Dislocations and morphological instabilities: Continuum modeling of misfitting heteroepitaxial films

We present a continuum model of nonequilibrium heterogeneous elastic systems, which includes both smooth and singular strains, as well as their coupling to free surfaces, in two spatial dimensions. It accurately includes nucleation, interactions, and dynamics of dislocations. In particular, we demonstrate that the model recovers the well-known Matthews-Blakeslee critical thickness for the nucleation of misfit dislocations. For misfitting heteroepitaxial films above the critical thickness, dislocations compete with the stress-induced instability of the film-vapor interface as a strain-relief mechanism. At early times, the dislocations slow down the initial instability by climbing to the film-substrate interface and relaxing the misfit strain partially. However, the late-time morphology is determined by the strong interaction between the stress concentration at the bottom of the grooves and the singular stresses due to dislocations.