Generalized drift-diffusion model for miniband superlattices

TL;DR

This paper derives a generalized drift-diffusion model for miniband transport in superlattices from the Boltzmann-Poisson equation, revealing non-Einstein relations at various temperatures.

Contribution

It introduces a new drift-diffusion model derived via Chapman-Enskog analysis, accounting for strong coupling effects and deviations from Einstein relation.

Findings

Model includes additional terms beyond classical drift-diffusion.

Diffusion and drift do not follow Einstein relation except at high temperatures.

Provides a more accurate description of miniband transport in superlattices.

Abstract

A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent Chapman-Enskog method to analyze the hyperbolic limit, at which collision and electric field terms dominate the other terms in the Boltzmann equation. The reduced equation is of the drift-diffusion type, but it includes additional terms, and diffusion and drift do not obey the Einstein relation except in the limit of high temperatures.