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 η(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
ρ(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 δ [gel ] 1.