First-principles envelope-function theory for lattice-matched semiconductor heterostructures

TL;DR

This paper derives a first-principles multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures, capturing interface effects and bulk properties using perturbation theory and pseudopotentials.

Contribution

It introduces a novel first-principles derivation of a multi-band envelope-function theory applicable to various heterostructures, incorporating interface band-mixing and response effects.

Findings

The theory accurately models interface band-mixing effects.

Quadratic response adds only bulk band offsets and interface dipoles.

Long-range Coulomb fields have limited impact in 2D systems.

Abstract

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent heterostructures with macroscopically neutral interfaces and no spontaneous bulk polarization. The key assumption -- proved in earlier numerical studies -- is that the heterostructure can be treated as a weak perturbation with respect to some periodic reference crystal, with the nonlinear response small in comparison to the linear response. Quadratic response theory is then used in conjunction with k.p perturbation theory to develop a multi-band effective-mass Hamiltonian (for slowly varying envelope functions) in which all interface band-mixing effects are determined by the linear response. To within terms of the same order as the position dependence of the effective mass, the quadratic response contributes only a bulk band offset term and an interface dipole term, both of which are diagonal in the effective-mass Hamiltonian. Long-range multipole Coulomb fields arise in quantum wires or dots, but have no qualitative effect in two-dimensional systems beyond a dipole contribution to the band offsets.