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

Abstract

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.

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

“…In this section, we first review a sharp-interface model obtained recently by the authors [30] for simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies in 3D. Based on this model, we then propose a variational formulation via the Cahn-Hoffman ξ-vector.…”

“…By using the approach in [30], we can obtain a sharp-interface model for simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies…”

“…where ∇ S is the surface gradient operator, and ξ := ξ(n) is well-known as the Cahn-Hoffman ξ-vector [13,24,29,30] which can be defined based on the homogeneous extension of γ(n) as…”

“…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].…”

“…The goal of this paper is to extend our previous works [5,29] from 2D to the 3D by using a variational formulation in terms of the Cahn-Hoffman ξ-vector for simulating solid-state dewetting of thin films. More precisely, the main objectives are as follows: (i) to derive a variational formulation of the sharp-interface model for simulating solid-state dewetting problems in 3D [30]; (ii) to develop a PFEM for simulating the solid-state dewetting of thin films in 3D; (iii) to demonstrate the capability, efficiency and accuracy of the proposed PFEM; and (iv) to investigate many of the complexities which have been observed in experimental dewetting of patterned islands on substrates, such as Rayleigh instability, pinch-off, edge retraction and corner mass accumulation.…”