Interaction of streamers and stationary corrugated ionization waves in semiconductors

A numerical simulation of evolution of an identical interacting streamers array in semiconductors has been performed using the diffusion-drift approximation and taking into account the impact and tunnel ionization. It has been assumed that the external electric field E0 is static and uniform, the background electrons and holes are absent, the initial avalanches start simultaneously from the nodes of the plane hexagonal lattice, which is perpendicular to the external field, but the avalanches and streamers are axially symmetric within a cylinder of radius R. It has been shown that under certain conditions, the interaction between the streamers leads finally either to the formation of two types of stationary ionization waves with corrugated front or to a stationary plane ionization wave. A diagram of different steady states of this type of waves in the plane of parameter E0,R has been presented, and a qualitative explanation of the plane partition into four different regions has been given. Characteristics of corrugated waves have been studied in detail and discussed in the region of R and E0 large values, in which the maximum field strength at the front is large enough for the tunnel ionization implementation. It has been shown that corrugated waves ionize semiconductors more efficiently than flat ones, especially in relatively weak external fields.