Investigation of diffusion and electromigration parameters for Cu–Sn intermetallic compounds in Pb-free solders using simulated annealing

An efficient numerical method was developed to extract the diffusion and electromigration parameters for multi-phase intermetallic compounds (IMC) formed as a result of material reactions between under bump metallization (UBM) and solder joints. This method was based on the simulated annealing (SA) method and applied to the growth of Cu–Sn IMC during thermal aging and under current stressing in Pb-free solder joints with Cu-UBM. At 150 °C, the diffusion coefficients of Cu were found to be 3.67 × 1017 m2 s−1 for Cu3Sn and 7.04 × 1016 m2 s−1 for Cu6Sn5, while the diffusion coefficients of Sn were found to be 2.35 × 1016 m2 s−1 for Cu3Sn and 6.49 × 1016 m2 s−1 for Cu6Sn5. The effective charges of Cu were found to be 26.5 for Cu3Sn and 26.0 for Cu6Sn5, and for Sn, the effective charges were found to be 23.6 for Cu3Sn and 36.0 for Cu6Sn5. The SA approach provided substantially superior efficiency and accuracy over the conventional grid heuristics and is particularly suitable for analyzing many-parameter, multi-phase intermetallic formation for solder systems where quantitative deduction for such parameters has seldom been reported.