A tangent-plane marker-particle method for the computation of three-dimensional solid surfaces evolving by surface diffusion on a substrate

Du, Ping; Khenner, Mikhail; Wong, Harris

doi:10.1016/j.jcp.2009.10.013

Cited by 29 publications

(19 citation statements)

References 39 publications

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“…Srolovitz and S.A. Safran proposed a sharp-interface model for the solid-state dewetting of thin films with isotropic surface energies [17]. Based on this model, the marker-particle method was presented for the simulation of the solid-state dewetting [18,19]. Recently, sharp-interface models were obtained rigorously via the energy variational method for the temporal evolution of open curves in 2D for the solid-state dewetting of thin films with weakly and strongly anisotropic surface energies.…”

Section: Introductionmentioning

confidence: 99%

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

Bao

Jiang

Wang

et al. 2017

Journal of Computational Physics

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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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Section: Introductionmentioning

confidence: 99%

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

Bao

Jiang

Wang

et al. 2017

Journal of Computational Physics

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“…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].…”

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confidence: 99%

Solid-state dewetting and island morphologies in strongly anisotropic materials

et al. 2016

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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...

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“…The first sharp-interface model for solid-state dewetting was proposed by Srolovitz and Safran [13] to investigate the hole growth of small slop profiles under the assumption of isotropic surface energy and cylindrical symmetry. This model was then generalized to both the two-dimensional case [15] and three-dimensional case [16] in Lagrangian representation. Besides, the "marker particle" method was simultaneously proposed for solving these geometric evolution models.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

2019

Journal of Computational and Applied Mathematics

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Based on the thermodynamic variation, we rigorously derive the sharp-interface model for solid-state dewetting on a flat substrate in the form of cylindrical symmetry. The governing equations for the model belong to fourth-order geometric curve evolution partial differential equations, with proper boundary conditions such that the total volume of the system is conserved and the total energy is dissipative during the time evolution. We propose a variational formulation for the sharp-interface model and then apply the parametric finite element method for solving it efficiently. Extensive numerical simulation results are presented lastly to demonstrate the morphological characteristics for solid-state dewetting.

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A tangent-plane marker-particle method for the computation of three-dimensional solid surfaces evolving by surface diffusion on a substrate

Cited by 29 publications

References 39 publications

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

Solid-state dewetting and island morphologies in strongly anisotropic materials

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

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