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

• Published in: Acta materialia 2007-05, Vol.55 (8), p.2805-2814
• Main Authors: Chao, Brook, Chae, Seung-Hyun, Zhang, Xuefeng, Lu, Kuan-Hsun, Im, Jay, Ho, P.S.
• Format: Article
• Language: English
• Subjects: AGING MECHANISMS; ANNEALING PROCESSES; Applied sciences; Brazing. Soldering; Copper; DIFFUSION; ELECTROMIGRATION; Exact sciences and technology; Intermetallic compound; INTERMETALLIC COMPOUNDS; Intermetallics; Inversion; Joining, thermal cutting: metallurgical aspects; Lead (metal); MATHEMATICAL ANALYSIS; Mathematical models; METALLIZING (FOR PLATING); Metals. Metallurgy; PARAMETERS; Simulated annealing; SOLDERING ALLOYS; Solders
• ISSN: 1359-6454; 1873-2453
• DOI: 10.1016/j.actamat.2006.12.019

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 × 10 17 m 2 s −1 for Cu 3Sn and 7.04 × 10 16 m 2 s −1 for Cu 6Sn 5, while the diffusion coefficients of Sn were found to be 2.35 × 10 16 m 2 s −1 for Cu 3Sn and 6.49 × 10 16 m 2 s −1 for Cu 6Sn 5. The effective charges of Cu were found to be 26.5 for Cu 3Sn and 26.0 for Cu 6Sn 5, and for Sn, the effective charges were found to be 23.6 for Cu 3Sn and 36.0 for Cu 6Sn 5. 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.