3×3R30°versus adatom–rest-atom phases on (111) semiconductor surfaces

Total-energy pseudopotential calculations are performed on several competing reconstructions for the Sn-covered and clean Ge(111) surfaces. Our results confirm that the Sn-Ge(111) $\ensuremath{\alpha}$ phase $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}R30\ifmmode^\circ\else\textdegree\fi{})$ with 1/3 ML Sn coverage, prevails over the adatom--rest-atom $2\ifmmode\times\else\texttimes\fi{}2$ phase (with 1/4 ML Sn coverage) for all allowed values of the Sn chemical potential. This is to be contrasted with the $2\ifmmode\times\else\texttimes\fi{}2$-based reconstructions which are known to prevail on the clean Ge(111) and Si(111) surfaces. Our results suggest that the stabilization of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}R30\ifmmode^\circ\else\textdegree\fi{}$ phase for Sn-Ge(111) is caused by the larger size of the adatom, which lowers the energy of the half-filled surface state band, and also increases hybridization with the underlying second-third layer bonding state. The same argument may explain why $\ensuremath{\alpha}$ phases are observed also in Pb-Ge(111), Pb-Si(111), and Sn-Si(111).