Unraveling effects of disorder on the electronic structure of ${\text{SiO}}_2$ from first principles

We present a first-principles systematic study of the electronic structure of ${\text{SiO}}_2$ including the crystalline polymorphs $\alpha$ quartz and $\beta$ cristobalite, and different types of disorder leading to the amorphous phase. We start from calculations within density functional theory and proceed to more sophisticated quasiparticle calculations according to the $GW$ scheme. Our results show that different origins of disorder have also different impact on atomic and electronic-density fluctuations, which affect the electronic structure and, in particular, the size of the mobility gap in each case.

Figure 1

(Color online) Topological structure of the WQ1 silica model: the ring-size distribution is made evident by recognizing the presence of 3- to 6-membered rings, respectively, in panels (a)–(d).

Figure 2

(Color online) DOS and normalized self-interaction for the DFT-LDA states of (a) cristobalite ${\text{C}}_0$ and quartz at 0 K, (b) cristobalite at 0 K, at 300 K ${\text{C}}_{300}$ and the WQ1 silica model, and (c) silica models FQ1, FQ2, and WQ2. The DOS are plotted with a Gaussian broadening of 0.27 eV, and have been aligned by the bottom of the valence band. The reported $\left|\text{SI}\right|$ is averaged over energy intervals of 0.09 eV.