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Acta Materialia 58 (2010) 6628–6636

Micropillar compression of Al/SiC nanolaminates

D.R.P. Singh a, N. Chawla a,⇑, G. Tang b, Y.-L. Shen b

a Materials Science and Engineering, Arizona State University, Tempe, AZ 85287-6106, USAb Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM, USA

Received 1 April 2010; received in revised form 12 August 2010; accepted 14 August 2010Available online 9 September 2010

Abstract

Al/SiC nanolaminates possess an excellent combination of mechanical strength and flexibility. While nanoindentation provides a rea-sonable estimate of the mechanical properties such as Young’s modulus and hardness of these materials, the stress state under nanoin-dentation is extremely complex. Micropillar compression has become an attractive method of studying the mechanical properties ofmaterials at small length scales in a nominally homogeneous stress state. In this work, micropillars of Al/SiC nanolaminate were fabri-cated using focused ion beam milling. Compression testing was carried out using a flat-end nanoindenter head. The actual displacementof the pillar during micropillar compression was deconvoluted by subtracting the “extraneous” displacements of the system. Fracto-graphic analysis showed that Al squeezes out between the SiC layers and that a mutual constraint is observed between the hard and softlayers. Numerical finite element modeling was also employed to provide physical insight into the deformation features of the multilayeredpillar structure and agreed well with the experimental observations.� 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Nanoindentation; Micropillar compression; Nanolaminate; Focused ion beam

1. Introduction

Multilayered materials at the nanoscale exhibit uniqueelectrical [1–3], magnetic [4], optical [5,6] and mechanicalproperties [7–9]. Metal–ceramic systems, in particular,can be tailored to obtain a combination of high strength,hardness and toughness [8–14]. Nanoindentation has beenused extensively to probe the modulus and hardness ofhomogeneous bulk materials and thin films. In multilay-ered materials, however, it has been shown that a highlycomplex and inhomogeneous stress state is developedunder the indenter [11,15]. Furthermore, the multilayeredstructure results in complex plasticity, which can take placeeven during unloading [15,16].

A more straightforward way of obtaining nominallyuniaxial stress–strain response at small volumes is bymicrocompression of pillars [17]. Pillars in the micrometerrange, or smaller, can be fabricated by the focused ion

1359-6454/$36.00 � 2010 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2010.08.025

⇑ Corresponding author.E-mail address: nchawla@asu.edu (N. Chawla).

beam (FIB) technique [17–21]. These pillars are then com-pressed using a flat punch in a nanoindenter, or by scan-ning electron microscopy (SEM). This method hasrecently been used to study the mechanical response ofmetallic single crystals [22,23], metallic alloys [24] andmetallic nanolaminates [25].

This paper reports on the microcompression behavior ofmodel Al/SiC nanolaminates. The pillars were fabricatedby FIB and tested in compression using a nanoindenter.The effect of pillar taper was studied. The evolution ofdamage was quantified by interrupted experiments andcross-sectioning of deformed pillars, also with the FIB.The finite element method (FEM) was used to model thedeformation behavior of the pillars numerically and to pro-vide a mechanistic understanding of deformation.

2. Materials and experimental procedure

Al/SiC multilayer samples were synthesized by physicalvapor deposition, using magnetron sputtering. Details ofthe sputtering method are discussed elsewhere [11–13].

rights reserved.

500 nm

Fig. 1. Microstructure of Al/SiC multilayer used in the study. A total of40 alternating layers of Al and SiC were grown on a Si(1 1 1) substrate.The layer thicknesses are homogeneous and show little variability.

D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636 6629

The samples were grown on a Si(1 1 1) substrate and theindividual layer thickness of Al and SiC were targeted tobe �50 nm. A total of 40 (20 layers of Al and SiC each) lay-ers were deposited. The cross-section of the as-depositedmicrostructure, as well as that of the damaged pillars wasstudied using FIB. Ten measurements of layer thicknesswere taken for each layer in the sample to obtain statisticsof the layer thickness.

The micropillars were fabricated using FIB. Two typesof samples were fabricated: (a) pillars using an annularmilling approach which resulted in a slight taper (�4�);and (b) pillars using a “lathe milling” procedure similarto that described by Uchic and Dimiduk [17], whichresulted in pillars with negligible taper (<1�). The latter pil-lars are termed “taper-free”. The tapered pillars weremilled in two steps. A relatively large current (7 nA) wasused to mill a pillar with a relatively large diameter(4 lm). This was followed by a second milling operationat a much lower current of 50 pA, which resulted in a finalpillar diameter of �2 lm. Straight pillars (with minimaltaper) were fabricated by initially milling a pillar of�3 lm, using the annular milling approach describedabove. Next, the sample surface was tilted so as to makea small angle with the initial sample surface (�28�). In thismanner, the ion beam impinged the sample tangent to thesurface. The sample was rotated in 5� intervals, and themilling operation was repeated. The milling current in thisstep was �50 pA. A thin layer of Pt was deposited in bothprocesses to protect the sample surface from ion beamdamage. To align the pillars during its rotation for latheoperation, a small central hole was drilled in the top Ptlayer. The hole served as a marker for centering the pillarafter each incremental rotation. Ion beam damage fromGa+ ion implantation can take place, although the depthof damage has been estimated to be no more than 60 nmat 30 kV beam under normal incidence [26,27]. For the pil-lars studied here, this is a very small fraction of the totalpillar diameter (�2 lm).

One of the major issues affecting microcompression datais the misalignment of the sample relative to the punch. Ithas been shown that even small degrees of misalignmentcan have a significant effect on the measured stiffness ofthe pillar [28]. In the present experiments, a novel nanoin-dentation in situ method was used to measure the misalign-ment of the sample. A sharp-tip nanoindenter was used asa high resolution displacement gauge to determine the sur-face profile of the sample. The indenter tip is brought incontact with the surface at various locations on the sample.The surface is “found” by the indenter, as measured by anextremely small contact stiffness (140 mN). This z displace-ment, measured across the surface, can be used to computeand, if necessary, correct the sample inclination. Using thisapproach, the sample inclination in the present experimentswas measured to be <0.3�.

Compression experiments were carried out using ananoindenter (MTS XP, Agilent Systems, Chandler, AZ).A Berkovich (three-sided pyramid) diamond indenter with

a flat triangular cross-section with a 10 lm side was used.The largest diameter circular cross-section that would fitin this triangle had a radius of �6 lm (three times as largeas the pillar diameter). The experiments were carried out ina continuous stiffness measurement (CSM) mode [29],enabling continuous measurement of contact stiffnessinstantaneously as a function of depth. The pillars werecompressed to varying depths to study the progression ofdamage with increasing load. Fractographic analysis afterdeformation was carried out by dual-beam FIB, and imag-ing was conducted by SEM.

3. Results and discussion

3.1. Micropillar compression experiments

The cross-section of the microstructure of the as-pro-cessed nanolaminate obtained by FIB is shown in Fig. 1.A total of 40 alternating layers of Al and SiC were grownon a Si(1 1 1) substrate. The individual layer thickness forAl was 58 ± 2 nm, while that for SiC was 73 ± 1 nm. Thiscorresponds to a volume fraction of SiC of �56%. A smalldegree of roughness is associated with the individual layersand is due to the columnar grain structure of the Al layers.Fig. 2 shows the two types of pillars that were fabricated(with taper and without taper). The average taper in thetapered pillar was �4�.

The total compliance measured during micropillar com-pression is a function of several factors, as shown in Fig. 3.These include a short Si post under the nanolaminate, theSi base and a small contribution from the diamond inden-ter. Thus, the total compliance of the system is the sum ofseveral compliances and can be written as follows:

Cmeasured ¼ Cp þ CSi-post þ CSi-base þ CDi þ CPt

where Cp is the compliance of the deformed pillar, CPt isthe deformation of the thin layer of Pt, CSi-post is the com-pliance due to deformation of the Si post, CSi-base is thecompliance due to the “punching effect” on the Si base(i.e. the Sneddon’s correction [30] described below), and

Tapered Pillar Taper-free Pillar

Fig. 2. FIB milled tapered pillars using annular milling pattern and taper-free pillars fabricated using the FIB lathe operation.

0

50

100

150

200

0 2 4 6 8 10 12

Dis

plac

emen

t (nm

)

Load (mN)

0

5

10

15

20

0 1 2 3 4 5D

efor

mat

ion

(nm

)Load (mN)

Plastic Deformation

in Pillar

Elastic Deformation in Multilayer

Elastic Deformation in Pt, Si Post &

Diamond Indenter

(a) (b)Fig. 3. (a) Schematic of the taper-free pillar system used to study the mechanical properties of the Al/SiC multilayer. The various elastic compliancesinvolved in the system are represented. (b) Deformations in various components of the pillar system that need to be accounted for measuring the truemodulus of the multilayer.

6630 D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636

CDi is the compliance due to minimal deformation of thediamond indenter.

By subtracting all the “extraneous” compliances, onecan obtain the compliance of the pillar. The elastic compli-ance (C) of cylindrical discs of Pt and the Si post can beestimated by:

C ¼ E � AL

� ��1

where E is the Young’s modulus of the material, A is thecross-sectional area of the pillar (measured at the top ofthe pillar), and L is the length of the pillar. The complianceof the tapered Si post, assuming a uniform taper, is calcu-lated by integrating the deformation over the length of thetapered Si, modifying the original expression by Lee et al.[31].

C ¼ P � h0

p � ESi � d0ðd0 þ h0 � sin hÞ

Here, P is the load on the sample, h is the taper angle ofthe post, h0 is the initial height of the pillar, ESi is the mod-ulus of Si, and d0 is the diameter of the top of the Si post.

Perhaps the most significant contribution in compliancecomes from the Sneddon’s effect [30]. Sneddon consideredthe case of elastic deformation associated with a rigid cylin-drical punch going into the substrate. The compliance asso-ciated with the Sneddon’s effect can be given as follows:

CSneddon ¼ffiffiffippð1� m2Þ

2Ebase

ffiffiffiffiffiAp

pwhere CSneddon is the Sneddon compliance associated withdeformation of the base material under the punch, Ebase isthe modulus of the base material (in this case, single crystalSi), Ap is the contact area of the pillar at the base, and m isthe Poisson’s ratio of base material. The Sneddon’s sink-inassumes the pillar to be rigid, which may result in a slightoverestimation of the compliance. Fig. 3 shows the relativecontributions of each of the above-mentioned factors to theoverall displacement of the pillar. Displacements in Pt, Si

D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636 6631

base and Sneddon’s displacements were computed fromtheir respective compliances. The deformation in the multi-layer pillar was then computed by subtracting the totalcompliance of the system (calculated from the experimen-tally measured CSM stiffness values, i.e. C = 1/S). TheCSM values were taken at depths between 100 nm and250 nm, since at smaller depths the indenter may not bein complete contact with the pillar, owing to slight mis-alignment and surface roughness. The elastic deformationof the multilayer (Fig. 3), then, was fairly linear, exceptfor the initial portion (<10 nm displacement), where theremay not have been perfect contact between the flat punchand the top of the pillar. The use of CSM to obtain the stiff-ness, and thus the compliance, is all the more important inmetal–ceramic multilayered materials, where microplastici-ty may take place at very low stresses. With the CSM, onlythe elastic response is measured. Using this analysis, theYoung’s modulus of the pillar was measured as122 ± 5 GPa, compared with 56 GPa when computed fromthe raw displacement. This compares very well with theanalytical rule of mixture calculation of the transverseYoung’s modulus of a laminate of Al and SiC calculatedas follows:

1

EML

¼ V Al

EAl

þ 1� V Al

ESiC

where EML is the Young’s modulus of the nanolaminate, VAl

is the volume fraction of Al, EAl is the Young’s modulus ofAl, and ESiC is the Young’s modulus of SiC. Using the mod-ulus of Al as 60 GPa and SiC as 280 GPa [11], the modulus ofthe nanolaminate is computed to be 107 GPa. The abovecalculation ignores Poisson’s expansion effects. A better esti-mate of the elastic modulus of the nanolaminate undermicrocompression is obtained using finite element simula-tion, which does not ignore Poisson’s expansion. For a nan-olaminate with equal thicknesses of Al and SiC with 41layers this value is 117 GPa. This is in excellent agreementwith the modulus values deduced from the micropillar com-pression study. The slight discrepancy may be attributed to aslight larger volume fraction of SiC in the experiment.

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

2 4 6 8 10 12

Stre

ss (G

Pa)

Strain (%)

(a) (b)

Fig. 4. Stress–strain plot comparison for taper and taper-free pillar. The stresspillar types.

After obtaining the true compliance of the pillar, the“corrected” load–displacement and stress–strain behaviorwere obtained. For the stress–strain plots, the stress wascalculated using the initial top cross-sectional area of thepillars, while the strain in the multilayer was computedfrom the difference between total displacement and “extra-neous” displacements, as discussed above. The stress–straincurves for tapered and straight pillars are shown in Fig. 4.The fracture stress of the pillars is �3 GPa. This stress rep-resents the point where catastrophic multiple SiC fractureoccurs and the pillar is unable to support any load. Thedeformation behavior of tapered pillars is compared withthat of taper-free pillars, as shown in Fig. 4. The taperedpillars tend to be somewhat more compliant than thestraight pillars. This can be attributed to more inhomoge-neous deformation and stress-concentration at the top ofthe pillar, and may lead to easier yielding. The deviationfrom linearity also occurs sooner for tapered pillars forthe same reason (yielding at lower stresses). The modulusmeasured from CSM is slightly higher for tapered pillarsand seems to increase with increasing depth. Higher mod-ulus in tapered pillars has also been observed in FEM sim-ulations of the effect of taper angle [28].

SEM fractography and FIB cross-sections were con-ducted to study the damage evolution in the multilayer pil-lars. Multiple pillars were compressed to various peakloads to study their deformation behavior at incrementaldepths (Fig. 5). The numbers indicate the order of the load-ing cycles. The deformed pillars were then cross-sectionedin the center to reveal the damage. Figs. 6 and 7 comparethe damage in straight and tapered pillars at variousstages/depths of deformation. It can be seen that, beforefracture, plastic barreling takes place in the straight pillars.This is expected, since the base of the pillar is fixed, andfriction is present in the top mating surface between the pil-lar and the indenter. The amount of barreling increaseswith the load applied. As seen from the load–displacementdata (Fig. 5), a significant amount of displacement occursduring the constant peak load segment. This is indicativeof viscoplastic deformation. It can be seen that this defor-

40

60

80

100

120

140

160

180

100 150 200 250

Youn

g’s

Mod

ulus

(GPa

)

Displacement (nm)

Straight

Tapered

–strain modulus derived from CSM stiffness is also compared for the two

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350

Load

(mN

)

Displacement (nm)

12

34

Fig. 5. Load–reload test for a pillar. The loading slope increases as thematerial is reloaded owing to decreased viscoplastic deformation duringreloading. The numbers indicate the order of the loading cycles.

6632 D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636

mation is associated with the viscoplastic deformation ofAl layers which squeeze out from between the SiC layers.As further load is applied, SiC layers start to fracture, whileAl continues to deform plastically. Finally, at the fracturepoint, multiple SiC layer fractures take place until the pillarcannot support the load, and catastrophic failure occurs.While most of the SiC layers fracture in the nanolaminatepillar, the bottom SiC layers are affected to a lesser extent,owing to constraint from the attached substrate. The plas-tic deformation of Al in the pillar appears to be homoge-neous throughout the length of the pillar. This is incontrast to the tapered pillar as shown in Fig 10. The taperin the pillar produces higher local stresses at the top where

(a) (b)

1 µm

1 µm

Fig. 6. Deformation during various stages of deformation in a straight pillarplastic and creep deformation in the Al layer is observed. Plastic barreling ofindenter side. Multiple catastrophic SiC layer fracture is observed above fract

the cross-sectional area is smaller. This creates localizeddeformation at the top of the pillar, and hence larger andmore inhomogeneous deformation. The squeezing out ofAl from between the SiC layers is also seen to be more pre-valent at the top of the tapered pillar. Also in the taperedpillars, fracture is restricted to fewer layers at the top ofthe pillar, rather than a homogeneous stress state through-out the pillar. A summary of the deformation mechanismsin the nanolaminates under compression is shown in Fig. 8.The Al flows plastically between the SiC layers. The flow ofthe Al is constrained by the SiC layers. The SiC layers can-not be compressed beyond a certain point, owing to the Allayers in-between. Thus, there exists a mutual constraintbetween the hard and soft layers in the nanolaminate,which results in the very high strength observed in thesematerials. This type of mutual constraint has also beenreported in conventional ceramic layered laminates [32].

3.2. Numerical modeling

To elucidate the experimentally observed deformationfeatures further, numerical modeling using the FEM wasperformed on the Al/SiC multilayered pillar structure.Fig. 9 shows a schematic of the axisymmetric model, inwhich the left vertical boundary is the symmetry axis.The multilayered pillar is attached to a large Si base (sub-strate). The radii of the pillar and base are 1 lm and500 lm, respectively, and the heights of the pillar and baseare 2 lm and 500 lm, respectively. The individual Al andSiC layers have an initial thickness of 50 nm. In additionto the case of a pillar with a straight side wall, tapered pil-

1 µm

1 µm

(c)

1 µm

1 µm

Extrusions

deformed to: (a) 120 nm; (b) 230 nm; (c) fracture. Al squeeze out due tothe pillar is observed due to one fixed end and frictional constraint on theure stress. Al extrusions are shown as bright layers in (b).

1 µm2 µm

1 µm

(a) (b)

(c)Fig. 7. Fracture in taper pillar: (a) pillar compressed to 200 nm; (b) pillar compressed to fracture; (c) cross-section of pillar compressed to fracture. Pillarfracture is pronounced at the top of the pillar owing to a small cross-sectional area. Al squeeze-out also seems to be higher in the top layers compared withtaper-free pillars.

Fig. 8. Deformation mechanism during multilayer pillar compression. Both Al and SiC are mutually constrained. Plastic deformation of Al layer results insqueezing out of Al on the free face of the pillar.

D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636 6633

lar models were also constructed for the simulations, asrepresented by the dashed line in Fig. 9. The flat-end dia-mond indenter is assumed to have perfect alignment withthe top surface of the pillar. A total of 111,176 linear ele-ments were used in the model, with a finer mesh size inside

and near the pillar. A representative local mesh configura-tion near the junction of the pillar and base, for the case of4� tapered pillar, is also included in Fig. 9. Note that themodel geometry does not exactly match the experimentalcondition (e.g. actual layer thicknesses, tapered Si post,

Diamond indenter

Si base

Al/SiC multilayer pillar

Symmetry axis

Fig. 9. Schematic showing the axisymmetric pillar model used in the finite element analysis. The dashed line at the pillar side wall represents the case withtaper. Local finite element discretization near the pillar/base junction for the case of 4� taper is shown.

0

0.5

1

1.5

2

2.5

3

0 0.03 0.06 0.09 0.12 0.15Strain

Stre

ss (G

Pa)

with taper

no taper

Fig. 10. Simulated stress–strain curves for the pillar structures withouttaper and with 4� taper.

6634 D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636

etc.). However, it is believed that they are sufficiently sim-ilar that useful insight can be gained from the finite elementmodeling.

During deformation, the left boundary was allowed tomove only in the vertical direction, and the bottom bound-ary of the Si base was allowed to move only in the horizontaldirection. The prescribed downward displacement wasapplied to the top surface of the indenter. The coefficientof friction between the top pillar surface and the indenterbottom surface was taken to be 0.1. The material propertiesused in the present model are identical to those in previouswork on indentation simulation [16], where details can befound. In short, the Al and SiC materials were both treatedas isotropic solids, with their elastic–plastic responseextracted from uniaxial tensile experiments or estimatedfrom the nanoindentation of single-layered films. TheYoung’s modulus E, Poisson’s ratio m, and initial yieldstrength ry used in the model are: EAl = 59 GPa, ESiC =277 GPa, mAl = 0.33, mSiC = 0.17 and ry,Al = 200 MPa. TheSi substrate and diamond indenters were assumed to be iso-tropic and elastic with the following properties: ESi =187 GPa, mSi = 0.28, Eindenter = 1141 GPa and mindenter =0.07. The finite element program ABAQUS (Version 6.8,Dassault Systemes Simulia Corp., Providence, RI) was usedto carry out the analysis.

Fig. 10 shows the modeled engineering stress–straincurves of the structures with a straight pillar (no taper)and with 4� taper. The stress is obtained by dividing thecompressive load by the initial cross-section area at thetop of the pillar. The strain is the applied displacement nor-malized by the initial pillar height. It can be seen that thetapered pillar resulted in a more compliant response. Thisis consistent with the experimentally measured response

shown in Fig. 5. The more compliant nature of the pillarwith taper is due primarily to the more localized deforma-tion near the narrower top portion, as evidenced by theexperimental results described above, as well as the model-ing results presented below.

Fig. 11a and b shows the deformed configurations andcontour plots of von Mises effective stress in the pillarand its vicinity, for the cases without and with taper,respectively, at the compression depth of 325 nm. It is clearthat the soft Al layers deformed much more easily than theSiC layers. In Fig. 11a, a significant portion of each Allayer was extruded out from the side. Note that the rela-tively free flow of Al out of the side surface implies lessdeformation constraint, which also resulted in generallysmaller effective stress near the side-wall regions. In thecase with taper (Fig. 11b), the extrusion process becomes

(a) (b)

Si base

Indenter

Si base

Indenter

Fig. 11. Deformed configurations and contour plots of von Mises effective stress in (a) non-tapered and (b) tapered Al/SiC multilayered pillar structures,when the applied displacement is at 325 nm.

(a) (b)

Si base

Indenter

Al

Si base

Indenter

Al

Fig. 12. Deformed configurations and contour plots of von Mises effective stress in (a) non-tapered and (b) tapered Al pillar structures, when the applieddisplacement is at 325 nm.

D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636 6635

highly non-uniform. Several Al layers near the top havebeen severely squeezed and extruded much further outcompared with the lower Al layers. The present resultrationalizes the experimental fractographic observationdiscussed above, where the squeezing out of Al betweenthe SiC layers was seen to be more localized near the pillartop in tapered pillars.

To explore further the localized deformation behaviorcaused by taper, simulations were carried out by replacingall SiC layers with Al. The entire pillar is thus homoge-neous Al material, with the Si base and all the other mod-eling parameters remaining unchanged. Fig. 12a and bshows the deformed configurations and contour plots ofvon Mises effective stress in the Al pillar and its vicinity,for the cases without and with taper, respectively, whenthe applied displacement is at 325 nm. With the soft andhomogeneous pillar under compression, it can be seen thatthe barreling effect becomes more evident. The barreling ismore apparent in the upper region in the case with taper(Fig. 12b). However, unlike the case of multilayers, thereis no severe localization of deformation near the top sur-

face of the pure metallic pillar. Therefore, the unevenextrusion of Al layers observed in Fig. 11b is caused bythe constrained deformation unique to the multilayeredconfiguration.

4. Summary

The deformation mechanisms in Al/SiC nanolaminatesduring micropillar compression were studied. The follow-ing conclusions can be made.

1. The actual displacement of the pillar during micropillarcompression can be deconvoluted by subtracting the“extraneous” displacements of the system. These includethe punching effect into the Si base (Sneddon’s effect), aswell as small elastic deformation of the diamond inden-ter and Si post.

2. Straight pillars had somewhat more stiff response thantapered pillars, although their strengths (as measuredby the cross-sectional area at the top of the pillar) wereequivalent.

6636 D.R.P. Singh et al. / Acta Materialia 58 (2010) 6628–6636

3. Fractographic analysis as well as FIB cross-sections ofthe compressed pillars showed that Al squeezes outbetween the SiC layers and that a mutual constraint isobserved between the hard and soft layers. Such a con-straint is responsible for the very high strengthsobserved in these materials.

4. Numerical finite element modeling was conducted torationalize some of the experimental results. The taperedpillar was shown to result in severe extrusion of Al lay-ers near the compressed pillar top, as observed in exper-iment. This feature is unique to the multilayer pillar andwas not seen in the homogeneous metallic pillar. Thehighly non-uniform deformation in tapered pillarsresults in a more compliant stress–strain response com-pared with straight pillars.

Acknowledgments

The authors are grateful for financial support for this re-search from the National Science Foundation (DMR-0504781, Drs. A. Ardell, H.D. Chopra and B.A. MacDon-ald, Program Managers). The authors acknowledge the useof processing and microscopy facilities at the LeRoy Eyr-ing Center for Solid State Science at Arizona StateUniversity.

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