First-principles envelope-function theory for lattice-matched semiconductor heterostructures
Year: 2005
Type: article
Abstract: In this paper a multiband envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles self-consistent 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 $\mathbf{k}∙\mathbf{p}$ perturbation theory to develop a multiband 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. The interface band mixing is therefore described by a set of bulklike parameters modulated by a structure factor that determines the distribution of atoms in the heterostructure. The same linear parameters determine the interface band-mixing Hamiltonian for slowly varying and (sufficiently large) abrupt heterostructures of arbitrary shape and orientation. 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. The method of invariants is used to determine the explicit form of the Hamiltonian for ${\ensuremath{\Gamma}}_{6}$ and ${\ensuremath{\Gamma}}_{8}$ states in semiconductors with the zinc-blende structure, and for intervalley mixing of $\ensuremath{\Gamma}$ and $X$ electrons in (001) $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{As}$ heterostructures.
Source: Physical Review B
Author: Bradley A. Foreman
Institution: Hong Kong University of Science and Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1972777282