Coarsening of 3D Thin Films under the Influence of Strong Surface Anisotropy, Elastic Stresses

We develop a diffuse interface model to investigate the three dimensional coarsening in thin films. In this model, both strong surface anisotropy with linear Willmore regularization, elastic stresses and deposition are included. The governing equation for the phase field parameter is a sixth order Cahn-Hilliard Equation due to the presence of surface anisotropy and the linear Willmore regularization. The simulated system is assumed to be in mechanical equilibrium with misfit in the film generated by lattice mismatch in the substrate. Thus, the Cauchy-Navier equations are solved for elastic displacements which lead to the elastic energy. Both the Cahn-Hilliard equation and the Cauchy-Navier equations are solved with an non-stiff, adaptive nonlinear multigrid method. Simulation results of coarsening in three dimensions with different strengths of the surface anisotropy, misfit strain, and deposition rates are shown. Comparison and analysis of these results help to explain their influence on coarsening processes in thin films.