Phase field microelasticity modeling of surface instability of heteroepitaxial thin films

A development of the nonlinear surface instability of heteroepitaxial films during annealing process has been studied by using the phase field microelasticity model. The developed model considers the diffusional surface profile evolution of nonlinear grooved and coarsened regime, which is driven by the strain energy relaxation and is not constrained by any ad hoc assumptions concerning possible surface morphology. The method is based on the numerical solution of the exact elastic equilibrium equations. The simulation has shown that an initial small amplitude random roughening of a flat film develops to form a quasi-periodical array of islands under a certain balance between the strain and surface energies. This occurs through the competitive growth of amplitudes with different wavelengths. The surface morphology simultaneously grows and coarsens. The fully coarsened morphology exhibits a dominant wavelength that is significantly greater than the one that follows from the linear analysis of initial instability. The equilibrium morphology corresponding to a periodic array of islands is reached independent of the initial fluctuations of the surface profile.