Adatoms on Si(111) and Ge(111) surfaces

First-principles calculations of energy and stress are performed on adatom-covered Si(111) and Ge(111) surfaces. The presence of adatoms is found to lower the surface energy and cause a large change in surface stress. While the 1×{}1 surfaces are under a weak compressive stress, the {}3×{}{}3 and 2×{}2 adatom-covered surfaces are under a strong tensile stress. Calculations at high plane-wave cutoff unambiguously identify the 2×{}2 top-site geometry as the energetically preferred adatom configuration. Relaxed geometries are presented and compared with x-ray structural measurements of adatoms in the Si(111)-7×{}7 structure. Vibrational mode frequencies and eigenvectors of the adatom unit are determined from a comprehensive set of frozen-phonon calculations for the Si 2×{}2 surface; we find two symmetric modes that are strongly localized at the surface, in agreement with electron-energy-loss--spectroscopy measurements. It is found that the 2×{}2 adatom-covered surfaces have three surface bands, and the dispersion relations are calculated along symmetry directions in the surface Brillouin zone. The surface band structures are in good agreement with angle-resolved photoelectron-spectroscopy data for the 7×{}7-Si(111) surface.