Stress relaxation of thin film due to coupled surface and grain boundary diffusion

A numerical scheme, based on an energy statement, is developed to simulate thin film morphology evolution and stress relaxation due to concurrent surface diffusion and grain boundary diffusion. Different from previously published works, this paper also explores the effects of mobility ratio of the two processes and the dihedral angle at the surface-grain boundary triple junction. The range of mobility ratio, in which the stress relaxation process is limited by either surface diffusion or grain boundary diffusion, is determined. It is found that, when the stress relaxation is limited by the rate of surface diffusion, the dihedral angle at the surface-grain boundary junction plays a significant role. A scheme of using both experimental and numerical results to determine grain boundary diffusivity is also presented. As an example, we obtain the activation energy and diffusivity for grain boundary diffusion in Cu thin film.