Symmetry implications for the selection of cluster sizes for semiconductor surfaces

Abstract

The implications of the intrinsic three-fold symmetry of the idealized (111) plane of the bulk crystals of the group iv semiconductors are examined. The highest occupied orbital of the asymptotically large clusters exhibiting this symmetry are shown to be expected to be of irreducible representation e and to be half-filled. The resulting electronic degeneracy is prone to a Jahn-Teller distortion leading to an expected reconstruction of the surface. The related phenomenon in solid state band theory, the Peierls distortion, has been previously suggested as the driving force behind the known reconstruction of this surface. The symmetry analysis supports this view. Finite clusters containing 8i + 3 or 8i + 4 surface atoms are recommended for cluster calculations examining the surface reconstruction problem because they are to be expected to have the appropriate (e)2 electronic configuration. A nearest-neighbor Huckel-like treatment of the problem gives analytical expressions for the eigenvalues for the idealized case and for one kind of 2 × 1 distortion. Calculations with this Huckel-like model exhibit the properties expected from the analysis of the three-fold symmetry.