of the DOP as a function of the QD shape asymmetry provides a
theoretical guidance for the continuing experimental efforts to achieve
tailored polarization properties from the QD nano-structures for the design of
optical devices.
