Reflectance anisotropy spectroscopy of the Si(111)−(5×2)Au surface

Hybrid DFT calculations of atomic structure, electronic band structure, and reflectance anisotropy (RA) are used to correlate atomic and electronic structures and optical transitions of eight structures for the $\mathrm{Si}(111)\text{\ensuremath{-}}(5\ifmmode\times\else\texttimes\fi{}2)\mathrm{Au}$ phase with Au coverage and Si adatom site occupancy. The structure recently proposed by Kwon and Kang (KK) [S. G. Kwon and M. H. Kang, Phys. Rev. Lett. 113, 086101 (2014)] and strongly supported by surface x-ray diffraction [T. Shirasawa et al., Phys. Rev. Lett. 113, 165501 (2014)] is found to be the most stable in the Au coverage range from 0.6 to 0.8 ML. The band structure of the Si adatom covered $(5\ifmmode\times\else\texttimes\fi{}4)$ surface has a surface state whose dispersion and position agree very well with the prominent ${S}₁$ surface state observed in angle-resolved photoemission experiment. Reflectance anisotropy spectra in the energy range 0.5 to 5 eV for the eight surface structures show variations with Au and Si adatom coverage which can be explained in terms of filling of this surface state. The best agreement between predicted and measured RA spectra, which are sensitive to both Au atom and Si adatom coverage, is found for coverages from 0.7 to 0.75 ML Au, when the surface has regions where Si adatoms are absent and where there are sufficient adatoms to cause surface-state band filling, in equal parts. Surface formation energy calculations favor a coverage of 0.7-ML Au. The structures of the $(5\ifmmode\times\else\texttimes\fi{}2)$ KK and $(6\ifmmode\times\else\texttimes\fi{}6)\mathrm{Au}$ phases on the Si(111) surface are compared and it is shown that the repeat unit of the KK phase also occurs in the $(6\ifmmode\times\else\texttimes\fi{}6)$ structure.