OPERATOR ORDERING AND BOUNDARY-CONDITIONS FOR VALENCE-BAND MODELING -APPLICATION TO [110]HETEROSTRUCTURES

A general method to derive the operator ordering and boundary conditio ns within the framework of the recently developed exact envelope-funct ion theory is presented. An ordered form of the familar Luttinger-Kohn Hamiltonian is derived which can be regarded as the natural starting point for calculations involving heterostructures, such that transform ing with an appropriate angular momentum basis, the derived ordering p rovides an unambiguous prescription for the boundary conditions across the interface. As an example, specific expressions are derived for st ructures with confinement along the [110] direction where the resultin g boundary conditions are found to differ significantly from those cur rently used in the literature. The effect on the calculated in-plane d ispersions is examined for two material systems, where it is found the greatest differences occur in systems with a large difference in Lutt inger parameters. Typically, the results show that employing the tradi tional boundary conditions tends to exaggerate any negative curvature of the valence bands near the zone center.