Int J Fract (2008) 152:37–49DOI 10.1007/s10704-008-9264-9

ORIGINAL PAPER

Fatigue fracture of SnAgCu solder jointsby microstructural modeling

M. Erinc · T. M. Assman · P. J. G. Schreurs ·M. G. D. Geers

Received: 15 February 2008 / Accepted: 1 October 2008 / Published online: 21 October 2008© The Author(s) 2008. This article is published with open access at Springerlink.com

Abstract The ongoing miniaturization trend in themicroelectronic industry enforces component sizes toapproach the micron, or even the nano scale. At thesescales, the underlying microstructural sizes and thegeometrical dimensions are comparable. The increas-ing influence of microscopic entities on the overallmechanical properties makes conventional continuummaterial models more and more questionable. In thisstudy, the thermomechanical reliability of lead-freeBGA solder balls is investigated by microstructuralmodeling. Microstructural input is provided by orienta-tion imaging microscopy (OIM), converted into a finiteelement framework. Blowholes in BGA solder ballsare examined by optical microscopy and a statisticalanalysis on their size, position and frequency is con-ducted. Combining the microstructural data with theappropriate material models, three dimensional localmodels are created. The fatigue life of the package isdetermined through a critical solder ball. The thermo-mechanical reliability of the local models are predictedusing cohesive zone based fatigue damage models. Thesimulation results are validated by statistical analysesprovided by the industry.

M. Erinc (B) · T. M. Assman · P. J. G. Schreurs ·M. G. D. GeersDepartment of Mechanical Engineering, Section ofMaterials Technology, Eindhoven University ofTechnology, 5600MB Eindhoven, The Netherlandse-mail: muge@live.nl

Keywords Lead free · Cohesive zone modeling ·Solder fatigue · Microstructural modeling

1 Introduction

In microelectronic packages, mechanical integrity andelectrical connection is provided by solder connections.The microelectronics industry has switched to lead-freesolders in 2006 due to the toxicity of lead (Pb). Sincethen, near-eutectic and eutectic compositions of SnAg-Cu alloy are being extensively used as a replacement forthe traditional SnPb solder. Solder joints in microelec-tronic devices are exposed to thermomechanical fatigueloading caused by the repeated heating and coolingof the device (Fig. 1). The different thermal expansioncoefficients (CTE) of package materials provoke cyclicmechanical strains which results in fatigue crack ini-tiation and propagation in solder joints. On top of theCTE mismatch, Sn based solders are prone to thermalfatigue deformation even without being mounted onthe package. The thermal anisotropy of the β-Sn phasecauses intergranular fatigue damage upon cyclic ther-mal loading (Matin et al. 2006; Subramanian and Lee2004; Telang et al. 2004; Vianco et al. 2004). Miniatur-ization, i.e. decreasing solder dimensions, pronouncesthis kind of failure since smaller joints with a few grainsare more likely to fail by intergranular crack propaga-tion.

Examples of both damage mechanisms are shownin Figs. 2 and 3. In Fig. 2, cross-section of a BGA

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Fig. 1 Solder joints are exposed to cyclic thermomechanicalloading resulting from the CTE mismatch between package com-ponents

package with eutectic SnAgCu solder balls subjectedto 2,000 thermal cycles between −40 and 125 ◦C isshown. In Fig. 3, a micrograph of a bulk SnAgCu spec-imen after 1,500 thermal cycles (between � T =−40and 125 ◦C) is shown. Here it is important to note, thebulk sample was only thermally cycled, it was mechan-ically not constrained. Thus it is clear that there is anintergranular damage mechanism, although not visiblein the presence of a joint. In a solder joint, cyclic ther-momechanical loading causes highly localized defor-mations at the bump/pad interface, generally leadingto overall failure. Thermal cycling of bulk specimensclearly reveals that extensive deformation on Sn grainboundaries also takes place. Both damage mechanismsare clearly dependent on the microstructure due to theirinterfacial nature. Motivated by this fact, cohesive zonebased interfacial fatigue damage models were charac-terized by inverse modeling through dedicated fatigueexperiments (Erinc 2007; Erinc et al. 2004, 2005, 2007,2008). Fatigue life predictions for BGA or flip-chip sol-

Fig. 2 SnAgCu BGA solder balls, N = 2,000, �T =−40 to125 ◦C, courtesy of J. W. C. de Vries, Philips Applied Tech-nologies, optical image

Fig. 3 Bulk SnAgCu, N = 1,500, �T =−40 to 125 ◦C, opticalimage

der balls are generally conducted using Coffin-Man-son, J-integral, power law or creep models (Tchankovet al. 2008; Desai et al. 1998; Li and Wang 2007; Teeet al. 2003; Zhang et al. 2008). In Towashiraporn et al.(2005), the fatigue crack trajectory and fatigue life of asolder joint is predicted through a coupled numerical-experimental approach. A review on solder joint fatiguemodels with respect to their applicability to chip-scalepackages is given in Lee et al. (2000).

Driven by the ongoing miniaturization trend in themicroelectronics industry, the underlying microstruc-tural sizes and the geometrical dimensions of micro-electronic components tend to be comparable. Theincreasing influence of microscopic entities on the over-all mechanical properties makes continuum material

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Fatigue fracture of SnAgCu solder joints by microstructural modeling 39

models increasingly questionable. In this study, thethermomechanical reliability of lead-free BGA solderballs is investigated by microstructural modeling. Theoriginal aspects which will be presented in this studyare: (i) full microstructural model of SnAgCu solderballs based on crystallographic scans, (ii) cohesive zonebased damage modeling of physical interfaces that areprone to fatigue damage in solder balls, and (iii) extend-ing the current cohesive zone based microstructuraldamage framework to three dimensions. It will beshown that microstructural modeling adequatelypredicts and explains the diversity and scatter in theavailable experimental data. The SnAgCu solder ballcrystallography and manufacturing defects (i.e. voids,under-flow, over-flow etc.) are discussed in Sect. 2. Thenumerical techniques and the simulations, includingthe cohesive zone formulation, microstructural model-ing and fatigue life predictions are presented in Sect. 3.

2 Experimental analysis

2.1 Blowholes in solder balls

In lead-freesoldersblowholesorsurfacevoidingismorecommon than tin lead solders. This is due to the sur-face tension of the alloy as well as interaction with theflux. Common tin fluxes are ammonium chloride androsin.Blowholesarecausedbyoutgassingofflux,mois-ture or other organics on board. Liquids or gases expandat high temperatures escaping through the solder, leav-ing behind a hole. Water based fluxes that are not com-pletely dried can also expand and cause the same effect(see http://www.circuitnet.com/articles/article_40062.shtml). Small voids may arrest a propagating crack andenhance fatigue life, however, voids that cause a signif-icant decrease in the cross-sectional area of the solderjoint may reduce the fatigue life. Determining an opti-mum void size for crack arrest is out of the scope of thisstudy. Nevertheless, a statistical analysis on the occur-rence of voids in BGA solder balls is presented below.

Six newly manufactured EFSOT-BGA256 packageswere cross-sectioned row by row. These packages con-tain 256 solder balls (760µm diameter) having the com-position Sn4.0Ag0.5Cu with Ni/Au metallization. Thesolder balls were examined by an optical microscope fordefects at their maximum diameter (∼760 µm). The im-ages were collected by a digital camera and voiddimensions were measured using image analysis soft-

ware. Figure 4 shows typical examples of manufactur-ingdefectsencountered inBGAsolderballs.Apart fromblowholes, defects due to under-flowing were alsoobserved.Thedatacollectedfromthesepackagesisplot-ted in Fig. 5. From all the solder balls examined, 57%containedvoidswithanaverageof1.5voidperball.84%of all the voids observed were on the chip side. Solderballs with big voids (>100µm) were rare (

40 M. Erinc et al.

Fig. 4 Manufacturingdefects, i.e. blowholes (left),under-flow gaps (right), inBGA packages withSnAgCu solder balls,optical images ×20

Fig. 5 Distribution ofblowholes in BGApackages. a Volumeoccupied by void(s) in asolder ball. b Void position.c Void diameter

43%

47%

9%1% 0%0−1%1−3%3−10%

84%

16% chip sideboard side

35%

39%

19%

6%< 1%

Fatigue fracture of SnAgCu solder joints by microstructural modeling 41

Fig. 6 OIM scans of760µm diameterSn4Ag0.5Cu solder balls

experimental evidence (Erinc et al. 2007). At the bump/pad interface, the microstructural morphology (scal-lops growing perpendicular to the pad surface) causesthe anisotropic behavior. The damage law is isotropicfor the grain boundaries (Erinc et al. 2008).

The 3D cohesive zone element is shown in Fig. 7.The local coordinate system is defined on the mid-planeABCD of the element. Four integration points, x1, x2,x3 and x4 in the mid-plane are considered. Two tangentvectors, �t1 and �t2, are located on the mid-plane, andthe normal vector �n is found by the cross-product of �t1and �t2. Opening vectors �� at the integration points arecalculated from the global openings at element nodesand rotated to the local coordinate system. Using thecomponents of ��, the components of the traction vec-tors in the normal and tangential directions, Tn, Tt1 andTt2, are calculated as follows:

Ti = ki(1 − Di)�i, where i = n, t1, t2 (1)

where ki is the initial stiffness and Di is an interfa-cial damage variable, which takes values between 0(no damage) and 1 (complete failure). The slope of theTi–�i curve for each fatigue cycle gives the instanta-neous stiffness, ki(1 − Di), which decreases due to theevolution of damage. The damage variable of a cohe-sive zone element is the sum of the cyclic incrementaldamage values for that element. The tangential tractioncomponents, Tt1 and Tt2, and opening components,�t1and �t2, compose the total tangential traction, Tt, andthe total tangential opening, �t , respectively:

Tt = (Tt12 + Tt22) 12 (2)

�t = (�t12 +�t22) 12 (3)

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Fig. 7 3D cohesive zoneelement, the mid-plane, andlocal coordinate system

1 2

34

5 6

78

A B

CD

IIII

I

I

NormalA B

CDX X

X X1 2

3 4

The evolution of the damage variable, Ḋ, is calcu-lated according to:

Ḋn,t = cn,t|�̇n,t|(1 − Dn,t + r

)mn,t〈 |Tn,t|

1 − Dn,t − σf〉

(4)

where �̇n,t is the rate of relative opening, σf is thefatigue limit, c, m and r are constants controlling thedecay of the cohesive interaction. Macaulay bracketsensure that damage evolution takes place only for stresslevels higher than the fatigue limit, σf . The fatigue limitis taken equal to σf = 17 MPa (Erinc et al. 2007). Theevolution law is typically phenomenological and is for-mulated in a way which takes into account the maindamage characteristics in solder joints.

3.2 The local model

A BGA package can be considered as a matrix of geo-metrically repetitive blocks composed of a solder ball,the printed circuit board PCB, and the molding com-pound, as shown in (Fig. 8). In this section, detaileddamage analyses on such blocks, further denoted as‘local models’, are presented.

In order to make a local model, first a 3D solderball incorporating the local grain orientations and themicrostructure is created. As explained in Sect. 2.2,760µm diameter solder balls were scanned by OIM.Grain boundaries are identified as a collection of linevectors and local Euler angles are used for each of thegrains. The grain boundary lines are directly transferredto the finite element discretization, along which the ele-ments are generated. The grain interiors are meshedusing hexagonal elements. The crystallographic orien-tations are assigned to the grains after rotating the local

Fig. 8 A BGA package is a 2D array of geometrically repeatingblocks composed of the solder ball, molding compound and thePCB

Euler angles (φ, θ, ψ) from the OIM reference frame tothe FEM reference frame. The OIM and FE referenceframes are shown in Fig. 9.

OIM scans relate the local crystal orientation to theOIM reference frame in Euler angles (φ, θ, ψ) accord-ing to the x-convention. The local crystal orientationwith respect to the OIM reference frame is found bythree subsequent rotations; 1st rotation around normaldirection (ND) by an angle φ (Rφ), 2nd rotation aroundreference direction (RD) by an angle θ (Rθ ) and 3rdrotation again around ND, by an angle ψ (Rψ ). TheOIM reference frame is rotated to the FE referenceframe by ROIM (90◦). All four rotations are combinedin a single rotation matrix R according to Eq. 5, whereeach matrix is defined with respect to the vector basisresulting from the previous rotation step.

R = RφRθRψROIM (5)where

Rφ =⎡

⎣cosφ − sin φ 0sin φ cosφ 00 0 1

⎤

⎦ Rθ =⎡

⎣1 0 00 cos θ − sin θ0 sin θ cos θ

⎤

⎦

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Fatigue fracture of SnAgCu solder joints by microstructural modeling 43

Fig. 9 OIM set-up andOIM and FEM referenceframes

Rψ =⎡

⎣cosψ − sinψ 0sinψ cosψ 00 0 1

⎤

⎦ ROIM=⎡

⎣0 1 0−1 0 00 0 1

⎤

⎦

A preliminary 3D analysis is performed on themicrostructural meshes, in order to coarsen the discr-etization without substantially altering the overallmechanical response. The discretization is coarsenedon a scale of f = 0−10, where f = 0 corresponds themesh created according to the original scan. An elas-to-plastic material model is used (Erinc et al. 2007).The models are thermally loaded by linearly increas-ing the temperature from 25 to 100 ◦C homogenouslyin 30 min, in other words, temperature is prescribed toall elements as a state variable and a heat transfer cal-culation is not done. The distribution of the equivalentVon Mises stresses, σvm, at 100 ◦C is compared. Se-lected meshes and contour plots of σvm are shown inFigs. 10 and 11, respectively. After coarsening four lev-els, f = 4, the number of elements significantly reduces.Coarsening level f = 6 seems to be an adequate com-promise since at this level the details in the results arewell captured while the number of elements is reducedby a factor of two.

The microstructure of ten solder balls is discret-ized from the OIM scans incorporating local crystal-lographic orientations and coarsening the mesh by afactor f = 6, as explained above. Different from the pre-liminary analysis shown above, very thin cohesive zoneelements are now placed at the grain boundaries, suchthat the normal direction corresponds to the crack open-ing between two grains, while the two tangential direc-tions reside in the grain boundary plane, representinggrain boundary sliding. Two examples of microstruc-tural meshes and the cohesive network at the grainboundaries are shown in Fig. 12.

The grain boundaries in the thickness direction areassumed to be straight and perpendicular to the surface.The resulting grain orientations are thereby approxi-mately expressed in the FEM coordinate system. In

Erinc (2007), it is shown on the basis of numerical re-sults that vertical grain boundaries touching the bump/pad interface have the highest stress level under thermalloading, whereas the stress level at a grain boundary de-creases as it becomes more horizontal.

Next, solder balls having a contact angle of 120◦ areextruded from the discs, which are then combined withthe rest of the local model shown in Fig. 13. The localmodel consists of (top to bottom): molding compound,substrate, solder mask, metallization (UBM: copper,nickel and Ni3Sn4 intermetallic layer), solder ball, met-allization, solder mask and the printed circuit board.The elastic and thermal material properties are givenin Table 1. SnAgCu is modeled by a time independentelasto-plastic material model (Erinc et al. 2007) com-bined with a steady-state creep model for bulk SnAgCugiven by Wiese et al. Wiese and Wolter (2004), shownin Eq. 6 where A1 and A2 are 4e-7 and 1e-12 s−1, Q1and Q2 are 26.8 and 61.4 kJ/mol, n1 and n2 are 3 and10 (different from the original value), respectively. Theplasticity model used is based on Von Mises yield crite-rion. Hardening is described by providing the measuredtensile curve using proper stress and strain definitions.Besides the grain boundary elements, two sets of cohe-sive zone elements are placed between the metallizationand the solder ball on both sides. The damage evolu-tion parameters for the bump/pad and grain boundaryelements have been identified previously (Erinc et al.2007, 2008) and are tabulated in Table 2.

ε̇ = A1(σ

σN

)n1exp

(− Q1

RT

)

+A2(σ

σN

)n2exp

(− Q2

RT

)(6)

Since all physical interfaces have a very small,though finite thickness, cz elements are given a 100 nminitial thickness (tcz). In classical cohesive zoneapproaches, cohesive zones do not need to have an ini-tial thickness. However, assigning a physically relevant

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Fig. 10 Reducing thenumber of elements (N) bycoarsening the mesh by afactor f. a f = 0,N = 564.b f = 5,N = 360.c f = 10,N = 140

Fig. 11 Correspondingequivalent Von Mises stress[MPa] distribution at 100 ◦C

finite thickness allows one to calculate a finite ini-tial stiffness which prevents the known initial stiff-ness problem and better represents the actual interphase(Chaboche et al. 2001). The initial stiffness of the cohe-sive elements for normal, kn, and tangential, kt, direc-tions are computed from the adjacent materials 1 and2, in order to provide an equivalent elastic deformationcompared to the case without the cohesive elements.The initial stiffness for tangential and normal directionsare given in Eq. 7, where E is the Young’s modulus andG is the shear modulus.

kt = 2G1G2tcz(G1 + G2) , kn =

2E1E2tcz(E1 + E2) (7)

Periodic boundary conditions are applied to the localmodel. A cyclic thermal loading is applied, being eithercyclic harmonic �T =−40 to 125 ◦C with a moder-ate temperature change rate (Fig. 14a), or cyclic shock�T =−55 to 125 ◦C with a strong temperature change

rate (Fig. 14b). Each cycle is computed in 10 incre-ments.

3.3 Fatigue life predictions

In the literature (Abdul-Baqi et al. 2005), Dn and Dt areaveraged to calculate an effective damage value Deffaccording to the following formulation:

Deff = (D2t + D2n − DtDn)12 (8)

According to Eq. 8, a Deff value lower than eitherDn or Dt can be calculated, leading to a decrease in thevalue of Deff (see Fig. 15, left). This is physically unre-alistic since damage is irreversible and cumulative. Inthis study a modified formulation is proposed, given inEq. 9:

Deff = 2π

arccos(

cos(π

2Dn

)∗ cos

(π2

Dt))

(9)

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Fatigue fracture of SnAgCu solder joints by microstructural modeling 45

Fig. 12 Microstructuralmeshes and the cohesivenetwork at grain boundaries.a Example 1, b Example 2

Fig. 13 A representativelocal model

1.17mm

Deff is defined in the range [0–1]. For low values ofDn and Dt, Deff follows a circular pattern (see Fig. 15,right). As they approach 1, Deff tends to a square pat-tern. Deff is thereby never smaller than its composingvalues Dn or Dt. The term 2/π is added to normalize

Deff towards unity. Values of Dn and Dt are calculated atthe end of every increment for every cz element accord-ing to Eq. 4.

After Deff is calculated for all elements, an aver-age damage value per interface is computed taking

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Table 1 Elastic materialparameters and CTE valuesused in simulations

a Hardening data is given inErinc et al. (2007)b Jang et al. (2004)c Lai et al. (2005)

Material E(GPa) ν α(ppm/◦C)

SnAgCua 64.1 0.4 [100], [110]:16.5,[001]:32.4

Cu 128 0.35 17Ni 197 0.31 12.96Ni3Sn b4 140.4 0.3 14.98PCBc 17.5 0.11 17.6Moulding compoundc 10 0.25 16.9Substratec 1 0.11 16Solder maskc 2.412 0.467 60

Table 2 Cohesive zoneelement parameters used insimulations

a Erinc et al. (2007)b Erinc et al. (2008)

Cz elements k(GPa/mm) c m r

bump/pad, normala 8.79e8 68,000 3.16 1e−6bump/pad, tang.a 3.21e8 47,000 3.135 4e−5grain bound, normalb 6.4e8 42,000 2.94 0grain bound, tang.b 2.28e8 42,000 2.94 0

Fig. 14 Cyclic harmonic(left) and cyclic shock(right) loading schemesprescribed as boundaryconditions in thesimulations

0 10 20 30 40 50 60

−40

−20

0

20

40

60

80

100

120

t (min)

T (

°C)

0 5 10 15 20 25 30 35 40−60

−40

−20

0

20

40

60

80

100

120

t (min)

T (

°C)

the surface average. The surface average is calculatedby weighing the integration point values to the corre-sponding face area of the element. Figure 16 showsthe average effective damage Davgeff at the interfaces,(1) top bump/pad interface, (2) bottom bump/pad inter-face, (3) grain boundaries. In all computations, the topbump/pad interface shows the highest damage,followed closely by the bottom bump/pad interface.Least damage was observed at the grain boundaries.Damage at the grain boundaries always evolved to astationary value early in the calculation. If the sol-der geometry is chosen such that it concentrates morestresses in the solder, i.e. through an hourglass shape,the grain boundaries will take most of the damage andeventually fail, whereas damage at the pads level-off.Hence, there is a competition between the grain bound-aries and the pads favored by a specific geometry.

Substantial CPU time can be saved if damage evo-lution could be predicted at an earlier stage in the cal-culation. Local models (examples 1 and 2 in Fig. 12)are loaded under thermal cycling,�T =−40 to 125 ◦C,for N = 5,000 cycles. In Fig. 17, the average damageevolution versus the number of cycles for both mod-els is plotted. In connection with the damage evolutionlaw given in Eq. 4, the shape of the curve suggests anexponential evolution (1 − e−a∗N ). However, a singleexponential parameter is not able to describe the entirespan of the damage evolution curve. Instead, a rationalfunction of quadratic polynomials with five parame-ters (p1x2 + p2x + p3)/(x2 + q1x + q2) is used. Asobvious from Fig. 17, with five parameters, the damageevolution curve can be described and predicted fairlywell. The fitting function is determined over the sim-ulation results between N = 0 and N = 1,000. Beyond

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Fatigue fracture of SnAgCu solder joints by microstructural modeling 47

Fig. 15 Contour plot ofDeff according to: Eq. 8(left), Eq. 9 (right)

0.05

0.1

0.150.2 0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9 0.9

0.9

0.95 0.95

0.95

Dn

Dt

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1

0.15 0.2

0.25

0.30.35

0.40.45

0.5

0.55

0.60.65

0.70.75

0.8 0.85

0.9

0.95

Dn

Dt

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

N

Dam

age

grain boundariesbottom bump/pad interfacetop bump/pad interface

Fig. 16 Damage at all interfaces in a representative local modelwith cyclic shock loading

N = 1,000, the extrapolated curve is compared with therest of the simulation results using least squares mini-mization, which provides an adequate prediction up toN = 5,000.

3.4 Numerical-experimental comparison

The numerical results obtained so far are comparedwith experimental analyses of BGA packages undercyclic harmonic and cyclic shock loading. For bothtypes of loading, damage evolution in all local modelsis calculated until N = 1,000 cycles and extrapolated toN = 5,000 cycles. According to Eq. 9, a critical effec-tive damage value Deff is defined to predict the num-ber of cycles to failure, that adequately reproduces theexperimental failure distributions provided by PhilipsApplied Technologies Eindhoven.

0 1000 2000 3000 4000

sim:slice 1rat22, N=1000

50000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

N

Dam

age

Fig. 17 Damage evolution curve is fit by a quadratic rationalfunction (rat22) between N = 0 and N = 1,000 cycles and extrapo-lated to N = 5,000 cycles. Extrapolation is compared with numer-ical results

First, the fatigue life of all local models are cal-culated without any defects, representing a theoreticalcase. Next, defects are introduced in the mesh, as sta-tistically determined in Sect. 2. This is done by settingthe initial damage value of the cz elements to D = 1 atplaces where a void is expected. In the case with de-fects, the average number of voids in a solder balls was1.5, 80% of the voids contained a void with diameterφ ≤ 50 µm (74% measured), 20% of the voids con-tained a void with diameter φ≤ 100 µm, (25% mea-sured). Voids with a diameter larger than 100µm arenot modeled (1% measured). Eighty percent of thevoids were placed at the chip side (84% measured).Finally, a data set consisting of good (45%) and defec-tive balls (55%) is constructed. Figure 18 shows that,with a critical damage level for failure equal to Dcriteff =0.87, a good agreement between the statistically con-structed data set and the experimental data is obtained.

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103

104

0

10

20

30

40

50

60

70

80

90

100

N

Fai

lure

%

experimentalsim: theoreticalsim: all defectivesim: statistical

103

104

0

10

20

30

40

50

60

70

80

90

100

N

Fai

lure

%

experimentalsim: theoreticalsim: all defectivesim: statistical

Fig. 18 Comparison of experimental results (De Vries et al.2007) with simulations for harmonic cycling (top), and cyclicshock (bottom)

The fatigue life of strongly resistant (N > 5,000) solderballs is over-estimated. This is an expected result; asmentioned previously, the cross-sectional defect anal-ysis hides many defects, yielding too optimistic results(45% of all solder balls were defect-free). In reality,more defects may be present, which have to be insertedinto the local models.

4 Conclusions

In this study, the thermomechanical reliability of lead-free BGA solder balls is investigated by microstructuralmodeling. Three dimensional solder joints are simu-lated incorporating the microstructure, local orienta-tions and initial defects, which were not handled inthe literature before. The fatigue life is determined us-

ing cohesive zone based damage models for bump/padcrack propagation and intergranular fatigue damageand compared with experimental values. The follow-ing conclusions are drawn from the current study:

• Microstructural modeling allows one to predict andunderstand the scatter in the solder ball fatigue lifeobserved in the engineering practice.

• A 2D cross-sectional analyses gives a qualitativeindication on the present initial defects. However,the numerical-experimental comparisons show thata 2D methodology yields an underestimate of ini-tial defects in real solder balls. 3D visual techniqueshave to be used for a complete description of thegeometry.

• Using cohesive zone elements to describe interfacialfatigue damage in solder joints, which is extended to3D in this paper, is shown to be an effective tool infatigue life prediction.

• The numerical results are compared with experimen-tal fatigue life analyses obtained from the indus-try. A critical effective damage value, describing theonset of failure for cohesive zone elements is deter-mined based on the numerical-experimental compar-ison. With the incorporation of initial defects intothe models, an adequate agreement between the pre-dicted and measured fatigue lives of solder joints isachieved.

Acknowledgements This research is supported by the Tech-nology Foundation STW, applied science division of NWO andthe technology programme of the Ministry of Economic Affairs.Special thanks to J. W. C. de Vries and Philips Applied Tech-nologies for the experimental input in Sect. 3.4, and to R. H. J.Peerlings for the useful discussions.

Open Access This article is distributed under the terms of theCreative Commons Attribution Noncommercial License whichpermits any noncommercial use, distribution, and reproductionin any medium, provided the original author(s) and source arecredited.

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Fatigue fracture of SnAgCu solder joints by microstructural modeling 49

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Fatigue fracture of SnAgCu solder jointsby microstructural modelingAbstractAbstract1 Introduction2 Experimental analysis2.1 Blowholes in solder balls2.2 Crystallography

3 Numerical analysis3.1 Cohesive zone model3.2 The local model3.3 Fatigue life predictions3.4 Numerical-experimental comparison

4 ConclusionsAcknowledgements

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