Research Papers

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

[+] Author and Article Information
X. J. Yao, J. J. Fang

School of Mechanical and Power Engineering,
Department of Material and
Equipment Engineering,
East China University of
Science and Technology,
Shanghai 200237, China

Wenjun Zhang

School of Mechatronics and Automation,
Shanghai University,
Shanghai 200444, China;
Department of Mechanical Engineering,
University of Saskatchewan,
Saskatoon, SK S7N 5A9, Canada
e-mail: chris.zhang@usask.ca

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received February 12, 2017; final manuscript received October 27, 2017; published online March 2, 2018. Assoc. Editor: Yi-Shao Lai.

J. Electron. Packag 140(1), 011001 (Mar 02, 2018) (6 pages) Paper No: EP-17-1019; doi: 10.1115/1.4038391 History: Received February 12, 2017; Revised October 27, 2017

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.

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Bear, J. , 1972, Dynamics of fluids in Porous Media, American Elsevier Publishing Company, Inc, New York.
Young, W. B. , and Yang, W. L. , 2002, “ The Effect of Solder Bump Pitch on the Underfill Flow,” IEEE Trans. Adv. Packag., 25(4), pp. 537–542. [CrossRef]
Wan, J. W. , Zhang, W. J. , and Bergstrom, D. J. , 2007, “ A Theoretical Analysis of the Concept of Critical Clearance Toward a Design Methodology for the Flip-Chip Package,” ASME J. Electron. Packag., 129(4), pp. 473–478. [CrossRef]
Wan, J. W. , Zhang, W. J. , and Bergstrom, D. J. , 2007, “ Recent Advances in Modeling the Underfill Process in Flip-Chip Packaging,” Microelectron. J., 38(1), pp. 67–75. [CrossRef]
Wan, J. W. , Zhang, W. J. , and Bergstrom, D. J. , 2005, “ An Analytical Model for Predicting the Underfill Flow Characteristics in Flip-Chip Encapsulation,” IEEE Trans. Adv. Packag., 28(3), pp. 481–487. [CrossRef]
Wan, J. W. , Zhang, W. J. , and Bergstrom, D. J. , 2005, “ Influence of Transient Flow and Solder Bump Resistance on Underfill Process,” Microelectron. J., 36(8), pp. 687–693. [CrossRef]
Wan, J. W. , Zhang, W. J. , and Bergstrom, D. J. , 2009, “ Numerical Modeling for the Underfill Flow in Flip-Chip Packaging,” IEEE Trans. Compon. Packag. Technol., 32(2), pp. 227–234. [CrossRef]
Fei, C. N. , Abas, A. , Abdullah, M. Z. , Ishak, M. , and Chong, G. Y. , 2017, “ CUF Scaling Effect on Contact Angle and Threshold Pressure,” Soldering Surf. Mount Technol., 29, pp. 173–190.
Abas, A. , Ishak, M. H. H. , Abdullah, M. Z. , Che Ani, F. , and Khor, S. F. , 2016, “ Lattice Boltzmann Method Study of Bga Bump Arrangements on Void Formation,” Microelectron. Reliab., 56, pp. 170–181. [CrossRef]
Abas, A. , Gan, Z. L. , Ishak, M. H. H. , Abdullah, M. Z. , and Khor, S. F. , 2016, “ Lattice Boltzmann Method of Different BGA Orientations on I-Type Dispensing Method,” PloS One, 11(7), p. e0159357. [CrossRef] [PubMed]
Abas, A. , Haslinda, M. S. , Ishak, M. H. H. , Nurfatin, A. S. , Abdullah, M. Z. , and Ani, F. C. , 2016, “ Effect of ILU Dispensing Types for Different Solder Bump Arrangements on CUF Encapsulation Process,” Microelectron. Eng., 163, pp. 83–97. [CrossRef]
Ishak, M. H. H. , Abdullah, M. Z. , and Abas, A. , 2016, “ Lattice Boltzmann Method Study of Effect Three Dimensional Stacking-Chip Package Layout on Micro-Void Formation During Encapsulation Process,” Microelectron. Reliab., 65, pp. 205–216. [CrossRef]
Wang, H. , and Wang, P. , 2016, “ An Experimental Investigation of the Permeability in Porous Chip Formed by Micropost Arrays Based on Microparticle Image Velocimetry and Micromanometer Measurements,” ASME J. Fluids Eng., 139(2), p. 021108. [CrossRef]
Young, W. B. , and Yang, W. L. , 2002, “ Underfill Viscous Flow Between Parallel Plates and Solder Bumps,” IEEE Trans. Compon. Packag. Technol., 25(4), pp. 695–700. [CrossRef]
Lai, C. L. , and Young, W. B. , 2004, “ A Model for Underfill Viscous Flow Considering the Resistance Induced by Solder Bumps,” ASME J. Electron. Packag., 126(2), pp. 186–194. [CrossRef]
Young, W. B. , 2003, “ Anisotropic Behavior of the Capillary Action in Flip Chip Underfill,” Microelectron. J., 34(11), pp. 1031–1036. [CrossRef]
Young, W. B. , and Yang, W. L. , 2006, “ Underfill of Flip-Chip: The Effect of Contact Angle and Solder Bump Arrangement,” IEEE Trans. Adv. Packag., 29(3), pp. 647–653. [CrossRef]
Yao, X. J. , Wang, Z. D. , Zhang, W. J. , and Zhou, X. Y. , 2014, “ A New Model for Permeability of Porous Medium in the Case of Flip-Chip Packaging,” IEEE Trans. Compon., Packag. Manuf. Technol., 4(8), pp. 1265–1275. [CrossRef]
Brunschwiler, T. , Zürcher, J. , Del Carro, L. , Schlottig, G. , Burg, B. , Zimmermann, S. , Zschenderlein, U. , Wunderle, B. , Schindler-Saefkow, F. , and Stässle, R. , 2016, “ Review on Percolating and Neck-Based Underfills for Three-Dimensional Chip Stacks,” ASME J. Electron. Packag., 138(4), p. 041009. [CrossRef]
Zhang, W. J. , and Luttervelt, C. A. V. , 2011, “ Toward a Resilient Manufacturing System,” CIRP Ann.-Manuf. Technol., 60(1), pp. 469–472. [CrossRef]
Zhang, W. J. , and Wang, J. W. , 2016, “ Design Theory and Methodology for Enterprise Systems,” Enterprise Inf. Syst., 10(3), pp. 245–248. [CrossRef]
Zhang, W. J. , Li, Q. , and Guo, L. S. , 1999, “ Integrated Design of Mechanical Structure and Control Algorithm for a Programmable Four-bar Linkage,” IEEE/ASME Trans. Mechatronics, 4(4), pp. 354–362. [CrossRef]
Li, Q. , Zhang, W. J. , and Chen, L. , 2001, “ Design for Control-a Concurrent Engineering Approach for Mechatronic Systems Design,” IEEE/ASME Trans. Mechatronics, 6(2), pp. 161–169. [CrossRef]


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Fig. 1

The schematic diagram of the porous medium specimen: (a) the main view and (b) the cross section. A: cross-sectional area; L: length of the medium; and P0: environmental pressure.

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Fig. 2

The schematic diagram of the gap space formed with the chip, substrate, and solder bumps

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Fig. 3

Superficial cross-sectional area As and pore average cross-sectional area Ap of single channel in an underfill porous medium: (a) the main view of a single channel, (b) the minimal cross-sectional area, (c) the pore average cross-sectional area Ap, and (d) the superficial cross-sectional area As (i.e., the maximal cross-sectional area)

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Fig. 4

The schematic diagram of the configuration of materials in series [15]

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Fig. 5

Schematic diagram of the capillary flow between two plates and solder bumps [17]

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Fig. 6

The model of the 3 unit cells of the underfill porous medium: (a) 3D diagram and (b) the front view and top view

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Fig. 7

The finite element mesh of the 3 unit cells of underfill porous medium

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Fig. 8

Velocity field at the midplane between the chip and substrate

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Fig. 9

Permeability for different models with respect to the variation of bump pitch. Numerical permeability refers to the permeability calculated with the CFD model.



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