Effective impact ionization threshold and piecewise linear approximation for impact ionization coefficients in a theory of superfast ionizing fronts in semiconductors

Abstract

We focus on theoretical description of superfast ionizing fronts in semiconductor p+−n−n+ structures and argue that in the context of this problem, Townsend's type field dependence of impact ionization coefficients α(E)=α0 exp[(−E0/E)m] can be well approximated by a threshold piecewise linear dependence α(E)=α0′(E−Eb)Θ(E−Eb), where Θ(x) is the unit step function. The possibility of such approximation explains the threshold square dependence υf∼(Em−Eb)2 of the front velocity υf on the maximum electric field Em that the theory of TRAPATT-like ionizing fronts predicts even for threshold-free Townsend's approximation. We suggest a procedure for finding the best-fit parameters of the piecewise linear dependence and determine the values Eb≈0.21 E0, α0′≈0.46α0/E0 for the power m=1 and Eb≈0.5 E0, α0′≈0.7α0/E0 for the power m=2.