A Parametric Three-Dimensional Phase-Field Study of the Physical Vapor Deposition Process of Metal Thin Films Aiming at Quantitative Simulations

In this paper, a parametric three-dimensional (3D) phase-field study of the physical vapor deposition process of metal thin films was performed aiming at quantitative simulations. The effect of deposition rate and model parameters on the microstructure of deposited thin films was investigated based on more than 200 sets of 3D phase-field simulations, and a quantitative relationship between the deposition rate and model parameters was established. After that, the heat maps corresponding to the experimental atomic force microscopy images were plotted for characterization of the surface roughness. Different roughness parameters including the arithmetic average roughness (R-a), root mean square roughness (R-q), skewness (R-sk), and kurtosis (R-ku), as well as the ratio of R-q to R-a were calculated and carefully analyzed. A quantitative relationship between the surface roughness and the deposition rate and model parameters was obtained. Moreover, the calculated R-q to R-a ratios for the thin films at the deposition rates of 0.22 and 1.0 nm s(-1) agreed very well with the experimental data of the deposited Mo and Ti thin films. Finally, further discussion about the correlative behaviors between the surface roughness and the density was proposed for reasoning the shadowing effect as well as the formation of voids during the thin film production.