Statistical Analysis of Mounded Surfaces: Application to the Evolution of Ultrathin Gold Film Morphology with Deposition Temperature

Extracting characteristic dimensions from mounded surfaces such as grain size or intergrain lengths is usually made by statistical analysis. Different statistical functions are used in the literature to extract characteristic lengths. The main issue is that depending on the choice of the statistical function the results can be very different. In this paper, we demonstrate using a series of model mounded surfaces for which characteristic dimensions are known, that a method (namely, interfacial differential function, IDF) is the most effective method to determine the different characteristic lengths. The influence on the statistical treatment of the variation of the different characteristic lengths is then studied and confirms the ability of the IDF analysis. The IDF method was used to analyze the evolution of ultrathin gold film morphology as function of deposition temperature. This approach allows us to demonstrate that the roughness increase with deposition temperature is mainly due to a grain height increase and not to a grain coarsening phenomena as it was claimed before.