The long-wave instability of the front of planar waves of impact ionization in semiconductors

Abstract

Theoretical analysis of the transversal stability of a planar front of a impact ionization wave in semiconductors having a finite thickness and doping concentrations, has been carried out. The formulas were developed for an increment s of an increase in long-wave perturbation in both the presence and the absence of background charge carriers ahead of the front. These formulas are applicable at arbitrary relationship between the wave vector of perturbation k and a distance L between the front and the electrode towards which the impact ionization wave propagates, if the thickness of a region in which the volume charge of electrons and holes is large, is far less than min(1/k, L). In the limiting cases, when kL ≪ 1 and kL ≫ 1, the theory leads to the results obtained previously. The practical result of the formulas developed is that at all actual values L perturbation with a wave vector k < 1/L decrease or increase much slower than short-wavelength perturbations do. Therefore it is just evolution of short-wave perturbations that should result in current pinching and limit the reliability of avalanche voltage sharpeners.