[Paper Review] Solid-State Dewetting and Island Morphologies in Strongly Anisotropic Materials

Wei Jiang, Yan Wang+3 more|arXiv (Cornell University)|Oct 12, 2015

Fluid Dynamics and Thin Films3 citations

TL;DR

This paper proposes a sharp-interface continuum model based on thermodynamic variational principles to study solid-state dewetting in strongly anisotropic materials. It demonstrates that multiple equilibrium and metastable island morphologies—beyond the classical Winterbottom construction—can emerge due to strong surface energy anisotropy, and numerically confirms that all such shapes are dynamically accessible under different initial conditions.

ABSTRACT

We propose a sharp-interface continuum model based on a thermodynamic variational approach to investigate the strong anisotropic effect on solid-state dewetting including contact line dynamics. For sufficiently strong surface energy anisotropy, we show that multiple equilibrium shapes may appear that can not be described by the widely employed Winterbottom construction, i.e., the modified Wulff construction for an island on a substrate. We repair the Winterbottom construction to include multiple equilibrium shapes and employ our evolution model to demonstrate that all such shapes are dynamically accessible.

Motivation & Objective

• To address the limitations of the classical Winterbottom construction in describing equilibrium island shapes under strong surface energy anisotropy.
• To develop a thermodynamically consistent continuum model that captures both surface diffusion and contact line migration in solid-state dewetting.
• To identify and classify multiple stable and metastable island morphologies that arise due to strong crystalline anisotropy.
• To validate the theoretical predictions through numerical simulations and construct a comprehensive phase diagram for wetting/dewetting behavior.
• To extend the applicability of continuum modeling to strongly anisotropic systems, enabling accurate prediction and control of nanostructure evolution.

Proposed method

• Formulates a sharp-interface continuum model using a thermodynamic variational approach to minimize total interfacial energy, including contributions from film/vapor, film/substrate, and vapor/substrate interfaces.
• Introduces a generalized Winterbottom construction that accounts for multiple equilibrium shapes by identifying critical boundary lines (L1–L5) in the parameter space of surface energy anisotropy and substrate energy mismatch.
• Derives analytical expressions for the boundary lines L1–L5 in the (σ, β) parameter space, which define transitions between different wetting/dewetting regimes.
• Employs a level-set based numerical scheme to simulate the time evolution of island morphology under surface diffusion and contact line migration.
• Validated the model by comparing numerical simulations with theoretical predictions across various parameter regimes, confirming consistency with the derived phase diagram.
• Generalizes the model to three dimensions, though notes the challenge of efficient numerical simulation for open surfaces with moving contact lines.

Experimental results

Research questions

• RQ1 What are the equilibrium island shapes that can form on a substrate when surface energy anisotropy is strong, beyond the classical Winterbottom construction?
• RQ2 How does the interplay between surface energy anisotropy and substrate energy mismatch lead to multiple stable and metastable morphologies in solid-state dewetting?
• RQ3 Can a continuum model accurately predict and simulate the dynamic accessibility of multiple equilibrium shapes during island evolution?
• RQ4 What is the complete phase diagram of wetting/dewetting behavior in terms of the anisotropy parameter σ and the substrate energy mismatch β?
• RQ5 How can the Winterbottom construction be mathematically repaired to include multiple equilibrium shapes in the presence of strong anisotropy?

Key findings

• For strong surface energy anisotropy, multiple equilibrium and metastable island morphologies can coexist, including shapes with 'ears' in the Wulff envelope that are not captured by the classical Winterbottom construction.
• The model identifies six distinct cases of wetting/dewetting behavior (Cases II–VI and IV′), each corresponding to different regions in the (σ, β) parameter space, with explicit boundary lines (L1–L5) defining transitions.
• Numerical simulations confirm that different initial island shapes dynamically evolve into either the equilibrium Winterbottom shape or one of the metastable shapes, demonstrating full dynamical accessibility.
• The phase diagram in Fig. 4, validated by simulations, shows perfect agreement between theoretical predictions and numerical outcomes across all parameter regimes.
• The equilibrium shape in Case IV (partial wetting with multiple stable shapes) includes four distinct configurations: symmetric blue, striped, and two asymmetric mirror-image forms, all dynamically accessible.
• In Case IV′, the equilibrium Winterbottom shape corresponds to complete dewetting, indicating that the same anisotropy can lead to either partial or complete dewetting depending on the substrate energy mismatch.