Adatoms, dimers, and interstitials on group-IV(113) surfaces: First-principles studies of energetical, structural, and electronic properties

Abstract

Using an ab initio plane-wave-pseudopotential code we study a variety of $3\ifmmode\times\else\texttimes\fi{}1$ and $3\ifmmode\times\else\texttimes\fi{}2$ reconstructions including adatom (A), dimer (D), and interstitial (I) models of Ge, Si, and diamond(113) surfaces. All reconstruction elements give rise to local minima on the total-energy surface. For Ge and Si, interstitial reconstructions are confirmed to be most favorable. Reconstructions without interstitials, even the oppositely puckered $3\ifmmode\times\else\texttimes\fi{}2$ AD model, do not open a surface-state gap. The semiconducting $3\ifmmode\times\else\texttimes\fi{}2$ ADI structure is the lowest one in energy for Si, since the occupied surface states appear below the valence-band maximum. The $3\ifmmode\times\else\texttimes\fi{}2$ AI surface with asymmetric pentamers is also semiconducting and, in the Ge case, it is even lower in energy. The $3\ifmmode\times\else\texttimes\fi{}1$ AD model is found to be the most stable (113) surface reconstruction for diamond, despite the vanishing gap. The measured structural data, the observed (in particular occupied) surface states, the scanning-tunneling microscopy images of Si and $\mathrm{Ge}(113)3\ifmmode\times\else\texttimes\fi{}2$ and $3\ifmmode\times\else\texttimes\fi{}1$ surfaces, as well as the temperature-induced phase transitions can widely be explained using models with subsurface interstitial atoms and accounting for the mobility of such atoms.