Eight-band calculations of strained InAs/GaAs quantum dots compared with one-, four-, and six-band approximations

The electronic structure of pyramidal shaped InAs/GaAs quantum dots is calculated using an eight-band strain-dependent $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian. The influence of strain on band energies and the conduction-band effective mass are examined. Single-particle bound-state energies and exciton binding energies are computed as functions of island size. The eight-band results are compared with those for one, four, and six bands, and with results from a one-band approximation in which $m_{\mathrm{eff}}\left(\overrightarrow{r}\right)$ is determined by the local value of the strain. The eight-band model predicts a lower ground-state energy and a larger number of excited states than the other approximations.