Analytical Solutions and a Numerical Approach for Diffusion-Induced Stresses in Intermetallic Compound Layers of Solder Joints

Intermetallic compounds (IMC) play a key role in the mechanical reliability of solder joints. The present work investigates the diffusion-induced stress developed in the Cu pad/IMC/solder sandwich structure during a solid-state isothermal aging process. An analytical model and a numerical approach are proposed to predict the stress. The model consists of a Cu6Sn5 layer sandwiched between a Cu pad and a solder layer, and it is assumed that the diffusivity of the Cu atoms is much greater than that of the Sn atoms. We use the Laplace transformation method to obtain the distribution of the Cu atoms concentration. The diffusion-induced stress is determined analytically by the volumetric strain resulted from the effect of the atomic diffusion. It is found that the Cu6Sn5 layer is subjected to compressive stress due to the Cu atoms diffusion. As the diffusion time is long enough, the diffusion-induced stress shows a linear relationship with the thickness of the Cu6Sn5 layer. A finite element approach to calculate the diffusion-induced stress is proposed, and it is compared and validated by the analytical solution. The results show that the proposed approach can give a well estimation of the diffusion-induced stress in the Cu6Sn5 layer, and is also efficient in predicting the diffusion-induced stress in the structures with more complex geometry. The distribution of the Cu atoms concentration and the diffusion-induced stress in the model with a scallop-like or flat-like Cu6Sn5/solder interface are calculated by the numerical approach. The results show that the interfacial morphology of the Cu6Sn5/solder has great influence on the evolution of the Cu atoms concentration, and the diffusion-induced stress in the Cu6Sn5 layer with the scallop edge is less than that with the flat edge.