Absolute surface energies of group-IV semiconductors: Dependence on orientation and reconstruction

We use a plane-wave-pseudopotential code to study the surface energetics for the elemental semiconductors Ge, Si, and diamond from first principles. Various reconstruction geometries including 1\ifmmode\times\else\texttimes\fi{}1, 2\ifmmode\times\else\texttimes\fi{}1, $c(4\ifmmode\times\else\texttimes\fi{}2),$ $c(2\ifmmode\times\else\texttimes\fi{}8),$ and 7\ifmmode\times\else\texttimes\fi{}7 of the low-index surfaces (100), (110), and (111) are optimized with respect to the atomic coordinates. The resulting total energies are related to the accompanying band structures. Chemical trends are derived. The different reconstruction behavior is discussed in terms of atomic sizes and orbital energies.