Assessing conformal thin film growth under nonstochastic deposition conditions: application of a phenomenological model of roughness replication to synthetic topographic images

In this work, a simple method to follow the evolution of the surface of thin films during growth on substrates characterised by high roughness is detailed. To account for real cases as much as possible, the approach presented is based on the hypothesis that deposition takes place under nonstochastic conditions, such as those typical of many thin film processes in industry and technology. In this context, previous models for roughness replication, which are mainly based on idealised deposition conditions, cannot be applied and thus ad hoc approaches are required for achieving quantitative predictions. Here it is suggested that under nonstochastic conditions a phenomenological relation can be proposed, mainly based on local roughening of surface, to monitor the statistical similarity between the film and the substrate during growth or, in other words, to detect changes of the bare substrate morphological profile occurring during the film growth on top. Such approximation is based on surface representation in terms of power spectral density of surface heights, derived from topographic images; in this work, such method will be tested on two separate batches of synthetic images which simulate thin films growth onto a real rough substrate. In particular, two growth models will be implemented: the first reproduces the surface profile obtained during an atomic force microscopy measurement by using a simple geometrical envelope of surface, regardless the thin film growth mechanism; the second reproduces the columnar growth expected under nonstochastic deposition conditions. It will be shown that the approach introduced is capable to highlight differences between the two batches and, in the second case, to quantitatively account for the replication of the substrate roughness during growth. The results obtained here are potentially interesting in that they account essentially for the geometrical features of the surfaces, and as such they can be applied to synthetic depositions that reproduce different thin film depositions and experimental contexts.