Updated Literature Summary
November 28, 1995

On the following pages is a summary of several papers that have been published in the area of solder joint geometry modeling. This material represents an updated version of the tables and bibliography that appear in the following reference:

Heinrich, S.M., "Prediction of Solder Joint Geometry," Chapter 5 of Mechanics of Solder Alloy Interconnects, Frear et al. (eds.), Van Nostrand Reinhold, 1994, pp. 158-198.

If you are aware of any relevant publications that are not included in this summary, please send copies to the address below:

Stephen M. Heinrich
Dept. of Civil Engineering
Marquette University
P.O. Box 1881
Milwaukee, WI 53201-1881
Ph.: (414) 288-5466
FAX: (414) 288-7082
E-Mail: [email protected]

Thank you.

Table 1. Literature Involving Models for Predicting 2-D Joint Geometries

Ref.	Applications	Solution Type	Main Results	Restrictions on Results
Klein Wassink & Verguld 1986	Reflow of Leadless Chips: Tombstone Prevention	Straight-Line Fillets	Gen'l Guidelines for Preventing Tombstoning	Straight-Line Fillet Assumption is Approximate
Alexander & Bello 1987	Reflow of Leadless Chips	Elastica Solution	General Recommendations to Increase Joint Compliance by Controlling Solder Volume	Elastica Solution is Approximate
Klein Wassink 1989	Reflow & Wave Soldering of Leadless Chips	Numerical Solution of BVP; Elastica Solution	Samples of Upright & Inverted Fillet Profiles	Numerical Results are Problem- Specific; Perfect Wettability; Infinite Tinning
Jopek 1989	Reflow of Leaded Fine-Pitch Components	"Piecemeal" Elastica	General Guidelines for "Optimal" Volume	Elastica is Approximate; Theory Underestimates "Optimal" Volume
Ellis & Masada 1990	Reflow of Leadless Chips: Tombstone Prevention & Self- Alignment Enhancement	Numerical Solution of BVP for Fillet Profile; Numerical Solution of Equations of Motion for Chip Dynamics	General Guidelines for Preventing Tombstoning and Promoting Self-Alignment	Specific Contact Angle (12 deg) Assumed at Chip Metallization
Heinrich et al. 1990a,b	Reflow of Leadless Chips	Explicit Integral Solution of BVP; Circular Arc Approximation (Zero- Gravity Solution)	Fillet Height & Length vs. Solder Area (Volume); Closed-Form Expressions for Small & Large Joint Profiles and for Maximum Fillet Height	Infinite Tinning Assumption; Acute Contact Angles
Rooks et al. 1991	Reflow of Leadless Chips	Numerical Solution of BVP; Circular Arc Approximation (Zero-Gravity Solution)	Samples of Fillet Profiles; Comparison of Exact and Zero-Gravity Solutions	Numerical Results are Problem- Specific; Infinite Tinning
Liedtke et al. 1991;	Wave-Soldering of Leadless Chips	Explicit Integral Solution of BVP	Fillet Size & Shape vs. Pad & Component Sizes (Dimensionless)	Perfect Wettability; Horizontal Conveyor Angle; Joint Size Estimated by "Equivalent Dipping Model"
Nambisan et al. 1995	Wave-Soldering of Leadless Chips	Circular-Arc Approximation (Zero-Gravity Solution)	Fillet Size, Shape, Contact Angles as Functions of Metallization Dimensions; Effect of Conveyor Angle Included	Perfect Wettability; Joint Size Estimated by "Equivalent Dipping Model"
Heinrich et al. 1993	Reflow of Leadless Chips	Explicit Integral Solution of BVP; Circular Arc Approximation (Zero- Gravity Solution)	Fillet Profiles as Function of Chip & Pad Geometry (Dimensionless Results); Closed-Form Expressions for Small Joints	Perfect Wettability; (Finite Tinning)
Nigro et al. 1993	Reflow of Leadless Chips	Energy Minimization by Finite Element Method	Samples of Fillet Profiles for Finite & Infinite Tinning	Numerical Results are Problem-Specific
Jahsman 1992	Reflow of Long (Channel-Type) Solder Bumps	Circular Arc Approximation (Zero-Gravity Solution)	Bump Volume and Bump Force vs. Contact Angle and Bump Height (Dim'less Results); Effect of "Count Ratio" of Two Bump Sizes on Dim'less Bump Height	Equal Pad Radii; Count Ratio Results are Problem-Specific

Table 2. Literature Involving Models for Predicting Axisymmetric Joint Geometries

Ref.	Applications	Solution Type	Main Results	Restrictions on Results
Goldmann 1969	C4 Joints in Flip-Chip Applications	Truncated Sphere	Approximate Analytical Expression Relating Pad Radii, Bump Height, and Solder Volume; Optimization of Joint Geometry	Truncated Sphere Assumption is Approximate
Chu 1975	Plated-Through-Hole Fillets Using Solder Preforms	Numerical Solution of BVP Coupled with Approximate Energy Minimization	Samples of Top & Bottom Fillet Profiles; Ideal Solder Volume vs. Board Thickness; Fillet Heights vs. Solder Volume	Numerical Results are for Specific Pin and Hole Diameters and Pad Radii; "Operationally Ideal" Solution is Arbitrarily Taken to be Within 0.5% of True Minimum- Energy State
Golachev et al. 1980	Melting of Tin-Lead Coatings in Plated-Through-Hole Apertures	Circular Arc Approximation for Meridian	Change in Hole Diameter vs. Volume of Plated Solder Alloy; Recommended Solder Layer Thickness vs. Pad and Hole Diameters	Circular Arc Approximation is Invalid for Larger Pad Diameters; Results are Problem- Specific
Kudryavtsev et al. 1982	Melting of Tin-Lead Coatings in Plated-Through-Hole Apertures	Circular Arc Approximation for Meridian	Change in Hole Diameter vs. Board & Plating Thicknesses and Pad & Hole Diameters	Circular Arc Approximation is Invalid for Larger Pad Diameters; Results are Problem- Specific
Oshima et al. 1982	C4 Joints in Flip-Chip Applications	Numerical Solution of BVP; Truncated Sphere; Circular Arc Meridian	Exact Results for Bump Height vs. Solder Volume; Optimization of Joint Geometry Using Approximate Solutions	Exact Numerical Results Limited to Equal Pad Diameters
Satoh et al. 1983, 1987; Oshima et al. 1985	C4 Joints in Flip-Chip Applications Using Self- Stretching Technique (SST), i.e., Height-Control Solder Bumps	Circular Arc Meridian	Bump Height vs. Volumes of Joint Solder and Control Solder; Optimization of Joint Geometry	Results are Problem-Specific
Klein Wassink 1985, 1989	Melting of Solder Coatings in Plated-Through-Hole Applications	Numerical Solution of BVP with and without Gravity; Circular Arc Meridian	Sample Profiles of Fused Solder Coatings; Comparisons of Exact and Approximate Profiles	Results are Problem-Specific
Klein Wassink 1989	Plated-Through-Hole Fillets	Numerical Solution of BVP	Samples of Top & Bottom Fillet Profiles	Results are Problem-Specific; Perfect Wettability
Rooks et al. 1991	Top Fillet in Plated-Through- Hole Applications	Numerical Solution of BVP; Elliptic Integral Solution for Zero Gravity	Samples of Top Fillet Profiles; Fillet Volume vs. Height (Dimensionless)	Results are Problem-Specific; Contact Angle at Pin is 15 deg
Katyl & Pimbley 1991	C4 Joints in Flip-Chip Applications	Numerical Solution of BVP; Energy Minimization by Ritz Method; Elliptic Integral and Approximate Polynomial Solutions for Zero Gravity	Sample Profiles of Sessile and Pendant Drops on Finite Pad; Sample Profiles of C4 Joints	Results are Problem-Specific
Nigro et al. 1993	C4 Joints in Flip-Chip Applications	Energy Minimization by Finite Element Method	Sample Profile for C4 Joint; Bump Force vs. Bump Height	Results are Problem-Specific
Ju et al. 1994	C4 Joints in Flip-Chip Applications	Approximate Numerical Solution of BVP Neglecting Solder Self-Weight	No Specific Geometry Results; Geometry Model was Integrated with Reliability Model to Predict Effect of Process Variability on Joint Fatigue Life	Numerical Results are Problem- Specific
Heinrich et al. 1994	BGA Joints	Circular-Arc Meridian	General Results for Joint Height and Mid- Height Width in Terms of Joint Volume, Array Size, Component Weight, Pad Size, and Solder Surface Tension: Upright or Inverted Reflow	Equal Pad Sizes; Identical Joint Shapes Throughout Array
Heinrich et al. 1995, 1996	Joints in Non-Uniform BGAs (Joint Shapes Vary Throughout Array)	Circular-Arc Meridian	Results for Joint Height and Mid-Height Widths in Terms of Joint Volumes and Count Ratio: Upright or Inverted Reflow	"Bi-Uniform Array" with 0.6-mm Pads
Subbarayan et al. 1995	BGA Joints	Energy Minimization by Finite Element Method	No Specific Geometry Results; Geometry Model was Integrated with Stochastic FEM and Neural Network Models to Predict Optimal Joint Shape	72 I/O OMPAC BGA with Stand- Off Spacers
Singler et al. 1995	Bump/Ball-Type Joints	Energy Minimization by Finite Element Program (Surface Evolver)	Illustrations of Joint Shapes for Different Heights and Volumes; Geometry Model was Integrated with FEM and Fatigue Models to relate Geometry to Reliability	Joint Height and Volume Specified Independently; Results are Problem-Specific

Table 3. Literature Involving Models for Predicting General 3-D Joint Geometries

Ref.	Applications	Solution Type	Main Results	Restrictions on Results
Landry et al. 1991	Realignment of C4 Joints in Flip-Chip Applications	Approximate Numerical Solution of BVP Neglecting Solder Self-Weight, Coupled with Curve-Fit of Oscillatory Realignment Motion	Sample Profiles of C4 Joints Before and After Realignment; Restoring Force & Equivalent Stiffness vs. Misalignment; Verification of Predicted Oscillatory Motion	Horizontal Cross-Sections Assumed to be Circular; Numerical Results are Problem- Specific
Patra & Lee 1991	Realignment of C4 Joints in Flip-Chip Applications	Approximate Numerical Solution of BVP Neglecting Solder Self-Weight	Sample Profiles of C4 Joints Before and After Realignment; Restoring Force vs. Misalignment	Horizontal Cross-Sections Assumed to be Circular; Numerical Results are Problem- Specific
Patra et al. 1992	Realignment of C4 Joints on Circular or Non-Circular Pads	Numerical (Finite-Difference) Solution of BVP Neglecting Solder Self-Weight	3-D Graphical Representations of Joints on Fully Wetted and Partially Wetted Circular and Rectangular Pads (Zero Misalignment); Joint Height vs. Rectangular Pad Aspect Ratio; Joint Height vs. Wetted % of Circular Pad Area	Numerical Results are Problem- Specific
Racz & Szekely 1993a; Racz et al. 1993	Prediction of Complex Joint Geometries, such as in Gullwing and J-Lead Fine-Pitch Applications	Energy Minimization by Finite Element Program (Surface Evolver)	3-D Graphical Representations of a Variety of Solder Joints; Dimensionless Design Nomographs for Selecting "Optimal" Solder Volume as a Function of Wettable Pad/Lead Area for Gullwing & J-Leads	Stand-Off Height Between Lead and Pad is Specified a Priori; Criteria for "Optimal" Joints are Qualitative "Rough Guidelines" Extrapolated from Through-Hole to Surface-Mount Technology
Yost et al. 1993	Realignment of C4 Joints in Flip-Chip Applications	Numerical (Finite-Difference) Solution of BVP Neglecting Solder Self-Weight	Horizontal and Vertical Force-Displacement Curves	Stand-Off Spacers Used; Numerical Results are Problem- Specific
Katyl 1993	Sessile Droplets on Circular and Rectangular Pads; Joint Spanning Parallel Rectangular Pads; Joint Connecting TSOP Lead to Rectangular Pad	Several Methods of Solution	Solution Methods are Compared for Accuracy and Efficiency; 3-D Profiles are Illustrated	Numerical Results are Problem- Specific
Racz and Szekely 1993b	Wetting Balance Measurements	Energy Minimization by FEM Program (Surface Evolver)	Relates Wetting Force to % of Sample Perimeter Having Poor Wettability	Numerical Results are Problem- Specific
Ju et al. 1993	Realignment of C4 Joints in Flip-Chip Applications	Numerical Solution of Laplace-Young Equation	Experimental Verification of Geometry Model for Circular and Square Pads	__________
Patra et al. 1993	Realignment of C4 Joints in Flip-Chip Applications	Numerical Solution of Laplace-Young Equation	Plots of Lateral Restoring Force vs. Misalignment, Solder Volume, and Surface Tension; Plots of Joint Height vs. Joint Volume and Vertical Loading	40 µm x 40 µm Square Pads
Lee et al. 1995	General	Energy Minimization by FEM	3-D Plots of Joints on Gullwing Leads	No Gap Between Lead and Pad; Solder Does Not Flow onto Top of Lead
Singler and Zhang 1995	Bridging of Solder Droplets Between Circular and Rectangular Pads	Energy Minimization by FEM Program (Surface Evolver)	Plots of Critical Solder Volume (at Which Stable Bridges May Form) vs. Pad Spacing for Different Pad Shapes; Plot of Critical Volume vs. Wettability of the Solder Resist Surface; To Minimize Bridges, Use Circular Pads and Solder Resist of Low Wettability	Results are for Specific Pad Area and for Mercury
Yost and Holm 1995	Solder Flow on Narrow Strips and in V-Shaped Grooves	Energy Minimization by FEM Program (Surface Evolver)	3-D Plots of Droplet Shapes on Circular Pad Connected to Thin Metallized Strip and in V-Groove	Droplet Shapes are Problem- Specific
Whalley et al. 1995	Globule Block Wetting Balance Test	Energy Minimization by FEM Program (Surface Evolver)	Plot of Globule Height vs. Solder Volume; Sensitivity Studies on Test Parameters	Numerical Results are Problem- Specific
Nigro et al. 1995	Sessile Droplets on Circular and Rectangular Pads	Parametric FEM	Droplet Shapes Plotted for Specific Pad Dimensions and Solder Volumes; Droplet height Plotted vs. Aspect Ratio of Rectangular Pad	Numerical Results are Problem- Specific

REFERENCES

Alexander, P.T., and Bello, D.C., "The Single Key Process Variable in SMT Solder Joint Reliability," Expo SMT '87, Technical Proceedings, Las Vegas, 1987, pp. 85-89.

Chu, T.Y., "A Hydrostatic Model of Solder Fillets," Western Electric Engineer, Vol. 19, No. 2, 1975, pp. 31-42.

Ellis, J.R., and Masada, G.Y., "Dynamic Behavior of SMT Chip Capacitors Durind Solder Reflow," IEEE Trans. on Components, Hybrids, and Mfg. Technology, Vol. 13, No. 3, Sept. 1990, pp. 545-552.

Golachev, S.M., Kudryavtsev, V.S., and Ovseevich, V.L., "The Hydrostatic Model of the Redistribution of the Tin-Lead Alloy in the Melting of the Coating of Printed Circuit Boards," Welding Prod. (Svar. Proiz.), Vol. 27, No. 2, 1980, pp. 19-21.

Goldmann, L.S., "Geometric Optimization of Controlled Collapse Interconnections," IBM J. Res. Develop., Vol. 13, May 1969, pp. 251-265.

Heinrich, S.M., Elkouh, A.F., Nigro, N.J., and Lee, P.S., "Solder Joint Formation in Surface Mount Technology -- Part I: Analysis," Journal of Electronic Packaging, ASME, Vol. 112, No. 3, 1990a, pp. 210-218.

Heinrich, S.M., Nigro, N.J., Elkouh, A.F., and Lee, P.S., "Solder Joint Formation in Surface Mount Technology -- Part II: Design," Journal of Electronic Packaging, ASME, Vol. 112, No. 3, 1990b, pp. 219-222.

Heinrich, S.M., Liedtke, P.E., Nigro, N.J., Elkouh, A.F., and Lee, P.S., "Effect of Chip and Pad Geometry on Solder Joint Formation in SMT," ASME Journal of Electronic Packaging, Vol. 115, No. 4, 1993, pp. 433-439.

Heinrich, S.M., Schroeder, S.A., and Lee, P.S., "Prediction of Solder Joint Geometries in Multiple Bump Arrays," Mechanics and Materials for Electronic Packaging: Volume 1, Design and Process Issues in Electronic Packaging, Chen, Nguyen, and Winterbottom (eds.), ASME AMD- Vol. 195, 1994, pp. 11-22; presented at the 1994 International Mechanical Engineering Congress and Exposition, Chicago, IL, November 6-11, 1994.

Heinrich, S.M., Wang, Y., Shakya, S., Schroeder, S.A., and Lee, P.S., "Selection of Design and Process Parameters for Non-Uniform Ball-Grid Arrays," Advances in Electronic Packaging 1995, Vol. 1, ASME EEP-Vol. 10-1, pp. 273-288; presented at InterPack '95, Lahaina, HI, 1995.

Heinrich, S.M., Shakya, S., Wang, Y., Lee, P.S., and Schroeder, S.A., "Improved Yield and Performance of Ball-Grid Array Packages: Design and Processing Guidelines for Uniform and Non- Uniform Arrays," to appear in Trans., Components, Packaging & Manufacturing Technology Society, Series B, IEEE, February 1996. (Also appearing in Proc., 45th Electronic Components and Technology Conference, Las Vegas, NV, May 1995, pp.793-803.)

Jahsman, W.E., "Channel Solder Bump Shape Analysis," Internal Correspondence, Intel Corporation, 1992.

Jopek, S., "Solder Volume Determination for Fine Pitch Packages," Printed Circuit Assembly, Vol. 3, 1989, pp. 15-20.
Ju, T.-H., Chan, Y.W., Lin, W., Lee, Y.C., Patra, S.K., and Lee, S.H., "Experimental Verification of a General Purpose Solder Profile Model," Advances in Electronic Packaging 1993, Vol. 2, ASME EEP-Vol. 4-2, 1993, pp. 1163-1168.

Ju, T.-H., Lin, W., Lee, Y.C., and Liu, J.J., "Effects of Ceramic Ball-Grid-Array Package's Manufacturing Variations on Solder Joint Reliability," ASME Journal of Electronic Packaging, Vol. 116, No. 4, December 1994, pp. 242-248.

Katyl, R.H., and Pimbley, W.T., "Shape and Force Relationships for Molten Axisymmetric Solder Connections," Mfg. Processes and Materials Challenges in Microelectronic Packaging, ASME AMD-Vol. 131/EEP-Vol. 1, 1991, pp. 57-63.

Katyl, R.H., "Calculation of Molten Solder Profiles for Rectangular Pad Geometries," Advances in Electronic Packaging 1993, Vol. 2, ASME EEP-Vol. 4-2, 1993, pp. 1095-1101.

Klein Wassink, R.J., "Notes on the Shape of Fused Solder Coatings of Metallised Holes in Printed Boards," Brazing and Soldering, No. 8, Spring 1985, pp. 5-7.

Klein Wassink, R.J., and Verguld, M.M.F., "Drawbridging of Leadless Components," Hybrid Circuits, No. 9, Jan. 1986, pp. 18-24.

Klein Wassink, R.J., Soldering in Electronics, 2nd ed., Electrochemical Publications Limited, 1989.

Kudryavtsev, V.S., Nikiforov, G.D., Dolgov, Yu. S., Golachev, S.M., and Oparin, M.I., "Effect of Design and Technological Factors on the Reduction in Diameter of Metallised Openings in Printed Circuits in Melting the Tin-Lead Coating," Welding Prod. (Svar. Proiz.), Vol. 29, No. 11, 1982, pp. 13-14.

Landry, M., Patra, S.K., and Lee, Y.C., "Experiment and Modeling of the Self-Alignment Mechanism in Flip-Chip Soldering," Manufacturing Processes and Materials Challenges in Microelectronic Packaging, ASME AMD-Vol. 131/EEP-Vol. 1, 1991, pp. 49-56.

Lee, T.S., Choi, T.P., and Yoo, C.D., "Finite Element Modeling of 3-Dimensional Solder Joint Geometry in SMT," Advances in Electronic Packaging 1995, Vol. 2, ASME EEP-Vol. 10-2, pp. 1031-1041; presented at InterPack '95, Lahaina, HI, 1995.

Liedtke, P.E., Heinrich, S.M., Elkouh, A.F., Nigro, N.J., and Lee, P.S., "Prediction of Wave-Soldered Fillet Geometry in SMT Applications," Manufacturing Processes and Materials Challenges in Microelectronic Packaging, ASME Applied Mechanics Division, Vol. 131; Electrical and Electronic Packaging Division, Vol. 1; pp. 65-72; presented at the ASME Winter Annual Meeting, Atlanta, GA, December 1991.

Nambisan, B.U., Heinrich, S.M., Fournelle, R.A., Elkouh, A.F., Nigro, N.J., and Lee, P.S., "An Approximate Model for Predicting the Size and Shape of Wave-Soldered Surface-Mount Joints," Journal of Electronics Manufacturing, Vol. 5, No. 3, September 1995, pp. 217-233. (Also appearing in Advances in Electronic Packaging 1993, Vol. 2, ASME EEP-Vol. 4-2, 1993, pp. 1079-1093.)

Nigro, N.J., Heinrich, S.M., Elkouh, A.F., Zou, X., Fournelle, R.A., and Lee, P.S., "Finite Element Method for Predicting Equilibrium Shapes of Solder Joints," ASME Journal of Electronic Packaging, Vol. 115, No. 2, 1993, pp. 141-146.
Nigro, N.J., Zhou, F.J., Elkouh, A.F., Fournelle, R.A.,Heinrich, S.M., and Lee, P.S., "Parametric Finite Element Method for Predicting Shapes of Three-Dimensional Solder Joints," Advances in Electronic Packaging 1995, Vol. 1, ASME EEP-Vol. 10-1, pp. 435-449; presented at InterPack '95, Lahaina, HI, 1995.

Oshima, M., Kenmotsu, A., and Ishi, I., "Optimization of Micro-Solder Reflow Bonding for the LSI Flip Chip," Proc., 2nd Annual Intl. Electronics Packaging Soc. Conf., 1982, pp. 481-488.

Oshima, M., Satoh, R., Hirota, K., and Ishi, I., "New Micro-Soldering Technology and its Application to VLSI," Proc., 1st IEEE CHMT Symposium: CHMT Tokyo '84, published in Aug. 1985, pp. 165- 170.

Patra, S.K., and Lee, Y.C., "Quasi-Static Modeling of Self-Alignment Mechanism in Flip-Chip Soldering. Part I: Single Solder Joint," ASME Journal of Electronic Packaging, Vol. 113, No. 4, Dec. 1991, pp. 337-342.

Patra, S.K., Sritharan, S.S., and Lee, Y.C., "Minimum-Energy Surface Profile of Solder Joints for Non-Circular Pads," Proc., ASME Winter Annual Meeting, Anaheim, CA, 1992.

Patra, S.K., Ma, J., and Lee, S.H., "Alignment Issue Relating to Flip-Chip Bonding Requirement for Holographic Optical Interconnects," Advances in Electronic Packaging 1993, Vol. 2, ASME EEP- Vol. 4-2, 1993, pp. 1191-1196.

Racz, L.M., Szekely, J., and Brakke, K.A., "A General Statement of the Problem and Description of a Proposed Method of Calculation for Some Meniscus Problems in Materials Processing," Trans., Iron and Steel Institute of Japan International, Vol. 33, No. 2, 1993.

Racz, L.M., and Szekely, J., "Determination of Equilibrium Shapes and Optimal Volume of Solder Droplets in the Assembly of Surface Mounted Integrated Circuits," Trans., Iron and Steel Institute of Japan International, Vol. 33, No. 2, 1993a.

Racz, L.M., and Szekely, J., "An Analysis of the Applicability of Wetting Balance Measurements of Components with Dissimilar Surfaces," Advances in Electronic Packaging 1993, Vol. 2, ASME EEP-Vol. 4-2, 1993b, pp. 1103-1111.

Rooks, S., Racz, L.M., Szekely, J., Benhabib, B., and Neumann, A.W., "Evaluation of Two- Dimensional and Three-Dimensional Axisymmetric Fluid Interface Shapes with Boundary Conditions," Langmuir, Vol. 7, 1991, pp. 3222-3228.

Satoh, R., Oshima, M., Komura, H., Ishi, I., and Serizawa, K., "Development of a New Micro-Solder Bonding Method for VLSIs," Proc., 3rd Annual Intl. Electronics Packaging Soc. Conf., 1983, pp. 455-461.

Satoh, R., Oshima, M., Hirota, K., and Ishi, I., "Optimum Bonding Shape Control of Micro-Solder Joint of IC and LSI," J. Japan Inst. Metals, Vol. 51, No. 6, 1987, pp. 553-560.

Singler, T.J., and Zhang, X., "Computer Simulation of Solder Bridging Phenomena," Advances in Electronic Packaging 1995, Vol. 2, ASME EEP-Vol. 10-2, pp. 1117-1127; presented at InterPack '95, Lahaina, HI, 1995.

Singler, T.J., Pitarresi, J.M., Holub, I.R., and Yin, H., "Towards an Optimization Algorithm for Solder Joint Reliability," Advances in Electronic Packaging 1995, Vol. 2, ASME EEP-Vol. 10-2, pp. 1155- 1166; presented at InterPack '95, Lahaina, HI, 1995.

Subbarayan, G., Li, Y., and Mahajan, R.L., "Reliability Simulations for Solder Joints Using Stochastic Finite Element and Artificial Neural Network Models," Advances in Electronic Packaging 1995, Vol. 1, ASME EEP-Vol. 10-1, pp. 459-471; presented at InterPack '95, Lahaina, HI, 1995.

Whalley, D.C., Conway, P.P., Sarvar, F., and Kalantary, M., "The Globule Block Wetting Balance Test," Advances in Electronic Packaging 1995, Vol. 1, ASME EEP-Vol. 10-1, pp. 89-94; presented at InterPack '95, Lahaina, HI, 1995.

Yost, B., McGroarty, J., Borgesen, P. and Li, C.-Y., "Shape of a Nonaxisymmetric Liquid Solder Drop Constrained by Parallel Plates," IEEE Trans. on Components, Hybrids, and Manufacturing Technology, Vol. 16, No. 5, August 1993, pp. 523-526.

Yost, F.G., and Holm, E.A., "Capillary Flow on Narrow Strips and in V-Shaped Grooves," Advances in Electronic Packaging 1995, Vol. 2, ASME EEP-Vol. 10-2, pp. 1265-1271; presented at InterPack '95, Lahaina, HI, 1995.