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

摘要

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? face='roman'>exp[(-E₀/E)m] can be well approximated by a threshold piecewise linear dependence α(E)=α₀′(E-E _{face='roman'>b})Θ(E-E _{face='roman'>b}), where Θ(x) is the unit step function. The possibility of such approximation explains the threshold square dependence υ _{face='roman'>f}～(E _{face='roman'>m}-E _{face='roman'>b})2 of the front velocity υ _{face='roman'>f} on the maximum electric field E _{face='roman'>m} 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 E _{face='roman'>b}≈0.21?E₀, α₀′≈0.46α₀/E₀ for the power m=1 and E _{face='roman'>b}≈0.5?E₀, α₀′≈0.7α₀/E₀ for the power m=2.