Electronic structure of crystalline and amorphous silicon dioxide

The electronic structure of α-quartz and a-${\mathrm{SiO}}_2$ has been calculated using the tight-binding recursion method. For a-${\mathrm{SiO}}_2$ two structural models were used. The first one consisted of the continuous-random-network model constructed by Bell and Dean (BD). The second model was generated by Doan from molecular-dynamics (MD) simulations by quenching the liquid ${\mathrm{SiO}}_2$ to room temperature. While the bond-length distortions in the BD model are small from the values in α-quartz, the MD model yields relatively large distortions. Our calculations show that the electronic structures of α-quartz and a-${\mathrm{SiO}}_2$ are, roughly speaking, quite similar. The valence band can be divided into three parts. A narrow band ∼2.5 eV wide at ∼-20 eV is dominated by the O 2s states. This band is separated by a gap from the silicon-oxygen bonding states. The top of the valence band is formed essentially of nonbonding oxygen states approximately 4 eV in width. A region of low densities of states separates the bonding-nonbonding states which have a width of 11.5–13 eV. The results for BD model are quite close to those for α-quartz but the MD model shows quantitative differences. In particular the bonding-nonbonding states have a slightly reduced bandwidth (11.5 eV compared to 13.0 eV in α-quartz and BD model) and the valley between the nonbonding and bonding states is shallower. The valence-band edge remains unchanged by disorder but the conduction-band edge moves down, thus slightly reducing the band gap from 8.4 eV in α-quartz to 7.5 eV in BD model and 7.2 eV in the MD model. We find effective charges of approximately 1.6 and 7.2 electrons at Si and O sites, respectively. A detailed analysis of the composition of the densities of states is presented and comparison with experimental data on x-ray emission, photoelectron spectra, and reflectivity made. The generally good agreement found between the experimental data and the MD model seems to indicate a large bond-length variation in amorphous silicon dioxide.