Free boundary problems describing two-dimensional pulse recycling and motion in semiconductors

TL;DR

This paper presents an asymptotic analysis of the Gunn effect in two-dimensional semiconductors, modeling pulse dynamics via free boundary problems and validating the approach with numerical solutions.

Contribution

It introduces a free boundary problem framework for analyzing pulse motion in 2D semiconductors and provides exact solutions in simple geometries, advancing understanding of the Gunn effect.

Findings

Exact solutions in 1D and axisymmetric geometries

Numerical solutions match full system with high accuracy

Free boundary approach effectively models pulse dynamics

Abstract

An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk n-GaAs with circular contacts is presented. A moving pulse far from contacts is approximated by a moving free boundary separating regions where the electric potential solves a Laplace equation with subsidiary boundary conditions. The dynamical condition for the motion of the free boundary is a Hamilton-Jacobi equation. We obtain the exact solution of the free boundary problem (FBP) in simple one-dimensional and axisymmetric geometries. The solution of the FBP is obtained numerically in the general case and compared with the numerical solution of the full system of equations. The agreement is excellent so that the FBP can be adopted as the basis for an asymptotic study of the multi-dimensional Gunn effect.