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.

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