Optical and electronic properties of Si${}_3$N${}_4$ and $\alpha$-SiO${}_2$

Self-consistent quasiparticle GW (sc-QPGW) calculations are used to calculate the electronic properties of $\alpha$-Si${}_3$N${}_4$ and $\beta$-Si${}_3$N${}_4$, as well as $\alpha$-SiO${}_2$ (quartz). The optical properties are evaluated by solving the Bethe-Salpeter equation in the Tamm-Dancoff approximation. For quartz, the predicted dielectric function is in good agreement with experimental data, with the onset of absorption located about 1.2 eV below the direct quasiparticle gap. For Si${}_3$N${}_4$, the theoretical dielectric function is fairly structureless and the onset of absorption corresponds to an exciton with a binding energy of 0.6 eV. The calculated sc-QPGW data are compared to more approximate calculations using G${}_0$W${}_0$, GW${}_0$, and a local multiplicative potential $V\left(r\right)$ designed to predict accurate one-electron band gaps. Although these calculations yield similar one-electron energies as the sc-QPGW approach, the bands are too narrow, leading to a “compressed” optical spectrum with too small excitation energies at higher energies. Finally, we report the absolute shifts of the conduction- and valence-band edges in silicon nitride and silicon to facilitate the prediction of band alignments at silicon/silicon-nitride interfaces.

Figure 1

(a) Band structure and (b) electronic density of states of $\alpha$-SiO${}_2$. The sc-QPGW results are shown as black lines, while the MBJLDA results are represented by red (gray) lines. In (b), the crosses correspond to the calculated QP band structure, and the black lines are the interpolation between these points using the wannier90 code.

Figure 2

(a) Band structure and (b) electronic density of states of $\beta$-Si${}_3$N${}_4$. The sc-QPGW results are shown as black lines, while the MBJLDA results are represented by red (gray) lines. For details, see the caption of Fig. 1.

Figure 3

(a) Band structure and (b) electronic density of states of $\alpha$-Si${}_3$N${}_4$. The sc-QPGW results are shown as black lines, while the MBJLDA results are represented by red (gray) lines. For details, see the caption of Fig. 1.

Figure 4

(a) Absorption spectra of $\alpha$-SiO${}_2$ predicted using BSE on top of sc-QPGW (solid line), independent particle spectrum (dotted line), and experiment (squares). The theoretical spectra have been broadened using a Lorentzian width of 150 meV. To facilitate comparison with experiment, only the response parallel to the hexagonal plane has been calculated; the out-of-plane response is not shown. (b) Absorption spectra of $\alpha$-SiO${}_2$ predicted using BSE on top of the MBJLDA (solid line) and scissor-corrected PBE calculations (dashed red line), and independent particle spectrum using MBJLDA (dotted line). Experimental data are from Ref.31.

Figure 5

Absorption spectra of $\beta$-Si${}_3$N${}_4$ (black solid line) and $\alpha$-Si${}_3$N${}_4$ (red dashed line) predicted using BSE. The theoretical spectra has been broadened using a Lorentzian width of 150 meV.