Geometry and material parameter dependence of InAs/GaAs quantum dot electronic structure

We examine the effects of island geometry and material parameters on confined state energies of an InAs/GaAs pyramidal quantum dot calculated using a strain-dependent eight-band $\mathit{k}\cdot \mathit{p}$ Hamiltonian. For a truncated pyramidal dot with 101-type sides the electronic confined state energies depend strongly on the base of the pyramid, but are insensitive to the height. The exciton recombination energy is primarily determined by the island volume. This apparent paradox is explained by the change in strain profile with shape, and the fact that truncating a pyramid has a small effect on the volume. For a typical island size, we compute the sensitivity of the electron and hole ground-state energies to variations in 17 different material parameters. The most critical parameters are the InAs Luttinger parameters, ${\gamma }_1$ and ${\gamma }_3$ for which a $10\%$ shift in either one changes the recombination energy by $20\hspace{0.5em}\mathrm{meV}.$