First-principles study of the atomic and electronic structure of theSi(111)−(5×2)−Ausurface reconstruction

We present a systematic study of the atomic and electronic structure of the $\mathrm{Si}(111)\text{\ensuremath{-}}(5\ifmmode\times\else\texttimes\fi{}2)\text{\ensuremath{-}}\mathrm{Au}$ reconstruction using first-principles electronic structure calculations based on the density functional theory. We analyze the structural models proposed by Marks and Plass [Phys. Rev. Lett. 75, 2172 (1995)], those proposed recently by Erwin [ Phys. Rev. Lett. 91, 206101 (2003)], and a completely different structure that was found during our structural optimizations. We study in detail the energetics and the structural and electronic properties of the different models. For the two most stable models, we also calculate the change in the surface energy as a function of the content of silicon adatoms for a realistic range of concentrations. Our model is the energetically most favorable in the range of low adatom concentrations, while Erwin's ``$5\ifmmode\times\else\texttimes\fi{}2$'' model becomes favorable for larger adatom concentrations. The crossing between the surface energies of both structures is found close to $1∕2\phantom{\rule{0.3em}{0ex}}\text{adatom}\phantom{\rule{0.3em}{0ex}}\text{per}\phantom{\rule{0.3em}{0ex}}5\ifmmode\times\else\texttimes\fi{}2\phantom{\rule{0.3em}{0ex}}\text{unit}\phantom{\rule{0.3em}{0ex}}\text{cell}$, i.e., near the maximum adatom coverage observed in the experiments. Both models, our structure and Erwin's ``$5\ifmmode\times\else\texttimes\fi{}2$'' model, seem to provide a good description of many of the available experimental data, particularly of the angle-resolved photoemission measurements.