This study presents a comprehensive exploration of numerical and mathematical models designed to elucidate the formation processes of nanofilms. Nanofilms, with their unique properties and applications in various fields such as electronics, optics, and material science, require a detailed understanding of their growth mechanisms to optimize their performance and functionality. This research integrates theoretical modeling with advanced numerical simulations to analyze the dynamics of nanofilm formation.

We develop and apply mathematical models to describe the key processes involved in nanofilm growth, including nucleation, surface diffusion, and film deposition. These models are based on partial differential equations that capture the spatial and temporal evolution of film thickness and composition. To complement the theoretical framework, we employ numerical simulations to solve these equations and visualize the formation dynamics under various conditions. Our study demonstrates how factors such as deposition rate, substrate temperature, and material properties influence the morphology and uniformity of nanofilms. We present detailed results from simulations that illustrate the impact of these parameters on film growth and quality. The models and simulations are validated against experimental data, ensuring their accuracy and relevance.

Nanofilm formation, Mathematical modeling, Numerical simulation

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