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

TLDR

The authors numerically model strain in pyramidal InAs/GaAs quantum dots, compare it with analytical solutions for simpler geometries, compute band‑gap shifts and piezoelectric effects, and solve the 3D effective‑mass Schrödinger equation for electrons and holes under strong confinement, treating Coulomb interactions perturbatively and including AlAs barriers. The study finds that hydrostatic strain is largely confined within the quantum dots while anisotropic strain leaks into the barrier, optical‑phonon energies match experimental values, and the calculated electronic structure agrees with luminescence measurements.

Abstract

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.