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) = α_0 exp[(-E_0/E)~m] can be well approximated by a threshold piecewise linear dependence α(E) = α'_0(E - E_b)Θ(E - E_b), where Θ(χ) is the unit step function. The possibility of such approximation explains the threshold square dependence υ_f ～ (E_m - E_b)~2 of the front velocity υ_f on the maximum electric field E_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_b ≈ 0.21 E_0, α'_0 ≈ 0.46α_0/E_0 for the power m=1 and E_b α 0.5 E_0, α'_0 ≈ 0.7α_0/E_0 for the power m = 2.