Electronic structure consequences of In/Ga composition variations in self-assembled ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}/\mathrm{GaAs}$ alloy quantum dots

Provided that the shape, size, and composition profile of semiconductor-embedded quantum dots are given, theory is able to accurately calculate the excitonic transitions, including the effects of inhomogeneous strain, alloy fluctuations, electron-hole binding, and multiband and intervalley coupling. While experiment can accurately provide the spectroscopic signature of the excitonic transitions, accurate determination of the size, shape, and composition profile of such dots is still difficult. We show how one can arrive at a consistent picture of both the material and the electronic structure by interactive iteration between theory and experiment. Using high-resolution transmission electron microscopy, electron-energy-loss spectroscopy, and photoluminescence (PL) spectroscopy in conjunction with atomistic empirical pseudopotential calculations, we establish a model consistent with both the observed material structure and measured electronic/optical properties of a quantum dot sample. The structural model with best agreement between measured and predicted PL is a truncated cone with height $35\hspace{0.5em}\AA ,$ base diameter $200\hspace{0.5em}\AA ,$ and top diameter $160\hspace{0.5em}\AA ,$ having a nonuniform, peaked composition profile with average 60% In content. Next, we use our best structure to study the effect of varying (i) the amount of In in the dots, and (ii) the spatial distribution of In within the dots. We find that by either increasing the amount of In within the dot or by concentrating a given amount of In near the center of the dot, both electrons and holes become more strongly bound to the dot. A small change of In content from 50 to 60% causes an exciton redshift of about 70 meV. Changing the composition profile from a uniform In distribution to a centrally peaked distribution can redshift the exciton by an additional 20–40 meV.