General rules for constructing valence band effective mass Hamiltonians with correct operator order for heterostructures with arbitrary orientations

Abstract

Working from the recently developed exact envelope-function theory, the question of how the envelope functions connect across a boundary is addressed for arbitrary growth directions. Using angular momentum basis functions that are expressed in terms of the desired growth orientation, a general form for a six-band Hamiltonian is presented. A set of general rules has been obtained which describe how unordered bulk elements can be replaced to conform to the ordering determined from the exact theory, thereby avoiding the use of ad hoc symmetrization procedures. One important result of this study is that the reduced interface coupling between the heavy-hole state and light/split-off-hole state found previously for [100] and [110] orientation is a general property valid for all growth directions.