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-indu ced impurity breakdown in p-type germanium at liquid-helium temperatur es. In our Monte Carlo simulation, the impurities are treated as two-l evel systems (ground state and first excited state) exchanging particl es 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 negativ e differential mobility and demonstrate the cooling effect of the impa ct-ionization process. For a detailed analysis of the nonequilibrium p hase 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 den sity in the phase-transition regime. Finally, we demonstrate that our Monte Carlo simulations can be used for a quantitative investigation o f the complex nonlinear dynamics of current filaments in semiconductor s.