Transverse instability of a plane front of fast impact ionization waves
- PDF / 310,118 Bytes
- 10 Pages / 612 x 792 pts (letter) Page_size
- 72 Downloads / 167 Views
ONIC PROPERTIES OF SOLID
Transverse Instability of a Plane Front of Fast Impact Ionization Waves A. S. Kyuregyan AllRussia Institute of Electrical Engineering, Moscow, 111250 Russia email: [email protected], [email protected] Received July 25, 2011
Abstract—The transverse instability of a plane front of fast impact ionization waves in p+–n–n+ semicon ductor structures with a finite concentration of donors N in the n layer has been theoretically analyzed. It is assumed that the high velocity u of impact ionization waves is ensured owing to the avalanche multiplication of the uniform background of electrons and holes whose concentration σb ahead of the front is high enough for the continuum approximation to be applicable. The problem of the calculation of the growth rate s of a small harmonic perturbation with wavenumber k is reduced to the eigenvalue problem for a specific homo geneous Volterra equation of the second kind containing the sum of double and triple integrals of an unknown eigenfunction. This problem has been solved by the method of successive approximations. It has been shown that the function s(k) for small k values increases monotonically in agreement with the analytical theory reported in Thermal Engineering 58 (13), 1119 (2011), reaches a maximum sM at k = kM, then decreases, and becomes negative at k > k01. This behavior of the function s(k) for shortwavelength perturbations is due to a decrease in the distortion of the field owing to a finite thickness of the space charge region of the front and “smearing” of perturbation of concentrations owing to the transverse transport of charge carriers. The simi larity laws for perturbations with k kM have been established: at fixed σb values and the maximum field strength on the front E0M, the growth rate s depends only on the ratio k/N and the boundary wavenumber k01 ∝ N. The parameters sM, kM, and k01, which determine the perturbation growth dynamics and the upper boundary of the instability region for impact ionization waves, have been presented as functions of E0M. These dependences indicate that the model of a plane impact ionization wave is insufficient for describing the oper ation of avalanche voltage sharpers and that fronts of fast streamers in the continuum approximation should be stable with respect to transverse perturbations in agreement with the previously reported numerical simu lation results. The results have been confirmed by the numerical simulation of the evolution of small har monic perturbations of the steadystate plane impact ionization wave. DOI: 10.1134/S1063776112030168
1. INTRODUCTION A pulsed electrical breakdown of various media is usually due to the appearance and propagation of impact ionization waves [1–3]. Steadystate plane impact ionization waves are the simplest such waves, but they are very rarely observed in practice. One of the reasons is that the fronts of plane impact ionization waves are instable with respect to transverse perturba tions even in the completely deterministic continuum approximation. The evol
Data Loading...
