electromigration enhanced intermetallic growth …ho/papers/brook jap 2006.pdfelectromigration...

Electromigration enhanced intermetallic growth and void formationin Pb-free solder joints

Brook Chao,a� Seung-Hyun Chae, Xuefeng Zhang, Kuan-Hsun Lu, Min Ding, Jay Im, andPaul S. HoLaboratory for Interconnect and Packaging, The University of Texas at Austin, Austin, Texas 78712

�Received 1 July 2006; accepted 22 July 2006; published online 31 October 2006�

A kinetic analysis was formulated for electromigration enhanced intermetallic evolution of a Cu–Sndiffusion couple in the Sn-based Pb-free solder joints with Cu under bump metallurgy. Thesimulated diffusion couple comprised the two terminal phases, Cu and Sn, as well as the twointermetallic phases, Cu3Sn and Cu6Sn5, formed between them. The diffusion and electromigrationparameters were obtained by solving the inverse problem of the electromigration enhancedintermetallic growth, and they were compatible with the literature values. Finite difference methodwas applied to the whole simulated domain to solve for the mass transport kinetics within theintermetallic phases and across each interface of interest. Simulation showed that, whenelectromigration effect was absent �zero current�, intermetallic growth followed a parabolic law,suggesting a diffusion controlled mechanism for thermal aging. However, under significant currentstressing �4�104 A/cm2�, the growth of the dominant intermetallic Cu6Sn5 clearly followed alinear law, suggesting a reaction controlled mechanism for electromigration. Simulation results wereconsistent with the experimental observations. The analysis of vacancy transport was alsoincorporated with the model, and the results showed substantial increase in vacancy concentrationat the Cu6Sn5 phase near the Cu3Sn/Cu6Sn5 interface. The peaking of the vacancy concentrationexplains the substantial Kirkendall void formation under electromigration at this region. © 2006American Institute of Physics. �DOI: 10.1063/1.2359135�

I. INTRODUCTION

The continuing demand for increasing packing densityand device performance has spurred significant interests re-cently to develop plastic flip-chip packages. Flip-chip pack-aging provides substantial advantages over wire bonding inhigher I /O density with area array, better power-ground dis-tribution and lower stress over active areas. Applicationssuch as cellular telecommunications and portable consumerelectronics also necessitate their use for small form factorand high speed.

The reliability of flip-chip packages has emerged as acritical concern because of the demand for increasing currentdensity with smaller solder bump size. A common failuremode for flip-chip packages is an electrical open due to voidformation induced by intermetallic compound �IMC� growthat the interface between the solder and under bump metal-lurgy �UBM�. Failures of this type have been reported afterprolonged current stressing at an elevated temperature andhave been identified as a result of electromigration �EM�.1

Under EM, IMC growth can be significantly enhanced bymass transport driven by the electron current.2 The IMCgrowth is accompanied by Kirkendall void formation, whichplays an important role in controlling the EM lifetime ofsolder joints in flip-chip packages. Gan and Tu reported dis-tinct characteristics for IMC growth at the anode and thecathode and formulated a kinetic model to account for thecurrent polarity effect on IMC growth.3 In their model, the

two intermetallic phases, Cu3Sn and Cu6Sn5, formed at thesolder/UBM interface were not distinguished but treated as asingle phase for simplicity. Following this study, Orchardand Greer recently analyzed the EM effect on compoundgrowth at interfaces, taking into account the effect of inter-facial reaction barriers but still treated only a single interme-tallic phase.4

Gurov and Gusak analyzed the kinetics of the diffusioncouple under an electric field, taking into account the forma-tion of dual intermetallics and present asymptotic solutionsat steady state.5 These authors found that the growth kineticsof the dual intermetallics can follow several possible growthmodes depending on the balance of the interdiffusion andelectromigration fluxes in individual compound layers. Thiswas designated as interdiffusion electromigration coefficientin the present paper.

This paper reports a kinetic analysis for current en-hanced growth of dual intermetallic layers under EM. Thesimulative model was applied to analyze experimental resultson IMC formation observed under EM between a Cu UBMand a Sn-based Pb-free solder. The interfacial reaction wastreated as growth of dual compound layers in a Cu-Sn diffu-sion couple taking into account the current-driven masstransport of Cu and Sn atoms. The complexity of the dualIMC formation under EM necessitated the use of a simula-tion scheme to analyze the IMC growth kinetics at each dis-cretized time step and to extract the interdiffusion EM coef-ficients from the experiments. Thus, a finite differencemethod �FDM� was adopted in this paper. Such numericalapproach enabled a detailed examination of the effect of cur-a�Electronic mail: [email protected]

JOURNAL OF APPLIED PHYSICS 100, 084909 �2006�

0021-8979/2006/100�8�/084909/10/$23.00 © 2006 American Institute of Physics100, 084909-1

Downloaded 10 Nov 2006 to 129.116.140.99. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp

http://dx.doi.org/10.1063/1.2359135

http://dx.doi.org/10.1063/1.2359135

http://dx.doi.org/10.1063/1.2359135

rent in enhancing the growth of individual compounds. Inaddition, the rate of vacancy transport could be deducedfrom the flux balance in the layered structure. The resultprovides insight to void formation induced by EM duringIMC growth, which controls EM damage formation.

II. THEORY

A Cu–Sn diffusion couple was considered, in which twointermetallic phases, Cu3Sn and Cu6Sn5, were formed be-tween pure Cu and pure Sn phases. The two intermetallicphases have very narrow composition ranges, as indicated bythe phase diagram �Fig. 1�a�� and the values of the boundarycomposition that are listed in Table I. Figure 1�b� shows the

schematic composition profile of the diffusion couple. Withineach phase, interdiffusion of Cu and Sn atoms occurs simul-taneously and, in addition, the electron current from theUBM toward the top surface metallurgy �TSM� exerts a di-rectional driving force causing atoms to diffuse in this direc-tion. Darken’s equation for interdiffusion6 can be modified toapply to this particular case, so that atomic flux induced byboth chemical potential driven diffusion and external electricfield can be taken into account.

Atomic flux due to chemical diffusion is expressed as

JCu,ichem = − DCu,i

�Ci

�x,

�1�

JSn,ichem = − DSn,i

�CSn,i

�x= DSn,i

�Ci

�x.

In the present paper, all compositions C are expressed asmole fractions of Cu and the subscript Cu is omitted forsimplificity unless otherwise denoted. The running index idenotes the phase in which interdiffusion takes place. It isassumed that the vacancy concentration is low, and thereforethe density of the phase is C0=CCu+CSn.

Current induced atomic flux is expressed as

JCu,iEM = CCu,i

DCu,i

kTZCu,i

* e�i j = CiDCu,i�Cuj ,

�2�

JSn,iEM = CSn,i

DSn,i

kTZSn,i

* e�i j = �C0 − CSn,i�DSn,i�Snj ,

where �= �Z* /kT�e� is the electromigration factor.Combining the chemical diffusion flux and current in-

duced flux into Fick’s second law gives the governing equa-tion of current enhanced interdiffusion within each phase.

�Ci

�t=

�

�x�D̃�Ci�

�Ci

�x+ �̃iCi�1 − Ci�j� , �3�

�̃i = DSn,i�Sn,i − DCu,i�Cu,i, �4�

where �̃i is the effective interdiffusion electromigration coef-ficient of phase i as defined in Ref. 5.

Figure 1�c� shows the descriptive diagram of the compo-sition of two adjacent phases and their associated interfacewith respect to spatial coordinates. � and � denote the twoadjacent phases of interest, and their compositions are func-tions of the spatial coordinate x. Their compositions at theinterface are restricted by the solute solubility according tothe phase diagram and are denoted as C�� and C��, respec-tively. As the interface moves to the left by a distance dx, forinstance, the amount of solute dissolving from � into � canbe expressed as �C��−C��dx. Mass conservation dictatesthat the flux of solute migrating across the interface is bal-anced by the diffusive flux in the two adjacent phases � and�. Assuming that chemical diffusion and current induced dif-fusion are the only contributions to atomic flux, the velocityof interface migration can be described in the followingbased on the mass conservation principle:

FIG. 1. �Color online� �a� Sn–Cu binary phase diagram. �b� Cu compositionprofile of Cu–Sn diffusion couple. �c� Cu composition profile near aninterface.

TABLE I. Cu composition �atomic fraction� at interfaces.

C12 C21 C23 C32 C34 C43

0.993 0.765 0.755 0.549 0.541 0.000 06

084909-2 Chao et al. J. Appl. Phys. 100, 084909 �2006�


� =dx

dt= �chem + �EM

=1

C�� − C��D̃�

�C�

�x− D̃�

�C�

�x

+ j�C��C0 − C��̃� − C��C0 − C��̃�� .

�5�

Both chemical diffusion and current induced diffusioncause the interfaces to move. Each compound phase growsor shrinks as a result of the movement of its interface bound-aries.

III. SIMULATION

The numerical simulation was programmed with a MAT-

LAB6.5 program using the finite difference method. The simu-lated domain was meshed into 1000 fixed elements �1001fixed nodes�, each of which had a size of 100 nm. At the twoboundaries of each phase, an extra cladding node was at-tached to the end of the nodal array in order to represent themoving boundary, as shown in Fig. 2. Overall, the simulationdomain contained 1001 fixed nodes and 6 movable nodesaddressing the moving interfaces. The fixed nodes had con-stant positions but variable composition, while the moveablenodes had variable positions but constant composition.

Equation �3� was applied in each phase and solved forthe boundary conditions listed in Table I. In dealing with thecladding interfacial nodes and their first and second adjacentnodes, partial differences were adopted according to the tem-poral position of the movable interfacial nodes. Once thecomposition profile of each phase was obtained, the move-ment of interfaces was determined by Eq. �5� and knowledgeof the local composition gradient at the interfaces. Forwardor backward differences were used to calculate the composi-tion gradient at the interfaces. Care was also taken to ensurethat interfaces moved by a distance less than 1/100 of theelement size in each iterative step in order to maintain the

stability of the iteration. Current density was an adjustableparameter in this program and could be set to zero to inves-tigate the intermetallic growth kinetics by thermal agingonly.

IV. MEASUREMENTS OF INTERMETALLIC GROWTH

A. Electromigration experiment

In this paper, previously reported experimental results ofintermetallic growth were used for comparative purposes.7

The experiments and key results are briefly summarized inthis section to facilitate better understanding of the entiretexts. EM experiments were performed on Sn–3.5Ag lead-free solder bumps with a Cu-based UBM stack, as shown inFig. 3�a�, to measure current enhancement effects on IMCgrowth kinetics and Kirkendall void formation. The teststructures were subjected to a high current stressing ��4�104 A/cm2� at an elevated temperature ��140 °C� for aprolonged period of time ��400 h�. It is also worth notingthat joule heating effect caused the actual solder temperatureto rise to approximately 10–15 °C higher than the nominaltemperature of 140 °C. Therefore the actual solder tempera-ture in this experiment was around 150–155 °C.

In the EM tests, electron current flowed from the UBMto the TSM. Cross-sectional images were taken using scan-ning electron microscope �SEM� to investigate the evolutionof IMC phases and the formation of Kirkendall voids. Eachphase was identified by energy-dispersive x-ray �EDX�analysis performed in the scanning electron microscope. Thegrowth rates of the intermetallics along the electron flowdirection were evaluated by averaging the area of each phasein the SEM images over the diameter of the bumps.

Control samples �Fig. 3�b��, which were subjected toonly thermal aging at the test temperature �140 °C� but nocurrent stressing, showed minimal IMC thickness changecompared with the current stressed samples after �300 h ofEM testing. Figure 4 shows the cross-sectional images of aSn–3.5Ag lead-free solder bump �a� after prolonged currentstressing and �b� prior to current stressing. Electron currentflowed from UBM to TSM causing the Cu UBM to dissolveinto the solder Sn phase. Cu6Sn5 was identified by EDX tobe the intermetallic phase that grew into solder and extendedto reach the TSM end. The other intermetallic phase, Cu3Sn,however, remained as a thin layer between the Cu6Sn5 andthe remaining Cu UBM. Figure 5 shows the experimentalgrowth rate of the intermetallics at the UBM. Intermetallicgrowth appeared to follow a linear dependency on time. Thegrowth rates of Cu3Sn and Cu6Sn5 were determined to be11.5 and 81.1 nm/h, respectively. Cu6Sn5 was by far thedominant growing intermetallic phase, and its morphologywas consistent with the path in which the electron fluxflowed through the solder, taking into account the currentcrowding effect. Conversely, Cu3Sn growth was much moregradual and it remained a thin and conformal layer betweenCu and Cu6Sn5.

B. Aging experiment

In our effort to derive the simulation parameters by solv-ing the inverse problem of intermetallic growth, an aging

FIG. 2. �Color online� Nodal arrays and moving interfacial nodes.



simulation was found advisable in order to separate the cur-rent induced effect from chemical diffusion due to thermalaging. An aging experiment reported by Siewert et al. wasadopted in this paper for the thermal aging intermetallicgrowth kinetics.8 In their experiment, Sn–3.5Ag solder wasdeposited onto a coupon plated with 45–50 �m Cu immedi-ately after properly cleaning the Cu surface. The coupon wasthen thermally aged in a furnace at 150 °C. The intermetallicgrowth was determined by measuring the thickness of eachphase in the cross-section images by SEM.

V. RESULTS AND DISCUSSION

A. Derivation of parameters

1. Diffusion coefficients

In the analysis of the intermetallic growth kinetics,knowledge of the diffusion coefficients of all diffusing spe-cies �Cu and Sn atoms� in all four phases �pure Cu and pureSn as the terminal phases and the two intermetallic phases� isnot only critical but also indispensable. The coefficient ofself-diffusion in pure Cu and pure Sn phases are readily

FIG. 3. �Color online� �a� Schematic of a solder bump prior to currentstressing. �b� Cross section of a control sample subject to 140 °C annealing,but not to current stressing, for 300 h.

FIG. 4. �Color online� �a� Cross section of a solder bump after currentstressing. �b� Cross section of a solder bump prior to current stressing.



available in the ASM handbooks �ASM International� anddiffusion handbooks.9–11 Sn has been identified to have atetragonal crystal structure,12 and anisotropic diffusion coef-ficients were reported.9 Since the interdiffusion model in thispaper was one dimensional, this anisotropy was neglectedand only one diffusion coefficient was used for Snself-diffusion.10 Dyson et al. reported the extremely rapidand anisotropic mobility of Cu in the pure Sn phase due to itsfast diffusion by an interstitial mechanism.13

The diffusion coefficients of Cu and Sn atoms in theintermetallics are not well documented. However, the inter-diffusion coefficients of the Cu–Sn intermetallics have beenreported by a number of research groups. Both Mei et al.14

and Onishi and Fujibuchi15 deduced the interdiffusion coef-ficients by conducting an annealing experiment and fittingthe analytical model to the experimental data. Although theintrinsic diffusivities and activation energies they deducedwere different, their results were reasonably consistent witheach other in the values of the interdiffusion coefficients atthe temperature of interest. Bader et al. investigated the for-mation and growth of IMC in thin Cu–Sn–Cu trilayers andreported that the interdiffusion coefficient for Cu3Sn in thinfilms was approximately twice that in single crystalexperiment.16 Tu derived the diffusion coefficients of Cu–Snthin films by investigating the aging effect of Cu–Snbilayer.17 He concluded that the mutual diffusion of theCu–Sn thin film stack caused Cu6Sn5 to form at all agingtemperatures but Cu3Sn only formed at the samples whichaged at a temperature above 60 °C. He also obtained theinterdiffusion coefficient of Cu6Sn5 to be �10−21 m2/s at25 °C.

2. Effective charge number

The electromigration driving force is measured by a di-mensionless parameter, the effective charge number Z*. Hun-tington derived this driving force comprising the electrostaticand the electron wind contributions,18

Feff � e Z*E = e �Ze + Zw�E . �6�

The electrostatic charge number Ze represents the direct elec-trostatic force on the moving ion, and hence its value isexpected to be the nominal valence of the ion. The electronwind charge number Zw accounts for the electron wind forceand is generally the dominant contribution.

Self-electromigration has been reported for both Cu andSn and their effective charge numbers have beendetermined.18–21 However, this parameter has not been re-ported for Cu and Sn as dilute solute in each other. Hsieh andHuntington reported the effective charge number for Cu asdilute solute in pure Pb.22 The value fell in the range of6–3.25. The electron wind charge numbers Zw of Cu in Pband in Sn are expected to be similar because Pb and Sn areboth quadrivalent metals in group IV with similar electronicconfigurations and Cu atoms diffuse interstitially in both hostmetals. The effect on Zw of ions taking on interstitial sites orsubstitutional sites was reviewed by Huntington.18 Therefore,the effective charge number of Cu in pure Pb is herein takenas that in pure Sn with reservation.

3. Simulation parameters

According to Eqs. �3� and �5�, knowledge of the inter-diffusion coefficients of all phases suffices for the simulationof intermetallic growth in thermal aging �j=0�. However, inthe case of the electromigration simulation �j�0�, the inter-diffusion electromigration factors �̃ are required parametersand knowledge of the diffusion coefficients of both diffu-sants, Cu and Sn, is necessary according to Eq. �4�. Theindividual diffusion coefficients of Cu and Sn in the phasesof interest are not readily available in literature. However,the diffusion coefficients can be obtained together with ef-fective charge numbers by virtue of the solution of the in-verse problem of the experimental intermetallic growth.23

The diffusion coefficients so derived can be verified by cal-culating the interdiffusion coefficients based on the compo-sition of each phase and comparing with the reported valuesin the literature.

The parameters �effective charge numbers and diffusioncoefficients� used in the simulation of this paper are listed inTable II. The diffusion coefficients of the diffusants Cu andSn were obtained individually using the above mentionedinverse optimization method. The interdiffusion coefficientscalculated accordingly were also listed and compared withthe literature reported values. They were found to be veryconsistent, and this suggests that these are reasonable values.It is worth noting that there is some deviation between thediffusivities derived for the aging case and the EM case. Thisdeviation may result from some uncontrollable experimentalconditions such as the inhomogeneous joule heating andIMC morphology caused by current crowding. However, thedeviation is considered minimal compared with the diffusiv-ity difference in different phases.

B. Kinetics of intermetallic growth

To investigate the current enhancement effect on IMCformation, the growth rates under EM were compared with

FIG. 5. �Color online� IMC growth rate of solder bumps under currentstressing.



the growth rates under thermal aging. Under thermal aging,the rate of diffusion controlled intermetallic growth can beexpressed as

�d =1

Cij − Cji�D̃j

�CCu,j

�x− D̃i

�CCu,i

�x . �7�

It is clear that diffusion controlled growth rate is propor-tional to the composition gradient. The composition at eachside of the intermetallic remains constant because they arelimited by the solubility of the solute. As the intermetallicthickens, the composition gradient across the phase de-creases: the compositions at each end remain constant whilethe phase thickness increases. Therefore, the growth rate de-cays over time and follows the parabolic law in general.

The EM contribution to the growth rate is obtained froma different equation,

�c =j

Cij − Cji�Cji�C0 − Cji��̃ j − Cij�C0 − Cij��̃i� . �8�

In contrast to Eq. �7�, the growth rate in Eq. �8� is a functionof the current density and the composition across the inter-face. Hence, under steady current density, current inducedgrowth remains at a constant rate even when the intermetallicthickens. The fact that this growth is only dependent on in-terfacial compositions not only leads to the conclusion thatthe time dependency is expected to be linear but also sug-gests that this mechanism is controlled by interfacial reac-tions.

The growth behavior for the two limiting cases can bereadily deduced. When the current density is very high, cur-rent induced growth dominates and the intermetallic growthbehavior follows a linear law. At low or zero current density,however, current induced growth is relatively negligible orcompletely absent and therefore the IMC growth should fol-low a parabolic law. In general, the growth behavior will bemore complicated, depending on the balance of the massfluxes driven by interdiffusion and electromigration.

1. Thermal aging simulation

To demonstrate the different kinetics of current inducedgrowth and diffusion controlled growth, an analysis was firstconducted for intermetallic growth due to thermal aging �j=0�. Figure 6 shows the variation of intermetallic thicknessdue to thermal aging at 150 °C along with the experimentaldata of a Cu–Sn thin film aging experiment.8 The currentdensity was set to zero for aging simulation. Note that theabscissa of the plot is square root of time. The simulationresults are in good agreement with the experimental data,and the intermetallic growth kinetics apparently followsparabolic law in the aging simulation.

2. Electromigration simulation

An electromigration simulation was then conducted forintermetallic growth under electromigration at nominal tem-perature 140 °C �joule heating corrected temperature�150 °C� and 4�104 A/cm2. Figures 7�a� and 7�b� showthe initial and final composition profiles of the solder jointafter 300 h of EM tests. The simulated results indicated thatCu3Sn and Cu6Sn5 both thickened at the expense of the CuUBM. Cu3Sn thickened but remained a thin layer betweenCu UBM and Cu6Sn5, whereas Cu6Sn5 grew far into the pure

TABLE II. Diffusion coefficients and effective charge number derived by solving the inverse problem ofintermetallic growth rate at 150 °C.

Phase Diffusant Z*Daging

�m2/s�DEM

�m2/s�

Interdiffusioncoefficient

�m2/s�

Interdiffusioncoefficient

literature �m2/s�

�Cu� Cu 5 5.83�10−31 5.83�10−31¯ ¯

Sn ¯ 1.67�10−28 1.67�10−28

Cu3Sn Cu 33 3.06�10−17 7.64�10−16 1.91�10−16 2.87�10−17a–3.81�10−16b

Sn 33 2.44�10−16 1.31�10−16

Cu6Sn5 Cu 33 5.56�10−16 5.83�10−16 5.86�10−16 1.61�10−16a–4.19�10−16b

Sn 33 6.11�10−16 2.64�10−16

�Sn� Cu 2 2.44�10−12 2.44�10−12¯ ¯

Sn 18 1.11�10−15 1.11�10−15

aReference 15.bReference 16.cReference 14.

FIG. 6. �Color online� Intermetallic growth due to thermal aging only whencurrent effect is absent �experimental data �Ref. 8��.



Sn solder. It is apparent that the consumption of the Cu UBMmoved the Cu3Sn layer to a new position where Cu UBMhad been at the onset of the experiment.

Figures 8�a� and 8�b� show the simulated time depen-dency of the thickness change of Cu3Sn and Cu6Sn5 underelectromigration and aging, respectively, together with thediscrete data points taken from the EM �Ref. 7� and the ther-mal aging8 experiments. The growth rates of these interme-tallic phases as a function of time are plotted in Figs. 9�a�and 9�b�. All aging data in Figs. 8 and 9 were directly trans-planted from Fig. 6.

In Fig. 8�a�, Cu3Sn thickened with time both under elec-tromigration and thermal aging. It may seem that Cu3Sn ex-hibited comparable thickening under both thermal aging andelectromigration. However, this in part resulted from the dif-ferent sample preparation schemes used in the EM and thethermal aging experiments. The solder joints of the EM ex-periment were subject to repeated reflow treatment duringthe soldering process, and therefore the intermetallics weresubstantially thicker than those of the thermal aging samples,

which were cooled to ambient temperature soon after thedeposition of solder. As a consequence, the initial interme-tallic thickness of the EM sample was much thicker than thatof the thermal aging sample at the onset of the simulation.The initial IMC thicknesses for the simulation are listed inTable III.

Although the thickening of Cu3Sn appears to be inhib-ited by electromigration as shown in Fig. 8�a�, the finalCu3Sn thicknesses �at t=300 h� of EM and aging samplesare actually comparable. The fact that Cu3Sn remains a verythin conformal layer between Cu UBM and the adjacentphase adds to the difficulty of experimental determination ofthe Cu3Sn thickness. This is made obvious by the peculiarconfiguration of Cu3Sn layer in Fig. 4�a� and the extensiveerror bars in Fig. 8�a�. However, in general, the simulationstill predicted the Cu3Sn thickening within the error bars ofthe experimental data.

While the electromigration effect on the thickening ofCu3Sn is not yet clear in the present paper, the thickening of

FIG. 7. �Color online� �a� Initial composition profile of simulation �0 h�. �b�Final composition profile of simulation �300 h�. �c� Vacancy accumulationderived from vacancy transport model. �d� Expanded SEM image of a fail-ing solder joint showing the interfaces of intermetallic phases.

FIG. 8. �Color online� IMC thickness change plotted as a function of time:�a� Cu3Sn and �b� Cu6Sn5.



Cu6Sn5 was clearly found to be significantly enhanced byelectromigration, as shown in Fig. 8�b�. Simulation accu-rately predicted the thickening of Cu6Sn5 of both electromi-gration and thermal aging experiments. Most important ofall, it shows that the thickening of Cu6Sn5 was not onlysignificantly enhanced by electromigration but had lineartime dependency.

Figures 9�a� and 9�b� show the simulated growth rates ofthe two intermetallics, Cu3Sn and Cu6Sn5, under thermal ag-ing and electromigration, respectively. Recall from Fig. 6that, during thermal aging, the thickening of both Cu3Sn and

Cu6Sn5 followed a parabolic law, that is, square root timedependency of thickness. However, their growth behaviorsevidently changed under the effect of electromigration. Ac-cording to Fig. 9�a�, Cu3Sn grew at a decaying rate where therate eventually approached zero. The thickening rate ofCu3Sn under electromigration decayed more rapidly whenthe sample was subject to electromigration than when it wasonly subject to thermal aging. Since Cu3Sn thickening duringthermal aging followed a parabolic law, this observation in-dicates that the power law which Cu3Sn followed shouldhave an exponent lower than 0.5.

As opposed to Cu3Sn thickening, the thickening rate ofCu6Sn5 remained relatively constant throughout the simula-tion time of 300 h, as shown in Fig. 9�b�. This further con-firms the conclusion that Cu6Sn5 thickening followed a linearlaw instead of a parabolic law. It grew into a very steady,constant rate approximately at the 100th hour of the simula-tion, and its thickness increased linearly with time.

At the onset of the simulation, the growth rates of Cu3Snand Cu6Sn5 were 15.3 and 87.4 nm/h, which were close tothe measured rates of 11.5 and 81.1 nm/h, respectively. It isworth noting that, although the growth of Cu6Sn5 approacheda steady state, its growth rate �Fig. 9�b�� did not reach aconstant until after 100 h. This indicates that there indeedwas a negative nonlinear term in Cu6Sn5 growth kinetics aspredicted by Gurov and Gusak.5 This term eventually de-cayed over time and the linear term finally dominated theCu6Sn5 growth.

The model successfully rendered a reasonably accurateprediction of intermetallic growth and shifting, which wasconsistent with the experimental observation. However, therewas still some discrepancy between simulation and experi-mental results. First, in the simulation, the Cu6Sn5 phase didnot extend itself as far into the solder and reach the TSM aswas evident in the experimental image �Fig. 4�a��. The dis-crepancy arose from the fact that the model was one dimen-sional while the solder bumps under test were three-dimensional structures. In a three-dimensional �3D� solderbump, Cu6Sn5 not only grows along the electron current pathdue to current crowding1 but also shrinks along lateral direc-tion due to dissolution of the Cu UBM. It is also interestingto compare the intermetallic morphology observed insamples subjected to current stressing �Fig. 4�a�� to thosesubjected only to thermal aging �Fig. 4�b��. Under thermalaging, both kinetics and energetics played a role in shapingthe intermetallics. This yielded distinct morphologies of thetwo intermetallic phases, leading to a layer-type Cu3Sn phaseand a scallop-type Cu6Sn5, as shown in Fig. 4�b�. However,under high current stressing, the morphological developmentof the intermetallic phases noticeably followed the distribu-tion of current flux divergence, as shown in Fig. 4�a�. Thisindicated that kinetics dominated the evolution of the inter-metallic morphology under EM.

C. EM enhanced void formation

As shown in Fig. 4�a�, crack formation in the interme-tallics was the dominant failure mode of solder joints underelectromigration.2,7,24 This failure mode has been attributed

FIG. 9. �Color online� IMC growth rate plotted as a function of time: �a�Cu3Sn and �b� Cu6Sn5.

TABLE III. Initial IMC thickness ��m� �Refs. 7 and 8�.

Cu3Sn Cu6Sn5

EM 2.00 10.00Aging 1.30 1.30



as the result of Kirkendall void formation accompanying theIMC growth due to reaction of Cu and Sn.2 Therefore, inorder to get a more comprehensive picture of the EM en-hanced void formation, it is essential to incorporate theanalysis of the vacancy concentration in the simulation.

In 1947, Smigelskas and Kirkendall reported the move-ment of the interface between Cu and Zn in brass at an el-evated temperature. Their experiment was consequently rec-ognized as an experimental evidence of vacancy mechanismof atomic exchange in solid state diffusion.25 In the diffusioncouple with different component diffusivities, the directionalflux of matter is counterbalanced by the opposite flux ofvacancies which can annihilate at dislocations or condenseinto voids. Many subsequent investigations indicated that thevoid formation was typically found in the component withhigher diffusivity due to the excess of vacancies. Seitz pro-posed that, for homogeneous nucleation of voids, an excessvacancy of twice the equilibrium concentration is requiredfor steady formation of voids based on thermodynamiccalculations.26 However, there has yet been compelling evi-dence that the locus of void formation can be predicted in thesame manner when one or more intermediate phases formbetween the diffusion couple.

For this purpose, vacancy transport was considered inthe following continuity equation:

�CV

�t= −

�JV

�x, �9�

JV = �DCu − DSn��C

�x− JCu

EM − JSnEM. �10�

The vacancy concentration increases at the infinitesimal dis-tance dx when

�DCu − DSn��2C

�x2 − j�DCu�Cu + DSn�Sn��C

�x 0. �11�

It is obvious that both the first and second derivative ofthe composition play a role in terms of the time variation ofthe vacancy concentration. Figure 10 shows the time varia-tion of composition profile of Cu6Sn5 with respect to normal-ized Cu6Sn5 thickness from the Cu3Sn/Cu6Sn5 interface to

the Cu6Sn5/Sn interface. The initial composition profile wasassumed to be linear. This is a valid assumption because thecomposition profiles of IMC were found to remain linear inthermal aging simulation and the initial condition of the EMsimulation can be considered as the result of a preliminaryaging simulation. The composition profile of Cu6Sn5 thenevolves with time and is no longer linear when the currentenhanced effect comes into play. It was also observed in Fig.10 that the longer period of time the electrical current isapplied, the further the composition profile deviates from thelinear initial condition. However, the evolution rate seems todecay with time and the composition on normalized thick-ness scale arguably approaches a steady state profile at theend of the simulation ��300 h�.

In Fig. 7�c�, the result from this analysis shows that un-der EM, a high concentration of vacancy can exist trailingthe advancing Cu/Cu3Sn interface. Given the high concen-tration of vacancy at this region, Kirkendall voids are likelyto form as a result of excess of vacancies. The predicted highvacancy concentration and subsequent void formation areconsistent with experimental observations. Under EM tests atthe nominal temperature of 140 °C, the dominant failuremode of the solder joints tested was due to void formation atthe Cu6Sn5 side of the Cu6Sn5/Cu3Sn interface.

This analysis of vacancy transport did not include anyvacancy annihilation effects; therefore vacancy concentrationin the Cu6Sn5 was overestimated. Provided vacancy annihi-lation at the sinks was considered, the peak vacancy concen-tration should be reduced and it should concentrate morelocally at a location behind but very close to the recedingCu3Sn/Cu6Sn5 interface, as observed in the experimental im-ages �Figs. 4�a� and 7�d��.

VI. CONCLUSION

A kinetic model of electromigration enhaced intermetal-lic growth in a Pb-free solder joint with Cu UBM was for-mulated, taking into account the interdiffusion and currentdriving forces. Simulation showed that the EM enhancedIMC growth followed a linear law, whereas the IMC growthfollowed a parabolic law when interdiffusion was the soledriving force. This result leads to the conclusion that IMCgrowth occurs in a reaction controlled mechanism under EM,while it occurs in a diffusion controlled mechanism underthermal aging �no EM�. The conclusion was verified with anEM experiment and a control aging experiment. The analysisof vacancy transport was incorporated with the model, andthe results showed substantial increase of vacancy concentra-tion at the Cu6Sn5 phase near the Cu3Sn/Cu6Sn5 interface.Experimental images indicated that significant void forma-tion takes place in the identical locus. This discovery sug-gests that the local escalation of vacancy concentrationplayed an integral role in the void formation and growth inthe intermetallics under current stressing.

ACKNOWLEDGMENTS

The authors would like to thank Dr. Peng Su, Dr. TrentUehlin, and Dr. Lakshmi N. Ramanathan of Freescale Semi-conductor for generous funding as well as support and assis-

FIG. 10. �Color online� Composition profile of Cu6Sn5 under current stress-ing on a normalized thickness scale.



tance in experiments. The authors would also like to thankProfessor Venkat Ganesan of Chemical Engineering, Univer-sity of Texas at Austin for healthy discussion in numericaltechniques.

1E. C. C. Yeh, W. J. Choi, K. N. Tu, P. Elenius, and H. Balkan, Appl. Phys.Lett. 80, 580 �2002�.

2K. Zeng, R. Stierman, T.-C. Chiu, D. Edwards, K. Ano, and K. N. Tu, J.Appl. Phys. 97, 024508 �2005�.

3H. Gan and K. N. Tu, J. Appl. Phys. 97, 063514 �2005�.4H. T. Orchard and A. L. Greer, Appl. Phys. Lett. 86, 231906 �2005�.5K. P. Gurov and A. M. Gusak, Phys. Met. Metallogr. 52, 75 �1981�.6L. S. Darken, Trans. AIME 175, 184 �1948�.7S.-H. Chae, X. Zhang, H.-L. Chao, K.-H. Lu, P. S. Ho, M. Ding, P. Su, T.Uehling, and L. N. Ramanathan, Proceedings of the 56th Electronic Com-ponents and Technology Conference, 30 May–2 June 2006, pp. 650–656.

8T. A. Siewert, J. C. Madeni, and S. Liu, Formation and Growth of Inter-metallics at the Interface Between Lead-Free Solders and Copper Sub-strates, Proceedings of the APEX Conference on Electronics Manufactur-ing, Anaheim, California, April, 2003.

9N. L. Peterson, Solid State Physics, Vol. 22, p. 409, edited by H. Ehren-reich, F. Seitz, and D. Turnbull �Academic, New York, 1968�.

10W. Seith and T. Heumann, Diffusion of Metals: Exchange Reactions�Springer, Berlin, 1962�, translated by U.S. Atomic Energy Commission,

pp. 65 and 68.11ASM Specialty Handbook: Copper and Copper Alloys, edited by J. R.

Davis �ASM International, Materials Park, OH, 2001�, p. 235.12V. T. Deshpande and D. B. Sirdeshmukh, Acta Crystallogr. 14, 355

�1961�.13B. F. Dyson, T. R. Anthony, and D. Turnbull, J. Appl. Phys. 38, 3408

�1967�.14Z. Mei, A. J. Sunwoo, and J. W. Morris, Jr., Metall. Trans. A 23A, 857

�1992�.15M. Onishi and H. Fujibuchi, Trans. Jpn. Inst. Met. 16, 539 �1975�.16S. Bader, W. Gust, and H. Hieber, Acta Metall. Mater. 43, 329 �1995�.17K. N. Tu, Acta Metall. 21, 347 �1973�.18B. Huntington, Diffusion in Solids: Recent Developments, edited by A. S.

Nowick and J. J. Burton �Academic Press, New York, 1975�, pp. 303–352.19A. R. Grone, J. Phys. Chem. Solids 20, 88 �1961�.20G. A. Sullivan, J. Phys. Chem. Solids 28, 347 �1967�.21C. Y. Liu, C. Chen, and K. N. Tu, J. Appl. Phys. 88, 5703 �2000�.22M. Y. Hsieh and H. B. Huntington, J. Phys. Chem. Solids 39, 867 �1978�.23B. Chao, S.-H. Chae, X. Zhang, K. H. Lu, J. Im, and P. S. Ho, Acta

Materialia �submitted�.24M. Ding, G. Wang, B. Chao, P. S. Ho, P. Su, and T. Uehling, J. Appl. Phys.

99, 094906 �2006�.25A. D. Smigelskas and E. O. Kirkendall, Trans. AIME 171, 130 �1947�.26F. Seitz, Acta Metall. 1, 355 �1953�.



electromigration enhanced intermetallic growth …ho/papers/brook jap 2006.pdfelectromigration...

Documents