An improved impact-ionization model for high-energy electron transport in Si with Monte Carlo simulation

A new model for impact ionization in Si is presented, which goes beyond the limitations of the Keldysh formula and is based on a more realistic scheme developed starting from a first-order perturbation theory. This scattering mechanism is modeled by an extended band structure which includes many bands for electrons and one band for holes in a finite Brillouin zone. Some processes have been identified to bring the dominant contribution to the scattering probability, in the present approach, for electron energies ranging up to 3 eV. Expressions for the differential and integrated scattering probabilities have been obtained which are consistent with the band model and can be included in a Monte Carlo simulation of the electron gas. Results for transport quantities are shown for a bulk material in presence of homogeneous and static electric fields under physical conditions where impact ionization influences the carrier dynamics. A comparison with theoretical and experimental data from the literature is also given.