Inelastic quantum transport in superlattices: success and failure of the Boltzmann equation

TL;DR

This paper compares quantum Green function calculations with Boltzmann equation results for electron transport in superlattices, highlighting where semiclassical models succeed or fail in nonlinear, inelastic scattering regimes.

Contribution

It provides a comprehensive analysis of quantum versus semiclassical transport models in superlattices, identifying the conditions under which the Boltzmann equation is valid or breaks down.

Findings

Quantum and Boltzmann results agree in linear response regime.

Discrepancies appear at high fields with negative differential conductivity.

The Boltzmann equation fails to capture certain quantum effects in inelastic scattering.

Abstract

Electrical transport in semiconductor superlattices is studied within a fully self-consistent quantum transport model based on nonequilibrium Green functions, including phonon and impurity scattering. We compute both the drift velocity-field relation and the momentum distribution function covering the whole field range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport situation in the presence of inelastic scattering.