Statistical Mechanical Calculation of Anisotropic Step Stiffness of a Two-Dimensional Hexagonal Lattice Gas Model with Next-Nearest-Neighbor Interactions: Application to Si(111) Surface

We study a two-dimensional honeycomb lattice gas model with both nearest- and next-nearest-neighbor interactions in a staggered field, which describes the surface of stoichiometrically binary crystal. We calculate anisotropic step tension, step stiffness, and equilibrium island shape, by an extended random walk method. We apply the results to Si(111) 7$\times$7 reconstructed surface and high-temperature Si(111) 1$\times$1 surface. We also calculate inter-step interaction coefficient.