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

Abstract

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.

Finite element methods for fourth order axisymmetric geometric evolution equations

“…The present authors have used the tangential degrees of freedom to improve the mesh quality during the evolution of discretized curvature flows, see [2,3,4,5]. There has been interest in numerical schemes for axisymmetric schemes for geometric evolution equations both for second and for fourth order flows, see [41,40,14,19,20,23,25,44,47]. However, the literature on numerical analysis of such schemes is sparse.…”

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

“…4.10), the shrinking instability dominates the evolution, and make it shrink towards the center. The shrinking instability for a toroidal island on a substrate has been studied in [31,58] under the assumption of axis-symmetric geometry. But it is still an open problem about quantitatively studying the competition effect by a simultaneous consideration of the shrinking instability and Rayleigh-like instability.…”

Application of Onsager's variational principle to the dynamics of a solid toroidal island on a substrate

“…For brevity, we denote Γ(t) = X(s, t) = (r(s, t), z(s, t)) as the crosssection profile of the surface S with 0 ≤ s ≤ L(t) and r(0, t) = r i , r(L, t) = r o . Based on a thermodynamic variational analysis, we previously proposed a sharp-interface model for simulating solid-state dewetting in three dimensions for axisymmetric geometries [42]. By choosing a length scale and surface energy density scale for normalization as L 0 and γ 0 respectively, the time normalized by L 4 0 /(Bγ 0 ), and the contact line mobility by B/L 3 0 , this leads to the following dimensionless sharp-interface evolution model (for isotropic surface energy) [42]:…”

“…We use the relaxed contact angle boundary condition (ii) in our numerical computations because it can improve numerical stability and, in the fast contact line motion limit, it is also physically important. The accurate, efficient parametric finite element method for numerically solving the above sharp-interface model is described in [12,42].…”