Impact of size-dependent non-local elastic strain on the electronic band structure of embedded quantum dots

Abstract

The effect of mechanical strain on the quantum confinement properties of quantum dots is appreciable and both qualitative and quantitative description of the electronic band structure of quantum dots requires proper incorporation of its effect. Although atomistic calculations such as tight binding or pseudopotential approaches are viable options, the typical and ‘standard’ practice is to employ the coarse-grained multiband envelope function method to compute the band structure of both strained and unstrained quantum dots. The typical recipe involves calculation of strain based on classical continuum elasticity and a subsequent link to the aforementioned eight-band envelope function model. The mechanical strain predicted by classical elasticity is not only size-independent but also departs qualitatively from the actual (atomistic) field owing to neglect of non-local effects that are prevalent at the nanoscale. In the present work, the authors employ the strain as calculated from a size-dependent non-local theory of elasticity (presented in work previously published by the current authors) and assess the qualitative and quantitative effects on the electronic band structure of an InAs-GaAs quantum dot system. Quantitatively, deviations of band gaps in the range of 100 meV are found when compared to classical elasticity-based estimates, while no significant qualitative differences were found. The non-local elastic effects, however, are appreciable only for very small quantum dots and certain materials (such as the InAs-GaAs system discussed in the present work).