Comparison of the electronic structure of $\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ pyramidal quantum dots with different facet orientations

Using a pseudopotential plane-wave approach, we have calculated the electronic structure of strained InAs pyramidal quantum dots embedded in a GaAs matrix, for a few height $\mathrm{}\left(h\right)\mathrm{}$-to-base$\mathrm{}\left(b\right)\mathrm{}$ ratios, corresponding to different facet orientations $\{101\}$, $\{113\},$ and $\{105\}$. We find that the dot shape (not just size) has a significant effect on its electronic structure. In particular, while the binding energies of the ground electron and hole states increase with the pyramid volumes ${(b}^{2}h)$, the splitting of the $p-$like conduction states increases with facet orientation $\mathrm{}(h/b),$ and the $p-$to-$s$ splitting of the conduction states decreases as the base size $\mathrm{}\left(b\right)\mathrm{}$ increases. We also find that there are up to six bound electron states (12 counting the spin), and that all degeneracies other than spin, are removed. This is in accord with the conclusion of electron-addition capacitance data, but in contrast with simple k⋅p calculations, which predict only a single electron level.