Advanced Statistical Model Calibration to Determine Manufacturing-Induced Variations of Effective Elastic Properties of SAC Solder Joints in Leadless Chip Resistor Assemblies

The unknown statistical distributions of two effective elastic properties of Sn-3.0Ag-0.5Cu solder joint of leadless chip resistors (LCRs), induced by an assembly condition, are determined by the advanced statistical model calibration. Two key elements are involved in the model calibration: an uncertainty propagation (UP) analysis and an optimization process using a calibration metric. In this paper, the UP analysis utilizes an advanced approximate integration method, which allows us to take into account the statistical variations of six additional known input variables, including die thickness, solder joint height, termination length, and thickness and elastic moduli of a printed circuit board. The cyclic bending test results of LCR assemblies are used in conjunction with the maximum-likelihood metric to obtain the statistical distributions of the effective properties. The cycles-to-failure distribution of the identical LCR assemblies subjected to a different loading level is predicted accurately by the calibrated model, which corroborates the validity of the proposed approach.