Roughening of vicinal surfaces and step step interactions: Application to Cu(1,1,11) by means of statistical analysis of STM images

The surface morphology of vicinal surfaces is governed by thermal kink creation energies and step-step interactions. Kink creation energies E(k) were measured first by means of the statistical analysis of STM images and within one-dimensional or free-step approximations. In the present paper a two-dimensional model is investigated where in addition to the simple no-crossing condition for steps, elastic like step-step interactions with A/L(2) dependence are considered. In the framework of this model, novel analytical expressions are obtained for the correlation function, G(0,y) parallel to steps and G(m,0) perpendicular to steps, in terms of microscopic energetic parameters E, and A. The good agreement observed between our approach, exact results (available for A=0 and one peculiar A value) and Monte Carlo (MC) simulations confirms its validity. By statistical analysis of STM images of Cu(1,1,ll), we have measured both G(0,y) and G(I,I,0) together with the terrace width distribution (TWD), All these measurements evidence a step-step interaction stronger than the mere no-crossing condition. This set of data can be consistently fitted within our approach with one couple of microscopic parameters E(k) = 1430 K and A = 70 K.