Comparison of cluster and slab models of the surface structure of Cl-terminated Ge(111) and GaAs(111) surfaces

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The surface reconstruction and bonding of Cl atoms on two semiconductor surfaces, namely, Ge(111) and GaAs(111), are studied using first-principles energy-minimization methods. We use (a) specially designed clusters which mimic the semiconductor-surface geometry and the GAUSSIAN quantum-chemistry program at various levels of basis-set refinement, and (b) slab calculations using plane-waves, pseudopotentials, and density-functional theory within the local-density approximation (LDA). We also calculate the vibrational spectra of the surface atoms and the Raman spectrum of Ge(111)Cl for comparison with future experiments. The surface vibrational modes predicted by the slab models are at least 30 ${\mathrm{cm}}^{\ensuremath{-}1}$ smaller than from the cluster models. The best cluster model tends to overestimate the Ge-Cl and Ga-Cl bond length by about 4%, while the LDA slab model underestimates the bond lengths by 1.8%. Very little reconstruction is found in the bond lengths of the ``substrate'' as modeled by the cluster, and in fact tend to overestimate the ``bulk'' bond lengths. In contrast, the slab calculation shows considerable reconstruction of the near-surface layers, shrinking the layer separations by pulling the surface toward the interior of the crystal.