Non-Newtonian Fluid Analytical Filling Time Model With Contact Line Jump Underfill Encapsulation - Ng, Fei Chong (2019)
The analytical filling time models to predict the capillary underfill flow in flip-chip are limited in amount; while the accuracy of existing models still has room of improvement due to the conventional porous media assumption. Moreover, the non-Newtonian behavior of underfill fluid was scarcely modelled. Therefore, this research presents a new filling time model based on novel bump-level analysis for the non-Newtonian power-law underfill fluid. Through the regional segregation approach, the filling times were separately studied at each filling stages. The formulation of current model had also incorporated both the spatial considerations of meniscus evolution and contact line jump, that were improvised in formulation and in-line to the experimental and numerical observations. Subsequently, three past underfill experiments were referred to validate with the current developed filling time model on top of the current scaled-up imitated flip-chip experiment and industrial package-on-package benchmarking. Overall, the current model predicted the filling times of least discrepancy among other existing analytical models for all validation cases. This had affirmed the capability of current model in terms of accuracy and versatility. Moreover, two new temporal analyses of individual filling time component and filling efficiency are introduced to further investigate the impact of bump pitch. Later, the well-validated analytical model is used to study the individual variation of underfill parameters on the filling progression. The parameters that affect the underfill flow prominently are gap height, contact angle and bump pitch. Lastly, a generalized filling time chart was generated using the current model to ease the direct computation of filling time.