Solder shape prediction is essential for accurate fatigue life determination and joint design optimization. In the present paper, a new solution approach using the surface tension theory is developed to simultaneously predict standoff height, wetted surface area, contact angles, and solder shape by including energy effects between a molten solder body and an arbitrarily shaped solid body. Existing models for solder shape prediction do not appear to determine all characteristics including joint standoff height, wetted surface area, and contact angles simultaneously. A general two-body axisymmetric finite element code is developed and coupled with a constrained optimizer to solve four illustrative examples. These examples include the shape of a sessile droplet on a fixed pad, a flip-chip joint, a sessile droplet on a free surface, and a typical ceramic ball grid array solder joint. In all four examples, the results predicted by the present approach compare favorably with available experimental and numerical results.
Issue Section:
Technical Papers
1.
Bachelor, G. K., 1991, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, Great Britain.
2.
Choi
H. C.
Gun
Y.
LaFontaine
W.
Lim
C. K.
1993
, “Solder Ball Connect (SBC) Assemblies Under Thermal Loading: 2. Strain Analysis via Image Processing and Reliability Considerations
,” IBM Journal of Research and Development
, Vol. 37
, pp. 649
–659
.3.
Delay, R., Prigogine, I., and Belemans, A., 1966, Surface Tension and Adsorption, John Wiley & Sons, Inc., New York, NY.
4.
Ellis, L. R., and Masada, G. Y., 1989, “Dynamic Behavior of SMT Chip Capacitors During Solder Reflow,” Proc., 5th IEEE/CHMT International Electronics Manufacturing Technology Symposium, San Francisco, CA.
5.
Gibbs, J. W., 1928, The Collected Works of J Willard Gibbs, Vol. 1: Thermodynamics, Yale University Press, New Haven, CT.
6.
Goldmann
L. S.
1969
, “Geometric Optimization of Controlled Collapse Interconnections
,” Journal of IBM Research and Development
, Vol. 13
, pp. 251
–265
.7.
Guo
Y.
Lim
C. K.
Chen
W. T.
Woychik
C. G.
1993
, “Solder Ball Connect (SBC) Assemblies Under Thermal Loading: 1 Deformation Measurement via Moire Interferometry, and its Interpretation
,” IBM Journal of Research and Development
, Vol. 37
, pp. 635
–647
.8.
Heinrich, S. M., 1994, “Prediction of Solder Joint Geometry,” The Mechanics of Solder Alloy Interconnects, D. Frear, H. Morgan, S. Burchett, and J. Lau, eds., Van Nostrand Reinhold, NY.
9.
Heinrich
S. M.
Elkouh
A. F.
Nigro
N. J.
Lee
P. S.
1990
, “Solder Joint Formation in Surface Mount Technology—Part I: Analysis
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 112
, pp. 210
–218
.10.
Heinrich
S. M.
Lee
P.
1997
, “Solder Geometry Prediction in Electronic Packaging: An Overview
,” Advances in Electronic Packaging
, Vol. 19-2
, p. 1371
1371
.11.
Heinrich
S. M.
Liedtke
P. E.
Nigro
N. J.
Elkouh
A. F.
Lee
P. S.
1993
, “Effect of Chip and Pad Geometry on Solder Joint Formation in SMT
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 115
, pp. 433
–439
.12.
Heinrich
S. M.
Schaefer
M.
Schroeder
S. A.
Lee
P. S.
1996
, “Prediction of Solder Joint Geometries in Array-Type Interconnects
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 118
, pp. 114
–121
.13.
Johnson, R. E., and Dettre, R. H., 1993, “Wetting of Low-Energy Surfaces,” Wettability, J. C. Berg, ed., Marcel Dekker, Inc., New York, NY.
14.
Katyl
R. H.
Pimbley
W. T.
1992
, “Shape and Force Relationships for Molten Axisymmetric Solder Connections
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 114
, pp. 336
–341
.15.
Liedtke, P. E., Heinrich, S. M., Elkouh, A. F., Nigro, N. J., and Lee, P. S., 1991, “Prediction of Wave-Soldered Fillet Geometry in SMT Application,” Proc, Symposium on Mechanics of Surface Mount Assemblies, ASME Winter Annual Meeting, ASME, NY.
16.
Nigro
N.
Heinrich
S. M.
Elkouh
A. F.
Zou
X.
Fournelle
R.
Lee
P.
1993
, “Finite Element Method for Predicting Equilibrium Shapes of Solder Joints
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 115
, pp. 141
–146
.17.
Nigro
N. J.
Zhou
F. J.
Heinrich
S. M.
Elkouh
A. F.
Fournelle
R. A.
Lee
P. S.
1996
, “Parametric Finite Element Method for Predicting Shapes of Three-Dimensional Solder Joints
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 118
, pp. 142
–147
.18.
Patra
S. K.
Lee
Y. C.
1991
, “Quasi-Static Modeling of the Self-Alignment Mechanism in Flip-Chip Soldering—Part 1: Single Solder Joint
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 113
, pp. 337
–342
.19.
Patra, S. K., Sritharan, S. S., and Lee, Y. C., 1992, “Minimum-Energy Surface Profile of Solder Joints for Non-Circular Pads,” Manufacturing Aspects in Electronics Packaging, Vol., EEP-Vol. 2/PED-Vol. 60, ASME, NY, pp. 197–210.
20.
Racz
L. M.
Szekely
J.
1993
, “Determination of Equilibrium Shapes and Optimal Volume of Solder Droplets in the Assembly of Surface Mounted Integrated Circuits
,” Transactions of the Iron and Steel Institute of Japan International
, Vol. 33
, pp. 336
–342
.21.
Racz
L. M.
Szekely
J.
Brakke
K. A.
1993
, “A General Statement of the Problem and Description of a Proposed Method of Calculation for Some Meniscus Problems in Materials Processing
,” ISIJ International
, Vol. 33
, pp. 328
–335
.22.
Schittkowski
K.
1985
, “NLPQL: A FORTRAN Subroutine Solving Constrained Nonlinear Programming Problems
,” Annals of Operation Research
, Vol. 5
, page 485
485
.23.
Subbarayan
G.
1996
, “A Procedure for Automated Shape and Life Prediction in Flip-Chip and BGA Solder Joints
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 118
, pp. 127
–133
.24.
Subbarayan
G.
Li
Y.
Mahajan
R. L.
1996
, “Reliability Simulations fur Solder Joints Using Stochastic Finite Element and Artificial Neural Network Models
,” ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol. 118
, pp. 148
–156
.25.
Trivedi, R., and Hunt, J. D., 1993, “Surface and Interface Energy Measurements,” chap. 7 in The Mechanics of Solder Alloy Wetting and Spreading, F. G. Yost et al., eds., Van Nostrand Reinhold, N York, p. 191.
26.
Zienkiewicz, O. C., and Taylor, R. L., 1989, The Finite Element Method, Vol. 1, McGraw-Hill, London.
27.
Zisman, W., 1964, Advances in Chemistry Series 43, R. F. Gould, ed., American Chemical Society, Washington, D.C., p. 1.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.
