Terrace-width distributions on vicinal surfaces: generalized Wigner surmise and extraction of step-step repulsions

From quantitative measurement of the equilibrium terrace-width (l) distribu tion (TWD) of vicinal surfaces, one can assess the strength A of elastic st ep-step repulsions A/l(2). Generally the TWD depends only on (A) over bar = A x (step stiffness)/(k(B)T)(2) From ideas of fluctuation phenomena, TWDs should be describable by the "generalized Wigner distribution" (GWD), essen tially a power-law in l/<l > times a "Gaussian decay" in l/<l >. The power- law exponent is related simply to A. Alternatively, the GWD gives the exact solution for a mean-field approximation. The GWD provides at least as good a description of TWDs as the standard fit to a Gaussian (centered at <l >) . It works well for weak elastic repulsion strengths A (where Gaussians fai l), as illustrated explicitly for vicinal Pt(l 1 0). Application to vicinal copper surfaces confirms the viability of the GWD analysis. The GWD can be treated as a two-parameter fit by scaling e using an adjustable characteri stic width. With Monte Carlo and transfer-matrix calculations, we show that for physical values of (A) over bar the GWD provides a better overall esti mate than the Gaussian models. We quantify how a GWD approaches a Gaussian for large (A) over bar and present a convenient, accurate expression relati ng the variance of the TWD to A. We describe how discreteness of terrace wi dths impacts the standard continuum analysis. (C) 2001 Elsevier Science B.V . All rights reserved.