A Further Study on the Analytical Model for the Permeability in Flip-Chip Packaging

The notion of permeability is very important in understanding and modeling the flow behavior of fluids in a special type of porous medium (i.e., the underfill flow in flip-chip packaging). This paper presents a new concept regarding permeability in a porous medium, namely two types of permeability: superficial permeability (with consideration of both the pore cross-sectional area and the solid matrix cross-sectional area) and pore permeability (with consideration of the pore cross-sectional area only). Subsequently, the paper proposes an analytical model (i.e., equation) for the pore permeability and superficial permeability of an underfill porous medium in a flip-chip packaging, respectively. The proposed model along with several similar models in literature is compared with a reliable numerical model developed with the computational fluid dynamics (CFD) technique, and the result of the comparison shows that the proposed model for permeability is the most accurate one among all the analytical models in literature. The main contributions of the paper are as follows: (1) the provision of a more accurate analytical model for the permeability of an underfill porous medium in flip-chip packaging, (2) the finding of two types of permeability depending on how the cross-sectional area is taken, and (3) the correction of an error in the others' model in literature.