Relaxation Time Approximation for the Wigner-Boltzmann Transport Equation

TL;DR

This paper develops a quantum transport model using the Wigner-Boltzmann equation with a relaxation time approximation, accounting for quantum confinement effects in nanostructures, and validates its applicability under specific conditions.

Contribution

It introduces a relaxation time expression within the quantum Wigner-Boltzmann framework that considers quantum number dependence for confined nanostructures.

Findings

Relaxation time approximation is effective for homogeneous defect distributions.

Derived relaxation time expression accounts for quantum confinement effects.

Model applies under linear response to external electric fields.

Abstract

A quasi-distribution function in phase space (based on Wigner functions) is used to write down the quantum version of Boltzmann equation (Wigner-Boltzmann transport equation). The relaxation time approximation is show to be a good approach when defects are homogeneously distributed and linear response to the external electric field is assumed. An expression for relaxation times based on this formalism is deduced, which consider the dependence in the quantum numbers when confinement effects are important (nanowires and nanosheets).