Calculations of Cleavage Processes, Surface Structures and Electronic Structure of Silicon and Germanium.

The cleavage processes, surface and step structures, and electronic structure of Si and Ge (111)2 x 1 surfaces were studied. The ab initio quantum chemistry programs KGNMOL-89 and DMol were used to study the cleavage of silicon and germanium clusters in the diamond structure. It was found that the potential energy of stretching and shearing glide planes increases much faster than for shuffle planes. The cleavage process is discussed and it is shown how glide -plane cleavage can occur, with consequences for surface structure models. The Keating strain-energy method has been applied to estimate the energies of surface and step structures on Si(111)2 x 1. Two minimum strain-energy TBS (Three -Bond Scission) model structures were obtained. Since angular strains are involved which go beyond the applicability limits of the Keating formula, a correction factor is used, derived by comparing Keating-type calculations of particular surface models of Si(111) with the results of more extensive calculations. The use of a simple correction factor gives results that agree with a calculation for the Pandey ( pi-bonded chain) model and one for the TBS model. Using this factor, a model for a 3-substep structure of the (322) step on Si is found to be quite stable, while the 2-substep structures are moderately stable. The surface band structure of the TBS and Pandey models have been computed using an ab initio HF LCAO program CRYSTAL-92. In the case of the TBS model, the results showed valence band dispersion that could be compatible with experiments. For the Pandey model, the calculated valence band dispersion seemed large. The surface band gap for both TBS and Pandey models was greatly overestimated. The significance is discussed. The surface electron density of states was calculated for the TBS model and the valence band generally matched experimental results from STM (scanning tunneling microscopy). The electron charge density of various surface regions was calculated. The corrugation amplitude at 5 A from the surface for the TBS model was found to be close to that of the Pandey model and STM measurements. STM would not be able to distinguish between the two models.