Monte Carlo Modeling of Electron Scattering in Nonconductive Specimens

Abstract

Very low energy electrons in a solid should behave like Bloch electrons and will interact with perturbations of the atomic lattice, that is, with phonons. So we use the acoustic phonon scattering for replacing the elastic binary encounter approximation of the Mott scattering for electrons with low energies E < 100 eV. For ballistic electrons (1 eV < E < Eg) and higher energies up to 1 keV we determined the acoustic phonon scattering and the impact ionization rate by means of the "backscattering-versus-range" proof and respective eta(E0) - R(E0) diagrams. Electron trajectories demonstrate the relatively short range of primary electrons (PE) with energies E > 50 eV due to strong impact ionization losses (cascading) and the much greater range of secondary electrons (SE) with E < 50 eV, finally as a consequence of less effective phonon losses. The field-dependent transport parameters allow us to model the self-consistent charge transport and charging-up of insulating SiO2 layers during electron bombardment maintained by the current components of primary electrons jPE, secondary electrons jSE, and associated ballistic holes jBH, as well as by Fowler-Nordheim field injection jFN from the substrate. The resulting distributions of currents j(x, t), charges p(x, t), electric fields F(x, t), and the potential V(x, t) across the dielectric layer explain the phenomena of field-enhanced and field-blocked secondary electron emission with rates delta >or<or=1.