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

Abstract

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.The hole generation factors m-1 quantitatively agree with substrate hole-current to channel-current ratios measured by the carrier separation technique in n-channel field effect transistors with gate oxide thicknesses ${\mathit{t}}_{\mathrm{ox}}$\ensuremath{\ge}25 nm. The field and thickness dependence of the measured positive charge buildup (hole trapping) near the Si/${\mathrm{SiO}}_{2}$ interface can be quantified in terms of impact ionization in the oxide film. The calculated carrier multiplication, however, cannot fully account for the substrate hole currents and the hole trapping measured in thinner oxides, ${\mathit{t}}_{\mathrm{ox}}$\ensuremath{\le}20 nm, indicating that another mechanism, likely related to hole injection from the anode, becomes the dominant source for hole currents in thin oxides. Dielectric breakdown of thin ${\mathrm{SiO}}_{2}$ films on silicon is reevaluated on the bases of all of these findings. It is proposed that time-dependent breakdown is the result of cumulative degradation of the oxide near its interfaces caused by impact ionization and by hot-electron-induced hydrogen release together. This ansatz is shown to yield a good understanding for the oxide field and thickness dependence of the interface-state generation and of the charge to breakdown. Since impact ionization is strongly suppressed in thin films, ${\mathit{t}}_{\mathrm{ox}}$25 nm, degradation and time-dependent breakdown appear to be largely caused by hydrogen release and its subsequent secondary reactions in these thin films.