Mathematical Modeling of Phase Separation and Branching Process of the Film Structure during Binary Thin Film Deposition

Abstract

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.