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Seungmin Cho

Bongtae HanMem. ASME

CALCE Electronic Products and Systems CenterDepartment of Mechanical Engineering

University of MarylandCollege Park, MD 20742

Jinwon JooDepartment of Mechanical Engineering

Chungbuk National UniversityCheongju Chungbuk, Korea

Temperature DependentDeformation Analysis of CeramicBall Grid Array Package AssemblyUnder Accelerated ThermalCycling ConditionA robust scheme of moire´ interferometry for real-time observation is employed to stuthe temperature dependent thermo-mechanical behavior of a ceramic ball grid apackage assembly. The scheme is implemented with a convection-type environchamber that provides the rapid temperature control required in accelerated thecycling. Thermal deformations are documented at various temperatures. Thermal-hdependent analyses of global and local deformations are presented. A significant near global behavior is documented due to complete stress relaxation at the maxtemperature. An analysis of solder interconnections reveals that inelastic deformaccumulates at the bottom eutectic solder fillet only at high temperatures.@DOI: 10.1115/1.1646426#

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IntroductionDesign and testing of microelectronics devices usually invo

stress analysis and fatigue life prediction. Finite element anal~FEA! has been used extensively to estimate stresses and stramicroelectronics packages. Although almost any kind of micelectronics device can be modeled, simplifications and uncertties are inevitable due to the complex loading and boundary cditions @1–3#. The models and the results usually requverification by other means before they are used for fatigueprediction. Accordingly, advanced experimental techniques arhigh demand to provide accurate solutions for deformation stuof microelectronics devices.

Moiré interferometry is a full-field optical method that has higdisplacement, strain and spatial resolution. In recent years,method has been used extensively in the electronics industrdetermine thermal strains—strains caused by temperachanges—in microelectronics devices@4–20#. In their originalcontribution, Guo et al. developed a new grating replication pcedure for specimens with complex geometry@7#. Later they em-ployed the procedure to document steady-state thermal defotions of a ceramic ball grid array~CBGA! package assembly@8#.

In the technique used in Refs.@7# and @8#, called bithermalloading @21#, the specimen grating was applied at an elevatemperature, and it was allowed to cool to room temperaturefore it was observed by moire´ interferometry. Thus, the deformation incurred by the temperature increment was locked intograting and recorded at room temperature.

In the applications shown in Ref.@8#, a temperature incremenwas260°C. Although they revealed the effect of local and globcoefficient of thermal expansion~CTE! mismatch, the results represented thermal deformations caused by cooling the assefrom 82°C to 22°C; the results did not represent the deformatiduring an actual thermal cycle. More importantly, time-dependdeformations were not included in the results. Later the bitherloading approach was extended to document inelastic defortions of solder column interconnections, accumulated during tmal cycles@15#. Yet, a complete deformation history over a the

Contributed by the Electronic and Photonic Packaging Division for publicationthe JOURNAL OF ELECTRONIC PACKAGING. Manuscript received July 2002. Associate Editor: Y. C. Lee.

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mal cycle was not clearly understood and the critical deformatmodes at the temperature extremes were not realized.

The objective of this paper is to study the temperature and tdependent thermo-mechanical behavior of a CBGA packagesembly subjected to an accelerated thermal cycling~ATC! condi-tion. A robust scheme of moire´ interferometry is implemented toachieve the goal. The experimental apparatus is based on atable moiréinterferometer and a computer controlled convectioven. Vibrations caused by the environmental chamber arecumvented by rigid links that connect the specimen to the mo´interferometer. Displacement fields are documented whilechamber is being operated. The results corroborate the trefound in earlier observations@8,10,15#, but they reveal the behavior in greater detail. Measurement of the real-time response ofassembly provides the most authentic data.

Real-Time Moiré Interferometry for ATC ConditionMoiré interferometry can map the deformations of advanc

engineering structures with extremely high resolution. The dare output as contour maps of in-plane displacements. A detadescription of moire´ interferometry can be found in Ref.@22#.

In this method, a high-frequency cross-line grating on the spmen, initially of frequencyf s , deforms together with the specmen. A pair of parallel~collimated! beams of laser light strike thespecimen and a portion is diffracted back, nominally perpendilar to the specimen, in the11 and21 diffraction order of thespecimen grating. Since the specimen grating is deformedresult of the applied loads, these diffracted beams are no loncollimated. Instead, they are beams with warped wavefrowhere the warpages are related to the deformation of the graThese two coherent beams interfere in the image plane ofcamera lens, producing an interference pattern of dark and lbands, which is the moire´ pattern.

These moire´ patterns are contour maps of theU andV displace-ment fields, i.e., the displacements in thex and y directions, re-spectively, of each point in the specimen grating. The relatiships, for everyx,y point in the field of view, are

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In routine practice of moire´ interferometry, f s51200 lines/mm~30,480 lines/in.!. In the fringe patterns, the contour interval1/2 f s , which is 0.417mm displacement per fringe order.

When deformation measurements are required during an acerated thermal cycling, it is necessary to implement moire´ inter-ferometry with an environmental chamber that provides convtion heating and cooling. The air inside the chamber mustcirculated vigorously to achieve the heating/cooling rate requifor a typical ATC condition. Consequently, the environmenchamber experiences vibrations, which are normally transmito the specimen. Moire´ interferometry measures tiny displacements and those inadvertent vibrations can cause the moire´ fringesto dance at the vibration frequency.

The real-time moire´ setup to circumvent the vibration problemis illustrated in Fig. 1@23#. Two major components are a portabmoiré interferometer~PEMI II, Photomechanics Inc.! and a com-puter controlled environmental chamber~EC1A, Sun Systems!.The specimen holder is not attached to the chamber. Instead,connected directly to the interferometer and it is essentially ffrom the environmental chamber. Furthermore, the interferomand the chamber are mounted on separate tables and thuinterferometer is mechanically isolated from the chamber. Wthis arrangement, moire´ fringes can be recorded while the chamber is being operated. Further details of the rod assembly andtemperature control can be found in Ref.@23#.

Deformation Analysis of CBGA Package AssemblyCeramic area array package technology allows attachmen

high I/O multilayer ceramic modules directly to an industry stadard epoxy/glass printed circuit board~PCB! @24,25#. The tech-nology has been used successfully for various flip chip applitions. The solder interconnection of the package assembly conof a high melting point solder ball~90%Pb/10%Sn! and a eutecticsolder fillet ~63%Pb/37%Sn!. The high melting point solder baldoes not reflow during assembly process, which provides a csistent and reproducible standoff between the ceramic packand the PCB.

The dominant mode of deformation of the solder interconntion is shear deformation, which is caused by the CTE mismaof the ceramic module and the PCB@8,26#. Consequently, theshear strains at the interconnection increase as the distancethe neutral point~DNP! increases.

The assembly used in the experiment was a 25 mm CBpackage with 361 I/O’s (19319 solder interconnection array! as-

Fig. 1 Schematic illustration of real-time moire ´ setup for ATCcondition

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sembled to an FR-4 PCB. A specimen with a strip array configration was prepared from the assembly, containing five cenrows of solder interconnection, as illustrated schematically in F2(a). The diameter of the solder ball was 0.89 mm. After thinterconnection was formed, the actual separation from the paage to the PCB was 0.97 mm. The pitch of the copper pads onPCB was 1.27 mm.

The cross section was ground flat by a 600 grit abrasive paThe drag method@8,17# was utilized to replicate a specimen graing using a room temperature curing epoxy~Tra-100, Tracon!.The initial null fields obtained at room temperature are shownFig. 2(b). The clean edges of the specimen grating achievedthe drag method are evident.

The specimen was subjected to a thermal cycle and the demations were documented as a function of temperature. Fig

Fig. 2 „a… Schematic diagram of CBGA package assembly withrelevant dimensions, „b… initial null fields obtained at room tem-perature and „c… temperature profile used in the experiment

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2(c) depicts the temperature profile used in the thermal cycle. Theating/cooling rate was 5°C/min. and the maximum and mmum temperatures were 100°C and220°C, respectively. To en-sure a uniform temperature distribution, the specimen was kepeach target temperate for five minutes before measurement.cording U and V moiré patterns was done within a fraction ominute and its effect was negligible.

Nonlinear Bending. Representative vertical displacemefields of the assembly are shown in Fig. 3. Relative vertical dplacements with respect to the axis of symmetry~referred to asbending displacements! along the middle line of the ceramic module were determined by Eq.~1! using the fringe orders,Ny , as-signed in the fringe patterns. The results obtained from the rihalf of the ceramic module are plotted Fig. 4. When the assemwas heated to 55°C~B!, the PCB expanded more than the moduwhich produced an upward bending of the module~ø!. The bend-ing displacement increased as the temperature increased to~C!. However, the bending displacement decreased when theperature further increased to 100°C. During the dwell period100°C, the bending displacement decreased to nearly zero. Wthe assembly was cooled to 55°C~E!, the module bent downward~ù!. The magnitude of downward bending increased continuouthroughout the entire cooling process.

Fig. 3 Representative V field fringe patterns of the CBGApackage assembly

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This significant nonlinear behavior is described schematicain Fig. 5. The initial heating produced the upward bending of tassembly, consistent with the CTE mismatch between the modand the PCB, and the coupling through the solder interconntions. At temperatures higher than 75°C, creep of the soldercame a dominant effect. As a result, deformation of the moddecreased while the temperature increased. At 100°C, thepling between the module and the PCB diminished until thesembly was in a nearly stress-free state. The solder intercontion experienced large inelastic deformations. During cooling,CTE mismatch produced downward bending of the assemsince the reference temperature of zero bending displacemchanged from room temperature to 100°C. There was virtually

Fig. 4 Relative vertical „or bending … displacements along themiddle line of the ceramic module obtained from the moire ´patterns

Fig. 5 Schematic illustration of the deformation of the CBGApackage assembly during the thermal cycle

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stress relaxation during cooling below 75°C. The magnitudethe bending displacement increased as the temperature decre

Deformation Mechanism of Two-Phase Solder Interconnec-tion. TheU ~or x) displacement fields corresponding to thoseFig. 3 are shown in Fig. 6. The inserts show a magnified viewthe rightmost solder interconnection. This solder interconnectwas analyzed to investigate the effect of the two solder materin the interconnection. It is important to note that the reflow prcess produced a thin eutectic solder bench between the soldeand the copper pad while there was no gap between the solderand the ceramic module. Consequently, the shear deformatiothe top eutectic fillet was constrained by the solder ball but

Fig. 6 U field fringe patterns corresponding to those of Fig. 3

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bottom eutectic fillet was free to deform in shear. A detailed dformation history of the bottom fillet is described below.

The development of inelastic strains during the thermal cyclexplained in Fig. 7, where the fringe patterns for the rightmsolder interconnection are shown. The corresponding horizodisplacements along the vertical centerlines are plotted for varstages in the thermal cycle.

As the temperature increased, a relative horizontal displacembetween the top and the bottom of the solder interconnectionproduced by the CTE mismatch between the module and the PThe relative displacement was nearly linear over the height ofsolder interconnection at the initial stage of heating~B!, whichindicated a nearly uniform shear strain in the interconnection.the temperature increased, however, the slope of the displaceat the high melting solder ball became distinctively different frothat at the bottom eutectic solder fillet. At the elevated tempetures, the shear strain of the bottom fillet became much largerthat of the solder ball. The eutectic solder had a lower meltpoint compared to the high melting solder, and thus it hadsmaller modulus and a higher creep rate at elevated tempera@15,26#. As a result, the shear strain of the bottom fillet increasat a much higher rate than that of the solder ball.

The most striking results were observed during cooling. Whthe assembly was cooled to 55°C~E! from the maximum temperature, the relative horizontal displacement~or average shear strain!of the high melting temperature solder ball was nearly identicathe deformation observed at the same temperature during he~B!. However, the shear strain in the bottom fillet was muhigher because the creep strain produced at the maximumperature was not recovered during cooling. When the assemwas cooled down to room temperature, this became more evidThe shear strain in the ball recovered completely but the shstrain in the bottom fillet did not. As the assembly was cooledcryogenic temperatures, the solder ball exhibited the opporelative horizontal displacement as expected, but the directiothe relative horizontal displacement in the bottom fillet remainunchanged. As a result, the sign of the shear strain of the soball became opposite to that of the bottom fillet.

It is worth noting that the fringes in the bottom fillet were todense to be resolved except for the initial stage of the thercycle. However, the relative horizontal displacement betweentop and the bottom of the fillet was determined readily usingwell-defined fringe orders at the solder ball and the coppersince the fringe orders at any point were unique, independenthe path of the fringe count used to reach the point@22#.

The displacement plots in Fig. 7 and the correspondingV dis-placement plots were analyzed to quantify the average sstrains in the bottom fillet using the following displacement-strarelationship

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fillet increased rapidly at high temperatures. Its maximum vawas'22.4% at 100°C, which was nearly six times as largethe shear strain in the solder ball. While the assembly was coto room temperature~F!, the shear strain magnitude decreased amuch slower rate. The permanent shear strain in the bottom fiwas'21.5% after the heating cycle. It is interesting to note ththe shear strain in the bottom fillet remained virtually unchangwhile the assembly was cooled from room to cryogenic tempetures.

DiscussionsIt was observed that the shear strain in the bottom fillet

mained nearly unchanged while cooling it from room to cryogetemperatures. At high temperatures, the modulus of eutectic so(Eeu) is much smaller than that of high melting solder (Ehm); at100°C, Eeu52.3 Gpa andEhm54.5 Gpa @26#. At low tempera-

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Fig. 7 U field fringe patterns of the rightmost solder interconnection and the corre-sponding horizontal displacements determined along the vertical centerline

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tures, however,Eeu becomes much larger thanEhm; at 0°C, Eeu516.5 Gpa andEhm58.5 Gpa@26#. This temperature dependenstiffness of eutectic solder was attributed to the deformationhavior of the bottom fillet at low temperatures, i.e., the bottoeutectic fillet deformed more than the solder ball at high tempetures, but less at low temperatures.

When an acceleration parameter is sought from ATC test resto predict cycles to failure in the actual operating condition, omust consider the cumulative damage from each cycle~inelasticstrain accumulation! as well as the maximum stress~crack propa-gation! that occurs at each cycle. Among many models availain the literature, the most widely used fatigue prediction modfor solder interconnections are based on the modified CofMansion’s relationship@27–28# and the unified creep deformatioapproach@1,2#.

In both approaches, damage caused by inelastic deformatiothe main parameter used to predict cycles to failure. The damis estimated from temperature change in a thermal cycle (DT) andgeometric parameters for the first model and plastic work calated from an FEM analysis for the second model. However, th

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parameters are not directly applicable to the solder deformatof the CBGA package assembly observed in this study. Theelastic deformation in the bottom fillet is governed only by tmaximum temperature; i.e., the maximum temperature is mcritical to the damage than the minimum temperature. Furthmore, due to complete stress relaxation at the maximum tempture, the maximum elastic stress occurs at the minimum tempture and its magnitude increases as the minimum temperaincreases. Consequently, the models also do not truly accounthe effect of the minimum temperature in the ATC cycle althoucrack propagation is considered in the second model.

The above argument is valid only when that the stressesduced by the CTE mismatch relax completely at the maximtemperature, i.e., stress-free state at the maximum temperaFor plastic ball grid array~PBGA! package assemblies, howevethe stresses are much lower and complete relaxation ofstresses does not always occur during an ATC test.

Figure 9 shows a preliminary result obtained from a flip-chPBGA package assembly. The cross section of the assemb

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shown in Fig. 9(a). It is important to note that the solder composition of the interconnection is identical to that of the CBGpackage assembly, i.e., high melting point solder balls with eutic fillets. The fringe patterns in Fig. 9(b) showU andV displace-ment fields of the right half of the assembly at 125°C. The pterns report very significant bending of the assembly, which wcaused by the low modulus and high CTE of the organic subst@29#. The maximum bending displacement (dmax) of the substrateand the PCB increased almost linearly as the temperaturecreased. The maximum displacement was about 25mm at 125°C.

The deformations were monitored continuously while thesembly was kept at 125°C for 15 minutes. The bending defortion remained unchanged. Stress relaxation did not occur atmaximum temperature because of the low level of stress inassembly, which otherwise would have been seen as a decreathe bending displacements during the dwell period. For the sreason, the damage concentration at the eutectic fillets wasobserved. The result was entirely different from that of the CBGpackage assembly and a stress-free temperature should bsumed carefully for the analysis of flip chip PBGA packaassemblies.

ConclusionsThermo-mechanical behavior of a CBGA package assem

was studied using moire´ interferometry. A robust scheme of moir´interferometry was implemented to document the whole-field dplacement patterns of the assembly during an accelerated thecycling condition. The results revealed a significant nonlinear gbal behavior due to complete relaxation of stresses. The lanalysis of the solder interconnection proceeded and the reindicated that the inelastic deformation was accumulated onlhigh temperatures. The results also implied that the fatigue cpropagation would be dominant at low temperatures becauslarger stresses in the assembly.

AcknowledgmentsThis work was supported by the CALCE Electronic Produ

and Systems Center of the University of Maryland. Their suppis gratefully acknowledged. The authors also wish to thank DrK. Lim of Photomechanics Inc., for lending the authors the PEII unit used in the study.

Fig. 8 Average shear strain history of the bottom eutectic fillet

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Fig. 9 „a… Schematic diagram of FC-PBGA package assemblyand „b… U and V field fringe patterns recorded at 125°C

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