Chaotic Motion of Space Charge Monopole Waves in Semiconductors Under Time-Independent Voltage Bias

Abstract

A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples and appropriate voltage bias - such that the sample is biased in a regime of negative differential resistance - we find period doubling and chaos in the propagation of nonlinear fronts (charge monopoles of alternating sign) of electric field. The chaos is always low-dimensional, but it still has a complex spatial structure, lack of spatial coherence; this behavior can be interpreted using a finite dimensional asymptotic model (which is exactly derivable from the full model in the limit of infinitely long samples) in which the front (charge monopole) positions and the electrical current are the only dynamical variables.