On the role of fractals dynamics in the evolution of microstructures in thin films and bulk materials

Fractal (micro)-structures are observed in many thin films, bulk specimens and fractured samples. A phenomenon that leads to the formation of these structures in thin films is diffusion-limited aggregation. The assumption in diffusion-limited aggregation is that formation of such structures is independent of the source conditions and relies only on film-substrate interactions with requirement of single crystallinity in both cases. The possibilities of fractal structures occurring in amorphous or crystalline film-on-amorphous or crystalline substrate have received limited attention. However, results on sputter deposited transition metal nitride thin films show that these combinations can indeed lead to fractal structures such as dendrites and snowflakes. In this work we postulate that the formation of these microstructures is perhaps related and sensitive to the initial conditions provided for growth, which leads to a conclusion that perhaps chaos-related dynamics is at work. We believe that a new theoretical framework is required to explain these phenomena. An attempt to identify the knowns and the unknowns in this area is made using our results as well as some available in the literature.