SIAM Journal on Applied Mathematics, Volume 80, Issue 4, Page 1654-1677, January 2020.
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 the Cahn--Hoffman ${\xi}$-vector) is clearer. By making use of the first variation, necessary conditions for the equilibrium shape of the solid-state dewetting problem are 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 numerical simulations to investigate the evolution of patterned films, e.g., the evolution of a cuboid and pinch-off of a long cuboid. Numerical simulations in 3D demonstrate the performance of the sharp-interface approach to capture many of the complexities observed in solid-state dewetting experiments.

中文翻译：

---

三维模拟固态去湿的Sharp-Interface模型

SIAM应用数学杂志，第80卷，第4期，第1654-1677页，2020年1月。
本文考虑了使用锐界面方法模拟三维（3D）薄膜的固态去湿问题。基于热力学变化，使用速度法来计算总表面能函数的第一个变化。与传统使用参数化曲线（或曲面）相比，速度方法具有更多优势。例如，它具有更强的内在性，并且其变异结构（与Cahn-Hoffman $ {\ xi} $-vector有关）更清晰。通过利用第一变化，给出了固态去湿问题的平衡形状的必要条件，并且还提出了包括表面能各向异性的动力学锐界面模型。这个尖锐的界面模型描述了3D界面的演变，它是通过表面扩散和接触线迁移而发生的。通过解决提出的模型，我们进行了数值模拟，以研究图案化薄膜的演变，例如长方体的长方体的捏和。在3D中进行的数值模拟表明，使用清晰界面方法可以捕获固态除湿实验中观察到的许多复杂性。