The Impacts of Material Uncertainty in Electro-Migration of SAC Solder Electronic Packaging by Monte Carlo-Based Stochastic Finite-Element Model

Electro-migration (EM) induced by electric current under the conditions of multi-physical fields in integrated circuits and electronic packaging is a crucial factor that affects reliability and safety of the entire system. The uncertainty quantification and propagation in the EM process are the challenging issues that deserve more attention. In this article, the uncertainties in the related material parameters of the Sn–Ag–Cu (SAC) solder and copper conductors are taken into consideration based on the stochastic finite-element model. The corners and edges of the contact surface in the SAC solder are the most dynamic and active places with the maximum concentration gradient. This reaches a satisfied agreement with the experimental results and parallel numerical investigations in the literatures. The extreme values of the concentration and its gradient in each time step are computed and recorded. The accuracy and convergence of results are confirmed by the comparison of different period durations and time step scales with discrete time points. Furthermore, the probability density distribution, mean, and variance of the extreme values in different time steps are recorded and compared. Based on the huge database provided by the Monte Carlo-based stochastic finite-element model (MC-SFEM), the correlations between the material parameters and the concentration as well as the concentration gradients are analyzed. The proposed MC-SFEM is a feasible and effective model for the comprehensive analysis of EM with the potential in uncertainty and reliability analysis.