Analysis of terrace width distributions on vicinal copper surfaces using the ‘Wigner surmise’: comparison with Gaussian approach

We have analyzed the terrace width distribution on a large number of Cu (100) and (111) vicinal surfaces using the standard Gaussian fit as well as by using an alternative analytical distribution, which comes from the perspective of fluctuation phenomena and is referred to as the generalized Wigner surmise. The chief motivation is to extract optimally the strength A of the elastic repulsion between steps. Both methods provide generally consistent estimates of the variance. We find the Wigner approach provides a viable alternative to the standard Gaussian approach. We review competing views on the proportionality constant relating A to the inverse square of the variance of a Gaussian fit; the experimental range of data seems to straddle the range over which various values are optimal. The previously suggested method for analyzing skewness proves unsatisfactory with actual data. By comparing data for different temperatures and misorientations with predictions based on scaling, we illustrate the difficulties of obtaining quantitative information about A.