Uncertainty analysis of solder alloy material parameters estimation based on model calibration method

Abstract

Quantification of the uncertainties in the material characterization of solder joint has been one of the major concerns in the microelectronics packaging industry to predict fatigue failure accurately. Therefore, in this study, a model calibration method based on Bayesian approach is proposed to quantify these uncertainties arising in the material parameter estimation of the solder alloy. A specimen is fabricated to this end, which closely simulates solder joint behavior of the actual package under a thermal cycle. Experiment is conducted to examine the deformation by using Moiré interferometry. Viscoplastic finite element analysis procedure is constructed for the specimen based on the Anand model. The uncertainties which include inherent experimental error and insufficient data of experiments are addressed by using the likelihood estimation. Two materials, one being conventional solder of Sn36Pb2Ag and the other the lead-free solder of Sn3.0Ag0.5Cu, are considered to illustrate the approach. As a result, material parameters are identified in the form of credible interval (CI), and the displacements and strains using these parameters are given by the predictive interval (PI). The results suggest that the proposed approach can be a useful tool in the probabilistic estimation of the unknown material parameters of solder joint by accounting for the uncertainties due to the experimental data.