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.Keywords: Solid-State Dewetting, Anisotropy, Winterbottom Construction, Surface Diffusion, Contact Line Migration.Solid-state dewetting is a ubiquitous phenomenon in thin film technology [1][2][3][4][5] which can either be deleterious, destabilizing a thin film structure, or advantageous, leading to the controlled formation of an array of nanoscale particles, e.g., used in sensor devices [6] and as catalysts for the growth of carbon or semiconductor nanowires [7,8]. Recently, solid-state dewetting has been attracting increased attention both because of interest in the underlying pattern formation physics and its potential application as an economical approach to obtain nanostructured surfaces and nanodevices [9][10][11][12][13][14][15][16][17][18].The dewetting of thin solid films deposited on substrates is similar to the dewetting of liquid films [19,20]. However, mass transport during solid-state dewetting is usually dominated by surface diffusion rather than fluid dynamics. Solid-state dewetting can be modeled as interfacetracking problem where morphology evolution is governed by surface diffusion and contact line migration [17,18]. In early studies, a number of simplifying assumptions were made in order to keep the analysis tractable. For example, under the assumption that all interface energies are isotropic, Srolovitz and Safran [9] proposed a sharpinterface model to analyze hole growth; based on the above model, Wong et al. [10,11] designed a "marker particle" numerical scheme to study the two-dimensional retraction of an island and a perturbed cylindrical wire on a substrate. Recently, we [17] solved a similar problem using a phase field approach that naturally captures the topological events that occur during evolution and is applicable in * Corresponding author.Email addresses: jiangwei1007@whu.edu.cn (Wei Jiang), matbaowz@nus.edu.sg (Weizhu Bao) any number of dimensions.However, many experiments have demonstrated that the morphology evolution that occurs during thin solid film dewetting is strongly affected by crystalline anisotropy [3]. Recent approaches that incorporate crystalline anisotropy have included a discrete model [12], a kinetic Monte Carlo method [13,14] and the crystalline method [15,16]. The main drawback of these approaches is that the evolution does not account for the full anisotropic free energy of the system or do not represent a completely mathematical description. To...

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharpinterface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th-or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.

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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 ξ-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.