The effective permeability of the underfill flow domain in flip-chip packaging

Connie Yang, Wen Bin Young

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


In order to reach the goals of high electrical performance and dense packaging within the limited space, the flip-chip technology becomes popular in electronics packaging. In the flip-chip assembly, difference between thermal expansion coefficients of the chip and substrate may cause 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. Because of the small space in the flow domain, the underfilling flow can be assumed as a flow in porous medium. Permeability is used to characterize the flow field of the space among the substrate, chip, and solder bumps. In this study, a numerical method is used to determine the effective permeability for the underfilling flow domain. Analysis of the three dimensional flow in a unit cell of the underfill flow domain is performed. The resulting average velocity and pressure gradient are used to calculate the apparent permeability. Comparison with the analytical approximation for the permeability in literature is also performed. The effective permeability calculated using the proposed numerical method gives reasonable prediction of the underfill flow as compared to the experimental result.

Original languageEnglish
Pages (from-to)1177-1186
Number of pages10
JournalApplied Mathematical Modelling
Issue number3
Publication statusPublished - 2013 Feb 1

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics


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