Intervalley kinetic energy terms in the effective mass equation: a one-dimensional analytical study

Abstract

We show that a one-dimensional analytical study allows us to test and clarify the derivation, assumptions, and symmetry properties of the intervalley effective mass equation (IVEME). In particular, we show that the IVEME is consistent with a two-band case, and is in fact exact for a model that satisfies exactly all its assumptions. On the other hand, an alternative formulation in k-space that includes intervalley kinetic energy terms is consistent with a one-band case, provided that intra-valley kinetic energy terms are also calculated consistent with one band. We also show that the standard symmetry assumptions for both real space and k-space formulations are not actually exact, but are consistent with a "total symmetric" projection, or with taking spherical averages in a three-dimensional case.