thermally induced deformation of solder joints in real packages: measurement and analysis

Microelectronics Reliability 46 (2006) 1148–1159

www.elsevier.com/locate/microrel

Thermally induced deformation of solder joints in realpackages: Measurement and analysis

Hua Lu *, Helen Shi, Ming Zhou

Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Canada ON M5B 2K3

Received 27 July 2005; received in revised form 2 October 2005Available online 18 November 2005

Abstract

The paper presents a hybrid experimental and analytical approach to track the deformation of solder joints in anelectronic package subject to a thermal process. The solder joint strain is directly measured using a computer visiontechnique. The strain measurement is analyzed following an approach that is devised based on an established solderconstitutive relation. The analysis leads to the determination of the solder joint stress and in turn, to the separationof the elastic, plastic and creep strain from the measured total strain. The creep strain rate and stress–strain hysteresisloop are also obtained. Two case studies are presented to illustrate the applications and to show the viability of theapproach. Each case involves a resistor package with SAC (Sn95.5Ag3.8Cu0.7) solder joints, which is subjected to atemperature variation between ambient and 120 �C. The results confirm that shear is a dominant strain componentin such solder joints. The shear strain varies nearly in phase with the temperature whereas the shear stress exhibits adifferent trend of variation due to stress relaxation. The peak shear stress of around 10 MPa to 15 MPa are found,which occur at near 70 �C in both cases, when the temperature ramps up at approximately 3 �C/min. The creep shearstrain goes up to 0.02 and accounts for over 80% of the total shear strain. The creep strain rate is in the order of mag-nitude of 10�5 s�1. Responding to the temperature cycling with such moderate rate, the creep strain shows modest rat-cheting while the stress–strain hysteresis stabilizes in two cycles.� 2005 Elsevier Ltd. All rights reserved.

1. Introduction

The global transition to lead-free solders has given anew thrust to the packaging reliability research e.g., [1–6]. The solder joint reliability performance as commonlyacknowledged is a complex issue due to its sensitivity tovarious factors such as the package structure and geo-metric scale, the manufacturing process and the servicecondition, etc. In the point of view of solid mechanics,

0026-2714/$ - see front matter � 2005 Elsevier Ltd. All rights reservdoi:10.1016/j.microrel.2005.10.002

* Corresponding author.E-mail address: [email protected] (H. Lu).

the stress and strain dictate the solder joint failure. Thedecades long studies have led to the establishment of aframework for quantitatively assessing the solder jointreliability. Based on that, some bunch mark structuresimulation and material modeling have provided neededguidance to the understanding of failure mechanismsunder different circumstances. Yet to date the packagethermal reliability assessment is heavily relied on theaccelerated test routines and failure statistic based dataanalysis. On the other hand, the interest in the physics-based, predictive methodologies is notably growingdriven mainly by the time and cost reduction for newpackage development, design and prototyping. The

ed.

mailto:[email protected]

Fig. 1. Experimental setup used for strain measurement: (a) a

Abbreviations

SAC Sn95.5Ag3.8Cu0.7 alloyDSC digital speckle correlation

LCCC leadless ceramic chip carrierPCB printed circuit board

H. Lu et al. / Microelectronics Reliability 46 (2006) 1148–1159 1149

existing solder joint failure theories are diverse as over-viewed and categorized by Lee et al. [7] in 2000, whichare recently enriched by the additions devoted to lead-free solders e.g., [8–12]. A class of the models [13–16] thathave gained wide acceptance attributes the thermal creepfatigue to the solders� microstructure damage that accu-mulates as the temperature cycles. Given that the damageand the strain energy dissipation are correlated to eachother, the solder joint creep fatigue can be demonstratedby the stress–strain hysteresis, and the per-cycle damagecan be quantified by the area enclosed in a stabilized hys-teresis loop. For a practical assessment, it is desirable toconduct such an evaluation on real assembly packagessubjected to a non-accelerated, operating thermal pro-cess. In a pioneering work, Hall et al. [17] used opticaland strain gauge techniques to observe the thermal defor-mation of LCCC (leadless ceramic chip carrier) assem-blies. Pan and Pao [18] studied the solder jointdeformation using a beam specimen. In both studiesthe solder joint hysteresis loops are examined. The pres-ent study, though similarly motivated, uses the methodof digital speckle correlation (DSC) to measure a solderjoint of a package. Specifically, the strain variation withthe temperature in a stress concentrated local area isobtained. The analysis uses a scheme that yields the solu-tion of solder joint stress based on the strain measure-ment. This in turn enables the separation of the elastic,plastic and creep strain components from the measuredtotal strain, and the determination of the creep rateand the strain energy density.

sketch of the system layout and (b) a picture of the system.

2. Solder joint strain measurement

2.1. DSC technique

The key of the study is to obtain direct strain mea-surement in the solder joints, which relies mainly onthe application of a technique called digital speckle cor-relation (DSC). With its high and adjustable resolution,DSC enables a gross search for the sites of strain concen-tration in a package, if necessary. When such sitesbecome apparent, the system can be zoomed in to obtaindetailed measurement. In Fig. 1 a sketch and a photo aregiven to help illustrate the experimental setup used. Themethodology is based on evaluating the correlationbetween a pair of the images that are recorded at differ-ent deformation states of a surface. A de-correlation fac-

tor is defined and related to the motion of the points in asubset of the deformed image with respect to the corre-sponding points in the un-deformed counterpart. Themotion is assumed to obey the continuum mechanicsbased deformation kinematics. An iterative algorithmis adopted to assess the factor initially calculated withgross estimates of the deformation parameters, and sub-sequently to improve the parameters. The iteration pro-ceeds to turn the deformed image back to its originalshape, evidenced by the progressively improved imagecorrelation. A good correlation reached at the end ofthe process signifies that the deformation parametersat the subset center have been converged to the respec-tive true values. The deformation of an area is deter-mined in a point-by-point manner repeating the aboveprocess. The computer vision technique is quick in

1150 H. Lu et al. / Microelectronics Reliability 46 (2006) 1148–1159

generating large quantities of measurements upon thetest completion. And its features of non-contact andnon-coherent make it suitable for thermal applications.Detailed descriptions of the methodology and the mea-surement procedures can be found in Refs. [19–21].

2.2. Test vehicles and sample preparation

The test vehicles used in the study are the type ofceramic resistor packages chosen to use in a Pb-free reli-ability research by National Electronics Manufactures�Initiative (NEMI). Fig. 2 gives a three-dimensionalsketch and another of a cross-section detailing the pack-age structure. The packages� feature dimensions arelisted in Table 1. The sample preparation includescross-sectioning, polishing, photographing and specklecoating, etc. Fig. 3 gives photos of a partial cross-sectionshowing the solder fillet and the surrounding area beforeand after a speckle pattern is applied to. The artificialspeckle pattern provides a desired random variation oflight reflectivity across the surface, which is criticallyrequired by the image correlation calculation. Should anaked cross-section be measured, the grey-value varia-tion across the image would be contributed mainly bythe surface texture or by variable reflectivity of individ-ual solder grains and cell boundaries in case a very large

Fig. 2. A 3D sketch and a sketch of a X–Y cross-section of atest package.

Table 1Geometric dimensions of the package cross-section

Test Solder-joint thickness(mm)

Copper trace thickness(mm)

Case A 0.044 0.068Case B 0.044 0.063

Fig. 3. Pictures showing a solder joint and its vicinity: (a) aphoto of a joint fillet and surrounding area with no specklecoverage, (b) a photo of same area covered by speckles, and (c)a sketch giving geometric dimensions of the joint.

optical magnification is used. Yet under heat and stress,the solder grains will grow to cause the solder micro-structure coarsening, which could affect the macroscopicappearance of the surface texture. Given that the meth-odology attributes the image de-correlation only to thesurface deformation, the microstructure coarseninginduced surface texture change could confuse the corre-lation calculation and thus cause measurement error.

2.3. Image recording and processing

In this study, each test records a series of images ofthe area centered at the solder joint fillet, as typically

Ceramic thickness(mm)

PCB thickness(mm)

Data area(mm2)

0.508 1.15 0.032 · 0.0440.508 1.15 0.050 · 0.044


shown by Fig. 3(b). The image processing involves a pairat a time, namely a reference image taken at the ambientand another at an elevated temperature. The processingrestricts to a portion of the image that covers a part ofthe solder joint. To exactly outline the solder joint underthe speckle coverage is assisted by feature lines andpoints that are commonly identifiable in both images.Upon the determination of the rectangular area andthe measurement resolution, a processing grid is laiddown in the reference image. The area is indicated bythe solid-line box in both schematics shown inFig. 3(a) and (c), as well as by the processing left traceson the image as seen in Fig. 3(b). Each processingobtains a set of the measurements at a grid point, includ-ing two displacement components and four displace-ment partial derivatives. It is noted that the DSCtechnique yields the six parameters simultaneously andindependently. Raw measurements in the solder layerobtained at a particular temperature are typically shownin Fig. 4 in the form of area contours. The displacementcomponents u and v are the direct output. The partialderivatives ou/ox and ov/oy are also direct output andrepresent approximately the respective normal strains.And the shear strain is obtained via ou/oy + ov/ox.Within the processed area, a small portion near the sol-der joint fillet is named the ‘‘data area’’. This chosensub-area, as indicated by a dash-line box in bothFig. 3(a) and (c), has linear dimensions of a few dozenmicrons. Based on the original data, the average shear

Fig. 4. Typical contour maps of strain and displacementcomponents directly obtained from image processing.

strain in the sub-area is calculated for off-setting the ran-dom errors that exist in the single-point measurements.In the analysis to follow, this average shear strain isreferred to as the measured ‘‘total shear strain’’.

2.4. Temperature control

A forced convective thermal chamber as seen inFig. 1(b) is used. The chamber temperature can be setto vary between �70 �C and 250 �C with chosen ratesand at the accuracy of ±3.5 �C. Since the sample tem-perature always lags behind the chamber reading, a sep-arate calibration test is conducted using thermal couplesdirectly attached to the test package. The test data andthe results from a finite-element thermal modeling bothconfirm a fairly uniform temperature distribution acrossthe sample surface and in the body. The modelingproves that the temperature in-uniformity throughoutthe package is limited and ranges from a fraction of adegree to a couple of degree Celsius. In actual testing,additional monitoring of the sample temperature is pro-vided by thermal couples attached to the sample stand atthe sample�s very vicinity. The system vibration and theair circulation, enhanced by the use of large optical mag-nification, are the main sources of disturbance to affectthe image stability and thus to cause scattered measure-ments. The chamber temperature control is automatedby adjusting the air flow, which functions well in keepinga limited temperature fluctuation during dwelling. Thenature of the control, however, appears to have contrib-uted to the data scatter. The troubling instable air flowbecomes apparently severer in the dwell periods duringwhich the feedback controls the electric fan to be alter-nately on and off. The resulted turbulence causes theoptical refractive index of the air to vary, and in turn,the image to distort. An effort made to counter that isto manually turn the fan off for a few seconds beforeeach image recording. This however results in that thesample temperature quickly drops from the preset testprofile by as much as 10 degree Celsius.

3. Strain analysis leading to solutions of stress and

separation of strain components

3.1. Solder constitutive relations

Numerous constitutive equations have been pro-posed for different solder alloys. This study gives theattention to those that are based on testing actual assem-blies e.g., [13,22,23]. For surface mount packages, it is awell documented e.g., [2] phenomenon that the sheardominates the thermally induced solder joint deforma-tion. This analysis focuses on the shear strain despitethe availability of normal strain measurements. Adoptedas follows is a commonly accepted, additive constitutive

Table 2Solder constitutive parameters [13]

G0 (GPa/Mpsi) 19.3/2.8

G1 (MPa/K/Kpsi/K) 69/10C6 2.04 · 1011

m 4.39C (K/s/Pa/K/s/psi) 0.454 · 10�6/3.13 · 10�3

a 1500n 5.5Q (eV) 0.5

Fig. 5. Test temperature vs. time curve: (a) for test package Aand (b) for test package B.


relation that regards the shear strain as a linear superpo-sition of separate components, each representing contri-bution of a different deformation mechanism. The ‘‘totalshear strain’’ ctl is expressed as

cel þ cpl þ ccr ¼ ctl ð1Þ

where cel, cpl and ccr are, respectively, the elastic, plasticand creep strain components. The specific model andparameters adopted are proposed by Darveaux et al.[13]. Darveaux�s model extends to several solder alloys(60Sn40Pb, 96.5Sn3.5Ag, 97.5Pb2.5Sn and 100In, etc.),covers a wide strain range and incorporates temperatureeffects in all the three components.

For the elastic portion, the model applies Hooke�slaw as follows:

cel ¼sG

ð2Þ

In the equation s is the shear stress, G is the temperaturedependent shear modulus expressed as G = G0 �G1(T � 273) where T is the temperature in Kelvin, G0

is the shear modulus at 0 �C and G1 is a constant.The Ramberg–Osgood type relation is used for the

time independent plastic deformation:

cpl ¼ C6sG

� �mð3Þ

cpl ¼ �C6

�sG

� �mð3aÞ

Eqs. (3) and (3a) are used when s is positive and nega-tive, respectively. C6 and m are material constants, thevalues for Sn3.8Ag0.7Cu are unavailable and are substi-tuted by those for Sn3.5Ag for the strain analysis. Con-sidering the similarities between their composition andmicrostructure as well as the minor plastic content inthe total strain, the substitution should contribute lim-ited error in the outcomes of this analysis.

Assuming the primary creep is negligible, the domi-nant steady state creep strain is expressed in a hyperbolicsine rate equation as follows:

dcs

dt¼ C

GT

� �sin h a0

sG

� �h inexp

�QkT

� �ð4Þ

dcs

dt¼ �C

GT

� �sin h a0

�sG

� �h inexp

�QkT

� �ð4aÞ

Similar as Eqs. (4) and (4a) are used alternately for po-sitive and negative shear stress. In both equations, C is aconstant characteristic of the underlying micro-mecha-nism, G denotes the temperature dependent shear mod-ulus, a0 prescribes the stress level at which the power lawdependence breaks down, n is the stress exponent, Q isthe activation energy for the deformation process, k isthe Boltzmann�s constant and T is the temperature inabsolute scale [13]. The values of the constitutive param-eters used in the analysis are listed in Table 2.

3.2. Solder deformation basics

Some basic aspects of the solder deformation arenoted in formulating the stress solution as presented inthe next section. First, the measured strain generallyconsists of mechanical and thermal components. Themechanical part is stress related and usually has morethan one contributor as indicated by Eq. (1); the thermalpart represents the material�s thermally induced dimen-sional change while the material is under no force andconstraints. The thermal strain is usually non-stress


related. Macroscopically, the solder materials may beconsidered as thermally isotropic. For such isotropicmaterials, temperature change induces no shear termof thermal strain. Second, the elastic strain componentis instant and recovers upon stress relaxation; the instantplastic strain and the time-lagged creep strain are bothpermanent and therefore stress-history dependent.

3.3. Step-wise stress formulation

For a test that obtains a set of n images, n � 1 imagepairs and n � 1 sets of solder joint deformation data canbe obtained upon processing. Let ti be the time instantthat the image i is recorded in a sequence ofi = 0, . . . , n � 1, and Dti = ti+1 � ti be the ith time inter-val where i = 1, . . . , n. The formulation aims to solvethe shear stress si in the interval Dti assuming that si isconstant. si is related to the elastic and plastic straincel and cpl at ti by Eqs. (2) and (3), respectively. si andthe creep increment Dccri

in Dti are related to each otherby integrating Eq. (4) over Dti as follows:

Fig. 6. Measured shear strain vs. time and fitting curve:

Dccri¼Z

Dti

_csidt

¼Z

Dti

CGT i

� �sin h a0

si

G

� �h inexp

�QkT i

� �dt if si > 0

ð5Þ

or

Dccri¼Z

Dti

�CGT i

� �sin h a0

�si

G

� �h in

� exp�QkT i

� �dt if si < 0 ð5aÞ

At the instant ti, the accumulated creep strain ccriis the

algebraic sum of all previous increments, namely

ccri¼Xi

j¼1

Dccrjð6Þ

Combining the Eqs. (2, 3 and 6), si and the measuredtotal shear strain ctli are put in one equation as follows:

(a) for test package A and (b) for test package B.


si

Gþ C6

si

G

� �mþXi

j¼1

Dccrj¼ ctli ð7Þ

Knowing all the relevant constitutive constants and test-ing parameters, shear stress si can be solved from Eq. (7).Noting that the inelastic content of the strain is cumula-tive, the stress solution is pursued step-by-step beginningwith the interval Dt1. Eq. (7) is a general form and theimplementation of it needs to consider specific stress con-dition at a respective time instant. This is in particularregarding the sign and the trend of variation of the stress.For instance, given that the plastic strain is instant andcumulative, Eq. (3) applies only up to an instant tk whena positive and increasing stress reaches the peak value.With a declining stress following tk, the plastic strain isheld at cplmax

¼ C6skG

� �muntil the stress falls further into

the negative territory. The change of stress direction sig-nals the sign reversal for both elastic strain and newinelastic strain. When that happens, the new plastic andcreep strain increments must be handled by Eqs. (3a)

0 10 20 300

5

10

15

t (min.)

She

ar s

tres

s (M

Pa)

(a)

0 20 40 60 80-15

-10

-5

0

5

10

15

t (m

She

ar s

tres

s (M

Pa)

(b)

Fig. 7. Shear stress solution vs. time curve: (a) fo

and (5a), respectively. Finally, the total inelastic (plasticplus creep) strain at any current time instant ti is the alge-braic sum of the portions that are reached in the previousperiods and possibly in different signs. The stress solutionfrom Eq. (7) is obtained numerically using a computerprogram. Difficulties may arise at certain points due tothe discrete and scattering input. To tackle that, ctli inEq. (7) is replaced by the value of a regression functionthat appropriately fits the raw data. Upon solving thestress si the elastic, plastic, and creep strains at ti are sep-arated via Eqs. (2, 3) and (6), respectively, and the creepstrain rate is calculated with Eq. (4).

4. Case studies

4.1. Case study A

Case A is designed to study the solder joint stressrelaxation and the creep behavior. The test profile in

40 50 60

100 120 140 160 180in.)

r test package A and (b) for test package B.


Fig. 5(a) shows a temperature ramp-up period followedby a dwell period, during which the package tempera-ture increases from the ambient at a rate of 3 �C/minfor 30 min, followed by 30 min dwelling at 120 �C. Atotal of 31 images are recorded in every 2 min, fromwhich 30 sets of data are obtained. The average strainis calculated based on 3 · 14 data points in an area of32 lm · 44 lm. The strain data of the ramp periodand dwell period are fit with a cubic polynomial regres-sion function and a linear function, respectively.

4.2. Case study B

Case B aims to study solder joint behavior inresponding to thermal cycling. The test subjects thepackage to two full temperature cycles as shown byFig. 5(b) to simulate a service condition. The tempera-

0 10 20 30 40

0.005

0.01

0.015

0.02

t (min.)

Cre

ep s

trai

n

T

(a)

0 20 40 60 800

0.002

0.004

0.006

0.008

0.01

0.012

0.014

t (m

Cre

ep s

trai

n

(b)

Fig. 8. Creep shear strain vs. time curve: (a) for

ture ramps 3 �C/min and dwells at 120 �C and 27 �C.Each ramp and holding period has 30 and 20 min dura-tion, respectively. A total of 91 images are recorded toyield 90 datasets. The average shear strain at 4 · 16 datapoints within a 50 lm · 44 lm area is calculated for eachtemperature. The stress, the strain rate, and the elastic,plastic and creep strain components in the solder jointfillet area are solved. The stress–strain curve is plottedto show the hysteresis loops.

5. Result presentation and discussion

5.1. Total shear strain measurement

A comparison of the strain contours obtained as typ-ically shown in Fig. 5 confirms the shear dominance in

0 50 60

est A, SnAgCu

100 120 140 160 180

in.)

test package A and (b) for test package B.


solder joint strain as commonly understood. It is notedthat the CTE mismatch and the temperature variationsubject the solder joint to a displacement/strain con-trolled boundary condition. The solder joint is sand-wiched in between the PCB (printed circuit board) andthe component substrate. Furthermore, the solder layeris two orders of magnitude thinner and much more com-pliant compared with the PCB and the substrate, thedevelopment of the solder joint deformation cannotbut closely follow the boundary displacement that isdominantly determined by the temperature variation.The above rationale appears help explain the trend ofvariation of the measured total strain as given inFig. 6. In case A, the total strain shows no substantialevolution during a 30-min dwell at 120 �C. In case B,the strain varies nearly in-phase with the temperatureand the comparison between the strain magnitudes inthe two cycles finds no significant difference.

0 10 20 300

0.5

1

1.5

2x 10-5

t (min.)

Cre

ep s

trai

n ra

te (

1/s)

(a)

0 20 40 60 80-0.5

0

0.5

1

1.5

2

2.5x 10-5

t (m

Cre

ep s

trai

n ra

te (

1/s)

(b)

Fig. 9. Creep shear strain rate vs. time curve: (a) fo

5.2. Shear stress

Fig. 7(a) shows for case A that the highest shearstress is about 15 MPa that reaches at 71 �C or 16 minentering the ramp-up. The stress relaxes from that pointthrough to the end of the test. For case B, Fig. 7(b) givesthe maximum of 10 MPa that occurs at 72 �C or 15 minentering the ramp-up. It is notable that the stress varia-tion in the first half-cycle in case B resembles the trend incase A. The stress relaxation continues throughout thehigh temperature dwell and it diminishes at a pointshortly after entering the ramp-down period, andchanges the sign. The maximum negative stress isaround �13 MPa that reaches near the end of that per-iod. The variation of the stress is out of phase with thetemperature, and the two stress cycles appear similar.In general, the stress will relax whenever the temperaturedrops or holds. Notably in this study, the relaxation

40 50 60

100 120 140 160 180in.)

r test package A and (b) for test package B.


happens during temperature ramp-up. This occursbecause that the rate (3 �C/min) is insufficient to exerton the solder layer a displacement boundary that isneeded to sustain a continued creep under the reachedlevel of stress.

5.3. Creep strain and creep strain rate

In both tests, the package temperature stays abovethe initial ambient temperature while varying. The creepstrain accumulates higher unless the stress changes sign.As seen from Fig. 8, the highest creep strain reaches0.017 in case A, and 0.011 in the first cycle and 0.013in the second cycle in case B. Although the total shearstrain remains more or less similar comparing the twocycles, the creep strain exhibits a modest but apparenttrend of ratcheting. The highest creep strain rate goesup to 0.17 · 10�5 s�1 in case A and 0.20 · 10�5 s�1 incase B as seen in Fig. 9. In both cases the sharp fall of

Fig. 10. Creep shear stress vs. creep shear strain curves: (a) for te

the creep strain rate starts during the temperature ramp-ing up, and the lowest rate occur during dwelling. Incase B the rate comes negative during the low extremedwell periods.

5.4. Stress–strain curve, hysteresis loops

Fig. 10 shows the shear stress vs. total shear straincurves for both cases. The stress–strain hysteresis forcase B is plotted in Fig. 10(b). The second loop notablyoverlaps the first one, which suggests a quick stabiliza-tion of the hysteresis.

5.5. Strain energy density

The strain energy density of 0.146 MJ/m3 is obtainedby numerically calculating the area included in the sec-ond loop in case B.

st package A and (b) for test package B (hysteresis loops).


6. Summary

The convective heating used in this experiment isproved a main source to cause disturbance to the sampleimage recording, especially during the temperature dwellwhen non-steady air flow dominates. The imagedistortion thus incurred is the main source responsiblefor the scatter of the measurement. While furtherimprovement is desired and can be realized, the presentstudy nevertheless demonstrates a feasible experimentalapproach that uses a high resolution vision techniqueto track the solder joint deformation in real packagessubject to a thermal process. With suitable material con-stitutive equations, the strain measurement can be ana-lyzed to yield the numerical solution of the stress.With the stress, the creep strain and creep strain rate

Fig. 11. Variations of measured shear strain, separated elastic, plastic a(b) for test package B.

as well as the elastic and plastic strains are also deter-mined. The study also points out a potential applicationof this approach to estimating the thermal creep fatiguelife for solder joints based on the evaluation of the dissi-pated strain energy density.

The case studies subject the lead-free resistor pack-ages to temperature extremes of 20 and 120 �C, dwelllength of 20 or 30 min and ramp rate of 3 �C/min. Undersuch circumstances, the results show that the variationof the total shear strain is synchronized with the temper-ature, whereas the shear stress is out of phase due to thestress relaxation. The peak shear stress of the magnitudeof about 10–15 MPa occurs at around 70 �C in bothcases. The creep strain, up to 0.02 in case A and 0.017in case B, accounts for over 80% of the total strain inboth cases (Fig. 11). Meanwhile the creep strain rate

nd creep component and shear stress: (a) for test package A and


reaches the order of magnitude of 10�5 s�1. Respondingto the temperature cycling, the creep strain appears rat-cheting modestly while the stress–strain hysteresisbecomes stabilized quickly. In case B, the per cycle dis-sipated strain energy density of about 0.15 MJ/m3 isobtained upon calculating the area of the second hyster-esis loop.

Acknowledgements

The financial support from NSERC (Natural Scienceand Engineering Research Council of Canada) andCMAP (Center for Microelectronics Assembly andPackaging of Ontario) is acknowledged. Professor J.Spelt of University of Toronto provided the test vehiclesand the material compositions and properties. Valuablediscussions with him and his students are appreciated.

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thermally induced deformation of solder joints in real packages: measurement and analysis

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