Origin of the Different Reconstructions of Diamond, Si, and Ge(111) Surfaces

Ab initio calculations of the 2x1, c(2x8), and 7x7 reconstructions of the diamond, Si, and Ge(111) surfaces are reported. The pi-bonded chain, adatom, and dimer-adatom-stacking fault models are studied to understand the driving forces for a certain reconstruction. The resulting energetics, geometries, and band structures are compared for the elemental semiconductors with different atomic sizes, and chemical trends are derived. We show why the lowest-energy reconstructions are different for the group-IV materials considered.