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.