Solid-state dewetting and island morphologies in strongly anisotropic materials

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.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...

Sharp-interface approach for simulating solid-state dewetting in two dimensions: A Cahn–Hoffman ξ-vector formulation

“…These earlier studies were focused on the isotropic surface energy, although recent experiments have demonstrated that the crystalline anisotropy could play important roles in solid-state dewetting. To include the surface energy anisotropy, many approaches have been proposed in recent years, such as a discrete model [13], a kinetic Monte Carlo model [42,15], a crystalline model [9,65] and continuum models based on partial differential equations [5,25,26,55]. From a mathematical perspective, theoretical solid-state dewetting studies can be categorized into two major problems: one focuses on the equilibrium of solid particles on substrates [4,33]; the other focuses on investigating the kinetic evolution of solid-state dewetting [25,26,55].…”

“…The above governing equation is well-posed when the surface energy is isotropic or weakly anisotropic. But when the surface energy is strongly anisotropic, some missing orientations will appear on equilibrium shapes [47,50]; in this case, the governing equation becomes ill-posed, and it can be regularized by adding regularization terms such that the regularized sharp-interface model is well-posed [25,5]. For the analytical criteria about the classification of surface energy anisotropy in 3D, interested readers could refer to [47].…”

A Parametric Finite Element Method for Solid-State Dewetting Problems in Three Dimensions

“…In order to understand this condition, we may consider two limiting cases as η = 0 and η = ∞: (i) when η = 0, the contact line moving velocity is zero, and we prescribe a fixed boundary condition such that the contact line does not move; and (ii) when η → ∞, as we always assume that the moving velocity should be finite, condition (ii) will reduce to the so-called anisotropic Young equation [30,4] (2.10) c γ Γ · n Γ − σ = 0. which prescribes an equilibrium contact angle condition. Therefore, condition (ii) actually allows a relaxation process for the dynamic contact angle evolving to its equilibrium contact angle [49,28]. The last condition (iii) ensures that the total volume/mass of the thin film is conserved during the evolution, i.e., no-mass flux at the moving contact line.…”

“…Solid-state dewetting of thin films belongs to the evolution of an open curve/ surface governed by surface diffusion and contact line migration [27,49,28,5,30]. In earlier years, the marker-particle method was firstly presented for solving sharpinterface models of solid-state dewetting in two dimensions (2D) [51,49] and three dimensions (3D) [18].…”

A sharp-interface model and its numerical approximation for solid-state dewetting with axisymmetric geometry

“…Moreover, the phase field approaches for solid-state dewetting have also been proposed for both isotropic [20,21] and anisotropic surface energy [22], which can naturally capture the complex topology change during the evolution. More recently, the two-dimensional solid-state dewetting has been fully studied via sharp interface models [23][24][25][26]. In these models, the interface between the thin film and vapor is assumed to be an open curve with two endpoints (the contact points) attached on the x axis (flat substrate).…”