[Paper Review] Sharp-interface model for simulating solid-state dewetting in three dimensions

Wei Jiang, Quan Zhao+1 more|arXiv (Cornell University)|Feb 14, 2019

Fluid Dynamics and Thin Films59 references4 citations

TL;DR

This paper proposes a 3D sharp-interface model for simulating solid-state dewetting with surface energy anisotropy, using the Cahn-Hoffman ξ-vector and shape derivatives to derive the first variation of the total surface energy functional. The model captures complex morphological evolution—such as edge retraction, corner accumulation, pinch-off, and faceting—through surface diffusion and contact line migration, accurately reproducing experimental features in numerical simulations of cuboid and square island films.

ABSTRACT

The problem of simulating solid-state dewetting of thin films in three dimensions (3D) by using a sharp-interface approach is considered in this paper. Based on the thermodynamic variation, a speed method is used for calculating the first variation to the total surface energy functional. The speed method shares more advantages than the traditional use of parameterized curves (or surfaces), e.g., it is more intrinsic and its variational structure (related with Cahn-Hoffman $\boldsymbolξ$-vector) is clearer and more direct. By making use of the first variation, necessary conditions for the equilibrium shape of the solid-state dewetting problem is given, and a kinetic sharp-interface model which includes the surface energy anisotropy is also proposed. This sharp-interface model describes the interface evolution in 3D which occurs through surface diffusion and contact line migration. By solving the proposed model, we perform lots of numerical simulations to investigate the evolution of patterned films, e.g., the evolution of a short cuboid and pinch-off of a long cuboid. Numerical simulations in 3D demonstrate the accuracy and efficacy of the sharp-interface approach to capture many of the complexities observed in solid-state dewetting experiments.

Motivation & Objective

• To develop a rigorous 3D sharp-interface model for solid-state dewetting that accounts for surface energy anisotropy.
• To derive the first variation of the total surface energy functional using the speed method and shape derivative theory.
• To establish necessary conditions for equilibrium shapes of solid particles on substrates via the Cahn-Hoffman ξ-vector formulation.
• To simulate kinetic evolution of thin films driven by surface diffusion and contact line migration in 3D.
• To reproduce experimentally observed morphological features such as corner accumulation, hole formation, and pinch-off in numerical simulations.

Proposed method

• The speed method is employed to compute the first variation of the total surface energy functional, offering a more intrinsic and geometrically clear variational structure than parameterized surface methods.
• The Cahn-Hoffman ξ-vector is used to describe surface energy anisotropy, derived from the gradient of the homogeneous extension of γ(n).
• A kinetic sharp-interface model is formulated, with evolution governed by surface diffusion and contact line migration, based on the first variation and thermodynamic principles.
• The model is solved numerically using a level-set or front-tracking method to capture the evolving interface and contact line in 3D.
• The anisotropic surface energy is modeled as γ(n) = 1 + a(n₁⁴ + n₂⁴ + n₃⁴) with a = 0.25 for cubic symmetry.
• Numerical simulations are performed on initial cuboid and square island films to study retraction, mass accumulation, and pinch-off dynamics.

Experimental results

Research questions

• RQ1 How can the first variation of the total surface energy functional be rigorously derived for 3D solid-state dewetting with anisotropic surface energy?
• RQ2 What are the necessary conditions for equilibrium shapes of solid particles on substrates under anisotropic surface energy?
• RQ3 How does the inclusion of the Cahn-Hoffman ξ-vector improve the modeling of interface evolution in 3D?
• RQ4 Can the sharp-interface model accurately reproduce complex morphological features such as corner accumulation and pinch-off in 3D simulations?
• RQ5 What role does surface diffusion play in the kinetic evolution of patterned thin films, and how does it interact with contact line migration?

Key findings

• Numerical simulations of a (1,12,1) cuboid island with anisotropic surface energy show progressive edge retraction and eventual pinch-off at t = 0.695, consistent with experimental observations.
• For a small (3.2,3.2,0.1) square island with isotropic surface energy, corner retraction leads to mass accumulation and eventual formation of a near-spherical shape by t = 0.080.
• In a large (6.4,6.4,0.1) square island, a central valley deepens over time and touches the substrate, forming a hole at t = 0.031, demonstrating the pinch-off phenomenon.
• Cross-sectional profiles in Fig. 10 confirm the development of a deep central valley and subsequent hole formation, validating the 3D evolution dynamics.
• The model successfully captures faceting, edge retraction, and Rayleigh-type instabilities, aligning with experimental and phase-field simulation results.
• The speed method provides a clearer variational structure than traditional parameterized approaches, with the Cahn-Hoffman ξ-vector offering a direct link to surface energy anisotropy.