Onset of thermally driven self-motion of a current filament in a bistable semiconductor structure

We perform an analytical investigation of the bifurcation from static to traveling current density filaments in a bistable semiconductor structure with S-shaped current-voltage characteristic. Joule self-heating of a semiconductor structure and the effect of temperature on electron transport are consistently taken into account in the framework of a generic reaction-diffusion model with global coupling. It is shown that the self-heating is capable to induce translation instability which leads to spontaneous onset of lateral self-motion of the filament along the structure. This may occur in a wide class of semiconductor structures whose bistability is caused by impact ionization due to the negative effect of temperature on the impact ionization rate. The increment of the translation mode and the instability threshold are determined analytically.