GE(100) 2X1 AND C(4X2) SURFACE RECONSTRUCTIONS STUDIED BY AB-INITIO TOTAL-ENERGY MOLECULAR-FORCE CALCULATIONS

The 2 X 1 and c (4 X 2) surface reconstructions on Ge(100) are investi gated by the ab initio, all-electron, molecular-cluster method, which solves the local-density-functional equations and provides analytical energy gradients. We use finite-size clusters (up to 71 atoms includin g 39 Ge atoms) to model the Ge(100) surfaces. Atomic-force calculation s are extensively used to obtain the minimum-energy geometry for the d ifferent structures investigated. We determine and compare the binding energy and geometry up to the fourth layer of the symmetric (2 X 1), buckled (2 X 1), as well as the higher-order c (4 X 2) reconstruction. Important energetic and structural differences are found compared to the corresponding Si(100)2 X 1 surface. The asymmetric dimer model is found to be 0.34 eV/dimer lower than the symmetric one with the up-dim er atom being 0.19 angstrom above the plane of the unreconstructed sur face and a dimer tilt of 15-degrees. The buckled 2 X 1 and c (4 X 2) r econstructions are found to be close in energy, which suggests that bo th could be present on the surface at room temperature. These results are in excellent agreement with scanning-tunneling-microscopy experime nts and previous theoretical studies using a slab geometry. This energ y is well below the energy of the symmetric dimer reconstruction indic ating that dimer flipping recently suggested for the Si(100)2 X 1 surf ace is unlikely to occur in the case of the Ge(100) surface. In signif icant contrast to the Si(100) surface, we found that the Ge-Ge dimer i s weaker with bond lengths that are slightly above the bulk value of 2 .44 angstrom, at 2.48 and 2.50 angstrom for the asymmetric 2 X 1 and c (4 X 2) reconstructions, respectively. It suggests that the Ge(I 00) surface might show some different behavior towards adsorption.