Extraction of step-re pulsion strengths from terrace width distributions: statistical and analytical considerations

Recently it has been recognized that the so-called generalized Wigner distr ibution may provide at least as good a description of terrace width distrib utions (TWDs) on vicinal surfaces as the standard Gaussian fit and is parti cularly applicable for weak repulsions between steps, where the latter fail s. Subsequent applications to vicinal copper surfaces at various temperatur es confirmed the serviceability of the new analysis procedure but raised so me theoretical questions. Here we address these issues using analytical, nu merical, and statistical methods. We propose an extension of the generalize d Wigner distribution to a two-parameter fit that allows the terrace widths to be scaled by an optimum effective mean width. We discuss quantitatively the approach of a Wigner distribution to a Gaussian form for strong repuls ions. how errors in normalization or mean affect the deduced interaction, a nd how optimally to extract the interaction from the variance and mean of t he TWD. We show that correlations reduce by two orders of magnitude the num ber of independent measurements in a typical scanning tunneling microscopy image. We also discuss the effect of the discreteness ('quantization') of t errace widths, finding that for high misorientation (small mean width) the standard continuum analysis gives faulty estimates of step interactions. (C ) 2000 Elsevier Science B.V. All rights reserved.