Morphology and Growth Kinetics of Straight and KinkedTin Whiskers

DONALD SUSAN, JOSEPH MICHAEL, RICHARD P. GRANT, BONNIE MCKENZIE,and W. GRAHAM YELTON

Time-lapse SEM studies of Sn whiskers were conducted to estimate growth kinetics and doc-ument whisker morphologies. For straight whiskers, growth rates of 3 to 4 microns per day weremeasured at room temperature. Two types of kinked whiskers were observed. For Type Akinks, the original growth segment spatial orientation remains unchanged, there are no otherchanges in morphology or diameter, and growth continues. For Type B kinks, the spatialorientation of the original segment changes and it appears that the whisker bends over.Whiskers with Type B kinks show changes in morphology and diameter at the base, indicatinggrain boundary motion in the film, which eliminates the conditions suitable for long-termwhisker growth. To estimate the errors in the whisker growth measurements, a technique ispresented to correct for SEM projection effects. With this technique, the actual growth anglesand lengths of a large number of whiskers were collected. It was found that most whiskers growat moderate or shallow angles with respect to the surface; few straight whiskers grow nearlynormal to the surface. In addition, there is no simple correlation between growth angles andlengths for whiskers observed over an approximate 2-year period.

DOI: 10.1007/s11661-012-1488-7� The Minerals, Metals & Materials Society and ASM International (outside the USA) 2012

I. INTRODUCTION

TIN (Sn) whiskers have become a concern in recentyears due to requirements for lead (Pb)-free solderingand surface finishes in commercial electronics. Pure Snfinishes are more prone to whisker growth than theirSn-Pb counterparts and high profile failures have beendocumented due to whiskers causing short circuits.[1] Itis generally understood that stress within the Sn layer,particularly compressive stress, provides the drivingforce for whisker growth. However, a full explanation ofthe whisker growth mechanism has yet to be developed.It is unlikely that mechanistic explanations of whiskergrowth can be fully developed without rigorous, detailedcharacterization of tin whiskers. The purpose of thiswork is to develop techniques for accurately measuringand characterizing whisker growth, morphology, length,and growth angle on a statistically significant popula-tion of whiskers.

Much has been learned about whiskers throughscanning electron microscopy (SEM) and related tech-niques.[2,3] Along with traditional SEM methods, an

efficient way to study growth kinetics is through time-lapse ‘‘in situ’’ SEM imaging, in which the samewhiskers are followed during the growth process.[4–6]

The difficulty lies in returning to the exact location ofthe whiskers after prolonged intervals. This can beaccomplished with sophisticated indexed removablesample holders or by simply leaving the sample in themicroscope chamber for long periods and using capa-bility to accurately reposition the SEM stage usingstored stage coordinates. This approach allows forsimultaneous determination of growth kinetics andchanges in whisker morphology or growth direction.With in situ SEM imaging, Jadhav et al.[4] showed thatthe removal of surface oxide was not enough to promotewhisker growth, indicating that the underlying grainstructure is important for whisker growth. They alsostudied hillock formation and found significant graingrowth and surface grain rotation associated withhillocks. Tu and Li[5] showed SEM time-lapse imagesthat confirmed that whisker growth occurs at the base ofthe whisker. Reinbold et al.[6] used in situ SEM imagingto observe the growth of whiskers in a bimetallic sampleof pure Sn and Sn coated with Cu. They were able tomeasure the extruded volume of whisker material as afunction of time with this technique. Jadhav et al.[4,6]

indicated that whisker growth was driven by compres-sive stresses derived from intermetallic compoundgrowth (IMC) at the Sn/Cu substrate interface.This paper presents an in situ time-lapse SEM study to

determine Sn whisker growth kinetics. The effects ofwhisker kinking on the growth process are also exam-ined. Kinks in Sn whiskers have been observed for manyyears.[7–9] However, whisker kinks have not been studied

DONALD SUSAN and W. GRAHAM YELTON, PrincipalMembers of Technical Staff, JOSEPH MICHAEL, Senior Scientist,RICHARD P. GRANT and BONNIE MCKENZIE, PrincipalTechnologist, are with the SandiaNational Laboratories, Albuquerque,NM 87185. Contact e-mail: dfsusan@sandia.gov

Manuscript submitted March 20, 2012.Article published online October 25, 2012Sandia National Laboratories is a multi-program laboratory

managed and operated by Sandia Corporation, a wholly ownedsubsidiary of Lockheed Martin Corporation, for the U.S. Departmentof Energy’s National Nuclear Security Administration.

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in detail using in situ techniques. During this work, theeffect of the SEM projected images became important.A technique to correct for image projection errors will bedescribed and, after applying this correction, a summaryof whisker growth angles and lengths is presented. It ishoped that the observations and data collected in thisstudy will be useful to researchers developing mechanis-tic explanations of the whisker growth process.

II. EXPERIMENTAL PROCEDURE

Electroplated Sn coatings were deposited on commer-cially pure annealed Cu sheet substrates. The substratethicknesses were either ~50 or 75 lm and the Sn coatingthicknesses were in the 1 to 2 lm range. Prior to plating,the substrates were mechanically polished, followed by achemical polish with a 50/50 vol. pct HNO3/H2SO4

mixture. The Sn was plated from a 0.375 M sodiumstannate alkaline bath at pH ~13 to 14 with 0.25 MNaOH, 0.15 M NaCOOCH3, and with or without0.0037 M Sorbital additive. A rotating disk electrodesetup was used at 1000 rpm and 70 �C. Plating wasperformed under various conditions, but those thatfavored Sn whisker growth were: �2 to �20 mA inchrono-potentiometrymode (CP) or�1500 to�2400 mVin chrono-amperometry mode (CA). A Pt foil auxiliaryelectrode and a Hg/HgO reference electrode were usedand nitrogen was bubbled through the plating cell toavoid oxidation of the plating bath.

The Sn-coated copper samples were stored underambient conditions and periodically examined for whis-kers by both light optical microscopy (LOM) and SEM.Time-lapse SEM imaging was performed on a Magellan400 XHR SEM at 5 kV accelerating voltage. Whiskergrowth was monitored with this technique for up to13 days. Other SEM imaging, length measurement, andwhisker angle determinations were performed on a ZeissSupra 55VP SEM. EBSD was also carried out in a ZeissSupra55VP field emission SEM. The SEM was equippedwith an Oxford/HKL Nordlys II EBSD detector and thepatterns were analyzed with Oxford/HKL Channel5 software. Tin whisker lengths and growth angles werealso characterized by laser confocal scanning micro-scopy (LCSM) on a Zeiss LSM 700 that allowed directcomparison with the SEM observations on the samewhiskers. LCSM is an optical microscopy technique thatprovides the ability to accurately obtain z-heights andother topographic information. The LCSM constructsan image from a stack of image slices (can be hundreds)using only the features in focus at each particular imageplane.

III. RESULTS AND DISCUSSION

A. Morphology and Growth Kinetics of Straightand Kinked Whiskers

Figure 1 displays time-lapse SEM photomicro-graphs of a tin whisker taken with a 45 deg sample tilt.

Fig. 1—Time-lapse in situ SEM photomicrographs of a straight tin whisker. Circles indicate a nucleated nearby growth with a change in orienta-tion. Arrows indicate electron beam damage on the whisker surface. Bottom-right photo shows close-up of other popped grains/nucleatedwhiskers.

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The whisker tip morphology remains unchangedthroughout the growth process with a so-called ‘‘capgrain,’’ indicating that growth occurs at the base of thewhisker. The diameter of the whisker is approximately1 lm, the approximate grain size of the Sn film. Thewhisker displays grooves along its length that are alsotypical of Sn whiskers seen in the literature.[10] Lebretand Norton surmised that the grooves are formed whena whisker nucleates from multiple grains.[10] Whiskersthat nucleate from a single grain do not show grooves.Examples of grooved and smooth whiskers are bothcontained in the present work, Figures 1 through 6. Asshown later, the extrapolated incubation period (afterSn plating) for whiskers was approximately 5 days.Similar incubation periods have been reported byothers.[11] If whiskers are held under the electron beamfor long periods or if the same location is repeatedlyimaged, slight beam damage can develop. This is shownby the arrows in Figure 1 as small voids along the lengthof the whisker. It is important not to interpret this arti-fact as a real morphological feature of the Sn whisker.The SEM photomicrographs in Figure 1 are typical fora ‘‘straight’’ whisker.

Also shown in Figure 1 is the occurrence of ‘‘poppedgrains.’’ These are apparent Sn whiskers that nucleated,but did not grow to an appreciable length. The circles inFigure 1 highlight a nucleated whisker that changesdirection as it breaks through the surface and severalother popped grains are visible in the bottom-rightregion of Figure 1. While they are not a concern forelectrical shorting, it may be important to includepopped grains when studying the mechanisms of whis-ker nucleation and growth. It appears that the nucleationof Sn whiskers is common in these samples. Forexample, by inspection of low magnification photomi-crographs, 57 popped grains were counted in one fieldof view that contained approximately 8000 grains(assuming a 1 micron grain size). Only one long whiskerwas contained within this field of view. These statisticssuggest that popped grains are present with an order ofmagnitude of ~1 in 100 grains, and long whiskers occurapproximately only once in every 10,000 grains. How-ever, the whisker density can vary widely depending onthe exact plating conditions used, thickness of the Snlayer, etc. Figure 2 shows an example of a dense forestof whiskers. Therefore, while the ratio of long whiskersvs. nucleated/popped grains can be determined, it isdifficult to make general statements about the overallwhisker density without a controlled study aimed at thisparticular parameter.

Other researchers have observed kinked or bentwhiskers[7–9] and several were characterized in thecurrent study. Figure 3 displays time-lapse SEM photosof a whisker that changes growth direction. When thisparticular whisker formed a kink (at/near its base), themorphology and orientation of the original growthsegment remained unchanged. This was labeled a TypeA kink, following the convention of Furuta, Reference8. Note that in this study, kinks are defined as sharplybent whiskers as opposed to curved whiskers like thoseshown by arrows in Figure 2. In general, whiskers withType A kinks continued to grow at a comparable rate

after kinking. In addition, Type A kinks do not showmorphological changes at their base and the apparentdiameter of the whisker remains unchanged duringgrowth. The whisker in Figure 3 also shows a slightchange in direction near its tip, indicating that thiswhisker also kinked very early in its growth process.In contrast, Figure 4 illustrates a Type B kinked

whisker. Type B kinks/bends are not as sharp as Type Akinks and they usually show other changes in morphol-ogy. In Type B kinks the spatial orientation of theoriginal growth segment changes (Figures 4, 6 to7 days). Type B kinks also display a change in diameterassociated with the kink process (bottom right, Fig-ure 4). This diameter change is caused by grain bound-ary movement near the base of the whisker. The changein diameter is gradual and, in Figure 4, striations areobserved around the whisker circumference at thislocation. Importantly, without time-lapse observations,the whisker in Figure 4 would probably not have beenidentified as a whisker that changed direction duringgrowth. The most significant aspect of Type B kinks,however, is that they are linked to a significant decreasein growth rate or complete stoppage of whisker growth(Figure 5 below). Thus, the grain boundary motion atthe base of the whisker also eliminates the localcrystallographic and/or diffusional conditions that werefavorable for Sn whisker growth. This growth stoppagemay account for the frequent observations of whiskerswith kinks near their base.[10] Jiang and Xian have alsoobserved periods of growth stagnation and, in theirstudy, a restart of whisker growth later on.[12] In theextreme, grain boundary motion at the base of a whiskercan bring about a transition from whiskers to hillockformation.[4,13,14] For limited grain boundary motion—perhaps the incorporation of a single extra grain into thewhisker—the consequences are a change in orientationof the whisker and cessation of growth.The results of whisker growth measurements of 23

straight and kinked whiskers are shown in Figure 5. Thetimes at which the kinks were observed are noted by ovalsin Figure 5(b). For straight whiskers, an average growthrate of about 2.7 microns per day (~3.1 9 10�5 lm/s)

Fig. 2—A dense forest of whiskers on a Sn-plated sample. Arrowsindicate curved whiskers.

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was determined, with the rate tapering off slightly overtime. The highest growth rate was about 4 microns perday (~4.6 9 10�5 lm/s). The highest observed rate is

likely more accurate due to the SEM projection effect, inwhich the apparent whisker length will always be lessthan or equal to its actual length. That is, the angle of the

Fig. 3—SEM time-lapse photos of a whisker with a Type A kink. The apparent orientation of the original segment remains unchanged after thekink. Circles indicate popped grains that nucleated during this sequence.

Fig. 4—Time-lapse SEM photos of a whisker that kinks and then stopped growing. The arrow indicates the nucleation point of a whisker thatbegan to grow between 10 and 11 days. Bottom right: close-up view of the base of the whisker.

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whisker with respect to the substrate surface is unknownin photomicrographs like those in Figures 1 through 4,which causes errors in length measurements. Even withthese errors, it is believed that the growth rate measure-ments are reasonable order-of-magnitude estimates, withthe projection effect contributing to the scatter towardlower growth rates. The SEM imaging effects and anestimation of measurement errors will be discussed indetail later.

Figure 5(b) shows the results for kinked whiskers.The times at which kinks were first observed are noted inthe plot and the kink process almost always results in asignificant reduction in growth rate or complete termi-nation of growth. When whisker growth stops, the SEMphotos appear completely unchanged. Again, the SEMprojection effect could produce changes in measuredgrowth rates, but based on the predominance of thisobservation, it is clear that the kink process does resultin growth stoppage for most whiskers. If the underly-ing process and crystallography for kinks could be

determined, it may be useful for understanding theconditions that govern whisker growth. Note, however,that the kink process is not necessary for whiskers tostop growing—some whiskers stopped growing withoutany apparent change in growth direction.The kink processes can be complex. Whiskers can

display multiple kinks of multiple types. Figure 6exhibits a whisker with two kinks—a Type A kinkfollowed by a Type B kink. Such behavior presents achallenge for explaining the whisker growth process andeven for simply measuring whisker lengths. One scenariofor the Type A kink process is shown schematically inFigure 7. In this two-dimensional view, it is assumedthat the grain boundaries at the whisker base form achevron ‘‘V’’ shape. This morphology has been observedwith focused ion beam (FIB) cuts by other research-ers.[15] It is further assumed that Sn is added to thewhisker base at one grain boundary and the other grainboundary is able to slide. The simplest case is if growthis parallel to boundary II and normal to boundary I. Asteady state in the rates of Sn addition and sliding ateach boundary must be achieved for straight whiskergrowth. This is a simplification because for three-dimensional whiskers, the whiskers are surrounded byseveral other grains and Sn atoms may be added to thewhisker at more than one grain boundary. As shown inFigure 7, during a Type A kink, the situation flips sothat the previous sliding boundary now becomes thelocation of Sn addition. The result is a kink and changein growth direction (Figure 7). In this simple 2-D modelwith two neighboring grains, the angle of the kink willdepend on the angle between these two grain boundariesat the base of the whisker. Growth does not have to benormal to the grain boundary as the whiskers tend toselect specific low index growth directions.[3,7,15] Theorientation, here in 2-D, of the original whisker segmentis maintained.Whiskers are single crystals as shown by EBSD

measurements (Figure 8). The single crystal is preservedon either side of a kink—the EBSD patterns do notchange as the electron beam is moved from one side of akink to the other. If the crystallographic growthdirections can be determined, then the possible kinkangles will be limited to the angles between crystallinedirections in Sn.[7] For example, a whisker growing in ah100i direction can continue to grow as a single crystalin a h010i direction with a 90 deg kink such as the oneshown in Figure 8. A 90 deg kink is possible forwhiskers growing at acute angles from the surface(Figure 7), but not for a whisker growing perpendicularfrom the substrate. The situation for a Type B kink ismore complex and involves the movement of one ormore grain boundaries at the base of the whisker. As thewhisker grain grows into an adjacent grain, there is asimultaneous change in growth direction. This can beachieved by a rotation of the crystal in order to maintainthe previous crystallographic growth direction or by achange in the crystallographic growth direction itself. Ineither case, the original whisker segment will be rotated.Such a rotation was predicted by Frolov et al.[16] usingmolecular dynamics simulation of hillock growth.As discussed in that reference, the sideways growth of

Fig. 5—(a) Whisker growth kinetics for straight whiskers. (b) Whis-ker growth kinetics for kinked whiskers. The times when kinks wereobserved are indicated by ovals.

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a hillock due to grain boundary movement at its base,coupled with different Sn accretion rates at the base andstill some pinning of grain boundaries, ‘‘might lead towhiskers that appear to change direction.’’[16] Thisrotation mechanism is different from the Type A truekink process described previously. Clearly, more work isneeded to understand complex Type B kinks.

B. SEM Projection Effect and Error Estimates

As mentioned previously, the fastest growth rates inFigure 5a are probably the most accurate, with the SEMprojection effect contributing to scatter toward lowergrowth rates. To estimate the measurement errors inFigure 5, it is necessary to determine actual whiskerlengths using two different views of the whisker achievedthrough the use of varying SEM stage tilt angles.Through geometry (parallax effect), the actual whiskergrowth angle and the correct length can be deter-mined.[17–19] The following describes one approach toobtaining accurate whisker lengths and growth angles.First, the sample is rotated so the whisker is aligned withthe tilt axis of the SEM. The projected length of thewhisker, x, is measured, Figure 9. Next, the distancefrom the whisker tip to a reference point on the samplesurface is measured (apparent z1). The sample is thentilted to a known angle. The whisker will appear tochange orientation (unless it is lying perfectly flat on thesurface). The distance from the whisker tip to the samereference point is measured again (apparent z2). The

following equations are used to determine the actualz-height of the whisker tip above the surface.[20]

Parallax ¼ P ¼ z1 � z2

Actual z� height � P= 2sin a=2ð Þð Þ;

where a is the SEM tilt angle. Now, the parameters xand z in a right triangle are known and the actualwhisker length and the growth angle with respect to thesurface are simply calculated from geometry. Thisprocedure was performed for 155 whiskers from fivedifferent samples and the results are shown in Figure 10.The majority of whiskers are observed to grow atshallow angles with respect to the surface (large angleswith respect to surface normal), most commonly 45 to60 deg with respect to normal or 30 to 45 deg withrespect to the surface. For whiskers measured with asingle SEM tilt, the growth angles of the whiskersrelative to the viewing direction will determine the errorin length measurements. Figure 11(a) shows a compar-ison of the apparent and calculated whisker lengthsdetermined for a subset of whiskers from three samples.In this study, the worst absolute errors were 45 to 50 lmfor long whiskers oriented at high angles from thesurface. The largest relative error was about 80 pct,which happened to be from a whisker with actual lengthof 10.7 lm and an apparent length of only 1.7 lm, againdue to its high growth angle. The apparent lengths arealways shorter than the actual (calculated) lengths, asexpected. The simple functional relationship of length

Fig. 6—Complex whisker growth showing a Type A kink followed by a Type B kink/bend. Circles indicate nucleated whiskers that appear, butdo not grow appreciably during this sequence.

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measurement error vs. whisker growth angle is shown inFigure 11(b) with the data points from the threesamples. Due to their shallow growth angles, mosterrors were in the 0 to 40 pct range. In the extreme,

whiskers growing nearly normal to the surface andviewed with zero tilt will appear to have almost noapparent length and the measurement error increasesdramatically. The results in Figure 11 can be used to

Fig. 7—Schematic diagram of Type A kink process.

Fig. 8—A kinked Sn whisker. The EBSD patterns remain unchanged showing that the whisker is single crystal (same crystallographic orientationthroughout). Only the crystallographic growth direction changes.

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estimate typical errors to be expected if whisker lengthsare measured at a single tilt. Note that the resultspresented above in Figure 5 were obtained with a 45 degSEM tilt, so the error estimates will be shifted withrespect to Figure 11.For comparison to Figure 5, the lengths of eight

whiskers from the time-lapse study were plotted togetherwith the data from Figure 11(a) and the results areshown in Figure 12. The eight whiskers represent themajor portion of the scatter in lengths and, thus, thescatter in growth rates in Figure 5. The scatter ofwhisker lengths from Figure 5 lies within the datadistribution obtained from measurements of apparentand actual lengths of other whiskers using the two-tilttechnique. The results in Figure 12 indicate that it is atleast possible that the scatter in Figure 5 comes primarilyfrom the projection effect when whisker lengths withunknown growth angles are measured. More work isrequired, with in situ time-lapse measurement of whis-kers with multiple tilt views of each whisker, to obtain a

Fig. 9—SEM photos showing the procedure for measuring whiskerlength and growth angle. The whisker is oriented along the tilt axis(x-axis for our SEM). Top: 0 deg tilt, Bottom: 10 deg tilt. Actualz-height is 50 lm, whisker length is 53.6 lm, and growth angle is 69deg wrt surface.

Fig. 10—Summary histogram of whisker growth angles for 155 whis-kers from 5 samples. The data were obtained from straight (non-kinked) whiskers only.

Fig. 11—(a) Comparison of apparent (projected) whisker lengthsand whisker lengths obtained with the SEM tilt technique describedin the text. (b) Error in whisker length measurements as a functionof the growth angle (for 0 deg SEM tilt).

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more accurate determination of the range of growthrates.

The error estimation discussed above only accountsfor errors due to the unknown angle of the whisker withrespect to the surface, i.e., the elevation angle. Therotational orientation (azimuth) is accounted for byrotating the whisker to align with the tilt axis of the SEM(Figures 9 through 11). An additional error is present inFigure 5, and other studies in the literature, due to therotational orientation of the whisker relative to theviewing direction. In our in situ growth study, whiskerswere rotated to a favorable angle for viewing, so thiserror should be minimal. Few studies of whisker growthactually correct for SEM perspective and published tinwhisker standards do not specify measurements at morethan one tilt. The standard JESD22-A121A recommendsthat whiskers be ‘‘positioned perpendicular to theviewing direction for measurement.’’[21] This methodrequires the whisker axis to be perpendicular to the tiltaxis of the stage and assumes that the stage has sufficienttilt range. This will minimize errors, but requires that thesample be tilted until the maximum apparent whiskerlength is obtained. The tilt angle required will be differentfor each straight whisker and each segment of a kinkedwhisker.

All of the whisker lengths and growth angles in thepresent study were obtained from straight whiskers. Itshould be recognized that a major concern with whiskersis the distance required for electrical shorting betweentwo conductors. Therefore, the distance from thewhisker tip to the sample surface is of interest, notnecessarily the combined length of kinked segments. Forwhisker growth mechanism studies, however, the fulllength is important. To minimize error, it is recom-mended that two SEM tilts be used to measure whiskerlengths.[17–19] With the method described above, thiswould require a sample rotation, whisker measurement,sample tilt, and another measurement for each datapoint (for example, in a plot such as Figure 5).To accurately measure the combined lengths of thesegments of a kinked whisker, the tilt-and-measure

technique must be repeated for each whisker segment.As such, the accurate measurement of the lengths ofkinked whiskers, as well as the kink angles, requiresextensive SEM analysis time.As a further check on the SEM analysis techniques

described above, whiskers were measured using laserconfocal scanning microscopy (LCSM). Figure 13shows an LCSM photomicrograph and a topographicrepresentation of a Sn whisker. The LCSM softwarerequires alignment of markers exactly along the whiskerlength to produce the topographic information inFigure 13(b). If the marker alignment is not exact, somedata dropout can occur, but relatively accurate deter-minations of growth angles and lengths are still pro-duced. LCSM was performed on six selected whiskersthat were also characterized by SEM. Figure 14 displaysa comparison of the two techniques. The length datawere comparable for both cases, which provides supportfor the accuracy of the SEM tilt-and-measure processdescribed previously. Both projected lengths (distance xin Figures 9(a) and 13(b)) and actual whisker lengths arecompared in Figure 14(a). For angle measurements,

Fig. 12—Scatter from eight straight whiskers from Fig. 5 superim-posed on Fig. 11 above. The scatter from the eight whiskers is with-in the scatter obtained from other whiskers with known apparentand actual lengths.

Fig. 13—(a) LCSM photomicrograph of a Sn whisker. The whisker’s‘‘shadow’’ is visible in the image. (b) Topographic informationobtained from the Sn whisker using LCSM.

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larger differences were found between the two tech-niques (Figure 14(b)). This is possibly due to difficultiesin determining the exact whisker origin, i.e., intersectionof the whisker with the substrate, using LCSM. Thebenefit of LCSM is faster analysis speed compared toSEM, especially if kinked whisker lengths and kinkangles are to be measured. A disadvantage of LCSM isthat crystallographic information cannot be directlyobtained, unlike that which can be determined by SEMwith electron backscatter diffraction (Figure 8). Inaddition, only longer whiskers can be characterizeddue to resolution limitations with LCSM. More work isneeded to further develop LSCM for both straight andkinked whiskers.

C. No Apparent Relationship Between Growth Angle andWhisker Length

Based on the analysis of whisker lengths and growthangles at multiple SEM tilts, a summary of approxi-mately 150 straight whiskers was compiled. The whis-kers were from multiple samples, observed at varioustimes after Sn deposition, but all within about 2 years ofplating. Figure 15(a) shows there is no correlationbetween whisker lengths and growth angles. Like

Figure 10 above, the plot also shows very few whiskersgrowing at high angles from the surface. The broaddistribution of whisker lengths is probably not due to abroad range of growth rates, but rather from thefollowing factors: (a) whiskers nucleate with differentincubation times (Figure 4), (b) whiskers stop growingat various times (Figure 5), and/or (c) whiskers stopgrowing and then restart growth later.[12] A carefulin situ time-lapse study of numerous whiskers over along time period, with corrections for SEM projectioneffects, would be required to determine the distributionof growth rates on individual samples.A similarly broad distribution of whisker lengths was

found by Panaschenko for 2-year-old samples.[18,19] Pan-aschenko also corrected the length measurements for theSEM projection effect. In the present study, the whis-ker length distribution was found to be approximately

Fig. 14—(a) Comparison of LCSM measured whisker lengths andthose determined by SEM tilt-and-measure technique for the samewhiskers. (b) Whisker growth angles for the same whiskers obtainedby LCSM and SEM.

Fig. 15—(a) Plot showing no correlation between whisker lengthsand their growth angles. (b) Probability plot of whisker length distri-butions obtained from samples approx. 2 years old. The length dis-tributions are similar for the present study and results fromPanaschenko.[19].

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log-normal and the results are plotted in Figure 15(b).Although the tails of the distributions differ, the relativeagreement between the results of the present study andthose of Panaschenko forms a quantitative basis forprobabilistic failure models of shorting between adjacentconductors.[22] However, more work is needed to deter-mine howwhisker length distributions evolve as a functionof time. Whisker shorting models should also account forkinked whiskers. If kinked whiskers are included, theeffective lengths and angles measured directly from thewhisker tip to the substratewill be different andwill includemore ‘‘growth angles’’ close to perpendicular from thesurface. In one respect, however, the lack of correlationbetween whisker lengths and growth angles (Figure 15(a))actually decreases the complexity involved in modelingshorting failures.

With regard to whisker growth mechanisms, it is notobvious how the results of the present work will relate toexisting theories. While compressive stresses or stressgradients are considered to be the driving force forwhisker growth, whether or not a particular grain willform a whisker needs to be addressed at the local scale.Several factors could be responsible for the localizationof whiskers to certain grains:

� Very localized stress (strain) gradients as proposedby Choi et al.[23]

� Heterogeneous nucleation at stochastic sites couldbe responsible for the initiation of whiskers (poppedgrains). The sustained growth of long whiskers couldthen occur at certain grains with favorable micro-structural conditions—stable grain boundary config-uration at the base—and the correct conditions ofstrain and strain rate as proposed by Vianco andRejent (dynamic recrystallization).[24,25]

� Whiskers could grow from certain grains with loweryield strength, i.e., low resistance to plastic deforma-tion, due to the anisotropic nature of Sn.[26]

� Whiskers could be the result of a favorable grainorientation for fast diffusion, in this case due to theanisotropy of diffusion in Sn,[27] or a local surround-ing network of grain boundaries that provide ananomalously fast diffusion path.

� Alternatively, whisker sites could be the result of theopposite effect of diffusion anisotropy, namely ‘‘bot-tlenecks’’ of material that build up at specific sitesbecause a local diffusion path is anomalously slow.

In any of these localized scenarios, it appears thatcrystallography could play an important role as well,especially for sustained growth of long whiskers. Whiskernucleation may be a stochastic event, such as the poppedgrains observed in this study, but favorable microstruc-tural and crystallographic conditions must be present forthe whiskers to continue to grow.

IV. CONCLUSIONS

In this work, a time-lapse in situ SEM study of Snwhisker growth was conducted and techniques were

developed to correct for SEM projection effects in orderto accurately measure whisker lengths and angles. Thefollowing points were compiled from this work:For straight whiskers, growth rates of 3 to 4 microns

per day were determined at room temperature. Since thegrowth angles were unknown, the SEM projection effectcontributes to the scatter in the measured growth rates.In this study, the whiskers displayed an incubation timeof about 5 days. For kinked whiskers, the kink processoften coincides with a significant slowdown or completestoppage in whisker growth.Two types of whisker kinks were observed. In Type A

kinks, the original segment spatial orientation remainsunchanged, there are no other changes in morphologyor diameter, and growth continues. In Type B kinks, theoriginal segment changes spatial orientation and itappears that the whisker bends over. Type B kinksdisplay changes in morphology and diameter at thebase, indicating grain boundary motion in the film.These changes at the whisker base eliminate the condi-tions suitable for long-term whisker growth.A technique was described using two SEM tilts to

correct for SEM image projection. Such techniques mustbe used to obtain accurate measurements of whiskerlengths and growth angles for studies of the growthmechanism. Based on this method, it was determinedthat most whiskers grow at moderate or shallow angleswith respect to the surface. Few straight whiskers grownearly normal to the surface. For general inspectionpurposes, the results of this study can be used toestimate typical errors if whisker lengths are onlymeasured with a single SEM tilt.There is no simple correlation between growth angles

and lengths for whiskers observed over an approximate2-year period. In addition, the distribution of lengths isbroad. The broad distribution may be due to differencesin the incubation periods and growth periods ofindividual whiskers in addition to the actual spread inindividual growth rates.

ACKNOWLEDGMENTS

Special thanks to Alice Kilgo and Lisa Deibler forlaser confocal microscopy analysis. Jamin Pillars isacknowledged for Sn plating and Mark Reece for sub-strate preparation. Thanks also to Dr. C. V. Robinofor an insightful review of the manuscript.

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