NEW RESULTS FOR TERRACE-WIDTH DISTRIBUTIONS: WIGNER SURMISE AND EXTRACTION OF STEP-STEP REPULSIONS

__T. L. Einstein__,1 O. Pierre-Louis,1,2 and M. Giesen3

[1] Dep't of Physics, Univ. of Maryland, College Park, MD 20742-4111, [2] Now at Lab. Spectro. Phys., UJF (CNRS) Grenoble I, B.P. 87, F-38042 Saint-Martin d'Hères, France, [3] IGV, Forschungszentrum-Jülich, D-52425 Jülich, Germany

*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 Ã admitting exact solutions, Pr(s) does far better than the standard mean-field expressions. From the single adjustable parameter r, Ã emerges via Ã = (r -2)r/4. Our results elucidate recent controversies about how best to extract Ã 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.