An efficient numerical method was developed in order to extract the diffusion and electromigration parameters for multi-phase intermetallic compounds. The method was based upon the simulated annealing method, and was applied to the growth of Cu-Sn intermetallic compounds during thermal aging and under current stressing in Pb-free solder joints with Cu. At 150C, the diffusion coefficients of Cu were found to be 3.67 x 10-17m2/s for Cu3Sn and 7.04 x 10-16m2/s for Cu6Sn5, while the diffusion coefficients of Sn were found to be 2.35 x 10-16m2/s for Cu3Sn and 6.49 x 10-16m2/s for Cu6Sn5. The effective charges of Cu were found to be 26.5 for Cu3Sn and 26.0 for Cu6Sn5. For Sn, the effective charges were found to be 23.6 for Cu3Sn and 36.0 for Cu6Sn5. The simulated annealing approach provided substantially superior efficiency and accuracy over conventional grid heuristics and was particularly suitable for analyzing many-parameter multi-phase intermetallic formation.

Investigation of Diffusion and Electromigration Parameters for Cu–Sn Intermetallic Compounds in Pb-Free Solders using Simulated Annealing. B.Chao, S.H.Chae, X.Zhang, K.H.Lu, J.Im, P.S.Ho: Acta Materialia, 2007, 55[8], 2805-14