Solid-State Dewetting of Polycrystalline Thin Films: a Phase Field Approach

Abstract

Solid-state dewetting is the process by which thin solid films break up and retract on a substrate, forming nanostructures. While dewetting of single-crystalline films is understood as a surface-energy-driven process mediated by surface diffusion, polycrystalline films exhibit additional complexity due to the presence of grain boundaries. Most theoretical and computational studies have focused on single-crystalline dewetting. Here, we present the application of the grandpotential multi-phase-field model to the dewetting of thin polycrystalline films in three dimensions, reproducing the key phenomenology of this process. By considering isotropic interface/surface energy, we illustrate its consistency with predictions based on energetic arguments and the morphological evolution towards equilibrium. We also provide novel analytical criteria for the onset of three-dimensional dewetting, serving as fundamental theoretical benchmarks, and highlight the critical role of triple junctions. Moreover, we unveil the dewetting behavior of polycrystalline patches, extending the scenarios of their single-crystalline counterparts.

Figures (5)

• Figure 1: Modeling and 2D simulation of polycrystalline SSD. (a) Scheme of the considered geometries and labeling of the phases as considered in the MPF model. The grain aspect ratio is defined as $r^{\rm 2D}=W/H$. (b) SSD simulations ($\epsilon=0.2H$) of a thin film with three grains. The central one has an aspect ratio of $r^{\rm 2D}=25$. The two at the border of the film have both $r^{\rm 2D}=12.5$. The timescale is relative to the one needed to reach equilibrium. The inset shows the vapour-solid-substrate trijunction. (c) MPF simulations of SSD with varying $r^{\rm 2D}$ for a film ideally formed by grains of the same size. A critical aspect ratio of $r^{\rm 2D}_{\rm c} \approx 9$ is obtained in simulations.
• Figure 2: Geometrical parametrization and estimation of the critical aspect ratios. (a) Schematics of 2D equilibrium morphology. The dashed line illustrates the thickness ($H$) of the conformal initial film. (b) Schematics (top view) of the idealized setting of hexagonal grains in 3D with equal size. (c) Spherical caps truncated by $n$-gons. (d) $r_{\rm c}(\theta)$ in 2D and 3D as predicted by Eqs. \ref{['eq:r2D']} and \ref{['eq:r3D']} for $d=0$ (sharp interface limit) and $d>0$ as in simulations. Symbols show $r_{\rm c}$ obtained by MPF simulations with $d=0.22$ (2D) and $d=0.25$ (3D). The inset illustrates the dependence of $r_{\rm c}$ on $d$ for $\theta=\pi/6$ (2D), as well as the average standard deviation of simulation results ($\pm 0.25$).
• Figure 3: Simulations (3D) of morphological evolution and SSD in polycrystalline thin films with an idealized initial microstructure ($\epsilon=0.22H$). (a) Perspective view of the equilibrium configuration for thin films with varying aspect ratio, except for $r^{\rm 3D}=16$ for which an intermediate stage is reported. (b) Representative stages of SSD for grains with $r^{\rm 3D}=8$ (top view). The timescale is expressed relative to the breakup time. (c) Representative stages of SSD for grains with $r^{\rm 3D}=32$ (top view). The timescale is set as in panel (b).
• Figure 4: SSD of square polycrystalline patches with an arbitrary internal grain structure. The two panels (a) and (b) show representative stages of the SSD with two different initial conditions obtained through a Voronoi construction over randomly generated points. The resulting domains are then randomly assigned to different phase fields. These initial conditions show significantly different variability of the numbers of grains per side, which are $\sim 7.25 \pm 0.69$ in (a) and $\sim 4.75\pm 3.69$ (b). Timescale is given relative to the polycrystalline patch breakup time (similar in both cases). Panel (b) shows the evolution up to the late stages. (c) SSD of a single-crystalline patch with the same size and aspect ratio as in (a) and (b).
• Figure S-1: Spherical cross-section (a) and $n$-gon unit cell (b) of a grain in the tile pattern.