Model of impact ionization in solid dielectrics

Yu. A. Volkov, F. N. Voronin, M. B. Markov, O. S. Kosarev

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Abstract: The Boltzmann equation for the electron gas in dielectric is constructed. Equations for the moments of the electron distribution function – concentration, drift velocity and energy density of the electron gas – are obtained. Closed equations for the electromagnetic field, concentration and temperature of nonequilibrium electrons are derived in the drift approximation. Under the assumption that the electron gas is nondegenerate and the density of energy states of electrons is quasiclassical, the rate of the impact ionization reaction of the dielectric near the ionization threshold is calculated.

Keywords: Boltzmann equation, transport equations, drift approach, electrical conductivity, impact ionization, dielectric breakdown.

Received: 09.12.2024
Revised: 04.06.2025
Accepted: 09.06.2025

DOI: 10.20948/mm-2025-06-08