Model for the on-site matrix elements of the tight-binding hamiltonian of a strained crystal: Application to silicon, germanium and their alloys

TL;DR

This paper presents a simplified yet accurate tight-binding model for strained diamond and zinc-blende crystals, effectively capturing strain effects on electronic properties with minimal parameters, demonstrated on silicon, germanium, and their alloys.

Contribution

It introduces a new on-site matrix element model for the tight-binding Hamiltonian that accurately accounts for arbitrary strains with few parameters and no ambiguity.

Findings

Model reproduces strain effects on band energies and effective masses

Good agreement with ab initio data for Si, Ge, and SiGe

Applicable to nanostructures and various strain conditions

Abstract

We discuss a model for the on-site matrix elements of the sp3d5s* tight-binding hamiltonian of a strained diamond or zinc-blende crystal or nanostructure. This model features on-site, off-diagonal couplings between the s, p and d orbitals, and is able to reproduce the effects of arbitrary strains on the band energies and effective masses in the full Brillouin zone. It introduces only a few additional parameters and is free from any ambiguities that might arise from the definition of the macroscopic strains as a function of the atomic positions. We apply this model to silicon, germanium and their alloys as an illustration. In particular, we make a detailed comparison of tight-binding and ab initio data on strained Si, Ge and SiGe.