Statistical mechanical calculation of anisotropic step stiffness of a two-dimensional hexagonal lattice-gas model with next-nearest-neighbour interactions: application to Si(111) surface

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