Energy Band Model Based on Effective Mass

TL;DR

This paper introduces a novel isotropic energy band model based on an effective mass approach, applicable to relativistic particles and solid state carriers, capturing non-parabolicity and velocity saturation phenomena.

Contribution

It extends the effective mass concept to anti-particles and zero rest mass particles, deriving a generalized energy-momentum relation that aligns with experimental observations.

Findings

Derives a non-parabolic energy-momentum relation with velocity saturation.

Applies the model to relativistic particles, solid state carriers, and graphene.

Proposes using effective mass for photons in energy band modeling.

Abstract

In this work, we demonstrate an alternative method of deriving an isotropic energy band model using a one-dimensional definition of the effective mass and experimentally observed dependence of mass on energy. We extend the effective mass definition to anti-particles and particles with zero rest mass. We assume an often observed linear dependence of mass on energy and derive a generalized non-parabolic energy-momentum relation. The resulting non-parabolicity leads to velocity saturation at high particle energies. We apply the energy band model to free relativistic particles and carriers in solid state materials and obtain commonly used dispersion relations and experimentally confirmed effective masses. We apply the model to zero rest mass particles in graphene and propose using the effective mass for photons. Therefore, it appears that the new energy band model based on the effective mass can be applied to relativistic particles and carriers in solid state materials.