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

The boundary conditions for the envelope functions at semiconductor heterointerfaces are calculated. They are obtained in a form of a 2×2 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/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As, HgTe/CdTe, and GaSb/InAs.