We have been studying a new class of defects called the grain boundary diffusion wedges in polycrystalline thin films. These diffusion wedges are formed by stress driven mass transport between the free surface of the film and the grain boundaries during the process of substrate-constrained grain boundary diffusion. The mathematical modelling involves solution to integro-differential equations representing a strong coupling between elasticity and diffusion. We show that the solution can be decomposed into diffusional eigenmodes reminiscent of crack-like opening displacement along the grain boundary which leads to a singular stress field at the root of the grain boundary. We find that the theoretical analysis successfully explains the difference between the mechanical behaviors of passivated and unpassivated copper films during thermal cycling on a Si substrate.
An important implication of our theoretical analysis is that dislocations with Burgers vector parallel to the interface can be nucleated at the root of the grain boundary. This is a new dislocation mechanism in thin films which contrasts to the well known Mathews-Freund-Nix mechanism of threading dislocation propagation. Recent TEM experiments at the Max Planck Institute have shown that, while threading dislocations dominate in passivated metal films, parallel glide dislocations dominate in unpassivated copper films with thickness below 400nm. This is fully consistent with our theoretical predictions.