Electron--electron scattering in linear transport in two-dimensional systems

TL;DR

This paper presents a numerical method to incorporate electron-electron scattering into quantum well transport calculations, enabling efficient and accurate analysis of mobility reductions due to interactions at finite temperatures.

Contribution

The authors develop a reusable matrix-based approach for including electron-electron scattering in linear-response Boltzmann equation calculations for quantum wells.

Findings

Electron-electron scattering can reduce mobility by about 40%.

The method accounts for finite-temperature dynamic screening effects.

A symmetric matrix simplifies repeated calculations for different conditions.

Abstract

We describe a method for numerically incorporating electron--electron scattering in quantum wells for small deviations of the distribution function from equilibrium, within the framework of the Boltzmann equation. For a given temperature $T$ and density $n$, a symmetric matrix needs to be evaluated only once, and henceforth it can be used to describe electron--electron scattering in any Boltzmann equation linear-response calculation for that particular $T$ and $n$. Using this method, we calculate the distribution function and mobility for electrons in a quantum-well, including full finite-temperature dynamic screening effects. We find that at some parameters which we investigated, electron--electron scattering reduces mobility by approximately 40\%.