W. Quade et al., MONTE-CARLO SIMULATION OF THE NONEQUILIBRIUM PHASE-TRANSITION IN P-TYPE GE AT IMPURITY BREAKDOWN, Physical review. B, Condensed matter, 49(19), 1994, pp. 13408-13419
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.