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.

References

References
1.
Bear
,
J.
,
1972
,
Dynamics of fluids in Porous Media
,
American Elsevier Publishing Company, Inc
,
New York
.
2.
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
.
3.
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
.
4.
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
.
5.
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
.
6.
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
.
7.
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
.
8.
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.
9.
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
.
10.
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
.
11.
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
.
12.
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
.
13.
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
.
14.
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
.
15.
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
.
16.
Young
,
W. B.
,
2003
, “
Anisotropic Behavior of the Capillary Action in Flip Chip Underfill
,”
Microelectron. J.
,
34
(
11
), pp.
1031
1036
.
17.
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
.
18.
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
.
19.
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
.
20.
Zhang
,
W. J.
, and
Luttervelt
,
C. A. V.
,
2011
, “
Toward a Resilient Manufacturing System
,”
CIRP Ann.-Manuf. Technol.
,
60
(
1
), pp.
469
472
.
21.
Zhang
,
W. J.
, and
Wang
,
J. W.
,
2016
, “
Design Theory and Methodology for Enterprise Systems
,”
Enterprise Inf. Syst.
,
10
(
3
), pp.
245
248
.
22.
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
.
23.
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
.
You do not currently have access to this content.