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The stochastic model for yield loss prediction proposed in Part I is implemented for a package-on-package (PoP) assembly. The assembly consists of a stacked die thin flat ball grid array (TFBGA) as the top package and a flip chip ball grid array (fcBGA) as the bottom package. The top and bottom packages are connected through 216 solder joints of 0.5 mm pitch in two peripheral rows. The warpage values of the top and bottom package are calculated by finite element analysis (FEA), and the corresponding probability of density functions (PDFs) are obtained by the eigenvector dimension reduction (EDR) method. The solder ball heights of the top and bottom package and the corner pad joint heights are determined by surface evolver, and their PDFs are determined by the EDR method, too. Only 137 modeling runs are conducted to obtain all 549 PDFs in spite of the large number of input variables considered in the study (27 input variables). Finally, the noncontact open-induced staking yield loss of the PoP assembly is predicted from the PDFs.

A comprehensive stochastic model is proposed to predict Package-on-Package (PoP) stacking yield loss. The model takes into account all pad locations at the stacking interface while considering the statistical variations of the warpages and the solder ball heights of both top and bottom packages. The goal is achieved by employing three statistical methods: (1) an advanced approximate integration-based method called eigenvector dimension reduction (EDR) method to conduct uncertainty propagation (UP) analyses, (2) the stress-strength interference (SSI) model to determine the noncontact probability at a single pad, and (3) the union of events considering the statistical dependence to calculate the final yield loss. In this first part, theoretical development of the proposed stochastic model is presented. Implementation of the proposed model is presented in a companion paper.