0
Research Papers

Reliability Analysis of Lead-Free Solders in Electronic Packaging Using a Novel Surrogate Model and Kriging Concept

[+] Author and Article Information
Hamoon Azizsoltani

Department of Civil Engineering and
Engineering Mechanics,
University of Arizona,
P.O. Box 210072,
Tucson, AZ 85721;
Department of Computer Science,
North Carolina State University,
P.O. Box 8206,
Raleigh, NC 27606
e-mail: azizsoltani@email.arizona.edu

Achintya Haldar

Department of Civil Engineering and
Engineering Mechanics,
University of Arizona,
P.O. Box 210072,
Tucson, AZ 85721
e-mail: haldar@u.arizona.edu

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received May 3, 2017; final manuscript received July 16, 2018; published online August 20, 2018. Assoc. Editor: Jeffrey C. Suhling.

J. Electron. Packag 140(4), 041003 (Aug 20, 2018) (11 pages) Paper No: EP-17-1047; doi: 10.1115/1.4040924 History: Received May 03, 2017; Revised July 16, 2018

A novel reliability evaluation procedure of lead-free solders used in electronic packaging (EP) subjected to thermomechanical loading is proposed. A solder ball is represented by finite elements (FEs). Major sources of nonlinearities are incorporated as realistically as practicable. Uncertainties in all design variables are quantified using available information. The thermomechanical loading is represented by five design parameters and uncertainties associated with them are incorporated. Since the performance or limit state function (LSF) of such complicated problem is implicit in nature, it is approximately generated explicitly in the failure region with the help of a completely improved response surface method (RSM)-based approach and the universal Kriging method (KM). The response surface (RS) is generated by conducting as few deterministic nonlinear finite element analyses as possible by integrating several advanced factorial mathematical concepts producing compounding beneficial effect. The accuracy, efficiency, and application potential of the procedure are established with the help of Monte Carlo simulation (MCS) and the results from laboratory investigation reported in the literature. The study conclusively verified the proposed method. Similar studies can be conducted to fill the knowledge gap for cases where the available analytical and experimental studies are limited or extend the information to cases where reliability information is unavailable. The study showcased how reliability information can be extracted with the help of multiple deterministic analyses. The authors believe that they proposed an alternative to the classical MCS technique.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Desai, C. S. , Somasundaram, S. , and Frantziskonis, G. , 1986, “A Hierarchical Approach for Constitutive Modelling of Geologic Materials,” Int. J. Numer. Anal. Met., 10(3), pp. 225–257. [CrossRef]
Desai, C. S. , 2015, “Constitutive Modeling of Materials and Contacts Using the Disturbed State Concept—Part 1: Background and Analysis,” Comput. Struct., 146, pp. 214–233. [CrossRef]
Desai, C. S. , 2015, “Constitutive Modeling of Materials and Contacts Using the Disturbed State Concept—Part 2: Validations at Specimen and Boundary Value Problem Levels,” Comput. Struct., 146, pp. 234–251. [CrossRef]
Higgins, W. , Chakraborty, T. , and Basu, D. , 2013, “A High Strain‐Rate Constitutive Model for Sand and Its Application in Finite‐Element Analysis of Tunnels Subjected to Blast,” Int. J. Numer. Anal. Met., 37(15), pp. 2590–2610. [CrossRef]
Zhou, M. , Huang, S. , Hu, J. , Lei, Y. , Xiao, Y. , Li, B. , Yan, S. , and Zou, F. , 2017, “A Density-Dependent Modified Drucker-Prager Cap Model for Die Compaction of Ag57. 6-Cu22. 4-Sn10-In10 Mixed Metal Powders,” Powder Technol., 305, pp. 183–196. [CrossRef]
Basaran, C. , and Nie, S. , 2004, “An Irreversible Thermodynamics Theory for Damage Mechanics of Solids,” Int. J. Damage Mech., 13(3), pp. 205–223. [CrossRef]
Gomez, J. , and Basaran, C. , 2005, “A Thermodynamics Based Damage Mechanics Constitutive Model for Low Cycle Fatigue Analysis of Microelectronics Solder Joints Incorporating Size Effects,” Int. Solids Struct., 42(13), pp. 3744–3772. [CrossRef]
Sosnovskiy, L. A. , and Sherbakov, S. S. , 2016, “Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems,” Entropy, 18(7), p. 268. [CrossRef]
Motalab, M. , Cai, Z. , Suhling, J. C. , and Lall, P. , 2012, “Determination of Anand Constants for SAC Solders Using Stress-Strain or Creep Data,” InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, San Diego, CA, May 30–June 1, pp. 910–922.
Basit, M. M. , Motalab, M. , Suhling, J. C. , and Lall, P. , 2014, “The Effects of Aging on the Anand Viscoplastic Constitutive Model for SAC305 Solder,” Fourteenth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), Orlando, FL, May 27–30, pp. 112–126.
Azizsoltani, H. , Kazemi, M. T. , and Javanmardi, M. R. , 2014, “An Anisotropic Damage Model for Metals Based on Irreversible Thermodynamics Framework,” Iran. J. Sci. Technol., 38(C1), pp. 157–173. http://ijstc.shirazu.ac.ir
Khaloo, A. R. , Javanmardi, R. , and Azizsoltani, H. , 2014, “Numerical Characterization of Anisotropic Damage Evolution in Iron Based Materials,” Sci. Iran. Int. J. Sci. Technol., 21(1), pp. 53–56.
Desai, C. S. , and Whitenack, R. , 2001, “Review of Models and the Disturbed State Concept for Thermomechanical Analysis in Electronic Packaging,” ASME J. Electron. Packag., 123(1), pp. 19–33. [CrossRef]
Shen, C. , Zhao, C. , Hai, Z. , Zhang, J. , Bozack, M. J. , Suhling, J. C. , and Evans, J. L. , 2015, “Sn-Ag-Cu Solder Joints Interconnection Reliability of BGA Package During Thermal Aging and Cycling,” International Symposium on Microelectronics, Orlando, FL, Oct. 27–29, pp. 135–140.
Zwick, J. W. , and Desai, C. S. , 1999, “Structural Reliability of PBGA Solder Joints With the Disturbed State Concept,” Pacific Rim/ASME International Intersociety Electronic and Photonic Packaging Conference, Advances in Electronic Packaging (Interpack '99), Maui, HI, June 13–19, pp. 1865–1874.
Whitenack, R. D. , 2004, “Design and Analysis of Solder Connections Using Accelerated Approximate Procedure With Disturbed State Concept,” Ph.D. dissertation, The University of Arizona, Tucson, AZ. https://repository.arizona.edu/bitstream/handle/10150/280662/azu_td_3145145_sip1_m.pdf?sequence=1
Sane, S. M. , 2007, “Disturbed State Concept Based Constitutive Modeling for Reliability Analysis of Lead Free Solders in Electronic Packaging and for Prediction of Glacial Motion,” Ph.D. dissertation, The University of Arizona, Tucson, AZ.
Tucker, J. P. , Chan, D. K. , Subbarayan, G. , and Handwerker, C. A. , 2014, “Maximum Entropy Fracture Model and Its Use for Predicting Cyclic Hysteresis in Sn3. 8Ag0. 7Cu and Sn3. 0Ag0. 5 Solder Alloys,” Microelectron. Reliab., 54(11), pp. 2513–2522. [CrossRef]
Desai, C. S. , 2000, Mechanics of Materials and Interfaces: The Disturbed State Concept, CRC Press, Boca Raton, FL.
Whitenack, R. , Desai, C. , and Rassaian, M. , 2007, “Parametric and Optimal Design in Electronic Packaging Using DSC: Computational, Geometrical, and Material Aspects,” ASME J. Electron. Packag., 129(3), pp. 356–365. [CrossRef]
Desai, C. S. , 2016, “Disturbed State Concept as Unified Constitutive Modeling Approach,” J. Rock Mech. Geotech. Eng., 8(3), pp. 277–293. [CrossRef]
Perzyna, P. , 1966, “Fundamental Problems in Viscoplasticity,” Adv. Appl. Mech., 9, pp. 243–377. [CrossRef]
Desai, C. S. , 2017, “Unified Approach for Constitutive Modelling for Geologic Materials and Discontinuities,” Numerical Methods in Geomechanics, 6th ed., Vol. 1, Routledge, Abingdon, UK, pp. 45–54.
Baladi, G. Y. , and Rohani, B. , 1984, “Development of an Elastic-Viscoplastic Constitutive Relationship for Earth Materials,” Mechanics of Engineering Materials, Wiley, New York, pp. 23–43.
Vianco, P. T. , Rejent, J. A. , and Kilgo, A. C. , 2003, “Time-Independent Mechanical and Physical Properties of the Ternary 95.5 Sn-3.9 Ag-0.6 Cu Solder,” J. Electron. Mater., 32(3), pp. 142–151. [CrossRef]
Xiao, Q. , and Armstrong, W. D. , 2005, “Tensile Creep and Microstructural Characterization of Bulk Sn3. 9Ag0. 6Cu Lead-Free Solder,” J. Electron. Mater., 34(2), pp. 196–211. [CrossRef]
Tummala, R. R. , and Rymaszewski, E. J. , 1989, Microelectronics Packaging Handbook, von Nostrand Reinhold, New York.
Zeng, Q. L. , Wang, Z. G. , Xian, A. P. , and Shang, J. K. , 2005, “Cyclic Softening of the Sn-3.8 Ag-0.7 Cu Lead-Free Solder Alloy With Equiaxed Grain Structure,” J. Electron. Mater., 34(1), pp. 62–67. [CrossRef]
Haldar, A. , and Mahadevan, S. , 2000, Reliability Assessment Using Stochastic Finite Element Analysis, Wiley, New York.
Haldar, A. , and Mahadevan, S. , 2000, Probability, Reliability, and Statistical Methods in Engineering Design, Wiley, New York.
Box, G. E. , 1954, “The Exploration and Exploitation of Response Surfaces: Some General Considerations and Examples,” Biometrics, 10(1), pp. 16–60. [CrossRef]
Gaxiola-Camacho, J. R. , Azizsoltani, H. , Villegas-Mercado, F. J. , and Haldar, A. , 2017, “A Novel Reliability Technique for Implementation of Performance-Based Seismic Design of Structures,” Eng. Struct., 142, pp. 137–147. [CrossRef]
Gaxiola-Camacho, J. R. , Haldar, A. , Azizsoltani, H. , Valenzuela-Beltran, F. , and Reyes-Salazar, A. , 2017, “Performance-Based Seismic Design of Steel Buildings Using Rigidities of Connections,” ASCE-ASME J. Risk Uncertain. Eng. Syst. Part A Civ. Eng., 4(1), p. 4017036. [CrossRef]
Villegas-Mercado, F. J. , Azizsoltani, H. , Gaxiola-Camacho, J. R. , and Haldar, A. , 2017, “Seismic Reliability Evaluation of Structural Systems for Different Soil Conditions,” Int. J. Geotech. Earthquake Eng., 8(2), pp. 23–38. [CrossRef]
Azizsoltani, H. , Gaxiola-Camacho, J. R. , and Haldar, A. , 2018, “Site-Specific Seismic Design of Damage Tolerant Structural Systems Using a Novel Concept,” Bull. Earthquake Eng., 16(9), pp. 3819–3843. [CrossRef]
Khuri, A. I. , and Cornell, J. A. , 1996, Response Surfaces: Designs and Analyses, CRC Press, New York.
Box, G. E. , and Wilson, K. B. , 1992, “On the Experimental Attainment of Optimum Conditions,” Breakthroughs in Statistics, Springer, New York, pp. 270–310.
Lucas, J. M. , 1974, “Optimum Composite Designs,” Technometrics, 16(4), pp. 561–567. [CrossRef]
Chakraborty, S. , and Sen, A. , 2014, “Adaptive Response Surface Based Efficient Finite Element Model Updating,” Finite Elem. Anal. Des., 80, pp. 33–40. [CrossRef]
Krige, D. G. , 1951, “A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand,” South. Afr. Inst. Min. Metall. Online J., 52(6), pp. 119–139. http://journals.co.za/content/saimm/52/9/AJA0038223X_4858
Lichtenstern, A. , 2013, “Kriging Methods in Spatial Statistics,” Ph.D. dissertation, Technische Universität München, München, Germany.
Wackernagel, H. , 2013, Multivariate Geostatistics: An Introduction With Applications, Springer Science & Business Media, Berlin.
Azizsoltani, H. , and Haldar, A. , 2017, “Intelligent Computational Schemes for Designing More Seismic Damage-Tolerant Structures,” J. Earthquake Eng. (epub).
Webster, R. , and Oliver, M. A. , 2007, Geostatistics for Environmental Scientists, Wiley, Hoboken, NJ.
Cressie, N. , 2015, Statistics for Spatial Data, Wiley, Hoboken, NJ.

Figures

Grahic Jump Location
Fig. 1

Solder ball schematic

Grahic Jump Location
Fig. 2

Solder ball (a) geometry and FE mesh and (b) layout

Grahic Jump Location
Fig. 3

Hierarchical single surface yield surface in J1−J2D space

Grahic Jump Location
Fig. 4

Variation of MFTD and MFT

Grahic Jump Location
Fig. 5

Probability of failure versus number of thermomechanical loading cycles profile

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In