Characterization of thin-film surfaces by fractal geometry

Abstract

The applicability of models based on fractal geometry to characterize thin-film surfaces is investigated. The fractal geometry of sputtered chromium nitride and silicon nitride thin film surfaces is described using Fourier profile analysis of scanning tunneling microscopy images and a box counting method. The CrN_x- and SiN_x-coatings were deposited on silicon wafers by reactive magnetron sputtering. The columnar structure of the amorphous silicon nitride varied with deposition similarly to the stucture of the polycrystalline chromium nitride films. For quantitative comparison of film morphology, an average column diameter has been used as a characteristic. The average column diameter increases with increasing gas pressure because of shadowing processes during deposition. The fractal dimension decreases with increasing pressure. Films with fine columnar structures are characterized by a larger fractal dimension than films with a coarse columnar structure. The fractal dimension determined by Fourier analysis is larger than the dimension calculated by the box counting method. The reason may be the limited pixel density of digitized images.