Anisotropic Effective Mass

TL;DR

This paper introduces a three-dimensional anisotropic effective mass for electrons in semiconductors, applicable to both isotropic and anisotropic materials, accounting for energy dependence and aligning with experimental measurements.

Contribution

It proposes a scalar anisotropic effective mass definition that extends traditional models to anisotropic and non-parabolic semiconductors, improving accuracy.

Findings

Effective mass depends on particle energy in non-parabolic semiconductors.

The new effective mass aligns with cyclotron mass measurements in isotropic materials.

The approach provides more accurate modeling for anisotropic semiconductors.

Abstract

In this work, we derive a three-dimensional effective mass that is suitable for treatment of electrons in anisotropic semiconductors. We show that it is possible to define a scalar anisotropic three-dimensional mass that reduces to a one-dimensional definition for isotropic materials. We extend the effective mass definition and apply it to electrons in non-parabolic semiconductors and demonstrate that the effective mass is generally dependent on particle energy. Finally, we show that the proposed definition of the effective mass is compatible with the experimentally measured cyclotron mass in isotropic materials while leading to a more accurate result in anisotropic semiconductors.