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

TL;DR

This paper develops a statistical mechanical model for the anisotropic step stiffness of a 2D honeycomb lattice gas with next-nearest-neighbor interactions, applying it to Si(111) surfaces to understand surface properties.

Contribution

It introduces an extended random walk method to calculate anisotropic step tension and stiffness in a honeycomb lattice gas model with complex interactions, applied to real silicon surfaces.

Findings

Calculated anisotropic step tension and stiffness for Si(111) surfaces.

Determined equilibrium island shapes based on the model.

Estimated inter-step interaction coefficients for the surfaces.

Abstract

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.