Theory of traveling filaments in bistable semiconductor structures

We present a generic nonlinear model for current filamentation in semiconductor structures with S-shaped current-voltage characteristics. The model accounts for the Joule self-heating of a current density filament. It is shown that the self-heating leads to a bifurcation from static to traveling filaments. Filaments start to travel when an increase of the lattice temperature has a negative impact on the cathode-anode transport. Since the impact ionization rate decreases with temperature, this occurs for a wide class of semiconductor systems whose bistability is due to the avalanche impact ionization. We develop an analytical theory of traveling filaments which reveals the mechanism of filament motion, finds the condition for bifurcation to traveling filament, and determines the filament velocity.