Analysis of terrace-width distributions using the generalized Wigner surmise: Calibration using Monte Carlo and transfer-matrix calculations

Abstract

Measurement of terrace-width distributions (TWD’s) of vicinal surfaces is used routinely to find the dimensionless strength à of the elastic repulsion between steps. For sufficiently strong repulsions, the TWD can be described by a Gaussian about the mean step spacing, but controversy has arisen on the correct prefactor in the relation of the TWD variance to Ã. Instead of the various Gaussian approximations, we have advocated for several years that the TWD be fit with the generalized Wigner distribution, essentially a gamma distribution in the normalized squared TWs. The basis for this idea stems from a mapping of the step model to the Sutherland model of fermions in one dimension. While several applications to experiment have been successful, definitive comparison of the various approximations requires high-quality numerical data. We report transfer matrix and extensive Monte Carlo simulations of terrace-step-kink models to support our contentions. Our work includes investigation of finite-size effects and of the breakdown of the continuum picture for values of à larger than in typical experiments.