Review Article

A Review on Water Vapor Pressure Model for Moisture Permeable Materials Subjected to Rapid Heating

[+] Author and Article Information
Liangbiao Chen

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: goodbill2008@gmail.com

Jiang Zhou

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: zhoujx@lamar.edu

Hsing-Wei Chu

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: chuhw@lamar.edu

Guoqi Zhang

Department of Microelectronics,
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: G.Q.Zhang@tudelft.nl

Xuejun Fan

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: xuejun.fan@lamar.edu

1Corresponding authors.

Manuscript received September 6, 2017; final manuscript received March 7, 2018; published online April 23, 2018. Assoc. Editor: Rui Huang.

Appl. Mech. Rev 70(2), 020803 (Apr 23, 2018) (16 pages) Paper No: AMR-17-1062; doi: 10.1115/1.4039557 History: Received September 06, 2017; Revised March 07, 2018

This paper presents a comprehensive review and comparison of different theories and models for water vapor pressure under rapid heating in moisture permeable materials, such as polymers or polymer composites. Numerous studies have been conducted, predominately in microelectronics packaging community, to obtain the understanding of vapor pressure evolution during soldering reflow for encapsulated moisture. Henry's law-based models are introduced first. We have shown that various models can be unified to a general form of solution. Two key parameters are identified for determining vapor pressure: the initial relative humidity and the net heat of solution. For materials with nonlinear sorption isotherm, the analytical solutions for maximum vapor pressure are presented. The predicted vapor pressure, using either linear sorption isotherm (Henry's law) or nonlinear sorption isotherm, can be greater than the saturated water vapor pressure. Such an “unphysical” pressure solution needs to be further studied. The predicted maximum vapor pressure is proportional to the initial relative humidity, implying the history dependence. Furthermore, a micromechanics-based vapor pressure model is introduced, in which the vapor pressure depends on the state of moisture in voids. It is found that the maximum vapor pressure stays at the saturated vapor pressure provided that the moisture is in the mixed liquid/vapor phase in voids. And, the vapor pressure depends only on the current state of moisture condition. These results are contradictory to the model predictions with sorption isotherm theories. The capillary effects are taken into consideration for the vapor pressure model using micromechanics approach.

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Zhang, G. Q. , Van Driel, W. D. , and Fan, X. J. , 2006, Mechanics of Microelectronics, Springer, New York. [CrossRef]
Fan, X. J. , and Suhir, E. , 2010, Moisture Sensitivity of Plastic Packages of IC Devices, Springer, New York. [CrossRef]
Antoon, M. K. , and Koenig, J. L. , 1980, “ The Structure and Moisture Stability of the Matrix Phase in Glass-Reinforced Epoxy Composites,” J. Macromol. Sci., Part C, 19(1), pp. 135–173. [CrossRef]
Baschek, G. , Hartwig, G. , and Zahradnik, F. , 1999, “ Effect of Water Absorption in Polymers at Low and High Temperatures,” Polymer, 40(12), pp. 3433–3441. [CrossRef]
Fan, X. J. , Lee, S. W. R. , and Han, Q. , 2009, “ Experimental Investigations and Model Study of Moisture Behaviors in Polymeric Materials,” Microelectron. Reliab., 49(8), pp. 861–871. [CrossRef]
Placette, M. D. , Fan, X. J. , Zhao, J.-H. , and Edwards, D. , 2012, “ Dual Stage Modeling of Moisture Absorption and Desorption in Epoxy Mold Compounds,” Microelectron. Reliab., 52(7), pp. 1401–1408. [CrossRef]
De'Nève, B. , and Shanahan, M. E. R. , 1993, “ Water Absorption by an Epoxy Resin and Its Effect on the Mechanical Properties and Infra-Red Spectra,” Polymer, 34(24), pp. 5099–5105. [CrossRef]
Zhou, J. , and Law, J. S. , 2008, “ Effect of Non-Uniform Moisture Distribution on the Hygroscopic Swelling Coefficient,” IEEE Trans. Compon. Packag. Technol., 31(2), pp. 269–276. [CrossRef]
Stokes, E. H. , 1993, “ Anomalous Swelling Behavior of FM 5055 Carbon Phenolic Composite,” AIAA J., 31(3), pp. 584–589. [CrossRef]
Benkeddad, A. , Grédiac, M. , and Vautrin, A. , 1995, “ On the Transient Hygroscopic Stresses in Laminated Composite Plates,” Compos. Struct., 30(2), pp. 201–215. [CrossRef]
Secrist, K. E. , and Nolte, A. J. , 2011, “ Humidity Swelling/Deswelling Hysteresis in a Polyelectrolyte Multilayer Film,” Macromolecules, 44(8), pp. 2859–2865. [CrossRef]
Shirangi, M. H. , and Michel, B. , 2010, “ Mechanism of Moisture Diffusion, Hygroscopic Swelling, and Adhesion Degradation in Epoxy Molding Compounds,” Moisture Sensitivity of Plastic Packages of IC Devices, X. J. Fan and E. Suhir , eds., Springer, Boston, MA, pp. 29–69. [CrossRef]
LaPlante, G. , and Lee-Sullivan, P. , 2005, “ Moisture Effects on FM300 Structural Film Adhesive: Stress Relaxation, Fracture Toughness, and Dynamic Mechanical Analysis,” J. Appl. Polym. Sci., 95(5), pp. 1285–1294. [CrossRef]
Dhakal, H. N. , Zhang, Z. Y. , and Richardson, M. O. W. , 2007, “ Effect of Water Absorption on the Mechanical Properties of Hemp Fibre Reinforced Unsaturated Polyester Composites,” Compos. Sci. Technol., 67(7–8), pp. 1674–1683. [CrossRef]
Toubal, L. , Cuillière, J.-C. , Bensalem, K. , Francois, V. , and Gning, P.-B. , 2016, “ Hygrothermal Effect on Moisture Kinetics and Mechanical Properties of Hemp/Polypropylene Composite: Experimental and Numerical Studies,” Polym. Compos., 37(8), pp. 2342–2352. [CrossRef]
Fan, X. J. , Zhang, G. Q. , van Driel, W. D. , and Ernst, L. J. , 2008, “ Interfacial Delamination Mechanisms During Soldering Reflow With Moisture Preconditioning,” IEEE Trans. Compon. Packag. Technol., 31(2), pp. 252–259. [CrossRef]
van Driel, W. D. , van Gils, M. A. J. , Fan, X. J. , Zhang, G. Q. , and Ernst, L. J. , 2008, “ Driving Mechanisms of Delamination Related Reliability Problems in Exposed Pad Packages,” IEEE Trans. Compon. Packag. Technol., 31(2), pp. 260–268. [CrossRef]
Shi, X. Q. , Zhang, Y. L. , Wei, Z. , and Fan, X. J. , 2008, “ Effect of Hygrothermal Aging on Interfacial Reliability of Silicon/Underfill/FR-4 Assembly,” IEEE Trans. Compon. Packag. Technol., 31(1), pp. 94–103. [CrossRef]
Chateauminois, A. , Vincent, L. , Chabert, B. , and Soulier, J. P. , 1994, “ Study of the Interfacial Degradation of a Glass-Epoxy Composite During Hygrothermal Ageing Using Water Diffusion Measurements and Dynamic Mechanical Thermal Analysis,” Polymer, 35(22), pp. 4766–4774. [CrossRef]
Chunhua, G. , Li, M. , Kewei, C. , Haibin, C. , and Jingshen, W. , 2012, “ Effects of Moisture Absorption and Temperature on the Adhesion Strength Between Die Attach Film (DAF) and Silicon Die,” 14th International Conference on Electronic Materials and Packaging (EMAP), Lantau Island, China Dec. 13–16, pp. 1–4.
Dai, T. , and Dai, H.-L. , 2016, “ Hygrothermal Behavior of a CFRR-Metal Adhesively Bonded Joint With Coupled Transfer of Heat and Moisture Through the Thickness,” Compos. Struct., 152, pp. 947–958. [CrossRef]
Yao, Y. , Long, X. , and Keer, L. M. , 2017, “ A Review of Recent Research on the Mechanical Behavior of Lead-Free Solders,” ASME Appl. Mech. Rev., 69(4), p. 040802. [CrossRef]
Fukuzawa, I. , Ishiguro, S. , and Nanbu, S. , 1985, “ Moisture Resistance Degradation of Plastic LSIs by Reflow Soldering,” 23rd Annual International Reliability Physics Symposium, Orlando, FL, Mar. 25–29, pp. 192–197.
Kitano, M. , Nishimura, A. , Kawai, S. , and Nishi, K. , 1988, “ Analysis of Package Cracking During Reflow Soldering Process,” 26th Annual Proceedings Reliability Physics Symposium, Monterey, CA, Apr. 12–14, pp. 90–95.
Liu, S. , and Mei, Y. , 1995, “ Behavior of Delaminated Plastic IC Packages Subjected to Encapsulation Cooling, Moisture Absorption, and Wave Soldering,” IEEE Trans. Compon. Packag. Manuf. Technol., Part A, 18(3), pp. 634–645. [CrossRef]
Gallo, A. A. , and Munamarty, R. , 1995, “ Popcorning: A Failure Mechanism in Plastic-Encapsulated Microcircuits,” IEEE Trans. Reliab., 44(3), pp. 362–367. [CrossRef]
Seol, K.-W. , Choi, C.-H. , Kim, S. , Son, S. H. , and Lee, J. K. , 2003, “ On the Mechanism of Popcorn Blistering in Copper Clad Laminates,” J. Adhes. Sci. Technol., 17(10), pp. 1331–1349. [CrossRef]
Xie, B. , Fan, X. J. , Shi, X. Q. , and Ding, H. , 2009, “ Direct Concentration Approach of Moisture Diffusion and Whole Field Vapor Pressure Modeling for Reflow Process—Part II: Application to 3-D Ultra-Thin Stacked-Die Chip Scale Packages,” ASME J. Electron. Packag., 131(3), p. 031011. [CrossRef]
Czabaj, M. W. , Zehnder, A. T. , and Chuang, K. C. , 2009, “ Blistering of Moisture Saturated Graphite/Polyimide Composites Due to Rapid Heating,” J. Compos. Mater., 43(2), pp. 153–174. [CrossRef]
Zehnder, A. T. , and Czabaj, M. W. , 2006, “ Delamination and Blistering due to Rapid Heating of Moist Composites,” ASME Paper No. IMECE2006-14669.
Tee, T. Y. , and Zhong, Z. , 2004, “ Integrated Vapor Pressure, Hygroswelling, and Thermo-Mechanical Stress Modeling of QFN Package During Reflow With Interfacial Fracture Mechanics Analysis,” Microelectron. Reliab., 44(1), pp. 105–114. [CrossRef]
Zhu, L. , Jiang, Z. , and Fan, X. J. , 2014, “ Rupture and Instability of Soft Films Due to Moisture Vaporization in Microelectronic Devices,” Comput. Mater. Continua, 39(2), pp. 113–134. http://www.techscience.com/doi/10.3970/cmc.2014.039.113.pdf
Sullivan, R. M. , 1996, “ The Effect of Water on Thermal Stresses in Polymer Composites,” ASME J. Appl. Mech., 63(1), pp. 173–179. [CrossRef]
Wong, E. H. , Koh, S. W. , Lee, K. H. , Kian-Meng, L. , Lim, T. B. , and Mai, Y.-W. , 2006, “ Advances in Vapor Pressure Modeling for Electronic Packaging,” IEEE Trans. Adv. Packag., 29(4), pp. 751–759. [CrossRef]
Shirley, C. G. , 2014, “ Popcorn Cavity Pressure,” IEEE Trans. Device Mater. Reliab., 14(1), pp. 426–431. [CrossRef]
Hui, C.-Y. , Muralidharan, V. , and Thompson, M. O. , 2005, “ Steam Pressure Induced in Crack-Like Cavities in Moisture Saturated Polymer Matrix Composites During Rapid Heating,” Int. J. Solids Struct., 42(3–4), pp. 1055–1072. [CrossRef]
Muralidharan, V. , Hui, C.-Y. , Krishnan, V. R. , and Papoulia, K. D. , 2006, “ A Flow Through Porous Media Model for Pore Pressure During Heating of Polymer–Matrix Composites,” Compos. Sci. Technol., 66(10), pp. 1409–1417. [CrossRef]
Fan, X. J. , and Lim, T. B. , 1999, “ Mechanism Analysis for Moisture-Induced Failures in IC Packages,” ASME International Mechanical Engineering Congress and Exposition, Nashville, TN, Nov. 14–19, Paper No. IMECE/EPE-14.
Fan, X. J. , Zhou, J. , Zhang, G. Q. , and Ernst, L. J. , 2005, “ A Micromechanics Based Vapor Pressure Model in Electronic Packages,” ASME J. Electron. Packag., 127(3), pp. 262–267. [CrossRef]
Xie, B. , Fan, X. J. , Shi, X. Q. , and Ding, H. , 2009, “ Direct Concentration Approach of Moisture Diffusion and Whole Field Vapor Pressure Modeling for Reflow Process—Part I: Theory and Numerical Implementation,” ASME J. Electron. Packag., 131(3), p. 031010. [CrossRef]
Fan, X. J. , Chen, L. , Wong, C. P. , and Zhang, G. Q. , 2015, “ Effects of Vapor Pressure and Super-Hydrophobic Nanocomposite Coating on Microelectronics Reliability,” Engineering, 1(3), pp. 384–390. [CrossRef]
Chen, L. , Zhou, J. , Chu, H.-W. , Zhang, G. Q. , and Fan, X. J. , 2017, “A Unified and Versatile Model Study for Moisture Diffusion,” 67th Electronic Components and Technology Conference (ECTC), Orlando, FL, May 30–June 2, pp. 2377–5726.
Bhattacharyya, B. K. , Huffman, W. A. , Jahsman, W. E. , and Natarajan, B. , 1988, “ Moisture Absorption and Mechanical Performance of Surface Mountable Plastic Packages,” 38th Electronics Components Conference, Los Angeles, CA, May 9–11, pp. 49–58.
Chen, L. , Chu, H. W. , and Fan, X. J. , 2015, “ A Convection–Diffusion Porous Media Model for Moisture Transport in Polymer Composites: Model Development and Validation,” J. Polym. Sci. B, 53(20), pp. 1440–1449. [CrossRef]
Chen, L. , Adams, J. , Chu, H.-W. , and Fan, X. J. , 2016, “ Modeling of Moisture Over-Saturation and Vapor Pressure in Die-Attach Film for Stacked-Die Chip Scale Packages,” J. Mater. Sci. Mater. Electron., 27(1), pp. 481–488. [CrossRef]
Alpern, P. , Lee, K. C. , Dudek, R. , and Tilgner, R. , 2000, “ A Simple Model for the Mode I Popcorn Effect for IC Packages,” Microelectron. Reliab., 40(8–10), pp. 1503–1508. [CrossRef]
Tay, A. A. O. , and Lin, T. Y. , 1996, “ Moisture Diffusion and Heat Transfer in Plastic IC Packages,” IEEE Trans. Compon. Packag. Technol., Part A, 19(2), pp. 186–193.
Wang, Z. , 2011, “ Vapour Pressure Modelling for Plastic Encapsulated Microelectronics Subjected to Lead-Free Solder Reflow Profile,” Strain, 47(s1), pp. e148–e155. [CrossRef]
Bao, L.-R. , and Yee, A. F. , 2002, “ Effect of Temperature on Moisture Absorption in a Bismaleimide Resin and Its Carbon Fiber Composites,” Polymer, 43(14), pp. 3987–3997. [CrossRef]
VanSant, J. H. , 1983, Conduction Heat Transfer Solutions, Lawrence Livermore National Laboratory, Livermore, CA.
Shirley, C. G. , 1994, “ THB Reliability Models and Life Prediction for Intermittently-Powered Nonhermetic Components,” 32nd Annual International Reliability Physics Symposium, San Jose, CA, Apr. 11–14, pp. 72–77.
Haynes, W. M. , 2013, CRC Handbook of Chemistry and Physics, 94th ed., Taylor & Francis, Boston, MA.
Hollenbeck, R. G. , Peck, G. E. , and Kildsig, D. O. , 1978, “ Application of Immersional Calorimetry to Investigation of Solid-Liquid Interactions: Microcrystalline Cellulose-Water System,” J. Pharm. Sci., 67(11), pp. 1599–1606. [CrossRef] [PubMed]
Tcharkhtchi, A. , Bronnec, P. Y. , and Verdu, J. , 2000, “ Water Absorption Characteristics of Diglycidyl ether of Butane Diol–3,5-Diethyl-2,4-Diaminotoluene Networks,” Polymer, 41(15), pp. 5777–5785. [CrossRef]
Yasuda, H. , and Stannett, V. , 1962, “ Permeation, Solution, and Diffusion of Water in Some High Polymers,” J. Polym. Sci., 57(165), pp. 907–923. [CrossRef]
Rouse, P. E. , 1947, “ Diffusion of Vapors in Films,” J. Am. Chem. Soc., 69(5), pp. 1068–1073. [CrossRef]
Chern, R. T. , Koros, W. J. , Sanders, E. S. , and Yui, R. , 1983, “ Second Component” Effects in Sorption and Permeation of Gases in Glassy Polymers,” J. Membr. Sci., 15(2), pp. 157–169. [CrossRef]
Koros, W. J. , Chan, A. H. , and Paul, D. R. , 1977, “ Sorption and Transport of Various Gases in Polycarbonate,” J. Membr. Sci., 2, pp. 165–190. [CrossRef]
Roussis, P. P. , 1981, “ Diffusion of Water Vapour in Cellulose Acetate—1: Differential Transient Sorption Kinetics and Equilibria,” Polymer, 22(6), pp. 768–773. [CrossRef]
Ghosh, M. , 1996, Polyimides: Fundamentals and Applications, CRC Press, Boca Raton, FL.
Basu, S. , Shivhare, U. S. , and Mujumdar, A. S. , 2006, “ Models for Sorption Isotherms for Foods: A Review,” Drying Technol., 24(8), pp. 917–930. [CrossRef]
Vieth, W. R. , Howell, J. M. , and Hsieh, J. H. , 1976, “ Dual Sorption Theory,” J. Membr. Sci., 1, pp. 177–220. [CrossRef]
Kanapitsas, A. , Tsonos, C. , Psarras, G. C. , and Kripotou, S. , 2016, “ Barium Ferrite/Epoxy Resin Nanocomposite System: Fabrication, Dielectric, Magnetic and Hydration Studies,” Express Polym. Lett., 10(3), pp. 227–236. [CrossRef]
Brunauer, S. , 1945, The Adsorption of Gases and Vapors, Physical Adsorption, Vol. I, Princeton University Press, Princeton, NJ.
McLaughlin, C. P. , and Magee, T. R. A. , 1998, “ The Determination of Sorption Isotherm and the Isosteric Heats of Sorption for Potatoes,” J. Food Eng., 35(3), pp. 267–280. https://doi.org/10.1016/S0260-8774(98)00025-9
Kapsalis, J. G. , 1987, “ Influence of Hysteresis and Temperature on Moisture Sorption Isotherms in Water Activity,” Theory and Applications to Foods, L. B. Rokcland and L. R. Beuchat , eds., Marcel Dekker, New York, pp. 173–213.
Poyet, S. , and Charles, S. , 2009, “ Temperature Dependence of the Sorption Isotherms of Cement-Based Materials: Heat of Sorption and Clausius–Clapeyron Formula,” Cem. Concr. Res., 39(11), pp. 1060–1067. [CrossRef]
Glicksman, M. E. , 1999, Diffusion in Solids: Field Theory, Solid-State Principles, and Applications, Wiley, Hoboken, NJ.
Zhang, M. , Ye, G. , and van Breugel, K. , 2014, “ Multiscale Lattice Boltzmann-Finite Element Modelling of Chloride Diffusivity in Cementitious Materials—Part I: Algorithms and Implementation,” Mech. Res. Commun., 58, pp. 53–63. [CrossRef]
Chen, L. , Zhou, J. , Chu, H.-W. , Zhang, G. , and Fan, X. , 2017, “ Modeling Nonlinear Moisture Diffusion in Inhomogeneous Media,” Microelectron. Reliab., 75, pp. 162–170. [CrossRef]
Bond, D. A. , and Smith, P. A. , 2006, “ Modeling the Transport of Low-Molecular-Weight Penetrants Within Polymer Matrix Composites,” ASME Appl. Mech. Rev., 59(5), pp. 249–268. [CrossRef]
Sawada, K. , Nakazawa, T. , Kawamura, N. , Matsumoto, K. , Hiruta, Y. , and Sudo, T. , 1994, “ Simplified and Practical Estimation of Package Cracking During Reflow Soldering Process,” IEEE International Reliability Physics Symposium, San Jose, CA, Apr. 11–14, pp. 114–119.
Yi, S. , Goh, J. S. , and Yang, J. C. , 1997, “ Residual Stresses in Plastic IC Packages During Surface Mounting Process Preceded by Moisture Soaking Test,” IEEE Trans. Compon. Packag. Manuf. Technol., Part B, 20(3), pp. 247–255. [CrossRef]
Liu, P. , Cheng, L. , and Zhang, Y. W. , 2003, “ Interface Delamination in Plastic IC Packages Induced by Thermal Loading and Vapor Pressure—A Micromechanics Model,” IEEE Trans. Adv. Packag., 26(1), pp. 1–9. [CrossRef]
Adamson, A. W. , 1990, Physical Chemistry of Surfaces, 5th ed., Wiley, New York.
Tuller, M. , Or, D. , and Dudley, L. M. , 1999, “ Adsorption and Capillary Condensation in Porous Media: Liquid Retention and Interfacial Configurations in Angular Pores,” Water Resour. Res., 35(7), pp. 1949–1964. [CrossRef]
Hunter, R. J. , 2001, Foundations of Colloid Science, Oxford University Press, Oxford, UK.
Soles, C. L. , Chang, F. T. , Gidley, D. W. , and Yee, A. F. , 2000, “ Contributions of the Nanovoid Structure to the Kinetics of Moisture Transport in Epoxy Resins,” J. Polym. Sci., Part B, 38(5), pp. 776–791. [CrossRef]
Chen, L. , Chen, C. F. , and Lee, J. H. , 2012, “ On the Modeling of Surface Tension and Its Applications by the Generalized Interpolation Material Point Method,” CMES, 86(3), pp. 199–224.
Yu, Y. , Sun, D. , Wu, K. , Xu, Y. , Chen, H. , Zhang, X. , and Qiu, L. , 2011, “ CFD Study on Mean Flow Engine for Wind Power Exploitation,” Energy Convers. Manage., 52(6), pp. 2355–2359. [CrossRef]
Sun, D. , Xu, Y. , Chen, H. , Wu, K. , Liu, K. , and Yu, Y. , 2012, “ A Mean Flow Acoustic Engine Capable of Wind Energy Harvesting,” Energy Convers. Manage., 63, pp. 101–105. [CrossRef]
Sakamaki, R. , Sum, A. K. , Narumi, T. , and Yasuoka, K. , 2011, “ Molecular Dynamics Simulations of Vapor/Liquid Coexistence Using the Nonpolarizable Water Models,” J. Chem. Phys., 134(12), p. 124708. [CrossRef] [PubMed]
Guo, T. F. , and Cheng, L. , 2002, “ Modeling Vapor Pressure Effects on Void Rupture and Crack Growth Resistance,” Acta Mater., 50(13), pp. 3487–3500. [CrossRef]
Chew, H. B. , Guo, T. F. , and Cheng, L. , 2004, “ Vapor Pressure and Residual Stress Effects on the Toughness of Polymeric Adhesive Joints,” Eng. Fract. Mech., 71(16–17), pp. 2435–2448. [CrossRef]
Chong, C. W. , Guo, T. F. , and Cheng, L. , 2004, “ Vapor Pressure Assisted Crack Growth at Interfaces Under Mixed Mode Loading,” Comput. Mater. Sci., 30(3–4), pp. 425–432. [CrossRef]
Chew, H. B. , Guo, T. F. , and Cheng, L. , 2005, “ Vapor Pressure and Residual Stress Effects on Failure of an Adhesive Film,” Int. J. Solids Struct., 42(16–17), pp. 4795–4810. [CrossRef]
Guo, F. L. , He, B. B. , and Niu, X. , 2015, “ Analysis of Vapor Pressure and Void Volume Fraction Evolution in Porous Polymers: A Micromechanics Approach,” Int. J. Solids Struct., 66, pp. 133–139. [CrossRef]
Guo, F. L. , Niu, X. , and He, B. B. , 2015, “ An Analytical Study on Steam-Driven Delamination and Stability of Delamination Growth in Electronic Packages,” Eng. Fract. Mech., 144, pp. 89–100. [CrossRef]
Suhir, E. , 1997, “ Failure Criterion for Moisture-Sensitive Plastic Packages of Integrated Circuit (IC) Devices: Application of Von Kármán's Equations With Consideration of Thermoelastic Strains,” Int. J. Solids Struct., 34(23), pp. 2991–3019. [CrossRef]


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Fig. 1

Cohesive failure of polymeric thin film induced by high water vapor pressure during soldering reflow process of a microelectronic package: (a) a side view and (b) a top-down view. Adapted from Ref. [28].

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Fig. 2

(a) Strain-temperature responses and (b) the microscopy of the damage of moisture-saturated graphite/polyimidecomposites during thermal spikes. Adapted from Ref. [29] with permission of SAGE Publications, Ltd.

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Fig. 3

A schematic water vapor pressure problem representing a cavity between a moisture saturated molding compound and water-impermeable lead frame. A step change in temperature is assumed to simulate the reflow soldering process.

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Fig. 4

Water vapor pressure results based on Shirley's solutions using Eqs. (18) and (19)

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Fig. 5

Schematic 1D crack-like cavity vapor pressure problem

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Fig. 6

Results of Chen's solution in Eq. (19) matches Shirley's in Eq. (10) with RH0 = 85% and ΔHs*=−1.5 kJ/mol and returns to Hui's solution with RH0 = 100% and ΔHs*=0 kJ/mol so that kH = constant. Results are based on w = 0.2 cm, l = 0.001 cm.

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Fig. 7

Capping effect of RH0 on cavity pressure under different values of α. Material constant ΔHs*=−1.5 kJ/mol.

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Fig. 8

Normalized cavity pressure versus normalized time under three different isosteric heat of sorption (ΔHs*) with RH0 = 85% and α = 100. Capping effect exists for ΔHs*<0 while unphysical pressure occurs for ΔHs*=3.0 kJ/mol.

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Fig. 9

Maximum cavity pressure against different values of ΔHs* at different temperatures

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Fig. 10

Comparison of Chen's solution and convection-only model for the 1D problem in Fig. 3

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Fig. 11

Schematic of convection-diffusion model (Reprinted with permission from Chen et al. [44]. Copyright 2015 by Wiley.)

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Fig. 12

A comparison of the three models. Material properties: D(T) = 2.86 × 10−8e−28,268/RT m2/s for both CD model and diffusion-only model; κ is 6.9 × 10−21 m2 for CD model and 1.1 × 10−20 m2 for convection-only model. Porosity is 5% based on Ref. [44].

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Fig. 13

Schematic of different water sorption isotherms

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Fig. 14

Three distinct sorption isotherms based on Henry's law and the Ferro Fontana model at (a) T = 85 °C and (b) T = 215 °C. All the isotherms assume Qst= 38.7 kJ/mol.

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Fig. 15

Results of moisture content and pressure for different isotherms (RH0 = 100%)

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Fig. 16

Representative elementary volume describing two distinct states of moisture in the microvoids of moisture permeable materials (Reprinted with permission from Fan et al. [39]. Copyright 2005 by ASME).

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Fig. 17

A comparison between the two-phased Fan's model and Chen's unified solution with w = 0.2 cm and l = 0.01 cm. ϕeq = 5% for Fan's model in Eq. (48).

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Fig. 18

A comparison of the cavity pressure for w → ∞ based on Eq. (51) in Ref. [46], Eq. (48) in Ref. [39], and Eq. (25) in Ref.[42]

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Fig. 19

Effects of pore radius to the saturated water vapor pressure and density: (a) σ = σrm N/m and (b) σ(Τ) = 0.072 − 0.0002 (Τ − 293.15) N/m

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Fig. 20

Cavity pressure based on the modified micromechanics-based model for different radius of microvoids with T1 = 215 °C: (a) σ = 0.072 N/m and (b) σ = σ(Τ ) based on Eq. (57)



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