AVS 45th International Symposium
    Surface Science Division Friday Sessions
       Session SS1-FrM

Paper SS1-FrM8
New Results for Analytical Approximants of Terrace-Width Distributions on Vicinal Surfaces, and Some Consequences@footnote 1@

Friday, November 6, 1998, 10:40 am, Room 308

Session: Surface Structure and Strain
Presenter: T.L. Einstein, University of Maryland, College Park
Authors: T.L. Einstein, University of Maryland, College Park
O. Pierre-Louis, University of Maryland, College Park
B. Joós, University of Ottawa, Canada
Correspondent: Click to Email
Quantitative measurement of the equilibrium terrace width distribution P(L) of vicinal surfaces has proved a powerful and convenient way to investigate the interactions between steps. Most analyses have relied on simple analytic results based on the Gruber-Mullins approximation: one "active" step wandering between two fixed straight steps separated by twice the average step spacing . For non-interacting, free-fermion (FF)-like steps, P(L) corresponds to the ground-state density of a confined fermion, going like sin@super 2@(@pi@L/2), while for significant repulsions decaying as A/L@super 2@, this density is a Gaussian.@footnote 2@ For both cases, P(L) vs. L/ can be written as a "universal function." Rather complicated analytic expressions can be written for FF@footnote 3@ and for a special value of A. For FF, H. Ibach concocted a simple but excellent approximation for P(L) involving a power law and a gaussian decay.@footnote 4@ This expression turns out to be the celebrated "Wigner surmise" for the distribution of energies in gaussian unitary ensembles, long known to correspond to free fermions. Based on this recognition and results from random-matrix theory, we present a general universal expression that has just one fitting parameter, the power, from which A can be easily estimated. We provide calibrations at the values of A for which exact solutions exist. We use these results to clarify recent controversies@footnote 5@ about how to extract A from P(L). We also discuss what can be learned from the third moment of P(L) and from the covariance of adjacent terrace widths. @FootnoteText@ @footnote 1@Work supported by NSF MRSEC grant DMR 96-32521. @footnote 2@N. C. Bartelt, T. L. Einstein, and E. D. Williams, Surface Sci. 240, L591 (1990). @footnote 3@B. Joós, T. L. Einstein, and N. C. Bartelt, Phys. Rev. B 43, 8143 (1991). @footnote 4@H. Ibach, private communcation; M. Giesen, Surface Sci. 370, 55 (1997). @footnote 5@L. Masson, L. Barbier, J. Cousty, and B. Salanon, Surface Sci. 317, L1115 (1994); L. Barbier, L. Masson, J. Cousty, and B. Salanon, Surface Sci. 345, 197 (1996); T. Ihle, C. Misbah, and O. Pierre-Louis, Phys. Rev. B 58, xxx (1998).