Self-sustained current oscillations in the kinetic theory of semiconductor superlattices

TL;DR

This paper presents the first numerical solutions of a kinetic theory model for self-sustained current oscillations in semiconductor superlattices, validating previous drift-diffusion approximations through detailed simulations.

Contribution

It introduces a numerical approach to solve the Boltzmann-Poisson equation with BGK collision term for superlattices, confirming the accuracy of prior analytical methods.

Findings

Numerical solutions match well with Chapman-Enskog derived equations.

The Weighted Particle Method effectively solves the kinetic model.

Results support the validity of drift-diffusion approximations at high fields.

Abstract

We present the first numerical solutions of a kinetic theory description of self-sustained current oscillations in n-doped semiconductor superlattices. The governing equation is a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary conditions for the distribution function describe electron injection in the contact regions. These conditions seamlessly become Ohm's law at the injecting contact and the zero charge boundary condition at the receiving contact when integrated over the wave vector. The time-dependent model is numerically solved for the distribution function by using the deterministic Weighted Particle Method. Numerical simulations are used to ascertain the convergence of the method. The numerical results confirm the validity of the Chapman-Enskog perturbation method used previously to derive generalized drift-diffusion equations for high electric fields because they agree very well with numerical solutions thereof.