A QUANTUM DESCRIPTION OF IMPACT IONIZATION IN SEMICONDUCTORS

We have studied impact ionization with a quantum-mechanical approach b eyond 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 re mains constant. A quantum Monte Carlo procedure has been extended, in the second-quantization formalism, to include variable numbers of elec trons and holes. The second-order correction to the number of electron s as a function of time has been evaluated. For delta-like initial dis tribution functions, quantum-mechanical and semiclassical results are compared. In contrast to a semiclassical treatment, non-conserving ene rgy transitions at short times and the intracollisional field effect i nfluence impact ionization above and below threshold.