Connection of envelope functions at semiconductor heterointerfaces. I. Interface matrix calculated in simplest models

Abstract

The boundary conditions for the envelope functions at semiconductor heterointerfaces are calculated. They are obtained in a form of a 2\ifmmode\times\else\texttimes\fi{}2 interface matrix, which gives two linear relations among the envelopes and their derivatives at interfaces. The two models considered are a linear-chain tight-binding model consisting of a cation s orbital and an anion p orbital and an empirical pseudopotential model containing a small number of basis plane waves. The results show that the so-called envelope-function approximation works surprisingly well in various heterostructures, including GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As, HgTe/CdTe, and GaSb/InAs.