Mechanical effects of isolated defects within a lead-free solder bump subjected to coupled thermal-electrical loading

In miniaturized lead-free solder bumps of electronic devices under high current density, isolated defects appear as voids and intermetallic compounds (IMCs) due to mass diffusion under the coupled thermal-electrical loading. Electromigration induced finger-shaped cracks between the interfacial IMCs layer and bulk solder interact with isolated defects when adjacent to each other. Consequently, crack propagation will be affected by an isolated defect and results in reduction of the mechanical strength of solder bumps and the service life of electronic products. In the present study, the induced variation of stress intensity factor (SIF) at the crack tip is investigated theoretically and numerically quantified by performing coupled thermal-electrical numerical simulations. With the temperature distribution that results from the applied electrical and thermal conditions, the crack-defect interaction analysis is conducted, based on the equivalent inclusion method, by treating the isolated void and IMCs as inhomogeneities with different mechanical properties. To facilitate the strength evaluation of lead-free solder bumps in practice, a simplified predictive equation for the effect of SIF variation is proposed by correlating the theoretical and numerical results. The toughening-weakening region is numerically differentiated under certain boundary conditions, which gives insight on the mechanical reliability of solder bumps with isolated defects.