The justification for applying the effective-mass approximation to microstructures

The assumptions of conventional effective-mass theory, especially the one of continuity of the envelope function at an abrupt interface, are reviewed critically so that the need for a fresh approach becomes apparent. A new envelope-function method, developed by the author over the past few years, is reviewed. This new method is based on both a generalization and a novel application to microstructures of the Luttinger-Kohn envelope-function expansion. The differences between this new method and the conventional envelope-function method are emphasized. An alternative derivation of the new envelope-function equations, which are exact, to that already published is provided. A new and improved derivation of the author's effective-mass equation is given, in which the differences in the zone-centre eigenstates of the constituent crystals are taken into account. The cause of the kinks in the conventional effective-mass envelope function, at abrupt effective-mass changes, is identified.