A Monte Carlo simulation method for {111} surfaces of silicon and other diamond-cubic materials

Abstract

We introduce a modified, solid-on-solid model for Monte Carlo computer simulation studies of equilibrium, growth and etching phenomena on the {111} surfaces of silicon and other diamond-cubic materials. Incorporation of the actual diamond-cubic crystal structure allows for the inclusion of possible effects of the structure's rotational symmetry, coordination and the layer-stacking periodicity (normal to the surface) on the surface properties and dynamics. Results of extensive equilibrium simulations, including surface energies, surface specific heats, step energies and surface roughness, are presented to characterize the basic model. A broad peak in the surface specific heat and the universal behavior of the height-difference correlation function indicate a roughening transition at temperature T R. A preroughening transition is indicated by a sharp peak in the surface specific heat and a dramatic decrease in the step energy at a temperature T PR ≈ 0.43 T R. The energies of stable and unstable steps differ significantly below T PR but become isotropic above T PR. Initially straight, unstable steps are observed to spontaneously microfacet below T PR. Preliminary simulations of growth and etching of surfaces, both with and without intersecting dislocations, are also presented.