Exact Solution of a Boundary Value Problem in Semiconductor Kinetic Theory

TL;DR

This paper provides an explicit solution to a boundary value problem in semiconductor kinetic theory, specifically for the linear Boltzmann equation with a high external field and velocity-dependent relaxation time.

Contribution

It introduces a novel method transforming the problem into a singular integral equation with an explicit solution, advancing analytical approaches in kinetic theory.

Findings

Explicit solution for the boundary value problem is derived.

Method handles high external fields and velocity-dependent relaxation times.

Solution advances analytical understanding of semiconductor transport models.

Abstract

An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be separable, which is also known as "relaxation time approximation"; the relaxation time may depend on the electron velocity. Our method consists in a transformation of the half-space problem into a nonnormal singular integral equation, which has an explicit solution.