The Gunn Effect: Instability of the Steady State and Stability of the Solitary Wave in Long Extrinsic Semiconductors

Abstract

A linear stability analysis of the stationary solution of a one-dimensional drift-diffusion model used to describe the Gunn effect in GaAs is performed. It is shown that for long semiconductor samples under do voltage bias conditions, and small diffusivity, the steady state may lose stability via a Hopf bifurcation. In the limit of infinitely long samples, there is a quasicontinuum of oscillatory modes of the equation linearized about the steady state that a acquire positive real part for voltages larger than a certain critical value. The linear stability of the solitary wave characteristic of the Gunn effect is proved for an idealized electron velocity curve in the zero diffusion limit.