FORMATION OF CRACK-LIKE DIFFUSION WEDGES AND COMPRESSIVE STRESS EVOLUTION DURING THIN FILM GROWTH WITH INHOMOGENEOUS GRAIN BOUNDARY DIFFUSIVITY

We consider the effects of inhomogeneous grain boundary (GB) diffusivity on the formation of crack-like grain boundary diffusion wedges and evolution of compressive stress during the growth of a polycrystalline thin film on a substrate with a perfectly bonded film-substrate interface. The problem is formulated as a class of moving boundary diffusion problems with fully coupled elasticity, GB diffusion and film growth. The inhomogeneous GB mobility leads to a set of hypersingular integro-differential equations which are solved by a special numerical scheme. During the film growth, atoms diffuse into the GBs due to the tensile coalescence stress in the film associated with GB formation. We show that, at deposition rates comparable to the diffusion time scale, such GB diffusion leads to temporal decay of GB traction and induces crack-like singular stress concentration at the roots of the GBs. For a slowly growing high mobility thin film, the stress intensity factor near the tip of the diffusion wedge is comparable to that of a GB diffusion wedge under annealing conditions and can lead to nucleation of dislocations, which in turn can influence stress evolution during film growth. Furthermore, the higher chemical potential at the film surface can overdrive adatoms into GBs and result in a final compressive stress in the film. Our simulations on cyclic film deposition and growth interruption processes qualitatively reproduced the experimentally observed behavior of GB mobility on the Stress-Thickness evolution during deposition, the stress relaxation during growth interruption, as well as the dependence of steady state stress on the deposition rate.