A numerical scheme, based on an energy statement, was 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 was limited by either surface diffusion or grain boundary diffusion, was determined. It was found that, when the stress relaxation was 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 was also presented. As an example, the activation energy and diffusivity for grain boundary diffusion in Cu thin films were obtained.

Stress Relaxation of Thin Film due to Coupled Surface and Grain Boundary Diffusion. Z.Liu, H.H.Yu: Thin Solid Films, 2010, 518[20], 5777-85