Vicinal surfaces: free energy, terrace width distribution and step correlation functions

The equilibrium morphology of vicinal surfaces is governed by thermal kink creation energies and step–step interactions. Such parameters can be determined within microscopic step models by means of the statistical analysis of surface images such as those provided by STM. A versatile multi-step transfer matrix (strip) method is introduced to calculate thermodynamical averages. The correlation function of step displacements along step edges, the terrace width distribution and the free energy are thus obtained. The applicability of various one-step and many-step formulae is discussed, and properties of the capillary wave approximation are given. Within this approximation, the width of the terrace width distribution at the roughening temperature is found to be universal.