Topological and Fractal Analysis of Nanostructured Metal–Dielectric Films

The surface topology and fractal dimension of ultrathin silver and gold films have been investigated utilizing atomic force microscopy. These films were formed at the early stages of metal deposition through thermal evaporation and have pre-percolation thicknesses. They contain both metallic and insulating (void) phases, making them metal–dielectric composites. We identified the main parameters of the microstructure, such as the size of the metallic particles and surface roughness, as well as the dependence of these parameters on the film thickness and substrate parameters. Approaches to processing data, including correlation analysis, were employed. An analysis of dependencies and an explanation of their appearance were conducted. The discussion also addressed the limitations of using atomic force microscopy for studying ultrathin metal films. We determined the various types of fractal dimensions, considering the film topology for two- as well as three-dimensional objects. Depending on the actual dimensions of the phase boundary for silver films, a maximum was found. Different approaches to determining the fractal dimensions in 3Ds case show a similar dependence, but different values.