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We used the molecular dynamics simulation based on the Stillinger–Weber (SW) interatomic potential to calculate the high-index surface energies of surfaces containing any of the stereographic surfaces of silicon at zero temperature. An empirical formula based on the structural unit model was generalized for high-index surfaces. Our simulated results show that the generalized formula can give a good estimation of the surface energy and structural feature of the high-index surfaces not only on the edge of stereographic but also within it. Our simulation and empirical formula results reveal that the closest surface has the lowest energy, so the closest (101) surface has the lowest surface energy and the (101), (111) and (001) surfaces are the extremum on the curve of surface energy versus orientation angle. Both the theoretical simulation results and the empirical formula calculation results are consistent with the available first-principles theoretical data.

Our first-principles calculation finds that only the Zn vacancy can induce a 1.0 μB magnetic moment in Er-doped ZnO, which comes from the unpaired 2p electrons at the ligand O atom and results in the room-temperature ferromagnetism property of ZnO.