measuringintrinsicelasticmodulusofpb/snsolderalloys · young’s modulus (e) values published in...

Measuring intrinsic elastic modulus of Pb/Sn solder alloys

Cemal Basaran *, Jianbin Jiang

UB Electronic Packaging Laboratory, Department of Civil, Structural and Environmental Engineering, University at Buffalo,

SUNY, 212 Ketter Hall, North Campus, Buffalo, NY 14260-4300, USA

Received 13 March 2001; received in revised form 28 February 2002; accepted 15 April 2002

Abstract

Young’s modulus (E) values published in the literature for the eutectic Pb37/Sn63 and near eutectic Pb40/Sn60

solder alloy vary significantly. One reason for this discrepancy is different testing methods for highly rate sensitive

heterogeneous materials, like Pb/Sn alloys, yield different results. In this paper, we study different procedures used to

obtain the elastic modulus; analytically, by single crystal elasticity and experimentally by ultrasonic testing and nano-

indentation. We compare these procedures and propose a procedure for elastic modulus determination. The defor-

mation kinetics of the Pb/Sn solder alloys is discussed at the grain size level. � 2002 Elsevier Science Ltd. All rights

reserved.

1. Introduction

Eutectic and near eutectic Pb/Sn solder alloysare the most commonly used interconnect materi-als in microelectronic packaging. In the micro-electronics industry it is widely accepted thatreliability of a package is assessed by the integrityof solder joints in it. Computational mechanicsis extensively used to simulate thermomechanicalreliability of these solder joints. During the anal-ysis stage elastic modulus is probably one of themost influential material constants as an input. Asmall change in elastic modulus value changes theresults significantly.

It is very well known that, in the literature,Young’s modulus value (E) varies significantly for

eutectic and near eutectic Pb/Sn solder alloys.Intrinsic (time-independent) Young’s modulusvalues of 9–48 GPa have been reported in theliterature (Basaran and Chandaroy, 1998; Das-gupta et al., 2001; Dun, 1975; Frear et al., 1995;Hacke et al., 1997; Knecht and Fox, 1990; Zu-belewicz, 1993; Frear et al., 1994; Harper, 1970;Pecht et al., 1999; Guo et al., 1991; Bonda andNoyan, 1996; Ling and Dasgupta, 2000). In com-putational mechanics analysis, results vary signif-icantly if 9 GPa is used instead of 48 GPa. In thispaper, our goal is to investigate this variation andto come up with a criterion for measuring andselecting Young’s modulus for eutectic and neareutectic Pb/Sn solder alloys. We believe that, to thebest of our knowledge, there is no published re-search in this subject other than the one by Adams(1986).

The study of thermomechanical fatigue failureof the solder joints in electronic packaging is an

Mechanics of Materials 34 (2002) 349–362

www.elsevier.com/locate/mechmat

*Corresponding author. Tel.: +1-716-645-2429; fax: +1-716-

645-3733.

E-mail address: [email protected] (C. Basaran).

0167-6636/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

PII: S0167-6636 (02 )00131-X

mail to: [email protected]

important field for the reliability of the packages.The solders are designed to maintain the me-chanical, electrical and thermal connection be-tween the substrates of the electronic packaging.Once there is any crack initiation or damage in thesolder joint, the whole package is consideredfailed. In microelectronics industry experiencewith field returns show that the failure is morelikely to occur in the solder joint than in the sub-strates under normal use conditions.

The material used as solder for the electronicpackaging is near eutectic 60Sn/40Pb or eutectic63Sn/37Pb solder alloy. Pb/Sn solder alloy is ahighly rate sensitive heterogeneous material with alow melting point (183 �C), hence during service itis operating at high homologous temperature. Pb/Sn solder alloy has good wetting characteristicsand adheres well to copper and nickel. The struc-ture of the alloy is non-homogeneous and deformsheterogeneously. Furthermore the size effect andmicrostructural evolution plays an important rolein the deformation of this alloy (Morris et al.,1994).

Quite a few researchers have developed constit-utive models to simulate the stress–strain responseof the Pb/Sn solder alloys (Adams, 1986; Basaranand Chandaroy, 1998; Basaran and Chandaroy,1997; Basaran and Tang, 2002; Chandaroy andBasaran, 1999; Dasgupta et al., 2001; Dasguptaet al., 1992; Rhode and Swearengen, 1980; Frearet al., 1995; Hacke et al., 1997; Kashyap andMurty, 1981; Knecht and Fox, 1990; Lau et al.,1987; Pan, 1991; Riemer, 1990; Subrahmanyanet al., 1989; Zubelewicz, 1993; Guo et al., 1991;Ling and Dasgupta, 2000; Wong et al., 1997; Tangand Basaran, 2001) and many others. The values ofelastic modulus researchers use in these publica-tions vary between 9 and 48 GPa.

The measurement of elastic modulus is quitecomplicated for highly rate sensitive microstruc-turally evolving materials. In the literature severalmethods have been used to measure the elasticmodulus of eutectic and near eutectic Pb/Sn solderalloys, such as monotonic uniaxial extension,simple shear, initial unloading of a stress-relation,cyclic loading and ultrasonic testing. The resultsof this study indicate that MTS Nano IndenterXP system with continuous stiffness measurement

(CSM) and ultrasonic testing yield results in thevicinity of single crystal elasticity bound theoremvalues. Other techniques, such as uniaxial exten-sion and simple shear, published in the literatureyield elastic modulus values much smaller thanbound theorem values. This research also showsthat voids in microelectronic solder joints cansignificantly influence the observed intrinsic elasticmodulus value.

2. Microstructural characteristics of Pb/Sn solder

alloy

At typical cooling rates used by the microelec-tronics manufacturers, the microstructure of thesolder consists of isolated and successive Pb islandsembedded in the Sn matrix, with classic eutecticmicrostructure. As cast eutectic and near eutecticPb/Sn alloy has a very high surface area per unitvolume and therefore it is a thermodynamicallyunstable material. Microstructure of Pb/Sn alloyevolves into a more coarser or more equiaxed grainlike structure by straining, aging and thermaleffects in order to minimize its surface energy(Morris et al., 1994). Under a microscope, grainswith different size and arbitrary boundary can beobserved. The macromechanical behavior of thesolder is attributed to the behavior of these grains,the local mechanism, in the deformation. The localfeatures include grain boundary sliding, grain ro-tation, void growth and coarsening. The influenceof these local features to the macrobehavior is timedependent and size scale dependent.

Microstructural coarsening occurs throughoutthe life of the solder, and has been found to affectthe damage initiation. There is a grain growthprocess that takes place in Pb/Sn solder alloys dueto two reasons. One is due to temperature andsecond one is due to strain. Callister (1999) statesthat after recrystallization is complete the strain-free grains will continue to grow if the metalspecimen is stored at an elevated temperature. Thisphenomenon is called grain growth. As grains in-crease in size the total boundary area decreases,yielding a reduction in the total energy, this isthe driving force for grain growth. Grain growthoccurs by migration of grain boundaries. Large

350 C. Basaran, J. Jiang / Mechanics of Materials 34 (2002) 349–362

grains grow at the expense of the small ones.Boundary motion is diffusion of atoms from oneside of the boundary to the other side of theboundary. Fig. 1 shows the scanning electron mi-croscope (SEM) images of the solder joint micro-structure before thermal cycling, where averagegrain size is 3.017 lm. Fig. 2 shows the SEM im-ages for the same solder joint after 300 thermalcycles, where the grain size is 5.23 lm. Each ther-mal cycle range varied from 0 to 75 �C with a 42min period after each cycle.

Grain boundary sliding and grain rotation cancause stress concentrations at grain boundary orat triple point junction and a corresponding de-crease of stress in the interior of individual grain.But as time goes on, these stresses will relax, andthe relaxation rate is dependent on its viscosity.These stresses will also cause void nucleation andgrowth.

The mechanism of the void nucleation andgrowth in Pb/Sn solder alloys is still not very wellunderstood (Morris et al., 1994).

The initial material properties of solder dependson manufacturing process and its solidificationrate, thus they vary with the size, location, thermaltreatment, grain size and interface metallurgy ofsolder joint. Solder mechanical properties changeduring service due to microstructural evolutionprocess. Therefore, microstructural evolution pro-cess can contribute to the variation in publishedelastic modulus values.

In practice it is difficult to produce void-freesolder joints. Usually voids, which form duringmanufacturing, are much larger than grain size.Fig. 3 shows Moir�ee interferometry images of a BallGrid Array package. Black circles, the fringelessareas in the middle of the solder joints, are thevoids, where no strain develops. Solder joints inFig. 3 are the ball like figures in the middle row,they are 500 lm in height. Voids in the solder jointare much larger than 3–5 lm grain size (Basaranand Wen, submitted).

3. Single crystal elasticity and bounding theorem

When tension testing is used to determineYoung’s modulus for Pb/Sn, significantly differentresults are obtained for each strain rate of loading,due to time-dependent deformation. Due to its lowmelting point, Pb/Sn solder is at high homologoustemperature (0:65Tm) point even in the roomtemperature. Thereby, uniaxial extension test isdominated by high creep strain even at very lowstress levels. One of the things we noticed in ourliterature survey is that researchers who use uni-axial extension tests to obtain elastic constantalways report a very low value of elastic moduluscompared to others. Therefore, using uniaxialextension test for determining intrinsic (time-independent) Young’s modulus for Pb/Sn alloyis unacceptable. Yet, this process is commonly

Fig. 1. Microstructure prior to thermal cycling, average grain

size d0 ¼ 3:017 lm.

Fig. 2. Microstructure after 300 cycles, average grain size

d300 ¼ 5:23 lm.

C. Basaran, J. Jiang / Mechanics of Materials 34 (2002) 349–362 351

reported in the literature (Westinghouse Defenceand Space center, 1968; Riemer, 1990; Pecht et al.,1999; Guo et al., 1991; Wong et al., 1997; Lau andChen, 1997) and many others.

Pb/Sn solder is a two phases alloy, in order toobtain the bounds of Young’s modulus (E) we willuse the Hashin and Shtrickman (1963) boundingtheorem using single crystal elastic constants forindividual phases and we follow the procedureproposed by Adams (1986). Young’s modulus ofthe individual phase is estimated from singlecrystal elastic constants, which were determinedfrom ultrasonic testing by Hellwege and Landolt-Bornstein (1979), Henkel and Pense, 2002.

The first step is calculating the bound of bulk(k) and shear moduli (l) of pure tin. The elasticstiffness of a single crystal tetragonal is given by

½CSn� ¼

C11 C12 C13 0 0 0C12 C11 C13 0 0 0C13 C13 C33 0 0 00 0 0 C44 0 00 0 0 0 C44 00 0 0 0 0 C66

26666664

37777775

ð1Þ

where Cij is the elastic moduli of the material.Voigt and Reuss bounds for polycrystalline

materials are used to calculate the shear and bulkmoduli. Voigt upper bounds are obtained by av-

eraging the single crystal elastic stiffness overallspace, and Ruess lower bounds are obtained bysimilarly averaging the single crystal elastic com-pliances that are the inverse of stiffness.

The Voigt upper bounds are given by

kV ¼ 13ðAþ 2BÞ

lV ¼ 15ðA� Bþ 3CÞ

ð2Þ

where kV is the bulk moduli and lV is the shearmoduli and A, B, C are given by

3A ¼ C11 þ C22 þ C33 ð3Þ

3B ¼ C23 þ C13 þ C12 ð4Þ

3C ¼ C44 þ C55 þ C66 ð5ÞThe Reuss lower bounds are given by

kR ¼ 1

3aþ 6b

lR ¼ 5

4a� 4bþ 3c

ð6Þ

where

3a ¼ S11 þ S22 þ S33 ð7Þ

3b ¼ S23 þ S13 þ S12 ð8Þ

3c ¼ S44 þ S55 þ S66 ð9Þwhere ½S� ¼ 1=½C�.

Fig. 3. Moir�ee interferometry image of the microelectronic package (specimen A). (a) Solder ball with a small void, (b) solder ball with a

large void (both (a) and (b) are for sample A).


Elastic modulus is calculated by using theelasticity relationship

E ¼ 9kl3k þ l

ð10Þ

Table 1 presents the upper and lower bounds ofelastic modulus for tin phase.

The second step is calculating the moduli ofpure lead. As the lead is a cubic metal, the singlecrystal stiffness matrix is given by

½CPB� ¼

C11 C12 C12 0 0 0

C12 C11 C12 0 0 0

C12 C12 C11 0 0 0

0 0 0 C44 0 0

0 0 0 0 C44 0

0 0 0 0 0 C44

26666664

37777775

ð11Þ

The Simmons and Wang (1971) bounds are usedto calculate the shear moduli for pure lead. Thelower bound is

lL ¼ l1 þ 35

l2 � l1

�þ 4

3 k þ 2l1ð Þ5l1ð3k þ 4l1Þ

� ��ð12Þ

The upper bound is

lU ¼ l2 þ 25

l1 � l2

�þ 6

3 k þ 2l2ð Þ5l2ð3k þ 4l2Þ

� ��ð13Þ

where

l1 ¼ 12ðC11 � C12Þ ð14Þ

l2 ¼ C44 ð15ÞFor cubic metal, the bulk moduli can be deter-mined by the equation:

k ¼ 13ðC11 þ 2C12Þ ð16Þ

The upper and lower bounds of the elastic mod-ulus of lead are presented in Table 2.

Finally, upper and lower bounds of the elasticmodulus for Pb/Sn alloy can be obtained byHashin and Shtrickman (1963) method. Using theindex a to denote tin, b to denote lead, and v toindicate volume fraction the bounds of moduli forPb37/Sn63 solder can be calculated as follows:

kU ¼ ka þvb

1

kb � kaþ 3va

3ka þ 4la

ð17Þ

kL ¼ kb þva

1

ka � kbþ 3vb

3kb þ 4lb

ð18Þ

lU ¼ la þvb

1

lb � la

þ 6 ka þ 2lað Þva

5la 3ka þ 4lað Þ

ð19Þ

lL ¼ lb þva

1

la � lb

þ6ðkb þ 2lbÞvb

5lbð3kb þ 4lbÞ

ð20Þ

Upper and lower bounds can be averaged to ob-tain an arithmetical average value.

k ¼ 12ðkU þ kLÞ

l ¼ 12ðlU þ lLÞ

ð21Þ

Table 1

Hashin–Strickman elastic modulus bounds for tin phase

T (�C) EU (GPa) EL (GPa)

�130 61.13102 58.29215

�55 57.48011 54.75473

�35 56.49389 53.78464

�15 55.50675 52.81354

5 54.51755 51.84041

22 53.67543 51.01557

50 51.93298 49.3002

75 50.3975 47.75107

100 48.83194 46.19578

125 47.23656 45.37358

150 45.65805 43.06591

Table 2

Upper and lower elastic modulus bounds for lead phase


�130 36.88 33.23785

�55 34.52532 31.0327

�35 33.86769 30.39405

�15 33.2093 29.72864

5 32.55065 29.11436

22 31.99627 28.55439

50 31.02894 27.60667

75 30.15662 26.75041

100 29.25685 25.89243

125 28.38114 25.05902

150 27.50369 24.17102


And finally the Young’s modulus for Pb/Sn can becalculated using Eq. (10)

Following the procedures presented above, theupper and lower bounds for the Young’s modulusof eutectic and near eutectic Pb/Sn alloy was cal-culated and presented in Tables 3 and 4.

4. Nano-indentation technique

Instrumented indentation testing (IIT) with anano-indenter is relatively new form of mechanicaltesting. Known as depth-sensing indentation, itcollects the indentation load–displacement data.Based on these data, it can measure the materialproperties such as hardness, Young’s modulus,yield stress, creep properties at very small-scale(micron) specimens Doerner and Nix, 1986; Nix,

1997. Nano-indentation is very helpful for micro-electronics packaging systems, because of sizeeffect on material properties. By testing specimensthe same size as the actual system itself the sizeeffect is eliminated. Bonda and Noyan (1996) haveshown very effectively that at small-scale materialproperties can be significantly different than bulkmaterial. With the development of IIT, the ad-vantage of this method becomes significant formeasuring the material properties at small scaleor thin films. Using a MTS Nano Indenter XPYoung’s modulus of the electronic packaging sol-ders joints can be measured in actual packagesrather than on bulk solder specimens.

CSM feature in nano-indenter allows measuringmaterial properties at very fast strain rates, up to0.2/s. When CSM feature is used during testing,the stiffness is measured continuously by super-imposing a small high frequency oscillation on theprimary loading signal and analyzing the resultingresponse of the systems by means of a frequencyspecific amplifier. In this case the rate of loading/unloading is indeed very high.

A schematic of the indentation process for anaxisymmetric indenter of arbitrary profile is shownas Fig. 4. Fig. 5 shows a section through an axi-symmetric indentation.

With MTS Nano Indenter XP unit with CSMsystem intrinsic elastic modulus can be determinedby the following relations (Hay and Pharr, 2000)

Er ¼ffiffiffip

p

2bSffiffiffiA

p ð22Þ

where S is the slope of the unloading curve, A isthe projected contact area at that load, Er is thereduced elastic modulus, and b is a constant de-pendent on the geometry of the indenter. For theMTS Nano Indenter XP which uses a Berkovichtip, b ¼ 1:012. Berkovich indenter tip has a three-sided pyramid shape (see Fig. 6). It has a center-line-to-face angle a of 65.3�, projected area of24:56d2 (d is the indentation depth), and volumedepth relation of 8:1873d3. For example, when thetip penetrates 1 lm into the specimen the projectedare is 24 lm2, which is much larger than 3 lmgrain size. Therefore nano-indenter penetration issufficient to obtain consistent material propertiesin solder joints tested in this study. As a matter of

Table 3

Bounds for Young’s modulus of Pb37/Sn63 at different tem-

peratures


�130 45.46 44.56

�55 42.11 41.31

�35 41.18 40.4

�15 40.23 39.48

5 39.26 38.54

22 38.43 37.74

50 36.9 36.27

75 35.44 34.87

100 33.92 33.42

125 32.36 31.94

150 30.67 30.32

Table 4

Bounds for Young’s modulus of Pb40/Sn60 at different tem-

peratures


�130 50.48 46.64

�55 47.4 43.7

�35 46.56 42.88

�15 45.71 42.03

5 44.86 41.21

22 44.15 40.51

50 42.75 39.16

75 41.5 37.94

100 40.23 36.71

125 38.95 35.46

150 37.69 34.21


fact penetration usually continues until modulusvalue does not change by depth anymore. Fig. 6show picture of an indentation. The width anddepth of the surface after polishing was about 350lm. The size of indentation was about 25 lm2.Therefore edge effect can be ignored.

The reduced modulus Er is used to account forthe fact that elastic displacement occurs in both

the indenter and sample. The elastic modulus ofthe tested material, E, is calculated by

1

Er

¼ 1� m2

Eþ 1� m2i

Ei

ð23Þ

where m is the Poisson’s ratio for the tested mate-rial, and Ei and mi are the elastic modulus andPoisson’s ratio of the indenter respectively.

For the purpose of calculating E and H, thecontact stiffness S and the projected contact area Aat that load must be accurately obtained. The mostwidely used method for deriving the contact areawas developed by Oliver and Pharr (1992). Thismethod begins with fitting the unloading portionof the load–displacement data to the power-lawrelation:

P ¼ BAðh� hfÞm ð24Þwhere B and m are empirically determined curvefitting parameters, and hf is the final displacementafter complete unloading (see Fig. 5). The contactstiffness is established by analytically differentiat-ing Eq. (24) and evaluating the result at the max-imum depth of penetration, that is

S ¼ dPdh

� �h¼hmax

¼ BAmðhmax � hfÞm�1 ð25Þ

Having established the theoretical framework ofmeasuring the Young’s modulus (E). We can seethat the only factor that will affect the test result isthe projected contact area A.

Fig. 5. A section through an axisymmetric indentation showing

variables.

Fig. 6. View of a solder joint with a Berkovich tip indentation.

Fig. 4. The basic components of an IIT system.


5. Sample preparation

Hay and Pharr (2000) indicate that surfaceroughness is extremely important in IIT, becausemechanical properties are calculated from thecontact depth, and contact area function on thepresumption that the surface is flat. Thus, the al-lowable surface roughness depends on the antici-pated magnitude of the measured displacementand tolerance for uncertainty in the contact area.The greatest problems are encountered when thecharacteristic wavelength of the roughness iscomparable to the contact diameter. In this casethe contact area is underestimated for valley andover estimated for peaks. For metallographicspecimens, ASTM E 380 provides the specimenpreparation guidelines. In this work ASTM E 380(1983) specimen preparation procedure was fol-lowed for all the specimens A, B and C.

Solder joints in actual microelectronic packagesin three different packages from three differentmajor US semiconductor manufactures were tes-ted. All packages contain Pb37/Sn63 eutectic solderjoints. Solder joints that were tested were actualproducts, not test vehicles. We will refer to thesesolder joints as A, B and C, where each letter refersto solder joints from a different manufacturer.

Each solder joint has approximate height of 500lm. In our testing program we tested a controlgroup of solder joints from each manufacturer A, Band C. In this paper only the results for a repre-sentative joint is presented for each manufacturer.Variation in material properties among the solderjoints from the same manufacturer was <5%. InFigs. 7–12 we present material response for a rep-resentative from each sample group A, B and C.

Fig. 7 shows the elastic modulus (GPa) forsolder joints in specimen A as a function of Ber-kovich tip penetration depth. Going beyond thefinal depth shown in the figure did not change theE value obtained, hence penetration is terminated.For each testing multiple penetration points wereused. Different elastic modulus values at the samepenetration depth in Fig. 7 account for differenttesting points in the solder joint.

Fig. 8 presents load–displacement curve forsolder joint A. Young’s modulus is obtained fromunloading portion of load–displacement curves.Negative portion of the displacement in to thesurface axis in Fig. 8 is due to uncontrollablefeatures in the MTS data post-processing software.

Figs. 9–12 show the elastic modulus (GPa) asa function of penetration (nm) and load–displace-ment (penetration) curves for solder joints B and

Fig. 7. Young’s modulus vs. displacement into surface for solder joint A.


C, respectively. In the nano-indentation testingBerkovich tip penetration varied from 5000 to8000 nm. Penetration is terminated when the ma-terial response becomes stable. In other words,going deeper than shown depth did not change theresults. Using different penetrations for Pb/Snsolder joints is a must due to voids in them.

The average Young’s modulus of specimen Ais EA ¼ 11:79 GPa, of specimen B is EB ¼ 38:64GPa, and for specimen C is EC ¼ 37:32 GPa. Us-ing the bounds theorem, we obtained the bounds

for Young’s modulus of Pb37/Sn 63 at 22 �C asEU ¼ 37:74 GPa, EL ¼ 37:68 GPa.

It is obvious that specimen A has an elasticmodulus 1=3 of the specimen B and C. This latterdiscrepancy is, we believe, due to the fact thatspecimen A had large voids, see Figs. 2 and 3. Onthe other hand, we did not observe any voids inspecimen B and C. We do realize the fact thatusing solder joint specimens with voids in themmay not make any sense to a reader unfamiliarwith electronic packaging. It should be pointed out

Fig. 8. Load–displacement curve for specimen A.

Fig. 9. Young’s modulus for specimen B.


that in the microelectronic packaging it is morecommon to have solder joints with voids thanvoid-free joints. In the microelectronics industry itis very well known that it is very difficult to makeuniform solder joints with no voids in them.Therefore including an actual solder joint from areal package with voids was intentional. The rea-son for voids is usually air bubbles trapped insolder paste during reflowing process.

The indentation depth dependence of elasticmodulus observed in this work agrees very well withresults published by Begley and Hutchinson (1998).

6. Ultrasonic testing

In a solid continuum the elastic modulus andthe material density define the speed of wave alongthe length of a bar;

V ¼ffiffiffiffiEq

sð26Þ

where V is velocity of waves in a medium, E iselastic modulus, and q is density.

Due to simple relationship between elasticmodulus and speed of compression wave in a

Fig. 10. Load–displacement curve for specimen B.

Fig. 11. Young’s modulus for specimen C.


material, ultrasonic testing is used for measuringelastic modulus of materials. Because loading isapplied instantaneously there is no time for creepdeformations. Therefore additional deformationsfrom creep are very low compared to other meth-ods. Simmons and Wang (1971) published ultra-sonic test data of Pb40/Sn60 solder alloy. Resultsare shown in Fig. 13. Ultrasonic testing yieldselastic modulus values higher than upper boundfor temperatures below 295 K and it gives modulusvalues between the lower and upper bounds fortemperatures above 295 K.

7. Comparison and discussion

Fig. 13 shows elastic modulus values obtainedby different testing methods and analytical methodas well as values reported in the literature. Figurecontains elastic modulus values for both Pb37/Sn63 and Pb40/Sn60. Figure indicates that ultra-sonic testing yields modulus values slightly higherthan upper bound at temperatures below 295 Kand values within the bounds at temperaturesabove 295 K. Nano-indenter CSM provides elasticmodulus of Pb37/Sn63 values slightly below thelower bound of EL ¼ 37:74 GPa for sample CEC ¼ 37:32 GPa and within the bounds for sampleB EB ¼ 38:64. Sample A Young’s modulus value

EA ¼ 11:79 GPa is significantly lower than thebounds theorem. It should be pointed out that inorder to crow the figure upper and lower boundsfor Pb37/Sn63 are not shown. Upper and lowerbounds for Pb40/Sn60 are shown to compare itwith ultrasonic data. Elastic modulus measure-ments obtained by all other methods consistentlyyield much smaller values than bound theoremusing single crystal elasticity constants. Because intension test (or shear test) total observed strainincludes elastic and time-dependent creep straincomponents, as a result, elastic modulus value issmaller. If one can subtract the influence of time-dependent creep response from the total observedresponse during testing they should be able to getthe same elastic modulus value as they would getfrom single crystal elasticity or ultrasonic testing.But, at small strain rates this may be difficult.

In ultrasonic testing and nano-indenter testingthe loading rate is very high (0.2/s) compared touniaxial extension (or shear testing) which is usu-ally around 10�2 to 10�5 therefore, there is verylittle creep deformation that takes place during thetesting process.

Another reason for significant difference be-tween modulus values obtained from tension andcompression type tests could be the behavior ofvoids in the material, which respond differently intension and compression.

Fig. 12. Load–displacement curve for specimen C.


In our nano-indenter testing it is obvious thatEB and EC are very close to the lower bound forYoung’s modulus of Pb37/Sn63 alloy obtainedfrom the bounds theorem. Hay and Pharr (2000)and Oliver and Pharr (1992) state that with MTSnano-system elastic modulus can usually be de-termined within �=þ10% of the analytical value.Yet, EA is much smaller than the analytical value.

One reason for variation in elastic modulusvalues among solder joints that were tested withnano-indenter could be the cooling rate used bythe manufacturers. During manufacturing differ-ent cooling and heating histories yield differentmicrostructures. Cooling rate determines the grainsize and microstructure of a solder joint. Kashyap

and Murty (1981), Tang and Basaran (2001) andBasaran and Chandaroy (1998) have presentedinfluence of grain size/microstructure on the be-havior of Pb/Sn solder alloys in great detail. Hencethe reader is referred to these references for furtherinformation. It is well known that grain size andgrain boundary surface area in a given volume ofany alloy can influence the mechanical properties.

As we mentioned above, the projected contactarea A is the only factor that will affect the accu-racy of the result in nano-indenter testing. Thepresence of the voids in solder joint will influencethe calculation of the projected area. The basicassumption of IIT is that the area function iscontinuous. When the indenter is drifting into the

Fig. 13. Elastic modulus vs. temperature curve from different references.


specimen, if there is a void, a jump will occur tothe function. It will overestimate the value ofprojected contact area A, and then the Young’smodulus will be small.

It should be pointed out that elastic modulusvalues measured in this work are time-independentintrinsic values. If one conducting thermal cyclinganalysis, which occurs over a long time period,would result in apparent modulus (the measuredmodulus which includes time-dependent creep be-havior) being lower than the intrinsic modulus.Hence the behavior should be separated into time-independent and time-dependent parts. Any anal-ysis assuming that the intrinsic modulus is thecorrect one for a complete time-dependent analysiswould not be acceptable, more in depth study ofthis subject can be found in Basaran andChandaroy (1998), Chandaroy and Basaran(1999), Tang and Basaran (2001) and Basaran andTang (2002).

8. Conclusions

Based on comparisons presented in Fig. 13 itis obvious that there is a significant discrepancyin elastic modulus values obtained by differentmethods. For a stress analysis obtaining elasticmodulus values from any reference withoutknowing how it was obtained can lead to seriouserrors in the computational stress analysis. Be-cause of its high strain rate sensitivity and in-homogenous medium, intrinsic elastic modulus foreutectic and near eutectic solder joints must beobtained by ultrasonic testing or nano-indenta-tion. Even when one of these testing techniques isused elastic modulus value could vary due to mi-crostructural differences and void ratio. Thereforefor computational stress analysis of Pb/Sn solderjoints elastic modulus should be obtained froman actual manufactured microelectronic packageusing a nano-indenter or ultrasonic tester.

Acknowledgements

This project is sponsored by National ScienceFoundation CMS Division Surface Engineering

and Material Design program and Office of NavalResearch Advanced Electrical Power Systemsprogram. Help received from program directorsDr. Jorn Larsen-Basse and Dr. George Campisi isgratefully acknowledged.

References

Adams, P.J., 1986. Thermal Fatigue of Solder Joints in Micro-

Electronic Devices. M.Sc. Thesis, Department of Mechan-

ical Engineering, MIT, Cambridge, MA.

Basaran, C., Chandaroy, R., 1997. Finite element simulation of

the temperature cycling tests. IEEE Trans. Comp. Packag-

ing Manuf. Technol.––Part A 20 (4), 530–536.

Basaran, C., Chandaroy, R., 1998. Mechanics of Pb40/Sn60

near eutectic solder alloys subjected to vibration. J. Appl.

Math. Modeling 22, 601–627.

Basaran, C., Tang, H., 2002. Implementation of a thermody-

namic framework for damage mechanics of solder intercon-

nect in microelectronic packaging. Int. J. Damage Mech.

11(1) 87.

Basaran, C., Wen, Y., submitted for publication. Grain growth

in eutectic Pb/Sn grid array solder joints. ASME J. Electron.

Packaging.

Begley, C., Hutchinson, J., 1998. The mechanics of size

dependent indendation. J. Mech. Phys. Solids 46 (10),

2049–2068.

Bonda, N.R., Noyan, I.C., 1996. Effect of the specimen size in

predicting the mechanical properties of PbSn solder alloys.

IEEE Trans. Comp. Packaging Manuf. Technol. A 19 (2),

112–120.

Callister Jr., W., 1999. Material Science and Engineering, An

Introduction. John Wiley & Sons, New York.

Chandaroy, R., Basaran, C., 1999. Damage mechanics of

surface mount technology solder joints under concurrent

thermal and dynamic loadings. Trans. ASME, J. Electron.

Packaging 121, 61–68.

Development of highly reliable soldered joints for printed

circuit boards, Westinghouse Defence and Space center,

contract NAS8-21233, August, 1968.

Dasgupta, A., Oyan, C., Barker, D., Pecht, M., 1992. Solder

creep-fatigue analysis by an energy-partitioning approach.

Trans. ASME J. Electron. Packaging 114, 19–25.

Dasgupta, A., Sharma, P., Upadhyayula, K., 2001. Micro-

mechanics of fatigue damage in Pb/Sn solder due to vibra-

tion and thermal cycling. Int. J. Damage Mech. 10 (2),

101–132.

Doerner, M.F., Nix, W.D., 1986. A method for interpreting the

data from depth-sensing indentation instruments. J. Mater.

Res. 1 (4), 75–81.

Dun, B.D., 1975. The properties of near-eutectic tin/lead solder

alloy tested between þ70 �C and �60 �C and the use of

such alloy in spacecraft electronics. European Space

Agency, Technical Memorandum ESA TM-162, Sep-

tember.


Frear, D.R., Burchett, S.N., Rashid, M.M., 1995. A micro-

structurally model of solder joints under conditions of

thermomechanical fatigue. In: Advances in Electronic

Packaging ASME, vol. 10-1.

Frear, D., Morgan, H., Burchett, S., Lau, J., 1994. The

Mehanics of Solder Alloy Interconnects. Chapman and

Hall.

Guo, Q., Cutiongco, E.C., Keer, L.M., Fine, M.E., 1991.

Thermomechanical fatigue life prediction of 63Sn/37Pb

solder. J. Electron. Packaging, 114, 145–151.

Hacke, P.L., Sprecher, A.F., Conrad, H., 1997. Microstructure

coarsening during thermo-mechanical fatigue of Pb–Sn

solder joints. J. Electron. Mater. 26 (7).

Harper, C.A., 1970. Handbook of Materials and Processes for

Electronics. Mcgraw-Hill, New York.

Hashin, Z., Shtrickman, S., 1963. A variation approach the

theory of the elastic behavior of multiple materials. J. Mech.

Solids 11, 127–140.

Hay, J.L., Pharr, G.M., 2000. Instrumented indentation testing.

In: Mechanical Testing and Evaluation. ASM Handbook,

vol. 8.

Henkel, Pense, A.W., 2002. Structure and Properties of

Engineering Materials. McGraw Hill, New York.

Hellwege, K.H., Landolt-Bornstein, J., 1979. Numerical data

and functional relationship in science and technology, group

III. In: Crystal and Solid State Physics, vol. 11. Springer-

Verlag, pp. 113–203.

Kashyap, B.P., Murty, G.S., 1981. Experimental constitutive

relation for the high temperature deformation of a Pb/Sn

eutectic alloy. Mater. Sci. Eng. 50, 263–269.

Knecht, S., Fox, L.R., 1990. Constitutive relation and creep-

fatigue life model for eutectic tin–lead solder. IEEE Trans.

Comp. Hybrids Manuf. Technol. 13 (2), 23–29.

Lau, J.H., Chen, K.L., 1997. Thermal and mechanical evalu-

ations of cost-effective plastic ball grid array package. J.

Electron. Packaging 119, 208–212.

Lau, J.H., Rice, D.W., Avery, D.A., 1987. Elasto plastic

analysis of surface mount solder joints. IEEE Trans. Comp.

Hybrids Manuf. Technol. CHMT-10 (3), 69–74.

Ling, S., Dasgupta, A., 2000. A nonlinear multi-domain

thermomechanical stress analysis method for surface mount

solder joints––Part II: Viscoplastic analysis. J. Electron.

Packaging 119, 177–182.

Morris, J.W., Goldstein, F.J.L., Mei, Z., 1994. Microstructural

influence on the mechanical properties of solder. In:

Burchett, M., Lau, J., (Eds.), The Mechanics of Solder

Alloy Interconnects. Chapman and Hall.

Nix, W.D., 1997. Elastic and plastic properties of thin film on

substrates: nanoindentation techniques. Mater. Sci. Eng. A

234–236, 37–44.

Oliver, W.C., Pharr, G.M., 1992. An improved technique for

determining hardness and elastic modulus using load and

displacement sensing indentation experiments. J. Mater.

Res. 7 (6), 102–113.

Pan, T., 1991. Thermal cycling induced plastic deformation in

solder joints. Part III: strain-energy based fatigue life model

and effects of ramp rate and hold time. In: Proceedings of

the ASME Winter Annual Meeting, pp. 1–6.

Pecht, M., Agarwal, R., mcClusket, P., Dishongh, T., Javad-

pour, S.M., 1999. Electronic Packaging Materials and Their

Properties. CRC Press.

Rhode, R.W., Swearengen, J.C., 1980. Deformation modeling

applied to stress relaxation of four solder alloys. J. Eng.

Mater. Technol. 102, 21–29.

Riemer, E.D., 1990. Prediction of temperature cycling life for

SMT solder joints on TCE-mismatched substrates. In: Proc.

Electronic Comp. IEEE.

Standard methods of preparation of metallographic specimen.

E 380, Annual Book of ASTM Standards, ASTM reap-

proved 1983.

Simmons, G., Wang, H., 1971. Single Crystal Elastic Constants

and Calculated Aggregate Properties: A Handbook, second

ed. MIT press.

Subrahmanyan, R., Wilcox, J.R., Li, C., 1989. A damage

integral approach to thermal fatigue of solder joints. IEEE

Trans. Comp. Hybrids Manuf. Technol. 12 (4), 61–68.

Tang, H., Basaran, C., 2001. Influence of microstructure

coarsening on thermomechanical fatigue behavior of Pb/

Sn eutectic solder joints. Int. J. Damage Mech. 10 (3), 235–

255.

Wong, T.E., Kachatorian, L.A., Tierney, B.D., 1997. Gull–

Wing solder joint fatigue life sensitivity evaluation. J.

Electron. Packaging 119, 171–176.

Zubelewicz, A., 1993. Micromechanical study of ductile poly-

crystalline material. J. Mech. Phys. Solids 41 (11), 1711–

1722.


measuringintrinsicelasticmodulusofpb/snsolderalloys · young’s modulus (e) values published in...

Documents