Growth of intermetallic compounds in solder joints based on strongly coupled thermo–mechano–electro–diffusional theory

Abstract

The growth of intermetallic compounds (IMCs) is one of the key problems that restrict the reliability of solder joints. A phase field model based on strongly coupled thermo–mechano–electro–diffusional theory is proposed to investigate the growth of IMCs and formation mechanism. Of which, the diffusion coefficients and effective charge numbers of Cu and Sn were regarded as a continuous function of concentration on the basis of experimental data. The effect of back stress can be determined to be equivalent to that of volumetric strain through the analogy of the diffusion equation in the strongly coupled theory and the classical diffusion equation. On this account, the evolution of back stress can be evaluated during the entire process.Simulation results demonstrate that the growth curves are well consistent with the experiment values at low current densities when the coupled phase field model is adopted. The reasons for the poor coincidence at high current density are investigated and explained. And then, the thermodynamic driving forces in the entire growth process of IMCs are quantitative assessed in detail. The result shows that the evolution of back stress is agree with the sum of Cu and Sn concentrations in the IMCs, which indicates that the analogy is practical. Lastly, the concentration factor of the total driving force is defined to characterise the effect of current crowding on the growth of IMCs in solder joints.