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. Thin film deposition onto rough surfaces is widespread among many industrial and technological applications such as photovoltaics, microelectronics, optics and biomedicine just to mention a few. In such cases, compared to substrate morphology, film deposition may be required to improve certain surface functionalities through roughening or smoothing of the pristine substrate morphology to accomplish different needs or applications. This raises a simple and legitimate question: how could the degree of replication of the substrate morphology after film deposition be determined? Quantitative approaches to this issue involve statistical descriptions of the two interfaces in terms of power spectral densities retrieved from scanning probe microscopy images of the surface. However, this requires an in-depth knowledge of the physics behind the process of film formation, leading to a complication in that models providing quantitative predictions for film conformality are based on ideal deposition conditions; thus, numerical results remained so far restricted to the case of atomically flat, and mostly unrealistic, surfaces. To tackle into this subject, an approximation is suggested that is based on phenomenological considerations and on the hypothesis that deposition is nonideal. On these premises, a simple conformality factor derived from a linear relation is introduced to relate the substrate and the evolving film morphology. Such approach is then applied to simulated atomic force microscopy images which describe the film growth onto a real substrate. Two models will be implemented: the first uses a simple geometrical envelope of the surface that uniquely matches with experiments without keeping into account the mechanism of growth, while the second reproduces the columnar growth expected under real deposition conditions. The application of conformality factors to the images so obtained shows that the second model accomplishes well to the final goal of obtaining quantitative results and enables to retrieve quantitative information especially in case of micro or nanometrically structured surfaces.

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