Vol.30 No.4

Editorial Office


  • Journal of the Microelectronics and Packaging Society
  • Volume 30(4); 2023
  • Article


Journal of the Microelectronics and Packaging Society 2023;30(4):50-60. Published online: Feb, 20, 2024

A Numerical Study on the Effect of Initial Shape on Inelastic Deformation of Solder Balls under Various Mechanical Loading Conditions

  • Da-Hun Lee1 , Jae-Hyuk Lim1 , and Eun-Ho Lee1,2,3†
    1School of Mechanical Engineering, Sungkyunkwan University, Seobu-ro 2066, Suwon-si, Gyeonggi-do, 16419, Republic of Korea, 2Department of Smart Fab. Technology, Sungkyunkwan University, Seobu-ro 2066, Suwon-si, Gyeonggi-do, 16419, Republic of Korea, 3Department of Intelligent Robotics, Sungkyunkwan University, Seobu-ro 2066, Suwon-si, Gyeonggi-do, 16419, Republic of Korea
Corresponding author E-mail: e.h.lee@skku.edu

Ball Grid Array (BGA) is a widely used package type due to its high pin density and good heat dissipation. In BGA, solder balls play an important role in electrically connecting the package to the PCB. Therefore, understanding the inelastic deformation of solder balls under various mechanical loads is essential for the robust design of semiconductor packages. In this study, the geometrical effect on the inelastic deformation and fracture of solder balls were analyzed by finite element analysis. The results showed that fracture occurred in both tilted and hourglass shapes under shear loading, and no fracture occurred in all cases under compressive loading. However, when bending was applied, only the tilted shape failed. When shear and bending loads were combined with compression, the stress triaxiality was maintained at a value less than zero and failure was suppressed. Furthermore, a comparison using the Lagrangian-Green strain tensor of the critical element showed that even under the same loading conditions, there was a significant difference in deformation depending on the shape of the solder ball.

Keywords Numerical analysis, Inelastic deformation, Fracture, Solder, Packaging

  • E. C. Noh, H. W. Lee, and J. W. Yoon, "Recent Advances in Fine Pitch Cu Pillar Bumps for Advanced Semiconductor Packaging", J. Microelecton. Packag., 30(3), 1-10 (2023).
  • A. Surrendar, K. H. Kishore, M. Kavitha, A. Z. Ibatova, and V. Samavatian, "Effect of thermo-mechanical fatigue and lower cycle fatigue interaction on performance of solder joints", IEEE Transactions on Device and Materials Reliability, 18(4), 606-612 (2018).
  • H. L. J. Pang, K. H. Tan, X. Q. Shi, and Z. P. Wang, "Microstructure and intermetallic growth effects on shear and fatigue strength of solder joints subjected to thermal cycling aging", Materials Science and Engineering: A, 307(1-2), 42-50 (2001).
  • S. Cho, Y. T. Kim, and Y. B. Ko, "A Study on Robust Design of PCB for Package on Package by Numerical Analysis with Unit and Substrate Level to Reduce Warpage", J. Microelecton. Packag. Soc., 28(4), 31-39 (2021).
  • Y. G. Kim, H. S. Kim, T. W. Kim, and H. S. Kim, "Sold er Alloy Types and Solder Joint Reliability Evaluation Techniques", J. Microelecton. Packag. Soc., 30(1), 17-29 (2023).
  • E. H. Lee and M. Rubin, "Modeling anisotropic inelastic effects in sheet metal forming using microstructural vectors-Part I: Theory", Int. J. Plast., 134, 102783 (2022).
  • E. H. Lee and M. Rubin, "Eulerian constitutive equations for the coupled influences of anisotropic yielding, the Bauschinger effect and the strength-differential effect for plane stresses", Int. J. Solids Struct., 241, 111475 (2022).
  • T. B. Stoughton and J. W. Yoon, "Anisotropic hardening and non-associated flow in proportional loading of sheet metals", Int. J. Plast., 25, 1777-1817 (2009).
  • J. W. Yoon, F. Barlat, R. E. Dick, K. Chung, and T. J. Kang, "Plane stress field function for aluminum alloy sheets-part II: FE formulation and its implementation", Int. J. Plast., 19(9), 1297-1319 (2003).
  • Y. Lou, H. Huh, S. Lim, and K. Pack, "New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals", Int. J. Solids Struct., 49, 3605-3615 (2012).
  • N. Park, H. Huh, S. J. Lim, Y. Lou, Y. S. Kang, and M. H. Seo, "Fracture-based forming limit criteria for anisotropic materials in sheet metal forming, Int, J. Plast., 96, 1-35 (2017).
  • G. R. Johnson and W. H. Cook, "Fracture characteristics of three metals subjected to various strains, strain rates, temperatures, and pressures", Eng. Fract. Mech., 21, 31-48 (1985).
  • W. K. Loh, R. Kulterman, H. Fu, and M. Tsuriya, "Recent trends of package warpage and measurement metrologies", Proc. International Conference on Electronics Packaging (ICEP), Hokkaido, Japan, 89-93 (2016).
  • F. Qin, T. An, and N. Chen, "Strain rate effects and rate-dependent constitutive models of lead-based and lead-free solders", J. Appl. Mech., 77, 01008 (2010).
  • J. H. Lim, D. H. Lee, and E. H. Lee, "Numerical investigation of the evolving inelastic deformation path of a solder ball joint under various loading conditions", Appl. Sci., 13(22), 12137 (2023).
  • E. H. Lee, "Elastic-plastic deformation at finite strains", J. Appl. Mech., 36, 1-6 (1969).
  • E. H. Lee and D. T. Liu, "Finite-Strain Elastic-Plastic Theory with Application to Plane-Wave Analysis", J. Appl. Phys. 38, 19-27 (1967).