InAs/GaAs pyramidal quantum dots: Strain distribution, optical phonons, and electronic structure

The strain distribution in and around pyramidal InAs/GaAs quantum dots (QD's) on a thin wetting layer fabricated recently with molecular-beam epitaxy, is simulated numerically. For comparison analytical solutions for the strain distribution in and around a pseudomorphic slab, cylinder, and sphere are given for isotropic materials, representing a guideline for the understanding of strain distribution in two-, one-, and zero-dimensional pseudomorphic nanostructures. For the pyramidal dots we find that the hydrostatic strain is mostly confined in the QD; in contrast part of the anisotropic strain is transferred from the QD into the barrier. The optical-phonon energies in the QD are estimated and agree perfectly with recent experimental findings. From the variation of the strain tensor the local band-gap modification is calculated. Piezoelectric effects are additionally taken into account. The three-dimensional effective-mass single-particle Schr\"odinger equation is solved for electrons and holes using the realistic confinement potentials. Since the QD's are in the strong confinement regime, the Coulomb interaction can be treated as a perturbation. The thus obtained electronic structure agrees with luminescence data. Additionally AlAs barriers are considered.