GENERAL K-CENTER-DOT-P THEORY OF LATTICE-MATCHED SEMICONDUCTOR HETEROSTRUCTURES

A 12-mode heterostructure theory employing an eight-band zone-center k . p model is formulated on a level comparable to the envelope-function approximation. The theory implements probability-flux-conserving interface boundary conditions, but also accounts for the often neglected material dependence of the zone-center Bloch functions. Such material differences lead to a coupling of the light- and heavy-particle states which is absent in many other schemes. Further, we find previously unidentified contributions to the eight-band-model transfer matrix, one describing the effect of spin-orbit coupling on interfacial scattering, another providing corrections required by the use of the finite eight-band bases. An important consequence of the theory is a unique perspective that exposes the relationships among, and implicit assumptions involved in, various schemes appearing in the literature. In particular, the usual envelope-function approximation results from adding simplifying assumptions to the theory.