Effect of diffusion on the velocity of stationary impact ionization waves in semiconductors

The known theory of stationary plane impact ionization waves in gases [U. Ebert et al., Phys. Rev. E 55, 1530 (1997)] has been generalized to the bipolar case characteristic of semiconductors, where a medium is ionized by hot charge carriers of both signs. In this case, the velocity u of bipolar waves (in contrast to monopolar waves) is determined by the processes in the leading region of the front at any nonzero impact ionization rates and for any propagation directions. This property makes it possible to derive analytical formulas for u as a function of material parameters, initial perturbation, and external field strength by analyzing a boundary value problem linearized near an unstable state. In the highest achievable fields (e.g., in streamers), diffusion must give rise to an increase in u by a factor of about 3 as compared to the average drift velocity at typical parameters of semiconductors.