Effective Kink Energy and Step Stiffness

We present a highly reliable statistical mechanical approach to calculate step-related quantities on the vicinal surface, which is comprised of the imaginary path-weight random walk method and the numerical renormalization group method. We applied the method to the studies of Si(001), Si(111) 7×7 and Si(111) 1×1 surfaces. From the effective kink energy, we obtain anisotropic step tension, step stiffness, equilibrium island shape, and step interaction coefficient, which allows quantitative comparison with experiments.