Multiphase Modeling and Machine Learning Analysis of Void Formation in Chip-to-Wafer Underfill Encapsulation

This study investigated void formation during capillary underfill (CUF) encapsulation in chip-to-wafer (C2W) assemblies using multiphase finite volume method (FVM) simulations and machine learning (ML) analysis. A three-dimensional volume-of-fluid (VOF)?based multiphase model was developed to capture the transient, capillary-driven flow of a shear-thinning epoxy underfill within the C2W BGA architecture. The numerical framework was validated against transparent-model flow visualization experiments, showing close agreement in flow morphology and filling time, with a maximum deviation of 6%, thereby confirming the predictive reliability of the model. Parametric investigations revealed that dispensing pattern was the dominant factor governing void formation, with I-type dispensing achieving approximately 71% reduction in average void content compared to L-type dispensing. Double-dispensing strategies further improved filling uniformity, with the 50-50 split ratio yielding the lowest void percentage, while BGA array density exhibited a secondary influence, as the denser 17 x 17 array produced slightly higher void formation than the 10 x 10 configuration due to increased flow resistance. ML-based prediction demonstrated that an RSM-style linear regression model achieved the lowest RMSE and highest R2, providing robust and interpretable prediction of void formation. The findings offer practical, data-driven guidelines for optimizing C2W underfill dispensing strategies to minimize void formation and enhance packaging reliability.