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Monte Carlo simulation of the nonequilibrium phase transition in p-type Ge at impurity breakdown.

We report an ensemble Monte Carlo simulation of impact-ionization-induced impurity breakdown in p-type germanium at liquid-helium temperatures. In our Monte Carlo simulation, the impurities are treated as two-level systems (ground state and first excited state) exchanging particles with the continuum of free holes by capture and thermal generation from the excited level and by impact ionization from both levels. From the simulation we directly obtain the experimentally observed negative differential mobility and demonstrate the cooling effect of the impact-ionization process. For a detailed analysis of the nonequilibrium phase transition between low and high conducting states we extract the characteristic relaxation times of fluctuations exhibiting ``critical slowing down'' and a strong increase of the current-noise spectral density in the phase-transition regime. Finally, we demonstrate that our Monte Carlo simulations can be used for a quantitative investigation of the complex nonlinear dynamics of current filaments in semiconductors.