Theory of high-field electron transport and impact ionization in silicon dioxide

A detailed theoretical study of impact-ionization-related transport phenomena in ${\mathrm{SiO}}_2$ thin films is presented. The Boltzmann transport equation is integrated by the Monte Carlo method using acoustic-phonon-scattering rates derived from photoinduced electron transmission experiments. It is shown that these empirical scattering rates necessitate the inclusion of impact ionization at fields F>${\mathit{F}}_{\mathrm{th}}^{\mathrm{ii}}$=7 MV/cm because phonon scattering alone can no longer stabilize the electron energy distribution below the ionization energy of 9 eV. However, even above ${\mathit{F}}_{\mathrm{th}}^{\mathrm{ii}}$, acoustic-phonon scattering is found to considerably delay the heating of electrons, leading to a wide dark space in which impact ionization cannot take place or is strongly reduced. Therefore, the electron multiplication factors m(F,${\mathit{t}}_{\mathrm{ox}}$) decrease rapidly with decreasing oxide thickness, ${\mathit{t}}_{\mathrm{ox}}$, for ${\mathit{t}}_{\mathrm{ox}}$<30 nm. These predictions are shown to be consistent with results of several high-field transport experiments in silicon–silicon-dioxide device structures. The calculated electron energy distributions develop high-energy tails which extend beyond the band-gap energy at fields larger than ${\mathit{F}}_{\mathrm{th}}^{\mathrm{ii}}$, as observed by vacuum emission experiments. The calculated impact-ionization coefficients are found to be in good agreement with values derived from experiments.