Energetics of the Si(111) and Ge(111) surfaces and the effect of strain

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Abstract
Using tight-binding models, the energies of a number of silicon and gemanium (111) surfaces are studied. These include reconstructed surfaces with dimers and stacking faults (DS), simple adatom surfaces such as 2×2 and c(2×8), and more complicated cases with dimers, adatoms, and stacking faults (DAS). For reconstructed surfaces containing adatoms, it is found that a simple correction term dependent on the adatom concentration is needed in the present total-energy model to account for the unusual geometry. Similarities between the silicon and germanium reconstructions are seen and compare well with ab initio results. There are also some differences between silicon and germanium; for example, the DS surfaces are lower in energy than the relaxed (1×1) for silicon, but higher for germanium. Si(111) reconstructs into the DAS structure while Ge(111) goes to the simple adatom c(2×8) surface. The c(2×8), 7×7 DAS, (1×1), and 7×7 DS surface reconstructions of Ge(111) were studied with in-plane strain. For these surfaces, a strain of about 2% was sufficient to make the 7×7 DAS/DS surface lower in energy than the c(2×8)/(1×1) surface. An analysis of the energy per atom showed that the dimer-row and associated first-layer atoms played a major part in the differing energy behavior, in agreement with an earlier proposal. An expansive strain was applied to the 2×2, 7×7 DAS, (1×1), and 7×7 DS surface reconstructions of Si(111). With a strain of about 2.5% the adatom surfaces switched relative energies, while the adatom free surfaces required only about 1.5% strain. As for germanium, the dimer-row and associated atoms were of major importance in the differing energy change.