Fracture Mechanics Analysis of Cracks in Solder Joint Intermetallic Compounds

M. o. Alamt, H. Lu, Chris Bailey*, and Y. C. ChantSchool of Computing and Mathematical Sciences, University of Greenwich

30 Park Row, London SEI0, 9LS, UKtM.O.Alam@gre.ac.uk, * C.Bailey@gre.ac.uk

tDepartment of Electronic Engineering, City University ofHong Kong83, Tat Chee Avenue, Kowloon Tong,

Hong Kong, China

AbstractThe trend towards miniaturization of electronic

products leads to the need for very small sized solderjoints. Therefore, there is a higher reliability risk that toolarge a fraction of solder joints will transform intoIntermetallic Compounds (IMCs) at the solder interface.In this paper, fracture mechanics study of the IMC layerfor SnPb and Pb-free solder joints was carried out usingfinite element numerical computer modelling method. Itis assumed that only one crack is present in the IMC layer.Linear Elastic Fracture Mechanics (LEFM) approach isused for parametric study of the Stress Intensity Factors(SIF, K1 and KII), at the predefined crack in the IMC layerof solder butt joint tensile sample. Contrary to intuition,it is revealed that a thicker IMC layer in fact increases thereliability of solder joint for a cracked IMC. Value of K1

and KII are found to decrease with the location of thecrack further away from the solder interfaces while otherparameters are constant. Solder thickness and strain ratewere also found to have a significant influence on the SIFvalues. It has been found that soft solder matrix generatesnon-uniform plastic deformation across the solder-IMCinterface near the crack tip that is responsible to obtainhigher K1 and KII•

1. Introduction

The demand for Pb-free solders in a greenenvironment and the increasing requirements for high­density interconnection technology to miniaturizeelectronic goods are the two most critical considerationsin the global electronics market. Such a two-fold criticalrequirement possesses a reliability threat in the selectionof proper materials and processes as a state-of-the-artrequirement of the electronics industries. Eutectic Sn-Pbsolders have long been used due to the advantages of theirmechanical properties, low melting temperatures, andexcellent wetting properties. In response to the concernover Pb used in electronic assemblies, much work isongoing over the last few years to find an acceptable Pb­free solder for various electronic attachment applications.Of all the Pb-free solders, Sn-based solders are the mostattractive materials for the replacement of conventionalSn-Pb solder [1].

During the soldering process, the formation ofintermetallic compound (IMCs) between Sn-containingsolders and substrates is inevitable[I-4]. Typically, a Cusubstrate is used as a wettable metallization pad inelectronic soldering applications. Interaction andinterdiffusion behavior between the solder and the Cubase metal have been intensively studied. It is now known

that at the Cu/solder interface, Sn reacts rapidly with Cuto form CU6Sns IMC during reflow soldering which growover the subsequent aging period. It has been reportedthat the strength of the solder joint decreases with anincreasing thickness of IMCs formed at the interface andtherefore, the IMC has been believed as an initiation sitefor microcracks. Depending on the IMC thickness anddifferent layers of IMCs at the interface as well as thelocation of the first critical crack, fracture propagateeither through the IMC layers or it switch from IMC tosolder and again solder to IMC [5]. In fact, a stresssingularity might always exist at the interface of IMC andsolder due to asymmetry in their elastic and plasticproperties. This stress singularity tend to exhibit higherstress intensity factors (SIFs) and mode mixity at the tipof a crack in the IMC layer as compared with equivalentcracks in homogenous materials.

There have been extensive theoretical andexperimental works carried out on the subject of stresssingularity and a fracture initiation criterion for bonedjoints of brittle and ductile materials at their interface [6-10]. Investigations into cracking near the interface ofceramic-metal bonding reveals that cracks in the ceramicregion deflected towards the ductile metal layer, however,they switch back again to brittle layer forming a jig-jagfracture path similar to that observed at the solderinterface. Fracture mechanics approach was used forthose theoretical studies. In-depth understanding of thefracture path at the solder interface demands similarapproach. Moreover, because of the viscoplasticproperties of solder alloys, cracks inside the IMC layerexperience complicated strain dependent stressconcentration that were not studies much.

Therefore, the present study addresses the effect ofdifferent solder alloys (such as SnPb and SnAgCu),location of the crack, solder joint thickness, and strainrates on the crack propagation propensity near the solderinterface. This explore liner elastic fracturemechanics(LEFM) approach by measuring stress intensityfactors (SIFs) for each condition.

2. Numerical method

2.1. Model for finite element analysis:

A tensile specimen of butt joint of solder alloyssandwiched between two copper plates is considered forthis study. It is assumed that 2-11 Jlm thick IMC layersare formed at the solder-copper substrate interfaces.Therefore, four parallel interfaces such as copper-IMC,IMC-solder, solder-IMC and IMC-copper are available inthe specimen as shown in Figure 1. A crack of 10 Jlm

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depth from the left edge and parallel to the interface isconsidered to be situated within one of the IMC layer.Distance of the position of this crack from the interface isvaried from 1 Jlm to 10 Jlm. Thickness of the solder layeris also varied from 0.3 mm to Imm. Specimens aremodelled in 2-dimensions under plain strain conditions.Finite element analysis has been conducted using acommercial FE software package, ANSYS-l1.

Figure 1. Model oflMC crack at the solder interfaceof tensile sample.

Following the work of Prakash et aI., Lee et aI., Quanand Bang et aI., [5, 11-13] fracture strength value of IMCat the solder interface is assumed 80 MPa, therefore,maximum load has been considered as 80MPa in oursimulation work.

2.2 . Material model:

In the computational model, Cu and IMC layer areconsidered to be isotropic linear elastic, whereas soldermaterials is considered to be viscoplastic materials. TableI lists material properties of Cu and IMC used in the FEManalysis.

Table I. material properties of Cu and IMC

Materials Elastic Modulus, E (Pa) Poisson' ration, U

Cu 128.7Xl09 0.34

IMC 85 XI09 0.31

To capture viscoplastic material model of the solderalloys, ANAND model has been used through theANSYS finite element code that deserve a bit moreexplanation.

758

2.3. Viscoplastic ANAND's model:

Previously, a specific viscoplastic constitutive lawneeded to be defined as a user-defined subroutine code torepresent the non-linear rate-dependent stress-strainrelations in some finite element programs, however,recent versions of ANSYS incorporated a well-acceptedrate dependent phenomenological model that was firstproposed by Anand. That Anand's constitutive modelconsiders large isotropic viscoplastic deformations butsmall elastic deformations. There are two main featuresin Anand model [14-15]:

1. no explicit yield condition and no loading/unloading criterion

2. a single scalar, the deformation resistance, S, isemployed as an internal variable to represent the averagedisotropic resistance to macroscopic plastic flow arosefrom strengthening mechanism such as dislocation filingup as well as solid solution strengthening, subgrain andgrain size effects, etc.

Anand model can be expressed as a flow equationand two evolution equations :

Flow equation:

~p = Aexp(- RQT{Sinh(;:)rm

Where,

£ p inelastic strain rate;

A pre exponential factor;Q activation energy;R gas constant;T absolute temperature;c; multiplier of stress;

(j equivalent stress;m strain rate sensitivity

Evolution equations:

A£ Qs* =s[-Lexp(_)]n

A RTho hardening/softening constanta strain rate sensitivity for hardening/softening

A

s coefficientn strain rate sensitivity for the saturation value of

deformation resistance

The values of the Anand's constant for SnPb andSnAgCu (SAC) solder were extracted from ref. 12 for thisresearch. The solder joints' part of the tensile sample wasmeshed using the viscoplastic element, VISCOI08, alongwith these values of materials parameters of Anand'sconstant.

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CDFigure 2. Quarter-point singular finite elements used

inANSYS.

K ll = CzO'"xy ..J1W

Although Kn is negligible for a homogenous elasticmaterial under uniaxial tensile loading, we have foundsignificant contribution of Kn value in our numericalanalysis that is sometime higher than KI values. This isbelieved to be the presence of highly viscoelastic soldermaterials in our specimen. Solder materials between Cuplates elongate viscoelastically with the applied load andtime. Therefore, similar to the case of Poissoncontraction, solder alloys contracts in the other direction.This generates strong shear contraction near the interface

that contributes to the shear stress, a in the solder/IMCxy

interface and is responsible for higher Kn value at theIMC crack tip.

Both of these KI and Kn values varied with:1. Alloys composition, i.e., materials properties of

solder alloys2. Location of the crack, i.e., distance from the

solder-IMC interface3. Solder joint thickness, i.e. volume of the solder

materials within the joint4. Strain rate, i.e., loading rate

Among these factors, distance from the interface has beenfound to be much more sensitive.

3.1 Effect of crack location relative to the interface:To understand the influence of the solder alloy on the

crack position near to the interface and further away, thesame size of cracks were considered at a distance of 1 J...Lm,2 J...Lm, 5 J...Lm, and 10 J...Lm from the solder-IMC interface.Loading rate of 0.8MPa/sec was used for both SAC andSnPb solder. Figure 3 shows the variation of KI and Knvalues with the crack location. It is clear from the figurethat SIF values increases sharply while the crack locationapproaches near to the interface, in particular, the Knvalue, i.e. the SIF of shear mode increases from theinsignificant values to a very high value that could lead toa very unstable crack. Pb-free solder (SAC) contributeshigher values compare to the SnPb solder. It is seen thatcracks within 5 fJm distance form the interface exertsmore than 1.5 MPa-mo.s - higher than the experimentalK1C values of IMC that could lead to fracture through theinterface. Among K1 and Kn values, Kn values were foundto be very sensitive to the crack location, in particular forPb-free solder. Effect of thickness of the IMC layer was

fracture toughness (KIC) of the CU6SnS IMC ranges from1.4 to 3 MPa-mo.s. Therefore, for a homogenous tensilesample of IMC, crack will not propagate under (j = 80MPa and crack size, a = 10 fJm. However, in ournumerical analysis, for the same loading stress, (j and thesame crack size, a, KI value of IMC varies from 0.1 to 3MPa-m°.5 due to the presence of solder alloys at theinterface.

While, KI is related to the SIF for opening modefracture solely due to tensile loading, Kn is related to theshearing mode fracture originated by shear loading asfollows:

PLANE183K

K] = CIO'">y&The specimen studied in this research is similar to

'Semi-infinite Plate with an Edge Through Crack underTension' where C =1.12. Throughout the simulation, weassumed 10 fJm size crack in the IMC layer. Ifwe put a =10 XI0-6m and applied load, (j = 80 MPa, we findanalytically KI= 0.503 MPa-mo.s. Numerically, by usingANSYS for the same model, we have found KI = 0.51MPa-mo.s when the whole body is elastic. From theexperimental findings of Balakrsinan et al. and Fields etal. [18-21], it was found that critical values for the

3. Results and discussionFor a tensile sample of homogenous elastic materials,

following analytical solution can be used to measure SIF[18],

2.3 Numerical methods for stress intensity factorevaluation:

Stress intensity factors (SIFs) play a major role inlinear elastic fracture mechanics (LEFM) analyses. Manynumerical methods using finite element analysis havebeen developed to obtain the SIFs along a pre-existingcrack front. The most common method of SIF calculationis the extrapolation of the displacements in the vicinity ofthe crack tip and uses the analytical expressions given bythe LEFM:

[u.E. J¥;]K r I tiP /"

a~ r~ (2+2vtip

)g/a l (1l") s;{a,i} = {I,1},{II,2},{III,3}

where, Ka ( a = I, II) are the SIFs, r is the distance of

the correlation point from the crack tip, Etip and Vtip areYoung's modulus and Poisson's ratio at the crack tip and

g}a) (B) are angular functions given by Anderson [16].

As the stresses and strains are singular at the crack tip,varying as l/r-Jl2

, singular finite elements with the mid­side nodes shifted to the quarter-point introduced byBarsoum are usually adapted in the FEA to improve thenumerical results in the vicinity of the crack tip [17].Elements are initially generated circumferentially about,and radially away, from the keypoint ( i.e., the crack tip)

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Figure 3: The variation of K1 and Kn values of Pb­free and SnPb solders with the crack locations.

Figure 4: vonMises stress distribution at the cracktips as well as crack openings for the cracks within (a) 1Jlm and (b) 2 Jlm distances for Pb-free solders.

12 Distance

5 from the10 interface,

JJ.mKII

4.5

4 /

3.5 /

3 .,-

an 2.5

~ 2dst 1.5

u.~ 1en

0.5

o

also studied where crack location was considered at themiddle of the IMC layer. IMC layer of 2 Jlm, 4 Jlm, 10Jlm, and 20 Jlm have resulted the same SIF values asshown in Figure 3 for cracks distance of 1 Jlm, 2 Jlm, 5Jlm, and 10 Jlm respectively. Therefore, we concludedthat thinner IMC layers have strong effect on the SIF ­leading to unstable cracks. Figure 4 shows vonMisesstress distribution at the crack tips as well as crackopenings for the cracks within 1 Jlm (a) and 2 Jlm (b)distances. Comparative crack opening displacements areclearly visible depending on the location of the crackfrom the interfaces.

4.5

4/

3.5/

3.,-

2.5 rnand E:JO.5E 2ds 1111

t 1.5

u: 1en

0.5

0

KII

Figure 5: The variation of K1 and Kn values of Pb­free and SnPb solders with the solder layer thickness atthe loading rate of 0.8MPa/sec.

It is worth mentioning that at a very slow loading rate,K1 values were found well below 0.5 MPa-mO.5

. Fromthe stress distribution contour, it is revealed that stressrelaxation of the solder materials near the edge interfaceat prolonged loading is responsible for lower value of SIFat slow strain rates.

Loading rates between 0.08 to 8 MPa/sec showedhigher K1 and Kn values for both solder joints. Yet, thereis a high jump for SIF values from loading rate 0.08 to

3.2 Effect of solder thickness:

Without any solder alloys between the Cu plate,sandwiched by only elastic IMC the K1 values lie within--0.5 MPa-mO.5

. Nevertheless, the SIF value increaseswith the presence of solder alloys - the thicker the solderlayer, the higher the values of SIFs. Here again, the effectis more significant for Pb-free solder (See Figure 5).Surprisingly, SIF values were also found well below 0.5MPa-mO.5

, however, at very slow loading rate. Effect ofloading rate is discussed in the next sections.

Higher values of SIF with the increasing solder layerthickness are considered to be related to the mass effect ofsolder alloys. Thicker solder layer exerts higherviscoelastic deformation that contributes higher stress andstrain near the crack tip at the solder interfaces.

3.3 Effect of strain rate:

Figure 6 shows the relationship between SIFs (K1 andKn) at the IMC crack tip and loading rates (MPa/sec) upto 80 MPa at 25°C for (a) SAC and (b) SnPb solder whilesolder thickness was Imm. The location of the crack isIJlm away from the solder-IMC interface. The trend issame for both Pb-free and SnPb, however SnPb soldershows lower SIF values for both K1 and Kn. At higherloading rates, solder alloys undergo less deformation aswell as less contraction. Therefore, we see lower value ofK1 and Kn when the strain rate is high.

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Figure 7: The extent of elemental deformation near theinterface as well as crack openings under (a) 0.008MPa/sec and (b) 0.8 MPa/sec loading rate.

1.00E+0!>

1.00E+05

1.00E+03

1.00E+03

1.00E+01

1.00E+01

5

4

Loading rate (MPa/sec)

Loading rate (M Pa/sec)

1.00E-01

1.00E-01

I-+-K1

1-.-KII

I-+-K1

1-.-KII

1.00E-03

1.00E-03

Figure 6: The relationship between KI and Ku at theIMC crack tip and loading rate (MPa/sec) for 80 MPaloading at 25°C for (a) SAC and (b) SnPb solder whilesolder thickness was 1mm. The location of the crack is1J.lm away from the solder-IMC interface.

0.01 MPa/sec. However, this peak value variesdepending upon the crack location and solder thickness.Further works need to be carried out to understand whyand how SIF values increase so sharply in this region.

Figure 7 shows elemental deformation near theinterfaces. Figure 7 (a) is for slow strain rate, whichshows significant deformation of the solder alloys at theinterfaces near the crack while in the Figure 7(b) which isfor high strain rate modelling, no such extendeddeformation is visible. As a result, we see higher cracktip opening that contributes higher SIF values.

3.4 Effect of loading:

Figure 8 shows the relationship between SIFs (KI andKu) at the IMC crack tip and applied loading (Stress,MPa) for (a) SAC and (b) SnPb solder for a constantloading rate (0.8MPa/sec) at 25°C while solder thicknesswas 1mm. The location of the crack is 1J.lm away fromthe solder-IMC interface. The trend is same for bothSnAg and SnPb, however SnPb solder shows lower SIFvalues for both K1 and Ku. Comparing with theexperimental fracture toughness mentioned earlier, safeload for SAC is found to be 50 MPa, whereas for SnPb, itis 70MPa. However, depending on the loading rate, this

safe loading limit could be changed. Among KI and Kuvalues, Ku values are initially low, however with theincrease of load, it increases sharply. On the other hand,Ku values were found to be insensitive while cracklocation was considered further away from the interface.

Conclusion

It is found that the cracks near the interface are moreprone to propagate. The thicker solder layer also hasdetrimental effect on the fracture characteristics of thesolder joints. In the solder joint using SnAgCu, the KI andKu values are higher than that of the SnPb solder. Strainrate showed a complex behavior - the highest range of KI

and Ku values were found at different rates depending onthe thickness of the solder layer and the distance betweenthe crack and the IMC-solder interface. It has beenconcluded that soft solder matrix generates a non-uniformplastic deformation across the solder-IMC interface that isresponsible for the higher KI and Kuvalues.

Acknowledgement

The authors would like to acknowledge the EDfunded Marie Curie Incoming International Fellowship,individual driven project MIFICT-2006-022113,"Reliability study of fine-pitch area-array Pb-free solderjoints for advanced electronic packaging - effect ofintermetallic compounds".

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7. 1. W. Hutchinson, M. E. Mear, J. R. Rice, "CrackParalleling an Interface Between DissimilarMaterials," J Appl Mech, Vol. 54:8, 1987, pp. 28-32.

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12. L. K. Quan, D. Frear, D. Grivas and J. W. Morris,"Tensile behavior of Pb-Sn solder/Cu joints" J.Electron. Mater., vol. 16, No.3, 1987, pp.203-208.

13. W.H. Bang, M.-W. Moon, C.-V. Kim, S.H. Kang,1.P. Jung and K.H. Ob, "Study of Fracture Mechanicsin Testing Interfacial Fracture of Solder Joints",Volun1e 37, Nun1ber 4,2008, pp. 417-428.

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15. G. Z. Wang, Z. N. Cheng, K. Becker, J. Wilde,"Applying Anand Model to Represent the ViscoplasticDeformation Behavior of Solder Alloys" Journal ofElectronic Packaging, Vol. 123,2001, pp. 247-253.

16. T. L. Anderson, "Fracture Mechanics: Fundamentalsand Applications", 2nd ed., CRC Press, London, BocaRaton (FL) (1995), pp. 29-96

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20. R. 1. Fields, R. R. Low and G. K. Lucey, "Physicaland Mechanical Properties of IntermetallicCompounds Commonly Found in Solder Joints" in"The Metal Science of Joining", edited by M.J.Cieslak, M.E. Glicksman, S. Kang Sand J. Perepezko(TMS, Ohio), (1991), pp.165

21. G. Ghosh, "Elastic properties, hardness, andindentation fracture toughness of intermetallicsrelevant to electronic packaging", 1. Mater. Res., Vol.19,No.5,2004,pp.1439-1454.

100

100

80

80

60

60

40

40

20

20

I--K1____ KII

O+----======-=--.--....-::::::::......-----.---~--__;_--____i

o

o+--.....a=====-~ ...-::~---.....,...._--____r-------i

o

Applied loading (Stress, MPa)

5,....---------------------,

Applied Loading (Stress, MPal

It)

Q 3

~ I--K11~ KII

u.M 2

en

Figure 8: The relationship between KI and Kn at theIMC crack tip and loading rate (MPa/sec) up to 80 MPa at25°C for (a) SAC and (b) SnPb solder while solderthickness was 1mm. The location of the crack is 1~maway from the solder-IMC interface.

References:

1. Puttlitz K. and Totta, P. A., Area Array InterconnectionHandbook, Kluwer Academic Publishers,Massachusetts, USA, 2001.

2. M. O. Alam and Y. C. Chan, "Effect of 0.5 wt% Cu inSn-3.5%Ag solder to retard the interfacial reactionwith the electroless Ni-P metallization in the IEEETransactions on Component and PackagingTechnology, Vol. 31, No.2, 2008, pp. 431-437.

3. M. o. Alam, B. Y. Wu, Y. C. Chan and L. Rufer,"Reliability of BGA Solder Joints on the Au/Ni/CuBond Pad - Effect of Thicknesses of Au and Ni layer"IEEE Transactions on Device and Materials Reliability,Volume 6, Issue 3, 2006, pp. 421 - 428.

4. M. O. Alam, Y. C. Chan and K. N. Tu, "Effect of 0.5wt.% Cu addition in Sn-3.5%Ag solder on thedissolution rate of Cu metallization", Joumal ofApplied Physics, Vol. 94 (12), 2003, pp. 7904-7909.

5. K. H. Prakash and T. Sritharan, "Tensile fracture oftin-lead solder joints in copper", Mater. Sci. Eng., vol.379,2004,pp.277

6. N. A. Fleck, J. W. Hutchinson, Z. Suo, "Crack pathselection in a brittle adhesive layer," Int J Sol Struct,Vol. 27(13),1991, pp. 1683-703.

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