Distribution of terrace widths on a vicinal surface within the one-dimensional free-fermion model

For the terrace-step-kink model of a stepped surface, the distribution P(L) of terrace widths L is calculated at low temperature by mapping the problem onto the one-dimensional free-fermion model. In this approximation, the only energetic interaction between steps is a hard-core repulsion. A skewed distribution with a parabolic rise and a Gaussian tail is found; the exact asymptotic forms are displayed. By plotting 〈L〉P(L) vs L/〈L〉, we obtain a ‘‘universal’’ curve nearly independent of the average terrace width 〈L〉. With use of this scaling property, analytic approximants are constructed and the role of correlations discussed. We present some results for steps with energetic interactions in two special cases.