Energetic stability, equilibrium geometry, and the electronic properties ofCa∕Si(111)surfaces

Abstract

We have performed an ab initio theoretical investigation of the energetic stability, equilibrium atomic geometry, and scanning tunneling microscope (STM) images of the $\mathrm{Ca}∕\mathrm{Si}(111)$ surface. We have considered the $(3\ifmmode\times\else\texttimes\fi{}1)$, $(3\ifmmode\times\else\texttimes\fi{}2)$, and $(2\ifmmode\times\else\texttimes\fi{}1)$ structural models for Ca coverage of $1∕3$ ML, $1∕6$ ML, and $1∕2$ ML, respectively. Our total energy results indicate that the $(3\ifmmode\times\else\texttimes\fi{}1)$ phase is not expected to occur, even for Ca-rich conditions. In the $(3\ifmmode\times\else\texttimes\fi{}2)$ phase the Ca adatoms lie on the $T4$ sites along the surface trench separated by Si honeycomb chains. Similarly, in the $(2\ifmmode\times\else\texttimes\fi{}1)$ phase the Ca adatoms are adsorbed on the $T4$ sites of the surface trench separated by Si zigzag chains. The equilibrium geometries and electronic charge transfers between Ca adatoms and Si(111) surface for the $(3\ifmmode\times\else\texttimes\fi{}2)$ and $(2\ifmmode\times\else\texttimes\fi{}1)$ phases have been detailed. Our simulated STM images indicate that the higher-lying occupied states are located on the topmost Si atoms along the chains, while the empty states lie on the Ca adatoms, forming bright spots and stripes on the $(3\ifmmode\times\else\texttimes\fi{}2)$ and $(2\ifmmode\times\else\texttimes\fi{}1)$ surfaces. For occupied states, the simulated STM images confirm the experimentally verified $2\ifmmode\times\else\texttimes\fi{}$ modulation along the honeycomb chains in the $\mathrm{Ca}∕\mathrm{Si}(111)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}2)$ surface, induced by attractive interactions between Ca adatoms and the nearest-neighbor Si atoms. Finally we have calculated the electronic band structures for the energetically stable $(3\ifmmode\times\else\texttimes\fi{}2)$ and $(2\ifmmode\times\else\texttimes\fi{}1)$ phases of the $\mathrm{Ca}∕\mathrm{Si}(111)$ surface, and compared (in detail) with the recent experimental findings.