Surface Evolution of Strained Thin Solid Films: Stability Analysis and Time Evolution of Local Surface Perturbations

A discrete formulation of the surface diffusion potential is developed taking into account both the capillarity and the elasticity contributions. This potential, also valid in the large curvature regime, is applied to study the surface evolution of strained thin solid films. The home made numerical tool MoveFilm, used to track the surface evolution due to surface diffusion, is coupled to a finite element solver Cast3M to calculate the mechanical problem. The numerical results are consistent with known analytic results in the small perturbation approximation. This validates the code and our formulation of the diffusion potential. To go further, some non-linear strain effects are analysed concerning the destabilization dynamics imposed by an initial local surface perturbation. For low biaxial strain (1%), the perturbation amplitude grows and reaches a maximum before a lateral expansion of the perturbation. During the evolution, the profile remains quasi-sinusoidal and selects a specific wavelength. For larger strain, a specific wavelength is also selected but the profile shape is highly asymmetric and exhibits sharp grooves similar to cracks.