Complex dynamics of current filaments in the low-temperature impurity breakdown regime of semiconductors

The formation of spatial and spatiotemporal patterns (current filaments) in semiconductors in the regime of low-temperature impurity impact ionization is investigated theoretically. Our model yields stable filaments, breathing filaments, and traveling filaments which show an intermittent spatiotemporal instability, resulting in chaotic oscillations of the average carrier density and of the current. The crucial role of the dielectric relaxation of the transverse electric field is singled out. Different strategies for the numerical treatment are discussed.