Smoothed boundary method modified phase-field modeling of growth dynamics of thin films on the surface of the planar substrate and the etch pit during physical vapor deposition

In this paper, we present a smoothed boundary method modified phase-field model for simulating the growth dynamics of thin films on the surface of the planar substrate and the etch pit during physical vapor deposition. This method effectively captures the complex interactions between film growth and substrate topology, providing insights into the microstructural evolution and mechanical properties of the films. The competition among the governing mechanisms such as the consumption of the grain growth, diffusion, and convection results in the unevenness of the film surface. Numerical results demonstrate that the grains with larger grain-dependent angle ${\theta }_i$ are eventually eliminated by the ones with lower ${\theta }_i$ for the thin film growth on a planar substrate. It was found that the increase of the incident vapor flux velocity leads to the increase of the final porosity in the defined characteristic region S while the final porosity decreases with the increase of the incident vapor flux. For the columnar grain growth on the surface of the etch pit, the final porosity strongly depends on the aspect ratio, the incident vapor flux velocity, and the incident vapor flux.