Space Charge Instabilities and Nonlinear Waves in Extrinsic Semiconductors

Abstract

We review the role of nonlinear space charge waves in the electrical conduction properties of extrinsic semiconductors, particularly ultrapure p-type Ge at low temperature. Recent experimental results can be interpreted using a drift-diffusion rate equation model which includes nonlinear electric field dependencies of the drift velocity and impurity capture and impact ionization rates. Under time-independent (dc) current bias, phase plane analysis of a reduced dynamical system indicates the presence of moving solitary waves which are dynamically unstable. Under dc voltage bias, numerical simulations for finite-length samples and Ohmic boundary conditions reveal dynamically stable solitary waves that travel periodically across the sample. Near the onset of time-dependent behavior we find a Hopf bifurcation to fast small-amplitude current oscillations which are associated with periodic motion of traveling waves that decay before reaching the end of the sample. Numerical estimates of wave speed, wave size and onset behavior are in excellent agreement with available experimental data. Finally, we discuss the sensitivity of dynamical behavior to material parameters such as impurity concentration.