√3X √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) alpha phase(root 3x root 3R30 degrees) with 1/3 ML Sn coverage, prevails over the adatom-rest-atom 2x2 phase (with 1/4 ML Sn coverage) for all allowed values of the Sn chemical potential. This is to be contrasted with the 2x2-based reconstructions which are known to prevail on the clean Ge(lll) and Si(lll) surfaces. Our results suggest that the stabilization of the root 3x root 3R30 degrees phase for Sn-Ge(lll) 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 alpha phases are observed also in Pb-Ge(111), Pb-Si(lll), and Sn-Si(111).