LBM simulation of capillary-driven underfill flow in flip-chip packaging

Capillary-driven underfill flow in flip-chip packaging is numerically investigated using a modified quasi-3D color-gradient LBM capable of handling various dispensing conFigurations. To accommodate complex inlet-outlet arrangements inherent in multi-side dispensing, Zou-He pressure boundary conditions and non-equilibrium extrapolation boundary conditions are introduced. The extended model effectively captures filling-front evolution and interfacial dynamics for both single-side (center-point and I-type) and multi-side (L-type and U-type) dispensing schemes—overcoming the limitation of the existing quasi-3D LBM, which is confined to I-type filling due to its reliance on modified periodic boundary conditions. A theoretical time-prediction formula incorporating Young's permeability model is established to estimate the filling speed. Benchmark simulations for I-type dispensing show excellent agreement with experimental data and the theoretical model, validating the accuracy of the proposed approach. Simulations for single-side and multi-side dispensing conFigurations yield results consistent with experimental observations and other numerical predictions, confirming the model's robustness under diverse conditions. Systematic parametric studies further elucidate the effects of contact angle, viscosity ratio, and solder bump density distribution on underfill behavior. The findings provide both fundamental insights and a reliable numerical tool for optimizing flip-chip underfill processes and enhancing encapsulation reliability.