A continuum model was presented, for non-equilibrium heterogeneous elastic systems, which included both smooth and singular strains, as well as their coupling to free surfaces, in 2 spatial dimensions. It accurately includes nucleation, interactions, and dynamics of dislocations. In particular, it was demonstrated that the model recovered the well-known Matthews-Blakeslee critical thickness for the nucleation of misfit dislocations. For misfitting hetero-epitaxial 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 was determined by the strong interaction between the stress concentration at the bottom of the grooves and the singular stresses due to dislocations.

Dislocations and Morphological Instabilities - Continuum Modelling of Misfitting Heteroepitaxial Films. M.Haataja, J.Müller, A.D.Rutenberg, M.Grant: Physical Review B, 2002, 65[16], 165414 (20pp)