T. L. Einstein,1 O. Pierre-Louis,1,2 and M. Giesen3

Quantitative measurement of the equilibrium terrace-width distribution (TWD) P(s) —s being the step spacing l ¸ á lñ —of vicinal surfaces facilitates assessment of the strength of elastic step-step repulsions A/l2. Step configurations can be viewed as time-lapse photos of fermions in 1D; the TWD then depends only on Ã, the dimensionless product of A and step stiffness over (kBT)2. Since equilibrium fluctuations exhibit "universal" behavior, random-matrix theory suggests that P(s) can be approximated by the "generalized Wigner surmise" Pr(s) º ar sr exp(-brs2), where ar and br are constants set by normalization and unit mean of Pr(s). At the three values of à admitting exact solutions, Pr(s) does far better than the standard mean-field expressions. From the single adjustable parameter r, à emerges via à = (r -2)r/4. Our results elucidate recent controversies about how best to extract à from experimental TWD's. We discuss the skewness of Pr(s) [at small Ã] and the covariance of adjacent terrace widths. For illustration we compare data analysis for various Cu(100) and Cu(111) vicinals at several T's using Pr(s) and traditional techniques. Since step-step correlations are much easier to calculate than TWD's, experiments should also monitor these multi-terrace functions.

[1] Work at UM supported by NSF MRSEC grant DMR 96-32521.—For more details, see TLE & OP-L, Surface Sci. 424, L299 (1999); MG & TLE, preprint.