A quantum description of impact ionization in semiconductors

The authors have studied impact ionization with a quantum-mechanical approach beyond the Boltzmann equation. The theoretical background is a two-band density-matrix formalism where, in an electron-hole picture, particle conservation means that only the difference of electrons and holes remains constant. A quantum Monte Carlo procedure has been extended, in the second-quantization formalism, to include variable numbers of electrons and holes. The second-order correction to the number of electrons as a function of time has been evaluated. For delta-like initial distribution functions, quantum-mechanical and semiclassical results are compared. In contrast to a semiclassical treatment, nonconserving energy transitions at short times and the intracollisional field effect influence impact ionization above and below threshold.