Theory for intermetallic phase growth between Cu and liquid Sn-Pb solder based on grain boundary diffusion control

Kinetics of phase formation during interdiffusion in solid-liquid diffusion couples are influenced by the morphology of the intermediate compound layer. In some cases, an intermediate compound layer is formed which has very fine grain size. This condition favors grain boundary diffusion as the predominant mechanism for transport through the layer. In systems where grain coarsening occurs, the coarsening kinetics will influence the interdiffusion kinetics. In addition, for some solid-liquid systems, a grain boundary grooving effect is observed which leads to a highly nonuniform layer thickness; the layer is thinner where the liquid phase penetrates the grain boundaries. As a consequence of the grooving effects, the diffusion path through the layer is shorter along the grain boundaries. This differs from standard interdiffusion models which assume that the diffusion distance is equal to the average layer thickness. A model for growth kinetics of an intermediate compound layer is presented for the case where grain boundary diffusion is the predominant transport mechanism. The model includes the geometric effects caused by grain boundary grooving. The model predicts layer growth which follows a t(1/3) dependence on time t. Experimental data for intermetallic growth between copper and 62Sn-36Pb-2Ag solder exhibit a t(1/4) dependence on time t. If experimental data are interpreted in terms of the grain boundary diffusion control model presented in this paper, the activation energy for grain boundary diffusion is 27 kJ/mole.