Density of States for Warped Energy Bands

TL;DR

This paper uses an angular effective mass formalism to analyze how band warping and corrugation affect the density of states in energy bands, highlighting the method's advantages for cubic materials and potential applications in heterostructures and thermoelectrics.

Contribution

It demonstrates the effects of band warping and corrugation on density of states and shows the effectiveness of angular effective mass formalism for valence bands in cubic materials.

Findings

Band warping may or may not increase the density-of-states effective mass.

Band corrugation can vary independently of band warping parameters.

Angular effective mass treatment is superior for valence band dispersions in cubic materials.

Abstract

An angular effective mass formalism previously introduced is used to study the density of states in warped and non-warped energy bands. Band warping may or may not increase the density-of-states effective mass. Band "corrugation," referring to energy dispersions that deviate "more severely" from being twice-differentiable at isolated critical points, may also vary independently of density-of-states effective masses and band warping parameters. We demonstrate these effects and the superiority of an angular effective mass treatment for valence band energy dispersions in cubic materials. We also provide some two-dimensional physical and mathematical examples that may be relevant to studies of band warping in heterostructures and surfaces. These examples may also be useful in clarifying the interplay between possible band warping and band non-parabolicity for non-degenerate conduction band minima in thermoelectric materials of corresponding interest.