Abstract
A novel model is presented for spatio-temporal pattern formation in semiconductors. It leads to self-generated nonlinear current oscillations due to “breathing” current filaments in the regime of impurity impact ionization. The four qualitatively different regimes which have been observed in Ge with increasing current are consistently explained as: a stationary nonconducting state; bulkdominated oscillations; breathing filaments; stable filaments. The physical origin of the breathing oscillations is impact ionization coupled with transverse diffusion and longitudinal dielectric relaxation. A method is developed to derive simple nonlinear dynamic equations for the filament radius and the position of the peak transverse electric field by a nonlinear mode expansion.
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