A comprehensive stochastic model is proposed to predict Package-on-Package (PoP) stacking yield loss. The model takes into account all pad locations at the stacking interface while considering the statistical variations of the warpages and the solder ball heights of both top and bottom packages. The goal is achieved by employing three statistical methods: (1) an advanced approximate integration-based method called eigenvector dimension reduction (EDR) method to conduct uncertainty propagation (UP) analyses, (2) the stress-strength interference (SSI) model to determine the noncontact probability at a single pad, and (3) the union of events considering the statistical dependence to calculate the final yield loss. In this first part, theoretical development of the proposed stochastic model is presented. Implementation of the proposed model is presented in a companion paper.
Issue Section:
Research Papers
References
1.
Loh
, W. K.
, Kulterman
, R.
, Purdie
, T.
, Fu
, H.
, and Tsuriya
, M.
, 2015
, “Recent Trend of Package Warpage Characteristic
,” International Conference on Electronics Packaging and iMAPS All Asia Conference
(ICEP-IACC
), Kyoto, Japan
, Apr. 14–17
, pp. 233
–238
.2.
Vijayaragavan
, N.
, Carson
, F.
, and Mistry
, A.
, 2008
, “Package on Package Warpage-Impact on Surface Mount Yields and Board Level Reliability
,” 58th Electronic Components and Technology Conference
(ECTC
), Lake Buena Vista, FL
, May 27–30
, pp. 389
–396
.3.
Ishibashi
, K.
, 2007
, “PoP (Package-on-Package) Stacking Yield Loss Study
,” 57th Electronic Components and Technology Conference
(ECTC
), Reno, NV
, May 29–June 1
, pp. 1403
–1408
.4.
Xie
, D.
, Geiger
, D.
, Shangguan
, D.
, Hu
, B.
, and Sjoberg
, J.
, 2008
, “Yield Study of Inline Package on Package (PoP) Assembly
,” 10th Electronics Packaging Technology Conference
(EPTC
), Singapore
, Dec. 9–12
, pp. 1202
–1208
.5.
Xie
, D.
, Shangguan
, D.
, Geiger
, D.
, Gill
, D.
, Vellppan
, V.
, and Chinniah
, K.
, 2009
, “Head in Pillow (HIP) and Yield Study on SIP and PoP Assembly
,” 59th Electronic Components and Technology Conference (ECTC
), San Diego, CA, May 26–29, pp. 752
–758
.6.
Huang
, C.-Y.
, 2013
, “Package-on-Package Assembly Yield Assessment in the ODM/EMS Environment Using Monte Carlo Simulation
,” IEEE Trans. Compon., Packag, Manuf. Technol.
, 3
(9
), pp. 1611
–1620
.7.
Huang
, C.-Y.
, 2017
, “Applying Monte Carlo Simulation to Analyze the Open Scenario in the Assembly of Electronic Components
,” IEEE Trans. Compon., Packag, Manuf. Technol.
, 7
(11
), pp. 1911
–1919
.8.
Katahira
, T.
, Scanlan
, J.
, Park
, J.
, and Oh
, K.
, 2007
, “0.3 mm Pitch CSP/BGA Development for Mobile Terminals
,” 40th International Symposium on Microelectronics (IMAPS 2007), San Jose, CA, Nov. 11–15, pp. 393
–401
.9.
Rubino
, G.
, and Tuffin
, B.
, 2009
, Rare Event Simulation Using Monte Carlo Methods
, Wiley
, New York.10.
Koch
, P. N.
, Simpson
, T. W.
, Allen
, J. K.
, and Mistree
, F.
, 1999
, “Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size
,” J. Aircr.
, 36
(1
), pp. 275
–286
.11.
Youn
, B. D.
, Xi
, Z.
, and Wang
, P.
, 2008
, “Eigenvector Dimension Reduction (EDR) Method for Sensitivity-Free Probability Analysis
,” Struct. Multidiscip. Optim.
, 37
(1
), pp. 13
–28
.12.
Wei
, H.-P.
, Han
, B.
, Youn
, B. D.
, Shin
, H.
, Kim
, I.
, and Moon
, H.
, 2017
, “Assembly Yield Prediction of Plastically Encapsulated Packages With a Large Number of Manufacturing Variables by Advanced Approximate Integration Method
,” Microelectron. Reliab.
, 78
, pp. 319
–330
.13.
Rahman
, S.
, and Xu
, H.
, 2004
, “A Univariate Dimension-Reduction Method for Multi-Dimensional Integration in Stochastic Mechanics
,” Probab. Eng. Mech.
, 19
(4
), pp. 393
–408
.14.
Sundararajan
, C.
, and Witt
, F.
, 1995
, “Stress-Strength Interference Method
,” Probabilistic Structural Mechanics Handbook: Theory and Industrial Applications
, Springer, Boston, MA, pp. 8
–26
.15.
Basu
, A. P.
, 2007
, “Stress–Strength Model
,” Encyclopedia of Statistics in Quality and Reliability
, Wiley, Hoboken, NJ.16.
Petrov
, V. V.
, 2012
, Sums of Independent Random Variables
, Springer Science & Business Media
, Berlin.17.
Puri
, P. S.
, 1966
, “Probability Generating Functions of Absolute Difference of Two Random Variables
,” Proc. Natl. Acad. Sci. U. S. A.
, 56(4), pp. 1059
–1061
.18.
Springer
, M. D.
, 1979
, “The Algebra of Random Variables
,” Wiley, New York.19.
Cox
, D. R.
, and Wermuth
, N.
, 1996
, Multivariate Dependencies: Models, Analysis and Interpretation
, Chapman & Hall
, Boca Raton, FL.20.
Kumar
, P.
, 2010
, “Probability Distributions and Estimation of Ali-Mikhail-Haq Copula
,” Appl. Math. Sci.
, 4
(14), pp. 657–666.21.
Taylor
, C. R.
, 1990
, “Two Practical Procedures for Estimating Multivariate Nonnormal Probability Density Functions
,” Am. J. Agric. Econ.
, 72
(1
), pp. 210–217.22.
Shan
, S.
, and Wang
, G. G.
, 2010
, “Survey of Modeling and Optimization Strategies to Solve High-Dimensional Design Problems With Computationally-Expensive Black-Box Functions
,” Struct. Multidiscip. Optim.
, 41
(2
), pp. 219–241.23.
Bogart
, K.
, and Stein
, C.
, 2002
, “Discrete Math in Computer Science
,” Department of Computer Mathematics and Department of Computer Science. Dartmouth College, Hanover, NH.Copyright © 2020 by ASME
You do not currently have access to this content.
