Vibrational Properties of Semiconductor Surfaces and the Indirect Substrate Mediated Adatom Interaction.

The vibrational properties of the reconstructed Silicon(100)2 x 1 surface have been studied using the Keating lattice dynamics model and a dimer bond description of the reconstructed surface. This model is sufficiently flexible that effects of variations in surface geometry and force constants can be examined easily. Calculations have been made of the on-site and intersite vibrational correlation functions and also of the wave-vector-dependent eigenstates which are localized in the surface region. The calculations were performed using a technique which Fourier transforms the dynamical matrix parallel to the surface and uses recursion calculations in the direction normal to the surface. Calculations were made for various surface dimer bond force constants and tilt angles. The surface mean square displacements and intersite correlation functions have been found to exhibit significant anisotropy and temperature dependence. The present results are compared with results of other calculations, and their implications to experiment are discussed. Bulk intersite vibrational correlation functions for neighbouring pairs of atoms in Silicon and Germanium have been calculated. Comparison with the results of the Si(100)2 x 1 surface indicates that the surface and bulk intersite correlation functions do not differ significantly. Thus in this case, the bulk intersite correlation functions should be useful for surface structure analysis. The indirect adatom interaction mediated by the lattice is investigated. A lattice dynamical treatment as opposed to a continuum elasticity approach is used. This permits the evaluation of the interaction at short adatom separations of the order of the surface lattice constant. In addition, the local structure of both the substrate and the adatom defect are properly reflected in the results of the positional dependence and anisotropy of the interaction. The system consisting of Arsenic dimer defects on the Si(100) surface is considered. For this system, the interaction is found to change from attractive to repulsive as the adatom separation is increased for a given orientation of the adatom defect separation relative to the cubic axes. This behavior has implications regarding the clustering of Arsenic dimer defects on the Si(100) surface.