Creep and stress relaxation in free-standing thin metal films controlled by coupled surface and grain boundary diffusion

An analytical solution is presented that interprets the effects of grain size, surface and grain boundary diffusivities, surface and grain boundary free energies, as well as grain boundary grooving on the creep rate in free-standing polycrystalline thin metal films. The Coble creep in the film plane is also taken into account; this has a significant effect on the creep rate of the film. The effects of diffusion ratio and free energy ratio between surface and grain boundary on film agglomeration are illustrated as well. A closed-form expression for stress relaxation in films under constrained strain conditions is derived from this solution. An exponential decay in stress is found as a function of the film microstructure. Results predicted by the solution are shown to be in agreement with the experiments.