Statistical characterization of surface morphologies

We implement and assess several statistical methods for rough surface morphology characterization, which can largely be divided into two classes. The first class is based on estimation of two-point, quadratic statistical functions and includes: estimates of the sample autocovariance function, sample height–height correlation (also, structure) function, and periodogram estimate of the surface power spectrum. The second class incorporates estimation of up to the fourth statistical moments of the local curvature on a fixed scale.We apply these methods first on computer-simulated epitaxial surfaces, which permits the characterization using large sets of “data” and rich statistics. Then we deal with real surfaces, whose roughness profiles are measured using atomic force microscopy (AFM). In both cases we infer and discuss scaling properties, degree of anisotropy and deviation from Gaussian distribution of surface heights.