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JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 9 1 NOVEMBER 2003

APPLIED PHYSICS REVIEWS—FOCUSED REVIEW

Recent advances on electromigration in very-large-scale-integrationof interconnects

K. N. TuDepartment of Materials Science and Engineering, University of California, Los Angeles, Los Angeles,California 90095-1595

~Received 4 February 2003; accepted 21 July 2003!

Today, the price of building a factory to produce submicron size electronic devices on 300 mm Siwafers is over billions of dollars. In processing a 300 mm Si wafer, over half of the production costcomes from fabricating the very-large-scale-integration of the interconnect metallization. The mostserious and persistent reliability problem in interconnect metallization is electromigration. In thepast 40 years, the microelectronic industry has used Al as the on-chip conductor. Due tominiaturization, however, a better conductor is needed in terms of resistance–capacitance delay,electromigration resistance, and cost of production. The industry has turned to Cu as the on-chipconductor, so the question of electromigration in Cu metallization must be examined. On the basisof what we have learned from the use of Al in devices, we review here what is current with respectto electromigration in Cu. In addition, the system of interconnects on an advanced device includesflip chip solder joints, which now tend to become weak links in the system due to, surprisingly,electromigration. In this review, we compare the electromigration in Al, Cu, and solder on the basisof the ratio of their melting point to the device operating temperature of 100 °C. Accordingly, grainboundary diffusion, surface diffusion, and lattice diffusion dominate, respectively, theelectromigration in Al, Cu, and solder. In turn, the effects of microstructure, solute, and stress onelectromigration in Al, Cu, and solder are different. The stress induced by electromigration inCu/low-k interconnects will be a very serious issue since the low-k dielectric ~with a value ofkaround 2! tends to be weak mechanically. In a multilevel interconnect, a electromigration force dueto current crowding, acting normal to current flow, has been proposed to explain why manyelectromigration induced damages occur away from the high current density region. Inmean-time-to-failure analysis, the time taken to nucleate a void is found to be much longer than thegrowth of the void in Al and solder interconnects. This is not the case for Cu interconnects for thenucleation of a void on a surface. On accelerated tests of electromigration in Cu interconnects, theresults gathered above 300 °C will be misleading since the mass transport will have a largecontribution of grain boundary diffusion, which is irrelevant to electromigration failure in realdevices induced by surface diffusion. ©2003 American Institute of Physics.@DOI: 10.1063/1.1611263#

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TABLE OF CONTENTS

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . .5452II. ELECTROMIGRATION IN Al

INTERCONNECTS. . . . . . . . . . . . . . . . . . . . . . . . . .5455A. Effect of microstructure on electromigration. . . 545B. Effect of solute on electromigration. . . . . . . . . . 5456C. Effect of stress on electromigration and vice

versa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5456III. ELECTROMIGRATION IN Cu

INTERCONNECTS. . . . . . . . . . . . . . . . . . . . . . . . .5458A. Effect of microstructure on electromigration. . . 545B. Effect of solute on electromigration. . . . . . . . . . 5460C. Effect of stress on electromigration and vice

versa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5461

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IV. ELECTROMIGRATION IN FLIP CHIPSOLDER JOINTS. . . . . . . . . . . . . . . . . . . . . . . . . .5461

A. Effect of current crowding on electromigration.. 546B. Effect of eutectic composition on

electromigration. . . . . . . . . . . . . . . . . . . . . . . . . .5464C. Polarity effect of electromigration on chemical

reactions at cathodes and anodes in solderjoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5465

D. Effect of stress on electromigration and viceversa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5467

E. Effect of solder composition onelectromigration. . . . . . . . . . . . . . . . . . . . . . . . . .5467

V. CURRENT CROWDING. . . . . . . . . . . . . . . . . . . . .5468A. Driving force of electromigration. . . . . . . . . . . . 5469B. Effect of contact resistance on current

crowding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5470

1 © 2003 American Institute of Physics

IP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

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5452 J. Appl. Phys., Vol. 94, No. 9, 1 November 2003 K. N. Tu

VI. ANALYSIS OF MEAN TIME TO FAILURE. . . . 5470A. Effect of current density. . . . . . . . . . . . . . . . . . . 5470B. Effect of activation energy of diffusion. . . . . . . 5471C. Effect of void nucleation and growth at

cathodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5471D. Effect of hillock and whisker formation at

anodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5472VII. SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5472

I. INTRODUCTION

An ordinary household extension cord conducts electity without mass transport because the electric current dsity in the cord is low, about 102 A/cm2. The free-electronmodel of conductivity of metals assumes that the conducelectrons are free to move in the metal, unconstrained byperfect lattice of ions except for scattering interactions duephonon vibration. The scattering is the cause of electrresistance and Joule heating. When an ion is out of its elibrium position, for example, a diffusing atom at the acvated state, it possesses a very large scattering cross seNevertheless, the scattering does not enhance displaceof the ion and it has no net effect on the diffusion of the iwhen the electric current density is low. However, the sctering by a high current density, above 104 A/cm2, enhancesatomic displacement in the direction of electron flow. Tenhanced atomic displacement and the accumulated effemass transport under the influence of electric field~mainly,electric current! are called electromigration. It is worth noing that a household cord is allowed to carry only a locurrent density, otherwise joule heating will burn the fusethin film interconnect in a device can carry a much highcurrent density, which facilitates electromigration, becathe Si substrates on which interconnects are built are vgood heat conductors. On the other hand, in a device haa very dense integration of circuits, the heat managementserious issue. Typically, a device is cooled by a fan or otmeans in order to maintain the operation temperature aro100 °C.

In very-large-scale-integration of circuits on a devicassuming an Al or Cu thin film line 0.5mm wide and 0.2mm

FIG. 1. SEM image of two-level Al~Cu! interconnect lines with W-plug viason a Si surface. The image was taken after etching away the interdielectric. The width of the line and the spacing between them is 0.5mm~Ref. 10!.


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thick carrying a current of 1 mA, for example, the curredensity will be 106 A/cm2. Such current density can causmass transport in the line at the device operation temperaof 100 °C and lead to void formation at the cathode aextrusion at the anode. These defects are the most persiand serious reliability failures in thin film integrated circuitAs device miniaturization demands smaller and smallerterconnects, the current density goes up, so does the pability of circuit failure induced by electromigration. This ia subject which has demanded and attracted mattention.1–7 In Ref. 7 a rather long list of literature~withtitles! about experimental studies of electromigration inand Cu interconnects is given.

In the past 40 years, Al has been the interconnect cductor in the microelectronic industry. A small amount of C1–2 at. %, has been added to Al to improve its resistancelectromigration,8 and the Al~Cu! interconnect has been usewithout serious reliability problems. Due to the trend of miiaturization, however, a better interconnect conductor thAl ~Cu! is needed in terms of resistance–capacitance deelectromigration resistance, and cost of fabrication. Thedustry has turned to Cu as the interconnect conductor, so

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FIG. 2. ~a! SEM image of an eight-level Cu interconnect structure takafter the interlevel dielectric was etched away.~Courtesy of Dr. Jeffrey Su,Institute of Microelectronics, Singapore. This image was suggested byAhila Krishnamoorthy, Institute of Microelectronics, Singapore.! ~b!Cross-sectional TEM image of a six-layered dual damascene Cu internect structure on a Si surface. The diameter of the narrowest Cu via ismm. There is a liner between a via and the line below it.~Courtesy of Dr. L.C. Hsia, Chartered Semiconductor Manufacturing, Singapore.!


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5453J. Appl. Phys., Vol. 94, No. 9, 1 November 2003 K. N. Tu

question of electromigration in Cu metallization must be eamined. We shall review what have we learned fromprevious studies and use of Al interconnect in devices.ask what is current with respect to electromigration behavin Cu interconnects. Since the system of interconnectsdevice includes solder joints on one end that link to packing circuits and also silicide contacts on the other end tlink to active Si transistors, we should also examine eltromigration in solder joints and silicide contacts. Becauthe geometry and eutectic compositions of solder jointsunique, electromigration in solder joints is different from thin Al and Cu. More importantly, it has become a reliabiliissue.9 We shall examine it here, too. Electromigrationsilicide contacts will not be reviewed.

Figure 1 shows a scanning electron microscopy~SEM!image of a two-level Al interconnect on a Si surface afterinsulating dielectric has been etched away.10 The width ofthe Al lines is 0.5mm and the spacing between them is 0mm, so the pitch is 1mm. On 1 cm31 cm area, we can hav104 lines and each of them has a length of 1 cm, so the tlength of interconnects in such a layer is 100 m. Whenbuild six such layers on a chip of the size of our fingernathe total length, if we include that of interlevel vias, is overkm. Figure 2~a! shows a SEM image of an eight-level Cinterconnect structure taken after the interlevel dielectric wetched away. Figure 2~b! shows a cross-sectional transmsion electron microscopic~TEM! image of a six-level Cuinterconnect structure built on a Si surface. There, the wof the narrowest interconnect via is 0.25mm. It is worthmentioning that a factory that can build this kind of structu

FIG. 3. ~a! Schematic diagram of the Blech structure consisting a shorstrip on TiN base line for electromigration tests. A void at the cathode anhillock at the anode are depicted.~b! SEM image of the top view of a Custrip tested for 99 h at 350 °C with current density of 53105 A/cm2. ~c!SEM image of the top view of a Cu~2 wt % Sn! strip tested at the samecondition ~Ref. 13!.


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on a 200 or 300 mm wafer would cost over billions of dolars. More than half of the production cost in processingwafer now is spent to make the interconnect metallizatio

One of the important differences between the Al inteconnect shown in Fig. 1 and the Cu interconnect shownFig. 2 is the vias between lines. In the Al interconnect, tvia is a W plug, so there are interfaces between Al andBut in the Cu interconnect, the via is Cu; typically, a via athe line above it are made in one step by electroplating usthe dual damascene process, so there is no interface betthem. On the other hand, there is an interface between aand the line below it in the multilevel Cu interconnects. This due to the use of the liner to improve the adhesion of Cuthe dielectric walls and the use of chemical–mechanical pishing to build the multilevel structure. In the threedimensional structure, if electromigration induces an openin any part of it, the device fails. We note that the thredimensional interconnect turns up and down and also leftright. There is current crowding at a turn where electromgration is enhanced. We shall address the effect of curcrowding on electromigration in Sec. V.

The phenomenon of electromigration can be obserfrom the response of a short Al or Cu strip on a base lineTiN as shown in Fig. 3~a!. This structure is called the Blecstructure for electromigration tests.11,12Figures 3~b! and 3~c!show, respectively, scanning electron microscope image

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FIG. 4. ~a! SEM image of mass depletion at cathode of a Cu strip at 2.5400 °C with current density of 2.13106 A/cm2, ~b! at 3.5 h, and~c! at 4.5h. The drift velocity is about 2mm/h as measured from the three imag~Ref. 13!.



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TABLE I. Melting point and diffusivities of Cu, Al, and eutectic SnPb.

Meltingpoint ~K!

Temperature ratio373 K/T m Diffusivities at 100 °C (cm2/s)

Diffusivities at 350 °C(cm2/s)

Cu 1356 0.275 LatticeDl57310228 Dl55310217

Grain boundaryDgb53310215 Dgb51.231029

SurfaceDs510212 Ds51028

Al 933 0.4 LatticeDl51.5310219 Dl510211

Grain boundaryDgb56310211 Dgb5531027

EutecticSnPb

456 0.82 LatticeDl5231029– 2310210 Molten stateDl.1025

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the morphology of a Cu strip and an alloyed Cu strip withwt % Sn in electromigration with current density of3105 A/cm2 at 350 °C for 99 h.13,14 At the cathode end othe strips, a depleted region can be seen, but at the aend, an extrusion is seen. By conservation of mass, bdepletion ~void! and extrusion occurs in the same strThese short strips were sandwiched between Ta thin fiand were deposited and patterned on a long W basewhich was deposited on an oxidized Si wafer. The applelectric current in the W line took a detour to go along tstrip because the latter is a path of low resistance. Whencurrent and temperature are high enough, atomic displment occurs and void and extrusion formations can beserved directly. We can measure the rate of depletion atcathode and calculate the drift velocity. Figure 4 is a seSEM images of the depletion at the cathode of a Cu staken at different intervals at 400 °C with current density2.13106 A/cm2. The drift velocity is about 2mm/h. It isimportant to note that the atomic displacement and mtransport are in the same direction as the electron flow.

Electromigration is the result of a combination of themal and electrical effects on mass transport. If the conding line is kept at a very low temperature~e.g., liquid nitro-gen temperature!, electromigration cannot occur becauthere is no atomic mobility. The contribution of thermal efects can be recognized by the fact that electromigrationbulk metal such as a eutectic solder bump occurs at athree quarters of its melting point in absolute temperatuand electromigration in a polycrystalline Al thin film linoccurs at less than one half of its melting point in absoltemperature. At these temperatures, there are atoms wundergo random walks in the bulk of the solder bump andthe grain boundaries of the Al thin film line, respectively, athese are the atoms which take part in electromigration unthe applied field. It is interesting to note that when the widof a thin film line is reduced to the submicron range, tgrain size in the line is comparable to the line width. Tgrains then become bamboo like in morphology so a contous grain boundary path of diffusion does not exist. WheCu thin film line possesses a bamboo-like microstructuelectromigration takes place on the surface of the lineabout one quarter of the melting point of Cu in absolutemperature. Indeed, we can assume the Si device opertemperature to be 100 °C, which is about three quarter

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the melting point of solders, about slightly less than halfthe melting point of Al, and about one quarter of the meltipoint of Cu. In this temperature scale, lattice diffusion, graboundary diffusion, and surface diffusion occur predomnantly at 3

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4 of the absolute temperature of a metarespectively.15

Table I lists the melting points and diffusivities whicare relevant to the electromigration behaviors in Cu, Al, aeutectic SnPb. The diffusivities for Cu and Al were calclated on the basis of the following equations from the maslogD vs Tm /T plot for face-centered-cubic metals, see F15 in Ref. 16:

Dl50.5 exp~234Tm /RT!,

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whereDl , Dgb, andDs are, respectively, lattice diffusivitygrain boundary diffusivity, and surface diffusivity.16,17 Tm isthe melting point, and the units of 34, 17.8, and 13Tm are incal/mol. As shown in Table I, at 100 °C the lattice diffusiviof Cu and Al is insignificantly small, and the grain boundadiffusivity of Cu is three orders of magnitude smaller ththe surface diffusivity of Cu. At 350 °C the difference btween surface and grain boundary diffusivity of Cu is muless, indicating that we cannot ignore the latter. The lattdiffusivity of eutectic SnPb~not a face-centered-cubic meta!at 100 °C given in Table I is an average value of tracer dfusivity of Pb and Sn in the alloy.18 It depends strongly onthe lamellar microstructure of the eutectic sample. Sincsolder joint has, typically, a few large grains, the smaldiffusivity is better for our consideration. The surface diffsivity of Cu, grain boundary diffusivity of Al, and latticediffusivity of the solder are actually rather close at 100 °To compare atomic fluxes transported by these three kinddiffusion in a metal, we should have multiplied the diffusiity by their corresponding cross-sectional area of path offusion. But the outcome is the same.

In face-centered-cubic metals such as Al and Cu, atodiffusion is mediated by vacancies. A flux of Al atoms driveby electromigration to the anode, requires a flux of vacancto the cathode in the opposite direction. If we can stopvacancy flux, we stop electromigration. To maintain a v


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cancy flux we must supply vacancies continuously. Henwe can stop a vacancy flux by removing the sources or splies of vacancies. Within a metal interconnect, dislocatioand grain boundaries are sources of vacancies, but thesurface is generally the most important and effective souof vacancies. For Al, its native oxide is protective, whimeans that the interface between the metal and its oxidnot a good source or sink of vacancies. This is also trueSn. It is known that an anodized Al line has a better eltromigration resistance than those that are not anodized

If the atomic or vacancy flux is continuous in the inteconnect, i.e., the anode can supply vacancies and the catcan accept them continuously, and if there is no flux divgence in between, there will be no electromigration inducdamage such as void and extrusion formation. In otwords, without mass flux divergence no electromigratdamage occurs in an interconnect when fluxes of atomsvacancies can pass through it smoothly. Hence, atomimass flux divergence is a necessary condition concerelectromigration failure in real devices. The most commmass flux divergences are the triple points of grain bouaries and interfaces between dissimilar materials.

In summary, electromigration involves atomic and eletron fluxes. Their distribution in interconnects is the moimportant concern in electromigration damage. In a regwhere both distributions are uniform, there will be no eletromigration damage. Concerning atomic or vacancy fluxthe most important factor is the temperature scale showTable I. Atomic diffusion must be thermally activated. Thsecond is the design and processing of the interconnect sture. For example, the difference in via structure betweenand Cu metallization is important. Nonuniform distributioor divergence occurs at microstructure irregularities suchgrain boundary triple points and interphase interfaces interconnects, and they are the sites of failure initiation.Secs. II, III, and IV, the effect of microstructure, solute, astress on electromigration in Al, Cu, and solder interconnewill be discussed, respectively. In Sec. VI, mean-time-failure analysis on the basis of void and hillock formatidue to flux divergence will be discussed.

Concerning the electron flux, the current density musthigh enough for electromigration to occur. Because trantors in devices are turned on by pulsed direct current,consider only electromigration under direct current. A brreview of electromigration by pulsed direct current canfound in Ref. 4. While a uniform current distribution is epected in straight lines, nonuniform current distribution ocurs at corners where a conducting line turns, at interfawhere conductivity changes, and also around voids or pcipitates in a matrix. In Secs. IV A and V, the effect of curent crowding on electromigration will be discussed.

Besides electrical forces due to the applied electric fiethere are gradients of mechanical stress, chemical potenand temperature acting on atomic diffusion in interconneHow these forces act together is of interest. In Secs. IIII C, and IV D, the interaction between electrical and mchanical forces will be reviewed. In Sec. IV C, the interation between electrical and chemical forces will be dcussed.


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II. ELECTROMIGRATION IN Al INTERCONNECTS

The microelectronic industry has used Al as the intercnect conductor for 40 years even though Cu is a better etrical conductor.1–4 This is because Al has certain advantagin lithographic processing. It has good adhesion to the S2

surface. It can be deposited by e-beam evaporation or stering, and it can be patterned by dry or reactive ion etchiIt does not poison Si as Cu does, so Al can be deposdirectly on Si to serve as contact metallization on Si devicElectromigration damage in Al lines was discovered in t1960s and was soon recognized to occur by grain bounddiffusion. The recognition has led to two major trends in tstudy of electromigration in Al; the effect of microstructuand the effect of solute.

A. Effect of microstructure on electromigration

The triple points of grain boundaries can serve as cenof atomic flux divergence. They lead to supersaturationvacancies and become locations of void nucleationgrowth near cathodes. Similarly, extrusions occur nearodes. Hence, the mechanism of void formation at a tripoint and growth into an opening along a grain boundwere studied. Consequently, the processing of Al intercnects with a bamboo-type microstructure, containinggrain boundary triple points and no continuous grain bouary path, attracted much attention. Interestingly, it was sorecognized that when the linewidth becomes smaller thangrain size, the microstructure naturally becomes bamlike. But it was also found to be very hard to fabricate a lihaving a perfect or 100% bamboo-type microstructure.

When a single level of Al interconnect was advanceda multilevel Al interconnect, atomic flux divergence shiftefrom grain boundary triple points to the interface betweenAl line and a W via. The interfacial divergence is due to tfact that atomic diffusivities in Al and W are very differenFigure 5 is a schematic diagram depicting a two-levelinterconnect with W vias. The curved arrow in Fig. 5 indcates the electron flow direction. Considering the W viathe left-hand side, we expect Al atoms to depart fromAl/W interface, so vacancies will accumulate above theterface and become supersaturated and eventually forvoid. When the void grows as big as the via, it becomesopening in the circuit. This phenomenon has been called‘‘wear-out’’ mode of failure. In actual devices having th

FIG. 5. Schematic diagram depicting a two-level Al interconnect withvias. The broken curve arrow indicates the direction of electron flow. A vis expected to form above the W plug on the left-hand side or the cathside.


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multilevel structure of Al lines and W vias, the lifetime habeen found to be reduced by a factor of 50 as comparethat of single level Al interconnects due to flux divergencethe interface. We shall reconsider this issue in Sec. V wwe discuss current crowding at the Al/W interfaces.

B. Effect of solute on electromigration

Methods for reducing grain boundary diffusion in Al iorder to improve its resistance to electromigration hastimulated much study, especially concerning the strucand atomic jump processes in grain boundaries. It is vdifficult to specify the atomic positions in an arbitrary largangle grain boundary, even with the help of atomic resoluttransmission electron microscopy and computer simulatIn turn, the activated configuration and activation energygrain boundary diffusion cannot be defined. Therefore,educated guess of grain boundary diffusion is based onknowledge of lattice diffusion.15,16

In bulk alloys, certain solutes have the effect of retardor enhancing solvent diffusion. For example, solute atomCu in bulk Al are known to enhance the lattice diffusionAl solvent atoms. This effect can be calculated on the baof atomic jump frequencies around a pair of Cu–vacancyan Al lattice. By this reasoning, of the use of alloyingretard grain boundary diffusion of Al, we would not chooCu. However, when a small amount of Cu was co-deposwith Al, the co-deposited thin film sample actually showmuch less electromigration.8 Now, it is a general practice inindustry to add 1 at. % or so of Cu to Al, and the lifetimimprovement against electromigration can be orders of mnitude better than that of pure Al. The excess Cu forAl2Cu precipitates in Al grain boundaries. These precipitadissolve and serve as sources of Cu to replenish the losCu in grain boundaries when electromigration depletes thby driving them to the anode. Why Cu is capable of retardgrain boundary electromigration in Al has been a questionkeen interest. Again, because of the difficulty in knowing tgrain boundary structure precisely, no definitive answerbeen given. Most likely, the answer is either a reductiondriving force or a reduction of kinetics or both. KineticallCu may either reduce the concentration of vacancies ingrain boundary or increase the activation energy of grboundary diffusion of Al. What is important to industriamanufacturing is the finding that the process of adding CuAl is forgiving, meaning that it tends to work well.

FIG. 6. Schematic diagram of a set of Al strips of different lengths patteron a base line of TiN. The longer the length, the larger the depletion acathode. Below the critical length, there is no electromigration damagdepicted by the last one on the left-hand side.


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C. Effect of stress on electromigration and vice versa

The interconnect structure shown in Fig. 1 has mashort segments. Electromigration in a short segment tendinduce back stress. This was first recognized by BlechHerring using a set of short Al strips patterned on a baseof TiN as depicted in Fig. 6.11,12 It was found that the longethe strip, the more the depletion at the cathode side in etromigration. Below a ‘‘critical length,’’ there was no observable depletion. The dependence of depletion on strip lenwas explained by the effect of back stress. In essence, welectromigration transports Al atoms in a strip from cathoto anode, the latter will be in compression and the formetension. On the basis of the Nabarro–Herring model of eqlibrium vacancy concentration in a stressed solid,19 the ten-sile region has more and the compressive region hasvacancies than the unstressed region, so there is a vacconcentration gradient decreasing from cathode to anoThe gradient induces an atomic flux of Al diffusing fromanode to cathode, and it opposes the Al flux driven by eltromigration from cathode to anode. The vacancy concention gradient depends on the length of the strip; the shothe strip, the greater the gradient. At a certain length defias the critical length, the gradient is large enough to balaelectromigration so no depletion at the cathode nor extrusat the anode occurs.

In analyzing this stress effect, irreversible proceshave been proposed by combining electrical and mechanforces on atomic diffusion. The electrical force proposedHuntington and Grone is taken to be20

Fem5Z* eE5~Zel* 1Zwd* !eE, ~2!

wheree is the charge of an electron andE is the electric field(E5r j , andr is resistivity andj is current density!. Zel* canbe regarded as the nominal valence of the diffusing ion inmetal when the dynamic screening effect is ignored; itresponsible for the field effect andZel* eE is called the directforce.Zwd* is the charge number representing the momentexchange effect andZwd* eE is called the electron wind forceand it is generally found to be of the order of 10 for a goconductor, so the electron wind force is much greater ththe direct force for electromigration in metals.Z* is the ef-fective charge number of electromigration. For a discussof the electrical force, see the review by Ho and Kwok,4 andother papers.21–25

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whereJem is atomic flux in units of atoms/cm2 s, andJe iselectron flux in units of coulomb/cm2 s. C is the concentra-tion of atoms per unit volume, andn is the concentration oconduction electrons per unit volume.D/kT is atomic mo-bility and me is electron mobility.L21 is the phenomenological coefficient of irreversible processes and it containsdeformation potential.26

In Eq. ~4a!, if we assumeJem50, i.e., there is no neelectromigration flux or damage, we obtain the expressfor the critical length as

Dx5DsV

Z* eE. ~5!

Since the resistance of the conductor can be taken toconstant at a constant temperature, we have, instead‘‘critical product’’ or ‘‘threshold product’’ of ‘‘ j Dx’’ by mov-ing the current density from the right-hand to the left-haside of the equation.

j Dx5DsV

Z* er. ~6!

Under a constant applied current density, a bigger valuecritical product in Eq.~6! means a longer critical length, iturn, a larger back stress in Eq.~5!. For Al and Cu intercon-nects, we takej 5106 A/cm2 and Dx510mm, we have atypical value of critical product about 1000 A/cm.

It has been proposed that if we can design interconnin a device to have a product ofj Dx less than the criticaproduct, we will have no electromigration. This might bpractical for devices approaching the nanoscale, but itnot been widely explored except in certain test samples.note that while the back stress in the above is induced

FIG. 7. Schematic diagram of a short strip confined by rigid walls. Copressive stress will build up at the anode as more and more atoms aredriven into the anode by electromigration.

FIG. 8. Solutions for stress evolution in a finite line as a function of tiunder electromigration~Ref. 27!.


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electromigration, the interaction between an applied strand electromigration is the same; for example, an appcompressive stress at the anode will retard electromigrat

The Blech structure has been used very often in expmental studies of electromigration for the following reasoWe can observe the damage directly and measure thevelocity by measuring the rate of depletion at the cathoAlso, we can study the effect of back stress. Neverthelethere has been a question about the nature of the back sIf we confine a short strip by rigid walls as shown in Fig.we can envisage easily the compressive stress at the ainduced by electromigration. Thus, we consider a fixed vume at the anode and we add atoms into it by electromigtion, the stress change in the volume is

Ds52BDC

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whereB is the bulk modulus. And the time dependencestress buildup in a short strip by electromigration canobtained by solving the continuity equation since stressenergy density and a density function obeys the continuequation,27,28

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The solution for a finite line and the manner of stress buildas a function of time is shown in Fig. 8. Clearly, in thbeginning of electromigration the back stress is nonlinalong the length of the strip; the curved lines. In reality, tbuildup is asymmetrical since the hydrostatic tensile stresthe cathode can hardly be developed.

In a fixed volume with a rigid wall, the compressivstress increases with the addition of atoms. However, in sstrip experiments, there are no rigid walls to cover thestrips, except native oxide. How can the back stress buildat the anode if the native oxide is not a rigid wall? Oplausible explanation is that the Al native oxide has removthe source of vacancies from the surface, therefore, welectromigration drives atoms into the anode region, the odiffusion of vacancies will reduce the vacancy concentrat

-ing

FIG. 9. Rate of resistance change of an Al line vs current density is shby the solid squares. The electromigration induced steady-state comprestress gradient vs current density is shown by the open squares~Ref. 29!.~Courtesy of Professor. G. S. Cargill III, Lehigh University.!


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in the anode region if there is no source to replenish it. Ieasy to envision the physical picture that under compresthere is less equilibrium vacancies, but the reverse situais not so easy to envision, i.e., when there is less equilibrvacancies in a region, the region is in compression. Wenot used to this latter concept. Furthermore, if we consiAu, which forms no oxide, and an unconfined Au strip wa clean surface, it is hard to imagine how a back stress cadeveloped in the strip under electromigration. This is bcause Au atoms can diffuse to the free surface at the anodrelieve the stress. It is equally hard to imagine the back stin Cu short strips. Since Cu grows a nonprotective oxide,surface can act as a source and sink for vacancies, althoumay not be as active as a free surface in ultrahigh vacuMore intriguingly, if electromigration in Cu interconnects ocurs by surface diffusion, how surface diffusion can produa back stress is unclear. We shall discuss this point lateSec. III C.

A serious effort has been dedicated to measuringback stress in Al strips during electromigration. It is noteasy task since the strip is thin and narrow; typically, itonly a few hundred nanometers thick and a few microwide, so a very high intensity and focused x-ray beamneeded in order to determine the strain in Al grains by pcision lattice parameter measurement.29–35 Alternatively, afocused laser beam has been used to measure the Rfrequency shift from the Si underneath the Al line due topiezospectroscopic property of Si.36

Microdiffraction x-ray beams using synchrotron radition have been employed to study the back stress. Whirays of 10mm310mm beam from the National SynchrotroLight Source ~NSLS! at National Brookhaven Laboratorwere used to study electromigration induced stress distrtion in pure Al lines.29 The line was 200mm long, 10mmwide, and 0.5mm thick with a 1.5mm SiO2 passivation layeron top, 10 nm Ti/60 nm TiN shunt layer at the bottom, a0.2 mm thick W pads at both ends which connect the linecontact pads. The electromigration tests were performe260 °C. The results of the steady state rate of resistancecrease, d(DR/R)/dt, and the electromigration inducesteady state compressive stress gradient,dsEM /dx, versuscurrent density are shown in Fig. 9. No electromigrationcurred below the threshold current density ‘‘j th’’ of 1.63105 A/cm2. Below the threshold current density, the eletromigration induced steady state stress gradient increlinearly with current density, wherein the electron wind forwas counterbalanced by the mechanical force, so no etromigration drift was observed.

The x-ray microdiffraction apparatus at the AdvancLight Source~ALS! in Lawrence Berkeley National Laboratory is capable of delivering white x-ray beams~6–15 keV!focused to 0.8–1mm by a pair of elliptically bentKirkpatrick–Baez mirrors.34,35 In the apparatus, the beamcan be scanned over an area of 100mm by 100mm in stepsof 1 mm. Since the diameter of the grains in the strip is ab1 mm, each grain can be treated as a single crystal wrespect to the microbeam. Structural information suchstress/strain and orientation can be obtained by using wbeam Laue diffraction. Laue patterns were collected wit


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large area (939 cm2) charge-coupled-device detector wian exposure time of 1 s or longer, from which the orientationand strain tensor of each illuminated grain can be deduand displayed by software. The resolution of the white beLaue technique is 0.005% strain. In addition, a four-crysmonochromator can be inserted into the beam to prodmonochromatic light for diffraction. The combined whitand monochromatic beam diffractions are capable of demining the total strain–stress tensor in each grain. The tenique and applications of scanning x-ray microdiffractihas been described by MacDowellet al.34,35

III. ELECTROMIGRATION IN Cu INTERCONNECTS

Although the Al~Cu! alloy has performed well as an interconnect conductor for a long time, the trend of miniatization has recently demanded a change due to the followreasons.37 First is the resistance–capacitance (RC) delay insignal transmission in fine lines. Second is the high cosbuilding a multilayered interconnect structure. Third is tconcern of electromigration.5–7,38–47For the use of narroweand narrower lines, not only the line resistance increasesalso the capacitance between lines will drag down sigpropagation. If we choose to maintain the dimensions ofAl interconnect without change, we must add more layersAl, from six to eight or ten. To make more layers of metalization on Si is very undesirable because of cost. Moreoif we have to add two more layers of interconnects, theditional processing steps can reduce yield. This is anoreason why the dual-damascene processing of Cu is attive. It has combined the steps of making one level of linand one level of vias together, so most of the steps of makvias have been removed. Using the same number of procing steps, we can build more levels of Cu than Al interconects.

Since Cu has a much higher melting point (1083 °than Al (660 °C), atomic diffusion should be much slowerCu than Al at the same device operation temperature.electromigration is expected to be much less in Cu intercnects. Surprisingly, the benefit is not as big as expectedwe have stated in the beginning, electromigration in Cucurs by surface diffusion which has a lower activation enethan grain boundary diffusion. Why has electromigratichanged from grain boundary diffusion in Al to surface dfusion, on Cu? Ironically, this is because of the use ofdamascene process to fabricate the Cu interconnect. In ation, it is because Cu intrinsically does not adhere to oxsurfaces. Why do we have to use damascene processproduce Cu interconnects? This is because Cu cannoetched or patterned by dry or reactive ion etching. Therefowe have to form Cu lines by electrolytic plating of Cu intrenches in dielectric,48 followed by a wet process ochemical–mechanical polishing~CMP! to planarize Cu withits surrounding dielectric. On the polished flat surfacerepeat the process and build the multilevel Cu interconnshown in Fig. 2. In the damascene process, via holesetched together with trenches in the dielectric layer, followby electroplating Cu into the trenches and via holes simuneously. Compared to the process of making Al lines a


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W-plug vias, the dual damascene process has saved theof making vias. In filling Cu into the trenches and via holin the dielectric, we need to improve the adhesion of Cuthe dielectric, so a liner such as Ta, TaN, or TiN is usedcover the bottom and sidewalls of the trenches and hbefore the electroplating of Cu.7 To plate the Cu, a seedinlayer of electroless Cu or vapor-phase deposited Cuneeded before the electrolytic plating.

Then, CMP is used to polish the top surface of Cwhich has no liner, and it is followed by the deposition ofdielectric layer so that the dual damascene process of bing another interconnect layer of vias and lines can bepeated. Thus, CMP produces a top surface of Cu interconwhich does not adhere to the dielectric layer over it. Atomdiffusion on the top surface of the Cu interconnect becomthe ‘‘built-in’’ path for electromigration. Furthermore, thliner between a Cu via and the Cu line below it is an intface of flux divergence.47 These are the two weak places felectromigration failure to occur. Which is the weaker omay depend on process control and it can lead to earlyure, resulting in a bimodal distribution of failures. Neverthless, the mechanism of how surface diffusion can leadvoid formation in a via is intriguing. It may be that a certaamount of interfacial diffusion can occur between Cu andliner. Then, the nucleation of a via–void could be thermstress induced due to poor adhesion. Moreover, the tmode of failure is stress-induced extrusion at the anodresulting in dielectric delamination or fracture, especiallylong interconnects with low-k dielectric insulation.

A. Effect of microstructure on electromigration

Because electromigration in Al interconnects takes plalong grain boundaries, the effect of microstructure is aissue. The knowledge leant from Al was applied to Cu intconnects with the intention to improve electromigrationsistance, but with less success. For example, no signifidifference in electromigration failure was found betwepolygranular and very long-grained bamboo Cinterconnects.41 The microstructure of electrolytic Cu has thunusual property that it undergoes abnormal grain growthrecrystallization near room temperature. It has a strong@111#texture in the as-plated state, yet the abnormal grain grohas weakened the texture due to twin formation.49 Why someof the grain boundaries in the electrolytic Cu have high mbility is unclear; it could be due to a minute amount of torganic and inorganic additives from the plating bath. Alwhether grain boundary diffusivity along these grain bounaries is the same as that given in Table I is of interest. Bgrain size and impurity may affect electrical conductivity agood conductivity is the first requirement of interconnemetallization. So far, this is not an issue for electrolytic CThe minute amount of additives from the plating bath hlittle effect on the conductivity and the grain size is, typcally, about 0.1mm before grain growth.

The room temperature grain growth has led to a nonuform distribution of large grains and clusters of small grain the interconnect. The large grains are bamboo liketheir grain boundaries to smaller grains have triple poinHence, the microstructure is undesirable if electromigrat


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is dominated by grain boundary diffusion. But, it becomirrelevant when electromigration occurs by surfadiffusion.47 On a surface, the triple point is not an effectivflux divergence point. The surface plane of the@111# orientedgrains and their twins is of interest since it affects surfadiffusion.

The microstructure of the seeding layer of electrolessvapor-phase deposited Cu is also interesting since its gsize is linearly proportional to its thickness. The grain growduring deposition is called flux-driven grain growth,50 yetafter deposition the grains do not grow at room temperatas those in the electrolytic Cu. Nevertheless, when eleclytic Cu is plated on the seeding layer, the microstructurethe latter is lost due to ripening. The interaction betwethese two types of Cu film is interesting, and it seems thatorganic and inorganic additives in the electrolytic Cu mighave diffused into the seeding layer to enhance its grboundary mobility.

The divergence at Al/W interfaces is no longer an issin Cu interconnects due to the dual damascene process.ertheless, the interface between a via and the line beneacan still be an interfacial discontinuity due to the liner. Bsides adhesion, the liner also serves as a diffusion barrieprevent Cu from reaching Si. As a diffusion barrier, tthicker the better. A thick liner will increase the resistancethe interconnect, so actually, the thinner the better. Whilcleaning of via holes is performed before depositingliner, if the cleaning is not done properly, it affects the adhsion between a Cu via and the Cu line beneath it. Henbesides being a flux divergence plane, the liner between aand a line is of reliability concern due to poor adhesion unthermal stress.

FIG. 10. Resistivity of Cu~0.5 wt % Sn! and Cu~1 wt % Sn! alloy thin filmsas a function of temperature~Ref. 13!.

TABLE II. Conductivity of Al and Cu thin film interconnects.

Film Resistivity ~mV cm! at 20 °C

Sputtered Cu 2.1Al ~2 wt % Cu! 3.2

Cu ~0.5 wt % Sn! 2.4Cu ~1 wt % Sn! 2.9


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B. Effect of solute on electromigration

Since the solute effect of Cu is beneficial to electromgration resistance in Al, we ask if a similar solute effect cbe found in Cu and what is the beneficial solute? Againwe try to find a solute to slow down grain boundary diffusiof Cu, it is irrelevant as we really need a solute that can sdown surface diffusion of Cu. There is no guideline to fisuch a solute until we realize that electromigration ininterconnects is dominated by surface diffusion. To sustacontinuous surface atomic flux of Cu, we must be ablerelease Cu atoms from kink sites on surface steps contously. In other words, the mechanism and energy neededissociate Cu atoms from kink sites, as in desorption andtemperature sublimation of atoms from a solid surface,51,52

are important in the consideration of surface electromigtion.

After adding and testing many elements in Cu, Sn wfound to show a significant effect in resisting electromigtion in Cu.13,14 Table II compares the conductivity of Al an

FIG. 11. Resistance change of Cu~0.8 at. % Sn! and pure Cu thin films in theelectromigration test at 250 °C with current density of 106 A/cm2 ~Ref. 14!.

FIG. 12. Plots to show the comparison of edge displacements vs time150-mm-long strips of Cu and Cu~Sn! alloys at 300 °C with current densityof 2.13106 A/cm2. The measured drift velocity ‘‘s’’ is given in the figure~Ref. 13!.


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Cu interconnects. Figure 10 shows the resistivity of Cu~0.5wt % Sn! and Cu~1.0 wt % Sn! alloys as a function of tem-perature using Van der Pauw test structures. Figure 11 shthe resistance change of Cu~Sn! and pure Cu thin films undeelectromigration at 250 °C and 106 A/cm2. While the resis-tance of the Cu in testing changed quickly with time, tresistance of the Cu~Sn! remained unchanged. Figure 1shows a comparison of the measured edge displacementsus time for 150-mm-long and 5-mm-wide Cu and Cu~Sn!test strips with a current density of 2.13106 A/cm2 at300 °C. The slope of the edge displacement vs. time githe average drift velocity for the Cu mass transport durelectromigration. The average drift velocity of the Cu matransport in the Cu~Sn! alloys strips is small at the beginninof testing, then it increases slowly with time, and eventuareaches a value comparable to that of pure Cu.

Why Sn is beneficial in resisting electromigration in Cis unclear. Since electromigration in Cu interconnectsknown to occur by surface diffusion, it is likely that somhow surface diffusivity of Cu is slowed down by Sn, anmore importantly, the supply of surface flux of Cu atomsreduced, especially, if the dissociation of Cu atoms fromkinks on Cu surface steps is retarded due to a strong binof Sn atoms to the kinks. Figure 13 is a schematic diagramsurface steps and kinks on a Cu surface. The shaded atokinks represent Sn atoms. If we assume a strong bindthere, the release of Cu atoms from the surface steps wiblocked. Moreover, when Sn segregates to Cu surfacesforms an oxide bond with the top dielectric layer that improves the adhesion between the Cu and the top dielelayer, it may further retard surface dissociation and diffusof Cu.

The device operation temperature is around 100 °which is only about 0.275 of the absolute melting tempeture of Cu. So, at 100 °C we can ignore both lattice and grboundary diffusion in Cu. We may still be able to ignore boof them at a testing temperature of 250 °C. But at 350 °which is about 0.46 of the absolute melting temperatureCu, we cannot ignore grain boundary diffusion in Cu. Henthe finding that there is no electromigration in Cu~Sn! up to250 °C ~see Fig. 11!, yet some has occurred at 350 °C~seeFig. 4!, tends to indicate that while Sn may be effectiveretarding surface diffusion of Cu, it is less effective in retar

or

FIG. 13. Schematic diagram of surface steps and kinks on a Cu surfaceshaded atoms at the kinks are Sn atoms.


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ing grain boundary diffusion. More importantly, what is thproper temperature range for conducting an acceleratedtromigration test for a Cu interconnect? On the basis offact that in devices the electromigration in Cu interconneis dominated by surface diffusion, we may conduct the teat 250 °C but not at 350 °C. The result at 350 °C is misleing since it may include grain boundary diffusion.

C. Effect of stress on electromigration and vice versa

The effect of applied compressive stress on electrogration in Cu is expected to be the same as that in Alretards electromigration at the anode. But, the effect of bstress on electromigration in Cu is unclear.7 The first ques-tion is whether there is any back stress to be inducedelectromigration in Cu strips at a temperature below 250If a Cu strip is not covered by a liner such as Ta, nor confinby rigid walls, it is hard to envision how back stress cangenerated under electromigration by surface diffusion. Tis because a free surface is the most effective source andof vacancies, so stress will be relaxed easily and willbuild up. Hence, definitive experimental measurementsback stress in Cu interconnects will be needed.13,43–46

In devices, the Cu interconnect is embedded in an inlayer dielectric, so it is confined. Electromigration will induce extrusion or hillock formation at the anode end, evthough the electromigration occurs by surface diffusion. Textrusion can deform the surrounding dielectric if it is socause delamination if its adhesion is poor, or crack theelectric if it is brittle. The effect of electromigration inducestress in Cu/low-k interconnects is unclear. This will beserious reliability issue when a low dielectric constant inlation having a constant near or below 2 is integrated wCu metallization. On the other hand, if the dielectric is rigelectromigration can lead to plastic deformation of the cfined strip.

IV. ELECTROMIGRATION IN FLIP CHIP SOLDERJOINTS

Flip chip technologies and flip chip solder joints habeen discussed in a recent article,53 so they will not be re-peated here. However, we need to discuss why electromtion in flip chip solder joints is of concern. In today’s circudesign, each solder joint will carry 0.2 A and it will bdoubled in the near future. At present, the diameter osolder joint is about 100mm and it will be reduced to 50mmsoon. In the most advanced device today, there are alreover 7000 solder joints on a chip. We can place 10 000 sojoints on a 1 cm31 cm chip if the diameter of the soldebumps and the spacing in between them is 50mm. The av-erage current density in such a 50mm joint is about104 A/cm2 when a current of 0.2 A is applied. This curredensity is about two orders of magnitude smaller than thaAl and Cu interconnects. Electromigration does occur inchip solder joints at such a low current density and it occby lattice diffusion.9,54,55 Often, it is explained by the lowmelting point or fast diffusion of solder. However, Tableshows that at device operation temperature of 100 °C, latdiffusion in solder is not much faster than grain bounda


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diffusion in Al or surface diffusion of Cu from the point oview of electromigration. While the total atomic flux in latice diffusion is much bigger, so is the volume of a vorequired to fail a solder joint. Therefore, a low melting poior fast diffusion is not the answer. Why electromigration ocurs in flip chip solder joints at such low current densitiwill be explained below.

We recall the critical product in Eq.~6!. If we replaceDsby YD«, whereY is Young’s modulus andD«50.2% is theelastic limit, we see in Eq.~9! that the critical product is afunction of Young’s modulus, resistivity, and effective charnumber of the interconnect material:

j Dx5YD«V

Z* er. ~9!

To compare the value of the critical product among CAl, and eutectic SnPb, we note that eutectic SnPb has asistivity that is one order of magnitude larger than thoseAl and Cu. The Young’s modulus of eutectic SnPb~30 Gpa!is a factor of 2–4 smaller that those of Al~69 Gpa! and Cu~110 Gpa!.56 The effective charge number of eutectic Sn(Z* of lattice diffusion!2,57,58 is about one order of magnitude larger than those of Al (Z* of grain boundarydiffusion!26 and Cu (Z* of surface diffusion!.7,13 Therefore,in Eq. ~9!, if we keepDx constant for comparison, we finthat the current density needed to cause electromigratioeutectic SnPb solder is two orders of magnitude smaller tthat needed for Al and Cu interconnects. This is the mareason why electromigration in flip chip solder joints canserious.

Furthermore, due to the unique geometry of a flip chjoint, current crowding occurs at the contact interface btween the solder bump and interconnect wire~to be dis-cussed in the next section!. The high current density due tcurrent crowding is about one order of magnitude highthan the average current density in the joint. The low threold of the current density needed to have electromigrationsolder and the high current density due to current crowdare the key reasons why electromigration in flip chip sold

FIG. 14. Schematic diagram of a flip chip solder bump joining an intercnect line on the chip side~top! and a conducting trace on the board~bottom!.The teeth-like structures depict the scallop-type intermetallic compouformed between the solder and conducting metals.


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joints can compete with electromigration in Al and Cu inteconnects as the major reliability problem in microelectrodevices.

In addition, owing to the eutectic composition of soldalloys and the thin film metallization used at the interfacesa joint, the nature of electromigration in flip chip soldjoints is very different from that in Al and Cuinterconnects.54–62 This will be discussed below.

A. Effect of current crowding on electromigration

Figure 14 is a schematic diagram depicting the geomof a flip chip solder bump joining an interconnect line on tchip side~top! and a conducting trace on the board or moule side~bottom!.55–60 Because the cross section of the lion the chip side is about two orders of magnitude smathan that of the solder bump, there is a very large currdensity change at the contact between the bump and thesince the same current is passing between them. The chleads to current crowding at the entrance into the sobump, so the current density there is about one ordemagnitude higher than the average current density inmiddle of the bump. It will be 105 A/cm2 when the averagecurrent density in the bump is 104 A/cm2. Figure 15~a! is atwo-dimensional~2D! simulation of current distribution in asolder joint. Figure 15~b! is a display of current density distribution in the joint, where the cross section of the jointplotted on thex–y plane and the current density is plotte

FIG. 15. ~a! 2D simulation of current distribution in a solder joint.~b!Display of current density distribution in the cross section of a solder jowhich is plotted on thex–y plane and the intensity of the current densityplotted along thez axis ~Ref. 59!.


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FIG. 16. Cross-sectional SEM images of asymmetrical dissolution of a thCu UBM due to current crowding by electromigration at 125 °C withapplied current of 1.2 A: ~a! 0 min, ~b! 15 min,~c! 45 min, and~d! 90 min.The electron current entered the bump from the upper-left corner. Assolder replaced the Cu at the upper-left corner, more and more intermeCu6Sn5 formed inside the solder bump near the anode.~Courtesy of Profes-sor C. R. Kao, National Central University, Taiwan.!


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FIG. 17. Cross-sectional SEM images of electromigration failure of achip solder joint due to void formation and propagation along the coninterface between the thin film Cu/Ni~V!/Al UBM and the eutectic SnPbsolder bump:~a! 37 h,~b! 38 h,~c! 40 h, and~d! 43 h at 125 °C with currentdensity of 2.253104 A/cm2 ~Ref. 59!.


along thez axis.59,60 It is the current crowding or the highcurrent density shown at the upper-right corner in Figs. 15~a!and 15~b! that leads to electromigration damage in the soljoint, not the average current density in the bulk of the joiConsequently, electromigration damage occurs near thetact between the line and the bump.

Figure 16 displays a set of scanning electron micscopic images at several different stages of a flip chip sojoint in electromigration. Figure 16~a! shows the cross section of the joint before electromigration. A very thick Cunderbump metallization~UBM! is at the upper interfaceThe electron flow comes from the upper-left-hand interconect and enters the bump at the upper-left corner. Figu16~b!, 16~c! and 16~d! are images of the cross section of thsolder joint after 15, 45, and 90 min, respectively, powered1.25 A at 125 °C. The left-hand side of the Cu UBM disapeared gradually and was replaced by solder. Correspoingly, more and more Cu6Sn5 intermetallic compound wasformed inside the solder bump. The asymmetrical dissolutof the Cu UBM is clearly due to the fact that the electrcurrent entered the solder bump from the upper-left cornecurrent crowding occurred there. Why the Cu UBM can

ct

FIG. 18. Corresponding voltage vs time curve of the solder joint shownFig. 16 ~Ref. 59!.

FIG. 19. Schematic diagram depicting the effect of void formation apropagation on the current entering the solder bump. While the currebeing displaced to the front of the void, there is little change in resistanOnly when the void has propagated across the entire contact interfaceresistance will jump abruptly~Ref. 59!.


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dissolved and why a large amount of intermetallic compoucan be formed in the solder joint will be discussed in SIV B.

Figure 17 displays another set of SEM images ofdamage in a flip chip solder joint caused by electromigratiThe upper interface of the solder joint consisted of a sethin films of Cu/Ni~V!/Al.59 The total thickness of the thinfilm UBM is about 1 mm, hence, it is not resolved in thSEM image. Electrons of the applied current enteredbump from the upper-right corner of the joint. Up to 37 h125 °C with a current density of 2.253104 A/cm2, no dam-age was observed as shown in Fig. 17~a!. Yet, after 38 and 40h, voids are seen at the upper-right interface, and the vpropagated along the interface from right to left, shownFigs. 17~b! and 17~c!, respectively. After 43 h, the joint failedby having a large void across the entire interface, shownFig. 17~d!. The corresponding curve of potential change vsus time is shown in Fig. 18. In the curve, the potenchange is insensitive to the void formation until the enwhere it showed an abrupt jump when the void has extenacross the entire interface. The arrows in Fig. 18 indicatecorresponding ‘‘time’’ when the images in Fig. 17 wetaken. Why the potential or resistance change of the sojoint is insensitive to void formation and propagation canexplained by two reasons. The first is shown in Fig. 1where a schematic diagram depicts the cross sectionsolder joint with a void formation at the upper interface. Tformation and propagation of the void displaced the currto the front of the void, so very little change in resistanceaffected by the void formation. An abrupt change occurs o

FIG. 20. Schematic binary eutectic phase diagram of Sn–Pb. Alongbroken line at constant 150 °C, there is no chemical potential changefunction of composition. Hence, we can have phase separation alongbroken line driven by electromigration.

TABLE III. Electromigration test of solder joints vs Al and Cu interconnects.

Al or Cuinterconnects Solder bumps

Cross section 0.530.2mm2 1003100mm2

Resistance 1–10V 1023 VCurrent 1023A 1 ACurrent density 106 A/cm2 103– 104 A/cm2


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when the void has extended across the entire joint or wthe contact becomes an opening. The second reason is gin Table III, where a comparison of the electrical behavbetween the Al~or Cu! interconnect and solder joint is givenThe resistance of a cubic piece of solder of 100mm3100mm3100mm ~the size of a solder joint! is about 1mV. The resistivities of Sn and Pb are, respectively, 11 a22 mV cm. The resistance of an Al or Cu line 100mm longwith a 1mm30.2mm cross section is about 10V. So, thesolder joint is a low resistance conductor, but the intercnect is a high resistance conductor. While the resistancthe latter is sensitive to a slight microstructure change,former is not. Often, a solder joint may contain a huspherical void due to residue flux in the solder paste, yetvoid has little effect on the resistance of the solder joint.

B. Effect of eutectic composition on electromigration

A major advantage of flip chip technology is that thosands of solder joints or electrical leads can be formedmultaneously by low temperature heating in forming gAlso, many joints can be placed near the center of a chiporder to avoid the voltage drop from a lead located atedge of the chip. The technology does require that alljoints melt or solidify at the same temperature, so a eutealloy is favored as solder. However, a eutectic alloy haunique property that at a constant pressure and tempera~below the eutectic temperature!, it has a two-phase microstructure and there is no chemical potential gradient afunction of alloy composition. A schematic diagram of thbinary phase diagram of Sn–Pb is depicted in Fig. 20illustrate the effect of eutectic composition. If we considerambient pressure and 150 °C, any composition alongbroken line shown in Fig. 20 will decompose into the twend phases at the two points indicated by the arrows. Thtwo phases are at equilibrium with each other, independof the amount of each phase. Consider the two alloyspoints ‘‘A’’ and ‘‘B’’ as shown in Fig. 20 to form a diffusioncouple. Upon annealing at 150 °C, we find that there isinterdiffusion or no homogenization, except some ripeniThus, if we subject a homogeneous~in average composition!two-phase eutectic alloy to electromigration, it becomeshomogeneous by driving one of the phases to the anodethe other to the cathode. We can have phase separation alarge amount of up-hill diffusion and yet there exists no cocentration gradient force to oppose it.62 This eutectic effect isdifferent from the classic Soret effect,15 in which a homoge-neous single phase alloy becomes inhomogeneous undtemperature gradient. The difference is not because a eutalloy is a two-phase alloy, rather that in the Soret effect, this a chemical potential or composition gradient to resist

ea

he

TABLE IV. Intersititial Diffusion of noble and near-noble metals in GrouIV elements.

Cu, Ag, Au, Ni, Pd, Pt..............................`.............................. Interstitial Diffusion

Si, Ge, Sn, Pb


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effect. But in a eutectic alloy, there is no chemical potengradient to resist phase separation driven by electromigraor other forces.

If we examine the binary phase diagram of Sn–CuSn–Ni, we find that Sn and Cu6Sn5 as well as Sn and Ni3Sn4

form eutectic couples. This means that below their eutetemperature we can form a large amount of these compouin a Sn matrix, and the compounds will be in equilibriuwith the matrix. Indeed, this has been observed in electrogration in solder joints. Since both Cu and Ni are being uas UBM in solder joints, they can be dissolved by electromgration into the solder joint and form a large amount oftermetallic compounds~IMCs! near the anode, especially, thPb-free solders which are Sn based. The dissolution rasurprisingly fast due to the fact that noble and near-nometals diffuse interstitially in group IV elements as shownTable IV.63,64 Electromigration of these metals in Sn andare very fast.65–68

C. Polarity effect of electromigration on chemicalreactions at cathodes and anodes in solder joints

Both noble and near-noble metals react with Sn to foIMCs at room temperature due to fast interstitial diffusion69

Since the IMCs formed at the solder joint interfaces areintegral part of the joint, they must be considered togetwith the solder bump in electromigration. Because of fdiffusion and rapid reaction, the chemical and electriforces interact at these interfaces.70 However, the interactionsat the cathode and the anode are different due to the poleffect. At the cathode, the electrons flow from the IMCsolder, but at the anode the flow direction is reversed. Welectromigration enhances IMC formation at the anodeenhances IMC dissolution at the cathode.

To investigate the polarity effect, we have designed tsamples of V-groove solder lines with Cu electrodes attwo ends.57,71,72Figures 21~a! and 21~b! show schematic diagrams of a V-groove sample and its cross-sectional vi

FIG. 21. Schematic diagram of~a! V groove along^110& direction on theSi~001! surface with two Cu wires at two ends, and~b! cross-section view ofa V-groove solder sample~Ref. 57!.


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,

respectively. The V-shaped grooves with a width of 100mmand a length along the@110# direction on a 4-in.-diam~001!silicon wafer were processed by standard lithographyetching techniques. Following wet oxidation of a thin SiO2

layer of 0.1mm, metal layers of 0.05mm of Ti, 1 mm of Cu,and 0.05mm of Au were deposited sequentially by e-beaevaporation. The wafer was cut into small pieces withV-groove line in the middle. For each piece, two Cu wirwere placed at the two ends of the V groove as electrodthen eutectic SnPb and Pb-free solder of SnAg3.8Cu0.7 wereregrown into the V groove between the two copper wirusing mildly activated resin flux.

Electromigration in eutectic SnPb V-groove solder linhas been studied at 150 °C and room temperature.57,62 At

FIG. 22. SEM images of morphological changes on a eutectic SnPb soline due to electromigration:~a! large lump formation at the anode afteapplying 2.83104 A/cm2 at 150 °C for 8 days;~b!void at the cathode in atop-down cross section of the sample shown in~a!; and~c! a sample at roomtemperature with 5.73104 A/cm2 for 12 days~Refs. 57 and 62!.


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150 °C, the extrusion at the anode became very appaafter 8 days’ stressing with current density of 23104 A/cm2, as shown in Fig. 22~a!. The void at the cath-ode is seen more clearly after polishing away a 10mm layerfrom the surface, see Fig. 22~b!. The extrusion at the anodside is a big lump, rather than small hillocks as in the anoof Al or Cu thin film interconnects.

The morphological change due to electromigrationless obvious at room temperature, as shown in Fig. 22~c!,although the stressing time is longer, 12 days, and curdensity is more than doubled.

Redistribution of Sn and Pb in eutectic SnPb solder linwas examined by x-ray dispersive analysis. At 150 °Csignificant accumulation of Pb occurs at the anode side, wa maximum concentration reaching 95 wt % Pb. In contrat room temperature Sn accumulates at the anode side, wmaximum concentration of about 92 wt % Sn. These pnomena suggest that in the SnPb system Pb is the domdiffusion species at 150 °C, but Sn is the dominant diffusspecies at room temperature. These results are in agreewith those of Guptaet al.18 obtained from tracer diffusions

FIG. 23. SEM images of thickness change at the anode and cathode,current stressing of~a! 0 h at the anode,~b! 10 h at the anode,~c! 0 h at thecathode, and~d! 10 h at the cathode with current density of 33104 A/cm2 at 180 °C~Refs. 71 and 72!.


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s

nt

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antnent

of 210Pb and113Sn in eutectic SnPb solder, that Pb diffusiois faster than Sn at temperatures above 120 °C, and Snfuses quicker than Pb at temperatures below 120 °C.

Knowing the volume of mass transport~the volume ofthe extrusion at the anode or void at the cathode!, we canobtain the flux of electromigration,Jem, by assuming thatVem5VJemAt, whereVem is the volume of mass transporV is the atomic volume,A is the cross section of the soldeline, andt is the time of electromigration. Then, the effectivcharge number,Z* , can be calculated. The average valuesZ* in high temperature and room temperature electromigtion in eutectic SnPb are calculated to be 33 and 39, restively, which are close to the reported values of 47 and 18self-electromigration in bulk Pb and bulk Sn, respectively2

The polarity effect of electromigration on the thickneand morphology changes of IMCs at the cathode and anin SnAg3.8Cu0.7 V-groovesolder lines has been investigated150 and 180 °C, with current density in the range103– 104 A/cm2.71,72 The same IMC of Cu6Sn5 and Cu3Sn

fterFIG. 24. ~a! Cross-sectional SEM image of a flip chip corner solder jojoining a chip to a board. Relative displacement of 10mm due to shearbetween the chip and the board can be seen.~b! Schematic diagram of asheared solder joint in which the electron current enters the joint fromcompressive ‘‘C’’ region.~c! Electron current enters the joint from the tensile ‘‘T’’ region.


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form at solder/Cu interfaces with or without applying electcurrent. The IMC formed after the initial reflow hadscallop-type morphology and transformed into layer-tymorphology in solid state aging, with or without electromgration.

Electromigration enhances the growth of IMCs at tanode and inhibits the growth at the cathode as compwith the no-current case. As shown in Figs. 23~a! and 23~b!,for the sample under current density of 3.23104 A/cm2 at180 °C, both Cu6Sn5 and Cu3Sn layers keep growing at thanode side with the application of current. The total thicness approaches 9mm after 87 h. This thickness is comparable with that grown for 200 h at 180 °C without current.the cathode side, shown in Figs. 23~c! and 23~d!, the IMCgrew much slower than that at the anode side and the Ialso became layer like. Voids started to appear in the sopart just in front of the solder/IMC cathode interface afterh.71,72 The growth of IMC at the anode obeys the parabogrowth rate, and the back stress in IMC might have playesignificant role in the parabolic growth.

The polarity effect of electromigration on IMC formation in eutectic SnPb solder, as a function of temperatureof interest because of the temperature dependence odominant diffusing species in the solder. For example,can use Ni instead of Cu as electrodes and the formatioIMC will be different. Then, the length of the solder linmight affect IMC formation at the cathode and anode, to

D. Effect of stress on electromigration and vice versa

In flip chip devices, the solder joints at the corners ochip are subjected to large shear during thermal cyclescause of different thermal expansion coefficients betweenchip and its substrate. In Fig. 24~a!, an SEM image of acorner solder joint in a flip chip is shown, where the upppart of the joint is sheared to the left with respect to tlower part of the joint. The shear displacement ‘‘x’’ was mea-sured to be 10mm. The height ‘‘h’’ of the solder in the jointis about 30mm, so the shear (s5x/h) is very large. Todemonstrate the relationship between the shear andtromigration, a schematic diagram of the cross section osolder joint under shear is shown in Fig. 24~b!. In the dia-gram a letter ‘‘T’’ is used to indicate the tensile region andletter ‘‘C’’ to indicate the compressive region. There arepair of ‘‘T’’ and a pair of ‘‘C’’ in the sheared joint. We notethat the electrons can enter the joint from a ‘‘C’’ regionshown in Fig. 24~b! or a ‘‘T’’ region as shown in Fig. 24~c!.Similarly, it can get out of a joint from either a ‘‘C’’ or ‘‘T’’region. Generally speaking, at the cathode, electromigrais enhanced by tension but retarded by compression. Atanode, the interaction is opposite. Hence, a favorable cotion should be the electron current entering the joint from‘‘C’’ region and leaving from the ‘‘T’’ region. We note thathere are no experimental data to verify the effect yet. If teffect is true, we should be able to take advantage of idesigning the circuit in packaging.

The question of back stress in flip chip solder jointsinteresting, yet no measurement has been conducted to intigate it. Under the constraints of underfill, back stress m


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build up in a flip chip solder joint. How the back stresinteracts with the thermal shear stress is also of interest.

E. Effect of solder composition on electromigration

The electronic industry has been searching for Pb-fsolders for benign manufacturing. Tentatively, eutecSnAgCu has been recommended to replace eutectic SThe composition of Sn in a solder joint is an interesting issin electromigration. For example, in eutectic SnAgCu, tcomposition of Sn is about 96 wt % and it matrix is essetially Sn. In eutectic SnPb, the composition of Sn is aboutwt %. In high-Pb solders, which have been widely usedmainframe computers to join chips to ceramic modules,composition of Sn is 3 wt % and its matrix is essentially PGenerally speaking, if we assume atomic diffusivity is prportional to melting point of the solder, we expect electromgration in eutectic SnPb to be the fastest, next will beeutectic SnAgCu, and the slowest will be the high Pb. Atmoment, we have preliminary data to show that indeed etromigration in eutectic SnAgCu is slower than that in eutetic SnPb.58,73

Figures 25~a! and 25~b! show, respectively, sideviewSEM images of eutectic SnPb and eutectic SnAgCu sojoints after electromigration. The test temperature w120 °C and the applied current was 1.5 A. In Fig. 25~a! a

FIG. 25. ~a! Cross-section SEM image of a side view of a eutectic Snsolder joint after electromigration. A dimple in the cathode side and a buin the anode side can be seen,~b! Cross-section optical image of a side vieof a eutectic SnAgCu solder joint after electromigration. The surfacemains flat, indicating that the electromigration damage is very little~Refs.58 and 73!.


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dimple in the cathode side and a bump in the anode sidebe seen after 40 h. In Fig. 25~b!, the surface remains flat afte200 h, indicating almost no obvious damage by electrogration.

Figure 26~a! shows a cross-sectional SEM image of tfront view of a eutectic SnPb solder joint after electromigtion. On the polished surface, embedded debris~polishingpowder! was found which served as diffusion markers for tstudy of atomic flux migration during electromigration. Tharrow in Fig. 26~a! indicates that electrons flowed downward, the same as the atomic flux of electromigration, henthe markers migrated upward. The marker displacemehave been measured as a function of time and they are shin Fig. 26~b!. The displacement is linear with time. Knowinthe displacement and the average cross-sectional areavolume displaced by electromigration, in turn the effecticharge number of electromigration, can be calculated ascussed in Sec. IV C. The obtainedZ* values are in agreement. Using the same marker measurement, the rate ofplacement was found to be much less in eutectic SnAgC

For electromigration in the high-Pb solder, there are litpublished data for comparison. Since the lattice diffusivityeutectic SnPb solder is about two orders of magnitude fathan that in the high-Pb solder, electromigration in the lais expected to be two orders of magnitude slower thanformer, assuming the other parameters as given in Eq.~9! arethe same. Atomic diffusivity in a eutectic SnPb alloy is afected by microstructure. Below the eutectic temperature,

FIG. 26. ~a! Cross-section SEM image of a front view of a eutectic Snsolder joint after electromigration. Surface markers are indicated bysmall circles with numbers.~b! Marker displacement plotted against tim~Refs. 58 and 73!.


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tectic SnPb alloy has a lamellar structure consisting of pmary Pb and primary Sn phases. Atomic diffusion alonglamellar interfaces has been found not to be as fast aspected due to habit or a semicoherent relationship betwthe lamellae.18 The activation energy of the interfacial diffusion is about 80%, not 50%, of that of lattice diffusion in thprimary phases. Then, in solid state aging of solder joinlarge grains of primary Pb and primary Sn are formed athe interfaces are disconnected and reduced, so the interfdiffusion is less dominant. Therefore, electromigration ineutectic SnPb solder joint is sensitive to the thermal histof the joint, since it was very different after reflow as compared to solid state aging, especially when we consider etromigration at the device temperature of 100 °C.

V. CURRENT CROWDING

In Sec. IV A, we discussed current crowding in a flchip solder joint and its effect on electromigration. We epect to find current crowding in a multilevel structure of Aand Cu interconnects due to interfaces, turns, and vias.review below experimental observations of the effect of crent crowding, and we introduce a driving force of electromgration on the basis of the current density gradient. We ephasize that this force is normal to the direction of electrflow, while the classic electron wind force is parallel to eletron flow.

Several observations of unexpected void formationlow current density regions in electromigration tests habeen reported. Using the Blech structure of short Al stripsa TiN base line as sketched in Fig. 27~a!, Okabayashi and

e

FIG. 27. ~a! Schematic diagram of the cross section of an Al short stripTiN and the formation of a void at the upper-left corner where currdensity is low.~b! Schematic diagram of the top view of a TiN base linhaving a U-turn and an Al short strip having an overhang~Refs. 74 and 75!.


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co-workers observed void formation to start at the upper-corner of the strip where current density is low.74 The mea-surement was performed by sidewise cross-sectional TAfter a long period of testing time when the anode sideformed a large hillock, they reversed the current directand found that voids started to form at the tip of the hillocAgain, the voids were found in the region of nearly no crent density. Figure 27~b! shows a schematic diagram of thtop view of a Blech structure of the Al strip on TiN havingU turn, and it was used to study electromigration by Shgubara and co-workers.75 Some of the Al strips had an ovehang outside the TiN and the overhang should have vlittle current. Nevertheless, voids were found in the ovhang.

In Figs. 28~a! and 28~b!, respectively, a schematic diagram and SEM image of electromigration damage in a mtilevel Cu interconnect are shown.40 The direction of electronflow is indicated by the long and curved arrow. Two kindsdamage were observed. First, surface void formationobserved in the upper surface of the Cu interconnect. Sond, a huge void formation was found at the lower extens

FIG. 28. ~a! Schematic diagram of a two-level Cu dual damascene intercnect. The electron current direction is indicated by a curve arrow.~b! SEMimage of void formation in the upper surface of the Cu interconnect anda large void formation in the overhang at the left-hand bottom of theinterconnect~Ref. 40!. ~Courtesy of Dr. C. K. Hu,et al., IBM T. J. WatsonResearch Center, Yorktown Heights, NY.!


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of the Cu interconnect. The extension should have had vlittle current density, nevertheless, a large void was fouthere.

In the above three cases, voids were found to form inlow current density region. The explanation given was tvacancies were driven by a stress gradient to the low curdensity region. Such an explanation is unsatisfactory becait has ignored the fact that void formation requires nucleatthat in turn requires a supersaturation of vacancies. Weconsider the case shown in Fig. 27~a! or 3~a!. According tothe classic electron wind force of electromigration, vacancare driven to the cathode in the opposite direction of electflow, hence, vacancies should accumulate at the lower-rcorner. Thus, there is a vacancy concentration gradientcreasing from the lower corner to the upper corner, whmay induce a flux of vacancies to go from the lower cornto the upper corner. What is hard to explain by this reasonis why vacancies can reach supersaturation at the upperner and nucleate a void there, since the vacancy gradiefrom the lower corner~high concentration! to the upper cor-ner ~low concentration!. Vacancies should have reached spersaturation at the lower corner first and nucleated a vthere. A different explanation has been offered on the basia new driving force of electromigration.76

A. Driving force of electromigration

In Figs. 29~a! and 29~b!, schematic diagrams of an inteconnect having a 90° turn and a current density distribut

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ou

FIG. 29. ~a! Schematic diagram of a 90° turn in an interconnect, whereFwd

is electron wind force andFgrad is current density gradient force.~b! Currentdistribution in the 90° turn, in which current crowding occurs at the inncorner~Ref. 76!.


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at the turn are shown, respectively. A very high current dsity exists at the inner edge of the turn, and there is a curdensity gradient that decreases from the inner edge toouter edge of the turn. If a potential is applied to the graent, it produces a force acting down the gradient. Considvacancy in the high current density region, it will be pushdown the current density gradient by a force,F, because thevacancy is a high resistance or a high potential entity:

F52dP

dr, ~10!

where P5qv jADrv , and qv is the effective charge of thevacancy (5Zv* e andZv* is the effective charge number!, j isthe current density,A is the scattering cross section of thvacancy, andDrv is the resistance of the vacancy in thlattice.76–78 The vacancy flux driven by the gradient forcwill be given as

Jgm5DCv

D

kT S 2dP

dr D , ~11!

whereDCv is the excess vacancy concentration in the crent crowding region relative to the constant current denregion.

Another way to envision the gradient force is to compathe scattering on the two sides of a vacancy. The scatteon the higher current density side is greater than that onlower current density side, hence, there is a net force pusthe vacancy down the gradient. While the scattering olattice atom can be calculated, the resistance of a lattice ais only about one hundredth of that of a vacancy,79 so thegradient force on an atom is much less. Besides, the mobof a vacancy is much higher than an atom.

On the basis of scattering, it is expected that the foshould have a square dependence on current density.force by scattering depends on the momentum of electrand the number of electrons scattered by an atom pertime; both are proportional to current density. This has b

FIG. 30. Effect of contact resistance on current crowding is to reduce icurrent spreading~Refs. 80 and 81!.


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enge

ngam

ty

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nsnitn

shown in Black’s equation of mean-time to failure of inteconnects, which will be discussed in Sec. VI A.

In Eq. ~10! and also in Huntington’s equation of electromigration, which is shown below,

Jem5CD

kTZ* er j , ~12!

the force is linear with current density. The discrepancould be due to the fact that in Huntington’s derivation,20 theeffect of momentum exchange between electrons and difing atoms has been lumped into ‘‘Z* ,’’ the effective chargenumber, althoughZ* does not appear to depend on curredensity explicitly. This is not so. Because electrons scatte~or very near! the Fermi surface, and their momentum tranfer per collision is on the order of the Fermi momentum anot the electron drift velocity~which is proportional to elec-tron current density!. Therefore,Z* contains the momentumexchange, but it does not contain the current density.force is linearly proportional to electron current density.25

Combining the classic electron wind force and the crent density gradient force in the cathode side of the Al shstrip shown in Fig. 3~a!, we have a vector sum of

Jsum5Jem1Jgm5Cv

Dv

kT~2Zv* eE!1DCv

D

kT S 2dP

dr D ,

~13!

where the first term is due to electromigration driven by telectron wind force and the second term by the current dsity gradient force. Hence, in Figs. 3~a! and 5, vacancies willbe pushed towards the upper corner before they reachlower corner. This will lead to accumulation and supersaration of vacancies in the upper corner. A void will nucleagrow, and eventually deplete the entire cathode end ofstrip. In comparison, if a void were nucleated at the lowcorner, it would not be able to deplete the entire cathodeof the strip.76

B. Effect of contact resistance on current crowding

Current crowding can be diffused or spread by contresistance as shown in Fig. 30.80,81 By changing the contacresistance between the Al strip and TiN base line, we fouthat a spreading of the current entering or leaving the Al cbe achieved, resulting in a reduction of current crowding

The beneficial effect of contact resistance can be appto vias and to flip chip solder joints. In the latter, we can ua thick underbump metallization such as a thick Cu or eltroless Ni~P!. It will move the high current density regionfrom the solder to the UBM. However, the high current desity in the UBM might enhance the dissolution of the UBas shown in Sec. IV A.

VI. ANALYSIS OF MEAN TIME TO FAILURE

A. Effect of current density

The electronic industry uses the mean-time-to-failu~MTTF! analysis to predict the lifetime of a device. In 196Black provided the following equation to analyze failureAl interconnects caused by electromigration:82

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MTTF5A1

j n expS Q

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The derivation of the equation was based on an estimof the rate of forming a void across an Al interconnect. Tmost interesting feature of the equation is the dependencthe MTTF on the square power of current density, i.e.n52.

In the MTTF equation, whether the exponentn is 1, 2, ora larger number has been controversial, especially wheneffect of Joule heating is taken into account. However,suming that mass flux divergence is required for failure athe nucleation and growth of a void requires vacancy supsaturation, Shatzkes and Lloyd have proposed a modesolving the time-dependence diffusion equation and obtaia solution for MTTF in which the square power dependenon current density is also obtained.83 Nevertheless, whetheBlack’s equation can be applied to MTTF in Cu interconects and flip chip solder joints deserves careful examtion.

B. Effect of activation energy of diffusion

Although the effect of microstructure was not taken inaccount in obtaining the MTTF equation, Black has studthree kinds of Al films with different microstructures anobtained three different values of activation energy ‘‘Q’’ inthe MTTF equation.82 It is clear that as linewidth has beereduced from 25 to 10mm ~in Black’s samples! to less thanhalf a micron today, the distribution of grain size and tdominant diffusion path in interconnects have changed.changes will affect the activation energy ‘‘Q’’ in the MTTFequation. To determine the activation energy, acceleratests at high temperatures are performed. We must pay ation to the temperature range in which lattice diffusion migoverlap grain boundary diffusion and also grain bounddiffusion might overlap surface diffusion. For exampwhile an accelerated test at 350 °C for Al interconnectsacceptable, it is not for Cu interconnects since grain bouary diffusion cannot be ignored at 350 °C for Cu as shownTable I, although Cu has a higher melting point than Al. Feutectic SnPb solder, it is more complicated because ofchange of dominant diffusion species above and be100 °C.

C. Effect of void nucleation and growth at cathodes

The formation of a void requires nucleation. If we ignoat this moment the barrier of nucleation of a void, we cjust consider the growth of a void by vacancies driven tovoid or by atoms driven away from the void. We assumevolume of the void to beV5VJemAdt, where V is theatomic volume of an atom or a single vacancy;Jem is theatomic or vacancy flux driven by electromigration;Ad is theeffective cross-sectional area of the diffusion flux, whichdifferent for lattice diffusion, grain boundary diffusion, ansurface diffusion; andt is time. To define the volume of thvoid that is large enough to become an opening, we consa void in an Al line above a W via and we take the vo


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volume to be equal to the cross section of the via timesthickness of the Al line. Ignoring nucleation, the time needto fail a test strip is the time needed to transport enouvacancies to grow the void of volumeV:

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We recall thatJem depends on back stress as shown in E4~a!. On the other hand, a simpler way to estimate the tiof growth of such a void is to divide the diameter of the vby the drift velocity measured from the Blech strip shownFig. 4 or the two-level test structure shown in Fig. 5,

t5d

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In measuring the drift velocity in Al~Cu! strips using thetwo-level test structure, it was found that there is a loincubation time before void growth. The incubation timedue to the depletion of Cu and nucleation of a void in tcathode end. After that the void growth by electromigratiin the pure Al cathode is very fast. This behavior is alfound in the testing of Cu~Sn! samples shown in Fig. 12, acompared to that of pure Cu in Fig. 12. Since the grboundary diffusivity in Al and surface diffusivity in Cu ashown in Table I are close to each other and their cosponding cross-sectional area of diffusion is also comrable, we expect their drift velocity near the device operattemperature to be similar.

The above calculation indicates that the time neededgrow a void to the size of an opening above a via ininterconnects is only a small fraction of the measured MTTherefore, the bulk part of the MTTF is taken up by the timneeded to deplete the Cu solute from the cathode anovercome the nucleation barrier of a void. In other woreven in the heterogeneous nucleation of a void in Al intconnects, the supersaturation of vacancies needed to ocome the nucleation barrier is important as assumed inmodel of Shatzkes and Lloyd.83

However, the case of the Cu interconnect is differentwe consider surface diffusion, it is hard to imagine why tnucleation of a void on a surface requires much supersattion. On the other hand, the growth of a void on a surfamay not be a localized event since it can spread out anddown the entire or a large portion of the interconnect. In sua case, it is the growth not nucleation that will take mostthe time to fail the device. Furthermore, a void spreadingbetween a via and the line below it is much more seriothan a void spreading out in the middle or other part ofline far away from a via.

In the case of a flip chip solder joint, Fig. 18 shows ththe time to failure is controlled not by the propagation ofvoid across the contact interface, but by void nucleation. Tlatter takes about 90% of the time before failure. The progation of the void across the entire contact takes only ab10% of the time. Furthermore, as shown in Secs. IV A andthe effect of current crowding cannot be ignored in the anasis of MTTF. Black did point out the importance of the cu


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rent or temperature gradient on interconnect failure, althohe did not take them into account in his equation explicitly82

On the basis of the failure mode of a flip chip solder jointshown in Figs. 16 and 17, the major effects of current crowing are to increase greatly the current density at the entraof the solder joint and also to increase the local temperadue to Joule heating.

The above discussion indicates that we may not apBlack’s equation directly to predict MTTF for Cu interconnects and flip chip solder joints. While Black’s basic assumtions are correct, we need to revise the equation for theure in Cu interconnects and flip chip solder joints. Tdistribution of failure time due to electromigration in a largnumber of interconnects has been found to obey a lonormal function. Why such a distribution function is obeyis unclear since no mathematical derivation of such a disbution function has been given.

D. Effect of hillock and whisker formation at anodes

The extrusion of hillocks and whiskers at anodes isother mode of interconnect failure. Such extrusion cancome a short or crack the interlayer dielectric. The latterconcern for Cu/low-k technology. Because of current crowing, the one-dimensional compressive stress distributionpresented in Fig. 8 for a short strip is inadequate. We expa stress center at the lower-right corner~anode! in Fig. 3~a!or 7 due to current crowding where current exits the stWhile the electron wind force pushes atoms to the lowright corner, there should be a current density gradient foto push atoms to the upper-right corner. Nevertheless,gradient force on an atom is small as we have discusseSec. V, so the effect of the gradient force at the anodedifferent from that at the cathode. We must use a twdimensional stress distribution to model the stress at theode. Measurement of the two-dimensional stress distribuis a challenging problem.

The atomic mechanism of growth of hillocks and whkers at the anode is of interest. Typically, spontaneous wkers grow from the bottom by pushing up or by extrusion84

This is also true for hillock growth since the electron winforce drives atoms to the bottom where the current exitsstrip at the anode end. If adhesion between the interconand its bottom dielectric is weak, extrusion occurs atbottom interface. If the bottom adhesion is good, extrusionhillocks occurs on the top surface of the strip, and a crackthe surface oxide~Al strip! is required. Vacancies can comin from the crack to mediate the diffusion of atoms. By usifocused ion beams, we can cut a thin slice of the anodeuse transmission electron microscopy to study the micstructure change and the growth mechanism.

A strip of Sn grows whiskers at the anode drivenelectromigration.55 On the other hand, it is well known thaSn whiskers grow spontaneously on a thin coating of SnCu.85,86 But, whether the mechanism of growth of these twkinds of Sn whiskers is the same or not is unknown. Whboth are driven by a compressive stress, it is unclear whethe stress distribution in the root area of a whisker issame.


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VII. SUMMARY

We have compared the electromigration behaviors inand Cu interconnects and solder joints on the basis ofratio of their melting point to the device operating tempeture of 100 °C. Accordingly, grain boundary diffusion, suface diffusion, and lattice diffusion dominate, respectively,electromigration in Al, Cu, and solder. In turn, the effectsmicrostructure, solute, and stress on electromigration areferent in Al, Cu, and solder. For example, while the trippoint of grain boundaries has been an important issueelectromigration in Al, it is not so in Cu interconnects bcause a triple point on the surface is not an effective mflux divergence. Therefore, while Cu solute in Al has reducgrain boundary diffusion of Al, we will need a solute in Cwhich can retard the surface diffusion of Cu. So far, Sn hbeen found to be very effective in retarding electromigratin Cu. For the damascene process, improving the adhesiothe Cu to the dielectric layer above it is a most challengissue of device fabrication because otherwise the surfacthe built-in mass transport path of electromigration. For Clow-k interconnects, the compressive stress at the anodeduced by electromigration will be a very serious issue sinthe low-k dielectric ~with a valuek around 2! tends to beweak mechanically. Several experimental observations hshown that void formation in electromigration occurs in locurrent density regions accompanying current crowdingelectromigration force is proposed; the current density graent force, acting normal to current flow, can explain welectromigration damage occurs away from the high currdensity region. In mean-time-to-failure analysis, the timtaken to nucleate a void is more important in Al interconects and flip chip solder joints than that on the surface oCu interconnect. For accelerated tests of electromigratthe temperature range must be relevant to the real faimechanism in actual devices, e.g., 350 °C is too high forinterconnects.

Finally, there are still many unanswered questions abelectromigration, therefore, much more study will be needAt the moment, the microelectronic industry is working othe integration of ultra-low-k dielectrics with Cu metalliza-tion. The question of what is beyond Cu will be challengin

ACKNOWLEDGMENTS

The author would like to acknowledge the supportNational Science Foundation Contract No. DMR 99874and Semiconductor Research Corporation Contract No.774. The author would like to thank Professor Y. C. Chanthe Department of Electronic Engineering at City Universof Hong Kong for hosting his one month leave~December2002! when a bulk part of this review was written. The traeling support provided by The Royal Society/Kan TongVisiting Professorship at City University of Hong Kongmuch appreciated. Also, the author would like to thank Pfessor R. S. Sorbello in the Department of Physics, Univsity of Wisconsin–Milwaukee, for comments on the linedependence of electromigration driving force on current dsity. The assistance by Albert Wu and Jong-ook Suh~UCLA!in collecting references and figures is appreciated, too.


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