Theory of high-field electron transport in silicon dioxide

A Monte Carlo technique is employed to simulate the electron transport in ${\mathrm{SiO}}_2$ at high electric fields (from 1.5×${10}^6$ to 12×${10}^6$ V/cm). Both the polar and the nonpolar electron-phonon scattering processes are considered. We show that the nonpolar interaction with the acoustic and band-edge phonons is a mechanism which must be included in order to explain the experimental evidence of a steady-state electron-transport regime at high average electron energy (≃3–4 eV) at these high fields. The LO phonons alone cannot prevent the electrons from running away at fields above 2×${10}^6$ V/cm, while at higher fields the main effect of the nonpolar scattering is that of randomizing the electron momenta via large-angle scattering, thus stabilizing the electron-energy distributions. The average energies and the energy relaxation distances obtained from the Monte Carlo simulation agree very well with the experimental data, particularly when collisional broadening effects are introduced in the simulation. Internal photoemission of electrons from an aluminum or a silicon electrode into ${\mathrm{SiO}}_2$ is also simulated, and the results agree with the well-known data indicating an effective relaxation length of about 3 nm for electrons in ${\mathrm{SiO}}_2$. Comparison is also made between the experimental and theoretical electron-energy distributions at high fields (≳8×${10}^6$ V/cm). The results indicate that at very high electron energies the band structure of ${\mathrm{SiO}}_2$ and quantum transport effects may reduce the effective scattering rates. While the semiclassical Monte Carlo solution seems to be reasonably valid for electron energies up to about 4 eV, more sophisticated approaches are needed to investigate the high-energy tails of the electron distributions.