Asymptotics of the trap-dominated Gunn effect in p-type Ge

TL;DR

This paper provides an asymptotic analysis of the Gunn effect in p-type germanium, revealing how solitary waves are generated, move, and annihilate during oscillations under specific conditions, supported by numerical simulations.

Contribution

It introduces a novel asymptotic framework for analyzing the Gunn effect in p-type Ge, accounting for electric-field-dependent processes and solitary wave dynamics.

Findings

Multiple solitary waves can be shed per oscillation cycle depending on boundary conditions.

The generation of waves is a faster process described by a canonical problem.

Numerical simulations validate the asymptotic analysis.

Abstract

We present an asymptotic analysis of the Gunn effect in a drift-diffusion model---including electric-field-dependent generation-recombination processes---for long samples of strongly compensated p-type Ge at low temperature and under dc voltage bias. During each Gunn oscillation, there are different stages corresponding to the generation, motion and annihilation of solitary waves. Each stage may be described by one evolution equation for only one degree of freedom (the current density), except for the generation of each new wave. The wave generation is a faster process that may be described by solving a semiinfinite canonical problem. As a result of our study we have found that (depending on the boundary condition) one or several solitary waves may be shed during each period of the oscillation. Examples of numerical simulations validating our analysis are included.