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

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 d.c. 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.