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In this study, we applied a mathematical model to explore the mechanism and factors leading to phase separation and the formation of branching structures with nanocolumns extending from larger clusters formed on the substrate of a grown film. The mathematical model simulated the growth of a thin film over time by using partial differential equations, including the processes of adsorption, phase separation, and diffusion due to the curvature of the thin film surface. The modeling results revealed the possible mechanism that could lead to the formation of the described branching structures. That mechanism can be divided into two main steps. The first step is the growth of a relatively large cluster (of a component that makes up the branching phase) on the substrate during the initial growth stages. The second step is the division process of that large cluster into smaller clusters in the later growth stages. The model parameters influencing the growth conditions that lead to the formation mechanism of the branching structures were determined, and their influences on the phase structure were analyzed. [ABSTRACT FROM AUTHOR]

The morphology of aluminum co-doped scandium stabilized zirconia (ScAlSZ) thin films formed by e-beam deposition system was investigated experimentally and theoretically. The dependencies of surface roughness, and the films' structure on deposition temperature and deposition rate were analyzed. It was shown experimentally that the dependence of the surface roughness on deposition temperature and deposition rate was not monotonic. Those dependencies were analyzed by mathematical modeling. The mathematical model includes the processes of phase separation, adsorption and diffusion process due to the film surface curvature. The impacts of substrate temperature, growth rate on surface roughness of thin films and lateral nanoparticle sizes are shown by the modeling results. Modeling showed that the roughness of the surface of grown films became higher in most cases as the substrate's temperature rose, but the higher deposition rate resulted in lower surface roughness in most cases. The results obtained by simulations were compared to the relevant experimental data. The non-linear relationships between surface roughness of grown films and lateral size of nanoparticles were also shown by our modeling results, which suggested that the variation in the surface roughness depending on the substrate temperature and growth rate was related to the lateral size of nanoparticles. [ABSTRACT FROM AUTHOR]

The dependences of the surface roughness and the phase structure of compound thin films on substrate temperature and flux of incoming particles are investigated by a proposed mathematical model. The model, which describes physically deposited thin compound film growth process is based on the Cahn–Hilliard equation and includes processes of phase separation, adsorption, and diffusion. In order to analyze large temperature range and assuming deposition of energetic particles, the diffusion is discriminated into thermal diffusion, radiation-enhanced diffusion, and ion beam mixing. The model is adapted to analyze surface roughness evolution during film growth. The influences of the substrate temperature and incoming flux particles on the surface roughness are determined by a series of numerical experiments. The modelling results showed that the surface roughness increased as the substrate temperature rose. Besides, a similar relationship was discovered between substrate temperature and size of nanoparticles formed in binary films, so the increase in the surface roughness with the substrate temperature was attributed to the increase in size of nanoparticles. [ABSTRACT FROM AUTHOR]