A New Model for Permeability of Porous Medium in the Case of Flip-Chip Packaging

Underfill flow control is an important step in flip-chip technology and it can be generalized to fluid flow control in a porous medium, so solving this problem is of generalized implication to many other applications. The size of pores (i.e., clearance between the two solder bumps) in the flip-chip medium is less than 100 micrometers. In this paper, a new analytical model for permeability of the porous medium or solder bump flip-chip package is presented for two configurations of pores or solder of bumps (i.e., quadrilateral and equilateral triangular configurations). The model is shown to be more accurate than the existing model in the literature for the same purpose. Besides, the proposed model explicitly relates permeability with the structural parameters that describe the underfill space in flip-chip technology, namely, diameter of solder bumps, pitch of solder bumps, and gap height. In fact, there are two models, one for Newtonian fluids and the other for non-Newtonian fluids. These models allow us to optimize the structure of flip-chip packages in flip-chip technology or pores mediums in other applications. The models also provide a foundation for more precise control of the underfill flow process in flip-chip packages and the fluid filling process in pores mediums.