Statistical and Fractal Analysis of Random Height Function

Abstract

Nanostructured semiconductor surfaces are commonly used for suppression of the light reflection. We prepared several kinds of surface structures on silicon substrate and analyzed the properties of the random height function used for the description of observed surface morphology. Statistical and fractal methods used in this analysis provide useful information for the optimization of the surface forming procedure. Multifractal analysis provides additional information about the surface morphology, not contained in the results of standard statistical methods. Numerical procedures used in the multifractal analysis were tested by using theoretical random height function created from large sets of Cantor numbers.