Terrace-width distributions of touching steps: Modification of the fermion analogy with implications for measuring step-step interactions

Abstract

Using Monte Carlo simulations, we compute the terrace-width distributions (TWDs) of surfaces in which steps can touch each other, forming multiple-atomic height steps, but cannot cross (no overhangs), and so inconsistent with the standard mapping to spinless fermions. Our results show that the generalized Wigner distribution with minor modifications at small step separations, gives a very good fit for TWDs of touching steps. The interaction strength derived from the fit parameter indicates an effective attraction between steps. The strength of this effective attraction decreases for larger mean-step separations and decreasing step-touching energies; describable via finite-size scaling. Hence, accurate extraction of the true repulsion strength requires multiple vicinalities.