Taguchi Robust Analysis of Fatigue of Lead-Free Sn3.5Ag Solders

This paper presents a study of the effects of selected geometry features on the fatigue life of the Sn3.5Ag lead-free solder ball on a multi-chip module (MCM) package. The features considered are both the upper and lower solder pad radii, the thickness of the substrate and that of the PC board. The components constituting the MCM include a heat spreader, thermal adhesive, chips, an underfill/Sn3.5Ag lead-free solder bumps mixture, structural adhesive, a substrate, a PC board, and Sn3.5Ag lead-free solder balls. To account for the time- and temperature-dependent behavior of the lead-free solders, a multi-linear isotropic hardening rule and a creep constitutive relation are considered. Linear elastic models are assumed for the rest components. In this study, the Surface Evolver is employed to determine the shape, including the height and pad radii, of the solder ball. A sliced 3D model is proposed using the finite element method to demonstrate the structural responses of the package subjected to ten temperature cycles between the high dwell temperature of 125°C and the low of −40°C. The structural responses of interest are deformation, stress distribution, and strain range of the solder ball having the greatest distance from the neutral point (DNP). A modified Coffin-Manson fatigue model is adopted to calculate the fatigue life cycle for the solders. In the course of the study, a parametric analysis is firstly conducted to characterize the influence of the geometry features on the fatigue life of the solders. An analysis of variation based on the Taguchi robust method is then exploited to investigate the optimal design for the fatigue life of the solders. Our results show that due to the mismatch of the coefficients of thermal expansion of the components, local deformations that do not comply with the global deformation are realized. Both the upper and lower pad radii have an opposite effect on the fatigue life of the solders. The fatigue life of the solders decreases as the thickness of the substrate or the PC board increases. The results using the Taguchi method reveal that among the four selected geometry features, both the upper pad radius and the PC board thickness are the most dominating factors. An optimal combination of the four features is recommended. This combination of the four features yields a fatigue life of 843 cycles that is a gain of 7.88 times of that of a reference package model.