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Mean time to failure of SnAgCuNi solder joints under DC

Conference Paper · May 2012

DOI: 10.1109/ITHERM.2012.6231474

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Shidong Li

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Electromigration time to failure of SnAgCuNi solder jointsCemal Basaran,1,a� Shidong Li,1 Douglas C. Hopkins,1 and Damien Veychard2

1Electronic Packaging Laboratory, State University of New York at Buffalo, Buffalo,New York 14260-4300, USA2PTM/CPA Group, STMicroelectronics, Grenoble F-38019, France

�Received 6 March 2009; accepted 23 May 2009; published online 9 July 2009�

Electromigration time to failure and electrical resistivity of 95.5%Sn–1.5%Ag–0.5%Cu–0.03W%Nimicroelectronics solder joints have been investigated experimentally. A Black-type electromigrationtime to failure equation is developed to describe the time to failure versus current density andtemperature. It is observed that resistance of a solder joint is not just a function of the temperaturebut also a function of the current density. The activation energy over the range of 83–174 °C ismeasured to be 0.77�0.12 eV, and the current density exponent is found to be �8.60�1.65�. It isalso shown that the most commonly used Black’s electromigration time to failure equation cannotbe used for solder joints. © 2009 American Institute of Physics. �DOI: 10.1063/1.3159012�

I. INTRODUCTION

Insatiable demand for higher functionality and miniatur-ization of electronics leads to higher density integrated cir-cuit �IC� devices with much smaller solder joints, which aresubjected to much higher current densities. As result, micro-electronics and power electronics solder joint failure due toelectromigration has been a major concern, recently. Accord-ing to International Technology Roadmap for Semiconduc-tors in next generation electronics electromigration will bethe dominant failure mode.

Electromigration is a mass transport process due to mo-mentum exchange between the mobile valence electrons andatoms �ions�. Due to the scattering phenomenon valenceelectrons bump into atoms and “electron wind force” movesthe atoms �ions� in the direction of electron movement.Hence, electromigration driving force moves the mass fromthe cathode side to anode side. As a result, on the anode side,the mass accumulation causes local compression and even-tually mass is squeezed out of material surface to form pro-trusions called hillocks.1,2 When the protrusions contact withcircuits nearby, short circuit failure occurs. While on thecathode side, mass depletion causes tension and vacancy ac-cumulation. Voids, which nucleate under tension, will growand coalesce causing increased localized resistivity and in-creased current crowding with eventual circuit failure. Thelatter mode is the major failure phenomenon that this study isconcerned with.

Basaran et al.,1 Abdulhamid et al.,3 Bastawros and Kim,4

Basaran and Abdulhamid5 have shown that when tempera-ture gradient is large enough, usually 1000 °C /cm, thermo-migration can overcome electromigration forces and can bethe dominant failure mechanism. Thermomigration is masstransport process due to temperature gradient, which happenin solids only under large temperature gradients.

A. Black’s law

In 1967, Black postulated that the lifetime of a metalthin film on a substrate is inversely proportional to the squareof the current density and has an Arrhenius relation withactivation energy, consistent with grain boundary diffusion.6

Based on experimental data, he proposed the following me-dian time to failure equation for electromigration failure ofthin films;

t50 =A

jn exp�Ea

kT� , �1�

where t50 is median time to failure defined by the time atwhich 50% of a large number of identical samples havefailed, A is an empirical material constant, j is the currentdensity, n is the current density exponent found to be 2 inBlack’s experiments, Ea is the activation energy consistentwith grain boundary diffusion activation energy, k is Boltz-mann’s constant, and T is the absolute temperature.

It has been reported in literature7 that for solder joints,Black’s equation cannot directly be used due to the influenceof current crowding and thermal gradient, which does notexist in straight thin films Black tested. Current crowding isnonuniform distribution of current density, similar to stressconcentration in solid mechanics. The major purpose of thisproject is to develop a similar simple electromigration timeto failure relationship for SACN solder joints.

II. EXPERIMENTAL SETUP

The test vehicles, shown in Fig. 1, were manufactured bySTMicroelectronics. The lead-free solder joints in the testvehicles have a composition by weight percentage of 95.5%tin, 1.0%–1.4% silver, 0.4%–0.6% copper, and 0.015%–0.03% nickel. The test vehicles is an actual 7.0�7.0�0.19 mm3 ball grid array �BGA� substrate is soldered to a50�50�1.5 mm3 BT printed circuit board substrate. Solderjoint dimensions are solder ball diameter is 320 �m, standoffheight is 127 �m, and passivation opening diameter is250 �m. During the experiments four-point method is em-ployed to measure the solder joint resistance. Software wasa�Electronic mail: cjb@buffalo.edu.

JOURNAL OF APPLIED PHYSICS 106, 013707 �2009�

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developed in LABVIEW to coordinate all the testing instru-mentations and collect the data every 5 s. Each test vehicleillustrated in Fig. 1 has several solder joints that can betested to failure independently.

During testing solder joints were subjected to dc currentonly. The testing started with stressing a solder joint to a 8 Afor about 12 h at room temperature �about 25 °C�, then cur-rent level was stepped up to 9 A, and then to 10 A. Mea-sured resistance time history is shown in Fig. 2. It was notuntil 10 A that a change in the slope of the electrical resis-tance time history was observed. It should be pointed out thatwhen a current is applied, due to Joule heating, resistanceincreases sharply at the beginning but then stabilizes withtemperature. Change in resistance discussed in the paper isnot the change that happens immediately following the cur-rent application but change after stabilization. By stressingthe test solder ball with 10 A current loading for 12 h, about3% irreversible resistance change was observed, Fig. 2, afterremoval of current and cooling down to room temperature.As a result of these initial trials, room temperature experi-ments started from 10 A.

Based on these experiments we observed that at roomtemperature, the solder joint will not fail or it will take verylong time to fail when it is stressed with a current lower than10 A. The corresponding nominal current density in the sol-der joint is about 2.04�104 A /cm2, where the nominalcurrent density is defined as the ratio of applied currentwith respect to solder mask opening area. This is in agree-ment with earlier studies reported by Basaran andco-workers.8–11,5,12,13

It was observed that the ambient temperature has signifi-cant effect on failure current density. When the temperaturewas raised to 60 °C, the electrical resistance started tochange, poststabilization period, when the applied current is9 A or higher.

In this study, measuring the temperature coefficient ofelectrical resistance in solder joints was one of the maintasks. However, it was quickly discovered that resistance insolder joints subjected to high current density is also a func-tion of the current density. Three samples, labeled P1, P2,and P3 individually, were placed in a thermal chamber. Theelectrical resistance was measured in room temperature�about 25 °C�; then the ambient temperature was increasedto 40, 50, and 60 °C. At each temperature level, five magni-tudes of electrical currents �I=0.2, 2, 4, 6, and 8 A, for

FIG. 1. �Color online� Test vehicle and measurement configuration.

FIG. 2. �Color online� Electrical resistance change under current loadings of 8, 9, and 10 A and then unloading to 1 A.

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sample P3 also I=10 A� were applied to measure the depen-dence of electrical resistivity on ambient temperature andcurrent density.

Following the first battery of tests, a second batch of testvehicles was tested under three different ambient tempera-tures: 25, 60, and 120 °C under higher currents than the firstbatch. In this series of tests applied current ranged from 9and 12.5 A, until solder joint failed. In these experiments,the failure criterion was a 10% change in resistance of testsolder ball after accounting for the influence of both ambienttemperature and Joule heating effect. The electrical resis-tance of a conductor under the high current loading can beexpressed by

R = R0 + �RT + �RJ + �REM, �2�

where R0 is the initial resistance defined before, �RT is theresistance change due to ambience temperature, �RJ is theresistance change due to Joule heating, and �REM is resis-tance change due to electromigration degradation.

Both �RT and �RJ reach steady state in a relatively shorttime. However, the resistance change due to electromigrationis a much longer process. Electromigration degradation con-tinuously increases the resistance of the solder joint and fi-nally causes device failure. In this work, the “failure criteria”threshold �REM is set as 10% of �R0+�RT+�RJ�. This is areasonable failure criterion because 10% resistance changecan lead to serious signal degradation in the device.

III. EXPERIMENTAL RESULTS

A. Temperature and current dependency ofresistance

It is difficult to eliminate the influence of Joule heatingduring the experiments. As a result, a numerical scheme wasadopted in order to remove the Joule heating induced resis-tance change from the total resistance change. Thermo-couples were placed on the surface of the tested solder ballsto measure the temperature. The relationship between mea-

FIG. 3. �Color online� Relationship ofelectrical resistance, current, and mea-sured temperature in Sample P1.

FIG. 4. �Color online� Relationship ofelectrical resistance, current, and mea-sured temperature in Sample P2.

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sured solder joint temperature and electrical resistance fortest vehicles P1, P2, and P3 are plotted in Figs. 3–5, respec-tively. In these figures, we observe that when the appliedcurrent is constant, the electrical resistance change is linearlyrelated to the actual measured temperature, which can beexpressed by the following relation:

R = Rref + ��T , �3�

where Rref is the electrical resistance at a reference tempera-ture which is 0 °C in this study, �T is temperature change,and � stands for the temperature coefficient of resistance.

However, as can be seen in Figs. 3–5, once the appliedcurrent is increased, both Rref and � change, which meansthat electrical resistivity of SACN solder alloy is both tem-perature and current dependent. In order to better describethe electrical resistivity of SACN solder joints, a model con-sidering both temperature dependence and current depen-dence is proposed below.

By using the method of least squares, each set of experi-mental data can be fitted to the following type of polynomialequation with the curve fitting coefficients listed in Table I.For sample P3 three extra data points were obtained with I=10 A,

R = R0�1 + �T + �I2� , �4�

where R0 is the initial electrical resistance, which is the re-sistance at T=0 °C �obtained by extrapolation�, � is the tem-perature coefficient of resistance, � is the current coefficient

of resistance, T is the ambient temperature in celsius, and I isthe direct current applied for measurement.

Using the coefficients given in Table I the experimentaldata were fitted to Eq. �4� for each sample. However, com-bining the data from all three samples into one regressioncurve yields smaller R-square value due to apparent differ-ences in initial manufacturing defects, which are very com-mon in solder joints. On the other hand, if we take R0 mea-sured from each sample �second column in Table I�separately, however, use the average values of � and � fromthree samples, using Eq. �4� leads to R-square coefficient of0.9678 for all 63 data points. Therefore, the relationship be-tween electrical resistivity and ambient temperature and elec-trical current can be expressed by

R = R0�1 + 4.567 � 10−3T + 3.828 � 10−3I2� . �5�

IV. FINITE ELEMENT SIMULATIONS

A finite element analysis was conducted, using ABAQUS

finite element analysis �FEA� code, to simulate the electricaland thermal responses of the test vehicles. For Joule heatinganalysis three-dimensional �3D� DC3D20E element for thesolder joints of interest, 3D element DC3D8E was used forother solder balls and the other components in the test ve-hicles, and 3D element DC3D6E was used for patches whichare used to mesh the irregular parts. The finite element meshis shown in Figs. 6–8.

At ambient room temperature �T=25 °C�, when 10 Acurrent is applied to the solder joint in position 1, the tem-perature contour in the test vehicle is shown in Fig. 9. FEATABLE I. Coefficients used for least-square curve fitting

Sample R0 �m�� � �

Number ofdata

points R-square

P1 1.673 4.589�10−03 3.403�10−03 20 0.9971P2 1.459 4.841�10−03 3.749�10−03 20 0.9980P3 1.828 4.272�10−03 4.332�10−03 23 0.9980

Average 4.567�10−03 3.828�10−03 63 0.9678

FIG. 5. �Color online� Relationship ofelectrical resistance, current, and mea-sured temperature in Sample P3.

FIG. 6. �Color online� Finite element mesh-global appearance.

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simulations indicate that the maximum temperature occurs atthe tapered �narrowing� section of the copper trace, labeledT1 in Fig. 9, where temperature is 90.8 °C. During FEAself-heat convection and heat radiation on the exposure sur-face were both taken into consideration. The simulation re-sults are very close to what is measured from the samples,for example, for solder joint S15P1 measured temperature is89.6 °C versus FEA computed temperature of 90.79 °C. Thedifference between simulation and measured value is small.In Fig. 10 it can be seen that the temperature inside the testsolder ball varies from 81 to 85 °C, which shows that thethermomigration effect can be neglected,8,3,11 Simulationsalso indicate that if we place the thermocouple at locationT1, the temperatures of the tested solder joints are overesti-mated by a few degrees of celsius. Therefore, it is reasonablefor us to assume that the measured temperature at T1 is theservice temperature of the tested solder joint.

Current crowding in solder joints subjected to high cur-rent densities is well known14,15,3 and it can be observed inFig. 11, which shows the current density contour in solderjoint P1. The nominal current density in the solder joint for acurrent of 10 A is 2.04�104 A /cm2, where the current den-sity is defined by the quotient of the applied current to thesolder mask opening area. However, from Fig. 11 we observethat the current distribution is not uniform throughout thesolder joint. In the left lower corner where the current entersfrom the solder joint to the copper trace, the current density�j=3.68�104 A /cm2� is about 1.5 times larger than thenominal value, while in the deep blue region of Fig. 11, thecurrent density is smaller than half the nominal value. There-fore, the geometry of the solder joint is an important factor

for its service life due to current crowding effect. Usually,the maximum current density at current crowding region ismuch higher than nominal current density, especially indrumlike solder joints.16,5

V. TIME TO FAILURE EXPERIMENTS

Test vehicles were also tested to failure to determinetheir time to failure. Failure was defined as 10% resistancechange after taking out Joule heating and current densityeffects. After an experiment starts initially, resistance willincrease during warm up period due to Joule heating andthen stabilize and remain constant for most the experiment.This 10% change in resistance was defined after the steady-state temperature in the solder joint was reached. In solderjoints resistance was also observed to be a function of thecurrent density. Therefore the influence of current densitywas also removed before calculating the 10% change. There-fore 10% change was due to electromigration only. Thethreshold was chosen because of electrical signal integrityconsiderations.

Time to failure �TTF� experiment results are listed inTable II. From these results we observe that there are threetypes of failure �and associated evolution of the electricalresistance� under different levels of current and temperature.

Type 1. Under a given ambient temperature, when thecurrent loading is small, there is no significant increase in theresistance due to electromigration. The electrical resistanceremains constant after Joule heating induced part reaches asteady state. The tests were stopped after a considerably longstressing time if no failure or change in resistance was ob-

FIG. 7. �Color online� Finite elementmesh-BGA.

FIG. 8. �Color online� Finite elementmesh-circuit in position 1.

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served. A typical Type 1 electrical resistance evolution canbe seen in Fig. 12 where joint S15P1 was stressed by acurrent of 10 A at room temperature. The test was terminatedafter 500 h with negligible irreversible resistance change.

Type 2. When current density is large enough, the resis-tance evolution follows a bilinear curve. In this case, theinfluence of electromigration is noticeable, which leads toincreasing resistance. For example, Fig. 13 shows the resis-tance evolution in solder joint S13P1, where we observe thatafter the warming up �initial Joule heating� period, the elec-trical resistance increases at an almost constant rate due toelectromigration. We should emphasize that during these ex-

periments temperature was continuously monitored at thesolder joints. Temperature in the solder joint stays stable, seeFig. 13, after the steady state is reached. Therefore we areconfident that change in resistance is not due to Joule heatingbut electromigration. After the 10% threshold �our pre-defined failure limit� was reached, the current loading onsolder joint S13P1 was kept for another 185 h. Then, whenthe current was removed the solder ball resistance, while it isstill hot, was measured to be 3.164 m� �78% increase frominitial resistance�. After the sample was allowed to cooldown, the resistance of the test ball was measured to be2.071 m� at 22.6 °C, which is 16.4% irreversible change

FIG. 9. �Color online� Temperature contour under room temperature with current loading of 10 A.

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compared to the initial resistance of 1.779 m� measured at23.8 °C.

Type 3. When current is very high �12 A�, heat generatedby Joule heating melts the solder joint in a very short time.

For example, sample S21P3 failed in 72 s, as shown in Fig.14. Because the entire process happens in a very short pe-riod, electromigration does not play an important role inType 3 failure. The mechanism can be explained by the de-

FIG. 10. �Color online� Temperature contour of test solder ball P1 �room temperature, I=10 A�.

FIG. 11. �Color online� Current density contour of test solder ball P1 �room temperature, I=10 A�.

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TABLE II. TTF of SACN solder joints.

TestI

�A�RT=0 °C

�m��Tsolder

�°C�Rreference

�m��Rthreshold

�m��TTF�h�

Failuretype

S21P1 9.0 1.766 83.49 2.674 2.942 No failure 1S18P2 9.0 1.477 82.83 2.392 2.632 No failure 1S20P3 9.0 1.821 88.35 2.913 3.204 No failure 1S22P1 9.0 1.683 149.41 3.218 3.54 14.42 2S21P2 9.0 1.631 146.05 2.907 3.197 68.16 2S22P3a 9.0 1.771 145.92 3.507 3.858 0.01 3S18P1 9.5 1.717 93.31 2.818 3.1 186.4 2S15P1 10.0 1.694 89.61 2.623 2.885 No failure 1S5P2 10.0 1.122 87.85 1.811 1.992 No failure 1S2P3 10.0 1.523 126.39 2.644 2.909 44.3 2S17P3 10.0 1.809 96.99 3.015 3.317 171.6 2S17P1 10.0 1.671 99.45 2.823 3.105 87.11 2S16P2 10.0 1.445 96.2 2.481 2.729 88.71 2S13P3 10.0 1.687 94.11 2.827 3.11 52.15 2S13P1 10.5 1.605 104.11 2.716 2.987 181 2S14P2 10.5 1.661 109.22 2.717 2.989 30.83 2S12P3 10.5 1.716 104.51 3.006 3.307 36.16 2S4P1 11.0 1.693 95.62 2.983 3.281 321 2S1P2 11.0 1.263 102.79 2.232 2.455 21.48 2S8P2 11.0 1.448 101.36 2.644 2.908 68.5 2S6P3 11.0 1.526 105.89 2.539 2.753 80.84 2S19P1 11.0 1.794 99.3 2.986 3.284 146.37 2S17P2 11.0 1.399 123.23 2.482 2.731 102 2S19P3 11.0 1.954 103.4 3.531 3.884 26.22 2S11P1 11.5 1.488 116.23 2.713 2.985 14.69 2S9P2 11.5 1.278 114.2 2.403 2.643 9.4 2S3P1 12.0 1.442 110.4 2.543 2.797 40.5 2S4P2 12.0 1.57 115.08 3.013 3.314 0.1 3S4P3 12.0 1.681 129.44 3.247 3.572 0.05 3S20P1 12.0 1.739 126.63 3.352 4.023 5.1 2S19P2 12.0 1.496 109.67 2.743 3.017 31.51 2S21P3 12.0 2.057 128.86 3.631 3.994 0.02 3

aWe believe that this data point is anomaly.

FIG. 12. �Color online� Sample S15P1I=10.0 A tested under room tempera-ture �failure mode: type 1�.

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generative amplification effect of Joule heating to electricalresistance. Increasing electrical resistance produces moreJoule heat under the constant current loading. Once the rateof heat generation exceeds the heat removal capacity of thestructure, temperature rises and conversely leads to the in-creasing electrical resistance, which again raises the tempera-ture until the solder joint melts.

Type 3 failure observed in solder joint SP22P3 is anaberration probably due to manufacturing defect, such as avoid which is common in BGA solder joints.

Using standard least squares method, an empirical timeto failure formula is developed from the data presented inTable II. For consistency, Type 3 failure data points are ex-cluded. In addition data points �S4P1, S17P2, and S13P3�

were also excluded because they were way outside the norm.The following electromigration time to failure equation is

TTF = A1

j8.60�1.65e�0.77�0.12� eV/kT ·1

�RT=0 °C�0.57�1.23 �6�

Moreover, in numeric terms the equation can be given by

ln�TTF� = �66.60 � 17.58� +�0.77 � 0.12� eV

kT

− �8.60 � 1.65�ln�j�

− �0.57 � 1.23�ln�RT=0 °C� . �7�

FIG. 13. �Color online� Sample S13P1I=10.5 A tested under room tempera-ture �failure mode: type 2�.

FIG. 14. �Color online� Sample S21P3I=12 A tested under room tempera-ture �failure mode: type 3�.

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The first three terms of Eq. �6� are similar to that ofBlack’s TTF equation, where A is a constant, which dependson the definition of failure threshold. For 10% net electricalresistance change after temperature reaches steady state, A=e66.60. T is the solder joint temperature in kelvins and j isnominal current density in A /cm2. The last term in Eq. �6�accounts for the manufacturing defect in the specimens,where RT=0 °C has been defined in Sec. IV. Manufacturingdefects lead to the scattered data we measure for the initialresistance. The coefficient of determination of Eq. �7� is R2

=0.81.The activation energy over the range of 83–174 °C is

measured to be 0.77�0.12 eV, which is very close to thevalues reported in the literature for SAC solder alloy, TableIII �0.72,17 0.89,18 0.83,14,17 and 0.76 eV �Ref. 15�� for SACsolder alloy. The current density exponent is found to be8.60�1.65.19,20 It was also observed that TTF of the SACNsolder joint is sensitive to its initial manufacturing defects,which leads to different initial resistance values.19,20

VI. CONCLUSIONS

In this study electromigration failure of SnAgCuNi BGAsolder joints was studied experimentally. It is observed thatresistance of solder joints is not just a function of the tem-perature but also a function of current density. An equation isproposed that correlates current density and temperature toresistance of a solder joint.

It is also shown that Black’s TTF equation cannot beused for solder joints. An electromigration time to failureequation for SACN BGA solder joints is proposed. Activa-

tion energy for SACN solder alloy is found to be very closeto published values of activation energy of SAC solder alloy.In TTF equation current density exponent for SACN solderjoints is 8.6.

Initial manufacturing defects cause serious differences ininitial resistance of solder joints.

ACKNOWLEDGMENTS

This research project has been partly sponsored by theSTMicroelectronics packaging team ATM which belongs toPTM/CPA groups in Grenoble, France. The project has alsopartly been sponsored by US Navy ONR under the directionof program Director Terry Ericsen.

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�2008�.

TABLE III. Activation energy for SnAgCu solder alloy.

Q�kcal/mol� Reference

0.72 Reference 170.89 Reference 180.83 Reference 140.76 Reference 15

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