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

Transverse instability of a plane front of fast impact ionization waves

“…Thus, the problem of the instability of slow impact ionization waves that are described in the min imal model (and, therefore, propagate at a velocity only slightly exceeding the average velocity v(E 0 ) of charge carriers drifting in the same direction [3,13,14]) is solved. In particular, the results obtained in [11,12] make it possible to explain the instability of the front with a small curvature that is revealed in the numerical simulation of the initial stage of the evolu tion of streamers in gases [16][17][18] and semiconductors [19].…”

“…The depen dences s(k) obtained in [11] are well described by the empirical formula (3) where k 01 and a are the fitting parameters depending on the kinetic coefficients of electrons in the field E 0 . This formula appears to ensure an acceptable accuracy for the minimal model of impact ionization waves in semiconductors [12] if the bipolarity of transport and impact ionization is appropriately taken into account [14]. Thus, the problem of the instability of slow impact ionization waves that are described in the min imal model (and, therefore, propagate at a velocity only slightly exceeding the average velocity v(E 0 ) of charge carriers drifting in the same direction [3,13,14]) is solved.…”

“…(1), s(0) < 0 at L > w [5]. In this case, the plane impact ionization wave is stable with respect to transverse perturbations with wavenumbers smaller than a certain critical value k 00 ≈ L ⎯1 [12]. In the particular case where 1 It should be calculated using the theory of steady state plane impact ionization waves in gases [3,13] (at N = 0) or semicon ductors [14,15].…”

“…The solution of this problem was discussed in numerous works [4][5][6][7][8][9][10][11][12]. The most general analytical results were obtained in [12], when the stability of steady state plane impact ionization waves in reverse biased semiconductor p + -n-n + structures was ana lyzed.…”

“…The most general analytical results were obtained in [12], when the stability of steady state plane impact ionization waves in reverse biased semiconductor p + -n-n + structures was ana lyzed. It was shown that the growth rate s of harmonic transverse perturbation in the long wavelength limit increases with the wavenumber k according to the law (1) where w = εE 0M /qN, q is the elementary charge, ε is the permittivity, N is the concentration of donors in the n layer, E 0M is the maximum field strength on the unperturbed front moving at a constant velocity u 0M , 1 = ∂u 0M /∂E 0M , and L is the distance from the front to the electrode (heavily doped n + layer) toward which impact ionization waves propagate.…”