Atomic and electronic structure of silicate adlayers on polar hexagonal SiC surfaces

Structural and electronic properties of silicate adlayers on $(\sqrt{3}\times \sqrt{3})R30\mathrm{}°$-reconstructed C-terminated $\left(0001\mathrm{}¯\right)$ and Si-terminated (0001) surfaces of hexagonal $6H-\mathrm{SiC}$ have been studied using the ab initio pseudopotential supercell method. Two significantly different structural models, previously suggested on the basis of a quantitative low-energy electron diffraction (LEED) analysis for the two adsorbate systems, have been investigated. Both of these models have been considered for both surfaces and the four respective structures have been optimized by total energy minimization calculations. The two structures with the lowest formation energy confirm the interpretation of the LEED data. In addition, they allow us to address the physical origin of the distinctly different reconstruction models for the two surfaces. The electronic structure of these surfaces according to local density approximation calculations is presented and discussed. Both models yield a number of oxygen-induced bound states and resonances within the projected valence band region and a band of localized dangling-bond states within the projected gap. Within the local density approximation, this dangling-bond band turns out to be half-filled in both cases, giving rise to metallic surfaces in contradiction to experiment. Therefore, the systems have also been studied within the framework of the Hubbard model and by employing the local-spin-density approximation. In both cases semiconducting surfaces are obtained in agreement with experiment. The dangling-bond bands resulting within the Hubbard-model calculation, in particular, are in quantitative agreement with most recent angle-resolved photoemission spectroscopy data for a ${\mathrm{Si}}_2{\mathrm{O}}_3$ silicate adlayer on $\mathrm{SiC}\left(0001\mathrm{}¯\right).\mathrm{}$