modeling thermally induced viscoplastic deformation and low cycle fatigue of cbga solder joints in a...

280 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING, AND MANUFACTURING TECHNOLOGY—PART A, VOL. 20, NO. 3, SEPTEMBER 1997

Modeling Thermally Induced ViscoplasticDeformation and Low Cycle Fatigue of CBGA

Solder Joints in a Surface Mount PackageBor Zen Hong and Lloyd G. Burrell

Abstract—A nonlinear finite element model was used to analyzethe thermally induced viscoplastic deformation and low cyclefatigue behavior of the lead-tin (Pb-Sn) solder joints in a 32 mmceramic ball grid array (CBGA) surface mount package. Theeffects of the cyclic frequency, hold (dwell) time, and temperatureramp rate on the response of the viscoplastic (creep and plastic)deformation for the CBGA solder joints were studied by applyingfour different low cycle thermal fatigue loads to the package.The modeling results show that the maximum viscoplastic strainsoccur in and around the edge CBGA solder joint. The cycliccreep strain (ratchetting) is very significant and dominates theconstituent of the accumulated viscoplastic strain. The equivalentplastic strain increases with the increase of cyclic frequency andramp rate, and decreases as the hold time increases. However,the equivalent creep strain decreases with the increase of cyclicfrequency and ramp rate, but increases as the hold time increases.In the solder joint, the Pb37-Sn63 solder paste has approximately2� larger equivalent plastic strains, and 10� larger equivalentcreep strains than that in the Pb90-Sn10 solder ball duringthermal cycling.

Index Terms—Ceramic ball grid array, creep, finite elementmodel, low cycle fatigue, plasticity, ratchetting, solder joints,surface mount package, thermal stress, viscoplastic deformation.

I. INTRODUCTION

T HE PAST five years have witnessed spectacular growthin high-density ceramic-based surface mount array inter-

connections technology. During this period, both the sophis-tication and the variety of ceramic ball grid array (CBGA)packages in development and production have increased cre-markably. The CBGA package was developed to serve asa mechanical and an electrical connection for attaching theceramic substrate to the printed circuit board (PCB) or cardusing lead-tin (Pb-Sn) solder joints [1]–[5]. As in many otherelectronic packages, the thermally induced stresses and defor-mation, resulting from the temperature changes and thermome-chanical mismatch, are the major concerns for the reliabilityand integrity of the CBGA packages.

When the CBGA package is subjected to a cyclic tempera-ture load, the ambient temperature may approach or exceedhalf the melting temperatures of the Pb-Sn solder alloysin package. Such changes in temperature can cause cyclicviscoplastic deformation and lead to low cycle thermal fatigue

Manuscript received August 27, 1996; revised April 9, 1997.The authors are with IBM Microelectronics Division, Hopewell Junction,

NY 12533 USA.Publisher Item Identifier S 1070-9886(97)06042-3.

failure in the solder joints. The literature recognizes that tofully understand the cyclic viscoplastic behavior and associ-ated thermal fatigue failure phenomena of the solder joints,appropriate modeling and tools are needed [6]–[17].

Most recent modeling approaches based on the finite ele-ment method have been widely used for studying the thermalstress and fatigue problems of the solder joints in variouselectronic packages. The major focus has been the com-plex characteristics of material nonlinearity (time/temperaturedependent behavior) with applications to the material selec-tion and structural design optimization of the solder joints[13]–[17].

In this paper, a nonlinear finite element model is used tostudy the thermally induced viscoplastic (creep and plastic)deformation of the solder joints in a CBGA package undervarious low cycle fatigue loads. The combined effects of thecyclic frequency, hold (dwell) time and temperature ramp rateare considered in this study. Detailed finite element modeling,results and discussions will be described as follows.

II. FINITE ELEMENT MODELING

In this study, a hermetic cavity-down, wire bond CBGAsurface mount package is modeled. The schematic of the crosssection for this surface mount package is shown in Fig. 1.

A. Model Descriptions

In the model example, a 32 mm square alumina ceramicsubstrate is connected to a 156107 mm FR-4 card with atotal of 256 CBGA Pb-Sn solder joints. These solder jointshave a dimension of 0.89 mm diameter and 0.94 mm height,and are placed in three rows on an I/O pitch of 1.27 mmaround the perimeter of the substrate. The CBGA solder jointconsists of a 0.89 mm Pb90-Sn10 solder ball surrounded bythe eutectic Pb37-Sn63 solder paste at both ends.

In the cavity of the substrate, the back (nondevice side)of a 13 mm square silicon chip is bonded to the substrateby a thin layer of 0.1 mm polymeric adhesive. The electricalconnections are made by attaching the 0.025 mm gold-wirefrom the device side of the chip to the substrate. Detailedmaterials and properties of the CBGA package are listed inTable I.

Taking advantage of symmetry, only one half of the crosssection in the longitudinal direction of the surface mountpackage is modeled. The finite element mesh was created using

1070–9886/97$10.00 1997 IEEE

HONG AND BURRELL: MODELING THERMALLY INDUCED VISCOPLASTIC DEFORMATION AND LOW CYCLE FATIGUE 281

Fig. 1. Schematic of a ceramic ball grid array (CBGA) package.

TABLE IMATERIAL PROPERTIES OFCBGA PACKAGE

the I-DEAS Program [18]. The mesh, as shown in Fig. 2,is made of three node linear, plane stress, triangular elementswith a total of 1979 elements and 1249 nodes. Convergencestudies were performed in I-DEAS to ensure that an optimalnumber of elements was suitably used and that there were no

Fig. 2. Finite element model of the CBGA package as shown in Fig. 1.

concerns with strain locking in regions of high strain gradients.The final mesh, as shown in Fig. 2, was obtained after fouriterations of the use of adaptive mesh procedures in I-DEAS.On the other hand, the use of plane stress assumption in thisstudy has the reason to accommodate the specific miniatureand complicated geometry of the solder joint based on thedimension of its diameter. It is noted that the strain responsein other components, such as substrate and card, should bejustified with the three-dimensional (3-D) results. The actual3-D results are bound between the plane stress and plane strainmodels [17].

B. Low Cycle Thermal Fatigue Loads

Engelmaier [7] described the cyclic thermal fatigue test andfield conditions for the electronic packages as recommendedby the Surface Mount Council as follows.

1) The temperature ramp rate is less than or equal to 30K/min.

2) The minimum hold time is 15 min.3) The cyclic frequency is less than or equal to 24 cycles

per day (cpd) or one cycle per hour (cph) for theaccelerated thermal cycling (ATC) test, and is less thanor equal to 100 cpd (4.2 cph) for the worst cases inrealistic field environment, respectively.

Base on the above information, four different conditionsof low cycle thermal fatigue loading were applied to themodeled package. Fig. 3 shows a typical temperature cycleprofile used in this study, while the four different conditions


Fig. 3. Temperature cycles of�55 to+125 �C. The symbol� denotes theend of each cycle.

of low cycle thermal fatigue load are specified in Table II.These low cycle thermal fatigue loading conditions were usedfor numerically studying the combined effects of the cyclicfrequency, hold (dwell) time, and temperature ramp rate onthe response of the viscoplastic (creep and plastic) strains ofthe CBGA solder joints.

C. Constitutive Behavior of Materials

In this work, metallic and alloy materials are assumed tobe elastic-plastic or elastic-viscoplastic, and the nonmetal-lic materials are linearly elastic. A constitutive theory ofthermoviscoplasticity based on classical creep and plasticityconcept was specially used in modeling the thermally induceddeformation behavior of the Pb-Sn solder joints. In the theory,the total strain is assumed to be the sum of the elastic,plastic, creep, and the thermal strains. The Garofalo hyperbolicsine law was applied to model the creep behavior, whilethe Prandtl–Reuss equation was used for rate-independentplastic deformation. The detailed description of the theory waspublished in Hong and Burrell [14]. The material properties ofthe surface mount package components are listed in Table I.All these properties were obtained from Hong and Burrell [14],and Pecht [19], except that the properties of eutectic Pb37-Sn63 solder was available in Pan [15]. It should be noted thatthe material constants for the creep law of Pb37-Sn63 solderwere modified to fit the original form of Garofalo equationwithout the effect of grain size.

D. Numerical Simulations

In the simulations, a total of 5 cycles for the various thermalfatigue loads as shown in Fig. 3 and Table II were applied tothe model. A stress-free temperature of 25C was assumedas the initial condition. The temperature at each specific timestep was assumed to be uniform across the whole model. Themodeled problems were solved by using a nonlinear finiteelement program, ABAQUS [20]. Numerical simulationswere carried out in an IBM RISC/6000 computer system.The computing times for simulating five cycles of thermalfatigue load were typically 2–5 h for the four studied cases.A preferred maximum time integration step of 10 s wasdetermined for ensuring the solution accuracy.

TABLE IIVARIOUS TEMPERATURE CYCLE CONDITIONS

III. RESULTS AND DISCUSSIONS

For convenience, the equivalent plastic strain, andthe equivalent creep strain, as defined in ABAQUS[20] are used for reporting the analysis results. The analysisresults show that the peak values of the equivalent plasticstrain and the equivalent creep strain occur in and around theedge CBGA solder joint during temperature cycling. This isconsistent with the results of other test and modeling studiesof CBGA packages [12]–[13]. The edge CBGA is locatedat the right corner of the package, as shown in Fig. 2. Twofinite elements are referred to describe the histories of themaximum viscoplastic strains in the edge CBGA solder joint.The element numbered 51 075 is in the Pb37-Sn63 solder pasteand located at the upper-right (northeastern) corner near to theinterface between the solder paste and the molybdenum pad.The element numbered 46 125 is in the Pb90-Sn10 solder balland positioned at the north pole near to the interface betweenthe upper solder paste and the solder ball.

Fig. 4(a) and (b) give the histories of maximum andfor the edge CBGA solder joint in the modeled surface mountpackage subjected to a total of five cycles of cyclic temperatureload of 55 C/ 125 C, with a frequency of 1 cph (cycleper hour), a 15-min hold time, and a temperature ramp rateof 12 C/min. We find that the values of in general, aregreater than that of with an exception at the very beginningof the temperature cycle. The results for Pb37-Sn63 solderpaste are shown in Fig. 4(a), and Pb90-Sn10 solder ball inFig. 4(b), respectively. Both and are accumulated withthe increasing numbers of temperature cycle. Thedevelopsmore significantly during the ramping session of either heat-up or cool-down, and stays as a plateau during the periodof the hold time. Inverse development is observed in thehistories. The difference between the accumulatedandgrows with the increase of temperature cycles.

In Fig. 5, a 3-cph frequency, a hold time of 5 min, anda 36 C/min ramp rate was simulated. When the cyclic fre-quency was increased to be 3 cph, we find that the strainresponse in the Pb90-Sn10 solder paste is different fromthat as shown in Fig. 4(b). The development of thetends to catch up and exceed that of as the number oftemperature increases as given in Fig. 5(b). This indicates that


(a) (b)

Fig. 4. (a) Histories of maximum equivalent creep and plastic strains of Pb37-Sn63 paste in the edge CBGA solder joint subjected to five cycles of�55�C/+125 �C with a frequency of 1 cycle per hour (cph) and 15 min hold time. The equivalent creep strain predominates the total inelastic deformationand (b) similar to Fig. 4(a), except that of Pb90-Sn10 ball is plotted.

(a) (b)

Fig. 5. (a) Histories of maximum equivalent creep and plastic strains of Pb37-Sn63 paste in the edge CBGA solder joint subjected to five cycles of�55 �C/+125 �C with a frequency of three cycles per hour (cph) and 5 min hold time. (b) Similar to Fig. 5(a), except that of Pb90-Sn10 ball isplotted. The almost equally competing deformation mechanism of the creep and plasticity is presented. The plasticity effect is more significant thanthecreep as the number of temperature cycle increases.

the increase of the loading rate by raising the cyclic frequencyand temperature ramp rate results in a fast-load response inthe modeled CBGA solder joint, which will mitigate the creepstrain and amplify the plastic strain in return.

Figs. 6 and 7 show the combined effects of the cyclic fre-quency, hold time and ramp rate on the maximum equivalentcreep and plastic strain response in the CBGA solder joint.The results for the Pb37-Sn63 solder paste is plotted in Fig. 6,


(a) (b)

Fig. 6. (a) The equivalent plastic strain is a function of temperature cycle for Pb37-Sn63 solder paste in the edge CBGA solder joint under five cyclesof �55 �C/+125 �C load as given in Fig. 3 and Table II. The accumulated plastic strain increases as the frequency increases, but decreases as thehold time increases. (b) Similar to Fig. 6(a), except that the quivalent creep strain is plotted. The accumulated creep strain decreases as the frequencyincreases, but increases as the hold time increases.

(a) (b)

Fig. 7. (a) Similar to Fig. 6(a), except that of the Pb90-Sn10 ball is plotted. (b) Similar to Fig. 6(b), except that of the Pb90-Sn10 ball is plotted.

and that for the Pb90-Sn10 solder ball in Fig. 7, respectively.We observe that the equivalent plastic strain increases withthe increase of cycle frequency and ramp rate, and decreasesas the hold time increases. While the equivalent creep straindecreases with the increase of frequency and ramp rate, butincreases as the hold time increases. Both the rate and the

accumulated magnitude of and in the Pb37-Sn63 arelarger than those in the Pb90-Sn10. The Pb37-Sn63 has anaccumulated that is approximately 2 larger, and 10larger, respectively, than those in the Pb90-Sn10. This may bedue to the fact that the Pb90-Sn10 has a stronger creep andfatigue resistance than the Pb37-Sn63 [11].


IV. CONCLUSION

In this paper, a numerical approach using a nonlinear finiteelement method was applied to study the combined effectsof the cyclic frequency, the hold time, and the temperatureramp rate on the viscoplastic (plastic and creep) deformationresponse of the CBGA solder joints in a surface mount packagesubjected to a cyclic temperature load of55 C to 125 C.

1) In the CBGA solder joint, the solders reveal that theequivalent plastic strain increases with an increase offrequency and ramp rate, and decreases as the holdtime increases. While the equivalent creep strain de-creases with an increase of frequency and ramp rate,but increases as the hold time increases.

2) The accumulated viscoplastic (creep and plastic) strainsincrease with the number of temperature cycle. Thecyclic creep strain dominates the constituent of theaccumulated viscoplastic strain. As a result, ratchetting(cyclic creep) behavior is very significant in the CBGAsolder joints.

3) In the edge CBGA solder joint, the equivalent creepstrain is developed approximately 10higher, and theequivalent plastic strain 2 higher, respectively, in thePb37-Sn63 solder paste than that in the Pb90-Sn10solder ball.

ACKNOWLEDGMENT

The authors wish to thank D. Agonafer and J. S. Fitch fortheir encouragement, G. Kromann for comprehensive com-ments and communication during the preparation of the finalmanuscript, and T.-D. Yuan for technical discussions. Finally,our special thanks go to D. Tempest, H. Lasky, and J. E.Heidenreich for management support.

REFERENCES

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[2] R. C. Marrs, B. J. Freyman, and J. A. Martin, “High density BGAtechnology,” inProc. Int. MCM Conf., ISHM, Denver, CO, Apr. 1993,pp. 326–329.

[3] J. Mearig, “An overview of manufacturing BGA technology,” inProc.1994 IEPS Conf., Atlanta, GA, Sept. 1994, pp. 565–569.

[4] J. U. Knickerbocker and M. S. Cole, “Ceramic BGA,”Adv. Packag.,pp. 20–25, Jan./Feb. 1995.

[5] G. Kromann, D. Gerke, and W. Huang, “High-density C4/CBGAinterconnect technology for a CMOS microprocessor,” inProc. IEEE44th ECTC Conf., Washington DC, May 1994, pp. 22–28.

[6] R. T. Howard, “Packaging reliability—How to define and measure it,”IEEE Trans. Comp. Packag., Manufact. Technol., vol. CHMT-5, pp.454–462, Dec. 1982.

[7] W. Englemaier, “Figures of merits tools for surface mount solder jointreliability,” Solder. Surf. Mount Technol., no. 10, p. 18, 1992.

[8] J.-P. M. Clech, J. C. Manock, D. M. Noctor, F. E. Bader, and J. A. Augis,“A comprehensive surface mount reliability model (CSMR) covering

several generations of packaging and assembly technology,” inProc.IEEE 43rd ECTC Conf., Orlando, FL, June 1993, pp. 62–67.

[9] M. Pecht and P. Lall, “Temperature dependence of microelectronicdevice failures,”Qual. Reliab. Eng. Int., vol. 6, pp. 275–284, 1990.

[10] T. J. Stadterman, M. Cushing, B. Hum, A. Malhotra, and M. Pecht,“Transition from statistical-field failure based models to physics-of-failure based models for reliability assessment of electronic packages,”Adv. Electron. Packag., vol. 10-2, pp. 619–625, 1995.

[11] J. S. Huang and R. M. Vargas, “Solder joint reliability—Can soldercreep?,”Solder. Surf. Mount Technol., no. 5, pp. 38–45, 1990.

[12] M. D. Ries, D. R. Banks, D. P. Watson, and K. G. Hoebener, “Attach-ment of solder ball connect (SBC) package to circuit cards,”IBM J. Res.Develop., vol. 37, no. 5, pp. 585–596, Sept. 1993.

[13] J. S. Corbin, “Finite element analysis for solder ball connect structuraldesign optimization,”IBM J. Res. Develop., vol. 37, no. 5, pp. 585–596,Sept. 1993.

[14] B. Z. Hong and L. G. Burrell, “Nonlinear finite element simulation ofthermoviscoplastic deformation of C4 solder joints in high density pack-aging under thermal cycling,”IEEE Trans. Comp., Packag., Manufact.Technol., vol. 18, pp. 585–591, Sept. 1995.

[15] T. Y. Pan, “Thermal cycling induced plastic deformation in solderjoints—Part I: Accumulated deformation in surface mount joints,”Trans.ASME, J. Electron. Packag., vol. 113, pp. 8–15, Mar. 1991.

[16] B. Ozmat, “A nonlinear thermal stress analysis of surface mount solderjoints,” in Proc. IEEE 40th ECTC Conf., Las Vegas, NV, May 1990,pp. 959–972.

[17] J. C. Suhling, R. W. Johnson, J. D. White, K. W. Matthai, R. W. Knight,C. S. Romanczuk, and S. W. Burcham, “Solder joint reliability of surfacemount chip resistors/capacitors on insulated metal substrates,” inProc.IEEE 44th ECTC Conf., Washington DC, May 1994, pp. 465–473.

[18] Structural Dynamics Research Corp., I-DEAS Master Series, V3, Mil-ford, OH, 1995.

[19] M. Pecht, Ed.,Handbook of Electronic Package Design. New York:Marcel Dekker, 1991.

[20] Hibbit, Karlson, and Sorensen, Inc., ABAQUS, V5.4, Providence, RI,1995.

Bor Zen Hong received the Ph.D. degree in me-chanical engineering from Rensselaer PolytechnicInstitute, Troy, NY, in 1989.

Fundamental and applied aspects of computa-tional and experimental mechanics of materials andstructures problems continued to be his researchinterests after joining IBM, East Fishkill, NY. Heis presently with IBM Microelectronics, HopewellJunction, NY, and involved in thermomechanicaldesign and reliability analysis for C4 flip chip,BGA and CGA packages, interconnection material

characterization, and assembly process development. He has contributed toover 30 technical publications in the areas of electronic packaging andcomposites.

Dr. Hong is a member of ASME, IEPS, and SAMPE.

Lloyd G. Burrell received the B.S. and M.S. degrees in mechanical engineer-ing from Polytechnic University, Brooklyn, NY.

He joined IBM in 1983 and is currently an Advisory Engineer in theSemiconductor Research and Development Center, Hopewell Junction, NY,engaged in process development and thermo-mechanical modeling of semi-conductor interconnections. His areas of interest include mechanical charac-terization of advanced electronic materials, and reliability of interconnectionsand solder joints.

Mr. Burrell is a member of ASME.

modeling thermally induced viscoplastic deformation and low cycle fatigue of cbga solder joints in a...

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