Periodic generation and propagation of traveling fronts in dc voltage biased semiconductor superlattices

TL;DR

This paper analyzes a continuum model for charge transport in semiconductor superlattices, revealing that traveling electric field fronts periodically form and propagate due to shock wave dynamics, supported by numerical and asymptotic analysis.

Contribution

It introduces an asymptotic theory explaining the periodic traveling fronts as shock wave recycling in a nonlinear hyperbolic integrodifferential model.

Findings

Time-periodic solutions are observed in numerical simulations.

Traveling fronts are caused by shock wave motion and recycling.

The model links shock dynamics to domain wall propagation in superlattices.

Abstract

The continuum limit of a recently-proposed model for charge transport in resonant-tunneling semiconductor superlattices is analyzed. It is described by a nonlinear hyperbolic integrodifferential equation on a one-dimensional spatial support, supplemented by shock and entropy conditions. For appropriate parameter values, a time-periodic solution is found in numerical simulations of the model. An asymptotic theory shows that the time-periodic solution is due to recycling and motion of shock waves representing domain walls connecting regions of the superlattice where the electric field is almost uniform.