Dynamics of nascent current filaments in low-temperature impurity breakdown

Formation of current filaments in n-type GaAs under crossed electric and magnetic fields

“…11. The experimentally observed bistability in the breakdown regime can be explained in terms of standard GR kinetics including impact ionization only if at least two donor levels, i.e., ground state and excited state, are taken into account.…”

“…These MC data are represented by fit functions to be adopted into the numerical scheme. 11 This approach serves to combine the microscopic physics of carrier scattering and GR processes and the macroscopic nonlinear spatiotemporal dynamics. The nonlinear dependence of the GR rate equations on n, n 1 , n 2 and Eϵ͉E͉ gives rise to an S-shaped current-density field characteristic of the homogeneous steady state.…”

“…28,29 To cope with the difficulties in the numerical treatment arising from the strong nonlinearity of the GR equations and the steep spatial gradients expected from the nature of breakdown phenomena, we have adopted a simulation algorithm based on a semi-implicit Euler scheme for time discretization with efficient time-step control. 11 The simulated sample represents a square epitaxial GaAs layer with side lengths L x ϭL z ϭ0.02 cm and thickness L y ϭ1.4ϫ10 Ϫ4 cm with point contacts in the center of two opposite sample edges, where the electron concentration is fixed to nϭ5ϫ10 15 cm Ϫ3 . This numerical value of the ͑Di-richlet͒ boundary condition at the contacts corresponds to the effective donor density N D *ϭN D ϪN A ͑see material parameters in Table I͒.…”

“…11 In order to solve these nonlinear space-and timedependent equations self-consistently for a realistic twodimensional sample geometry, we use an implicit finite element scheme. 28,29 To cope with the difficulties in the numerical treatment arising from the strong nonlinearity of the GR equations and the steep spatial gradients expected from the nature of breakdown phenomena, we have adopted a simulation algorithm based on a semi-implicit Euler scheme for time discretization with efficient time-step control.…”

“…In this phenomenon, S-shaped negative differential conductivity and self-organized current filaments, i.e., spatially inhomogeneous current flow, are often observed, accompanied by a variety of spatiotemporal instabilities. Steady state and dynamical properties of impurity breakdown have been modeled in the framework of nonlinear generation-recombination ͑GR͒ processes, [1][2][3][4][5][6][7][8][9][10][11] and investigated experimentally in various materials.…”