Isothermal stress relaxation in electroplated Cu films. II. Kinetic modeling

Abstract

In Part I we reported experimental results obtained from isothermal stress relaxation tests of electroplated Cu thin films with and without a passivation layer and deduced grain-boundary and interface diffusivities based on a kinetic model. Here in Part II we describe the detail of the model, which is based on coupling of grain-boundary diffusion with surface diffusion for unpassivated films and with interface diffusion for passivated films. Numerical solutions are obtained for the coupled diffusion problems and analytical solutions are obtained for several limiting cases. The effects of surface diffusivity and interface diffusivity on stress relaxation of polycrystalline thin films are analyzed and compared with experiments. The model predicts a transient behavior of stress relaxation and provides a quantitative correlation between stress relaxation and the kinetics of mass transport. In particular, the models can be used together with isothermal stress relaxation tests to characterize interface diffusion and to evaluate selected cap layers for improving electromigration reliability of Cu interconnects.