Theory of defects in vitreous silicon dioxide

Models for defects in Si${\mathrm{O}}_2$ fall into the two basic categories of "vacancy-bridge" and valence-alternation models. We have calculated the local electronic structure of the main defects in each model, using the tight-binding and recursion methods. The localization of each level is found and compared to that measured by ESR for the paramagnetic centers. The silicon dangling bond, the neutral oxygen vacancy, and the positively charged oxygen vacancy ($E^{\prime }$ center) all give deep states near mid-gap. The Si—Si bond gives a bonding state in the lower gap and an antibonding state near the conduction-band minimum. The positive, threefold-coordinated oxygen site $\mathrm{O}_3^{}{}_{}{}^{+}$(${\mathrm{Si}}_3$) gives a state bound only by its Coulombic field. In general, all positively charged centers possess a "shallow" bound state 1-2 eV below the conduction-band minimum. Such shallow states account for the prevalence of optical absorption around 7.6 eV in Si${\mathrm{O}}_2$. The nonbridging oxygen introduces states just above the valence-band maximum. The peroxyl bridge and radical give states both at mid-gap and in the lower part of the gap. A broad absorption band around 5-6 eV is associated with the peroxyl radical, for the first time. It is suggested that valence-alternation defects must still be present in $v-\mathrm{S}\mathrm{i}{\mathrm{O}}_2$, but at a much lower concentration, of order ${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$, than previously supposed, due to a higher valence-alternation creation energy in Si${\mathrm{O}}_2$ than in $a-\mathrm{S}\mathrm{e}$ or $a-{\mathrm{As}}_2{\mathrm{Se}}_3$.