Charge transport in a superlattice: a numerical study using moment methods

TL;DR

This paper presents a numerical study of charge transport in semiconductor superlattices using moment methods, demonstrating accurate, conservative solutions and observing self-sustaining current oscillations under voltage bias.

Contribution

It introduces a moment-based numerical approach that guarantees current conservation and achieves high accuracy, enabling future exploration of more complex quantum charge transport models.

Findings

Spectral convergence with respect to moments

First-order convergence in spatial discretization

Observation of self-sustaining current oscillations

Abstract

A semiclassical model of charge transport in a semiconductor superlattice is solved, using moments in the wavenumber direction and finite elements in the spatial direction (first order). The selection of numerical methods guarantees the conservation of current while allowing for high accuracy results. When a dc voltage bias is held between the ends of the sample, self-sustaining oscillations of the current through the superlattice are observed in a narrow range of voltages. the calculated solution displayed the expected accuracy: Spectral convergence in the number of moments used, and first-order convergence in the number of grid-cells. This result paves the way for higher-order methods (in the spatial direction) and the numerical solution of more complex models of charge transport including quantum models based on the Wigner function.