Non-Newtonian Flow Formulation of the Underfill Process in Flip-Chip Packaging

In the packaging process, the difference between thermal expansion coefficients of the chip and substrate causes thermal fatigue at solder joints. To avoid this thermal fatigue, epoxy encapsulant is filled into the gap between the substrate and chip by the capillary force. In modeling the underfilling process, the viscosity of the encapsulant may show the behaviors of shear thinning, shear thickening, or both. A formulation based on Hele-Shaw model is employed in this paper to simulate the underfill process by considering the bump resistance as a source term in the equation. A control volume finite element together with the finite difference is used to solve the equations. A penalty method is used to evaluate the pressure iteratively and assures the mass balance as convergence is reached. The result shows the ability to incorporate with the complicated viscosity model in the simulation. The effects of the shear rate on viscosity and the velocity field are also shown to be important.