An envelope function formalism for lattice-matched heterostructures

Abstract

The envelope function method traditionally employs a single basis set which, in practice, relates to a single material because the k · p matrix elements are generally only known in a particular basis. In this work, we defined a basis function transformation to alleviate this restriction. The transformation is completely described by the known inter-band momentum matrix elements. The resulting envelope function equation can solve the electronic structure in lattice matched heterostructures without resorting to boundary conditions at the interface between materials, while all unit-cell averaged observables can be calculated as with the standard envelope function formalism. In the case of two coupled bands, this heterostructure formalism is equivalent to the standard formalism while taking position dependent matrix elements.

Band-to-band tunneling in III-V semiconductor heterostructures

“…However, only one set of basis functions can be chosen to expand the wavefunction over the entire structure which forces us to make a choice of which basis set to use. As a solution to this problem, we map the basis set of one material to that of the other as explained in [11], [12]. This mapping is expressed by a unitary transformation S,…”