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Tutorial review

Depth-sensing indentation of nanomaterialsand nanostructures

Manuel L.B. Palacio, Bharat Bhushan⁎

Nanoprobe Laboratory for Bio- & Nanotechnology and Biomimetics, The Ohio State University, Columbus, OH 43210, USA

A R T I C L E D A T A

⁎ Corresponding author.E-mail address: Bhushan.2@osu.edu (B. B

1044-5803/$ – see front matter © 2013 Elseviehttp://dx.doi.org/10.1016/j.matchar.2013.01.0

A B S T R A C T

Article history:Received 1 November 2012Received in revised form7 January 2013Accepted 18 January 2013

Keywords:Indentation

Due to its capacity for applying ultralow loads and detecting nanometer-scale deflections,nanoindentation has been used to investigate the mechanical behavior of various materialconfigurations at the micro- and nano-scales. The emphasis of the article is on thenanoscale deformation of nanoparticles, micro/nanopillars, microbeams, micro/nanofibers,nanocomposites, membranes and monolayer films, which are all ubiquitous structures innanotechnology. The small volumes of these structures have led to the elucidation ofmaterial deformation mechanisms that are not the same as their bulk counterparts.Advances in instrumentation have enabled nanoindentation experiments to be conductedin situ in conjunction with scanning electron microscopy (SEM), electron backscatterdiffraction (EBSD), transmission electron microscopy (TEM), electrical contact resistance(ECR) measurements, atomic force microscopy (AFM), among others, and examples of thesestudies will be discussed.

© 2013 Elsevier Inc. All rights reserved.

NanoindentationNanotechnologyNanoparticlesNanostructures

1. Introduction

Nanotechnology encompasses the production and applicationof physical, chemical and biological systems at length scalesthat range from individual atoms or molecules to submicrondimensions, as well as the integration of the resulting nano-structures into larger systems [5,6]. The numerous applicationsof nanotechnology require the understanding of the mechan-ical properties of the materials being selected. Among themechanical properties of interest that can be obtained usingcommercial and specialized indentation testers are elastic–plastic deformation behavior, hardness, Young's modulus ofelasticity, scratch resistance, film–substrate adhesion, residualstresses, time-dependent creep and relaxation properties,fracture toughness, and fatigue. Indentation experiments canassess structural heterogeneities on and underneath thesurface such as diffusion gradients, precipitates, buried layers,

hushan).

r Inc. All rights reserved.09

grain boundaries, and surface composition modification,amongmany others [8,17,37,46].

Starting fromconventional indentation (ormicroindentation)test techniques, the need to apply very small loads and deformvery small volumes has given rise to depth-sensing nano-indentation. There is a need to measure the depth accuratelybecause the impressions created by the loads are too small tovisualize by optical microscopy. Schematic diagrams of twocommon nanoindentation apparatus designs are shown inFig. 1, along with typical data from an experiment. Fig. 1a is astand-alone nanoindenter unit consisting of an indenter head(where the load is applied by a coil/magnet assembly), an opticalmicroscope for indent visualization, and an x–y–z motorizedtable for positioning and transporting the sample between theindenter assembly and optical microscope [8,44,45]. Fig. 1b isanother indentation platform that uses the controller system ofan atomic force microscope (AFM), where the indenter trans-

Fig. 1 – Schematic diagrams of (a) a stand-alone nanoindentation system, (b) a nanoindentation system connected to ascanning probe microscope (SPM) controller, and (c) an example of the load–displacement curve obtained from thenanoindentation experiment [8,9].

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ducer replaces the AFM head. The load is applied to the sampleelectrostatically and a capacitive displacement sensor on thetransducer detects the displacement of the indenter tip into thesample [9,10].

Fig. 1c is a schematic of a basic load–displacement curve thatcan be obtained from an experiment. It consists of two portions,the loading and unloading curves. The exact profile of theloading andunloading curves depends on the loading conditionsand the mechanical properties of the material being investigat-ed, and deviations from the profile shown in this diagram are

common. In Fig. 1c, S is the material stiffness, hf is the finaldepth, hp is the plastic depth, hc is the contact depth and hmax isthe maximum depth of penetration. These parameters are usedto evaluate constitutive properties such as the elastic modulus(E) and hardness (H) [45,46]. In the study of bulk materials andthin films, the data from the load–displacement curve has beenused to determine the size (or length-scale) dependence of theirmechanical properties. But other experiments are accessibledepending on the available instrumentation. For example,imposing a constant load or holding the indenter tip at a

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constant displacement over a certain period of time enables theobservation of material properties such as creep and loadrelaxation at the nanoscale. By equipping the indenter with asensor at an axis perpendicular to the shaft, lateral forces can berecorded. The relative motion of the sample relative to the tipenables scratching of the surface and the determination of thefriction force [8,61]. The indenter tip can oscillate on the surfaceat various frequencies during application of the load, enablingthe measurement of viscoelastic properties at the nanoscale[29,56].

Nanoindentation is an established experimental techniquefor investigating the deformation of bulk materials and thinfilms [4–9,45,46,56]. The use of nanoindentation to probe themechanical properties of micron/nanometer-scale structures,(such as those found in micro/nanoelectromechanical system(MEMS/NEMS) devices) and biomaterials (such as bones andtissues), is steadily gaining acceptance among researchers. Withthe advent of advanced instrumentation methods, nanoinden-tation experiments can now be performed in conjunction withother techniques, such as electron microscopy, diffraction andcontact resistance measurements, and the synergy of theseexperimental methods aids in elucidating material deformationmechanisms involved.

This review article will discuss select examples of howdepth-sensing nanoindentation has been applied in the inves-tigation of theelastic andplastic deformation, aswell as fracturebehavior of various nanomaterials and micro/nanostructuressuch as nanoparticles, micro/nanopillars, microbeams, micro/nanofibers, nanocomposites, membranes andmonolayer films.A review of the application of nanoindentation to thin films andbiomaterials will not be discussed here, as it is beyond theintended scopeof this article, andhas beenpresentedelsewhere(for example, reviews by [1,8,16], as well as the June 1999,January 2004, August 2006, March 2009 and January 2012 focusissues of the Journal of Materials Research). The concepts learnedfrom studies on nanomaterials and nanostructures provide aninsight on themechanical properties at small length scales, andon how these properties can be used to implement thesenanomaterials and micro/nanostructures in various nanotech-nology applications.

Fig. 2 – (a) SEM images of a representative gold nanoparticlebefore (left) and after (right) compression with a diamondnanoindenter tip. (b) Load–displacement plots showingelastic loading (top), the displacement burst (middle) andreloading (bottom) during the compression of a goldnanoparticle.Adapted from Mook et al. [39].

2. Nanoindentation of Nanoparticles

Nanoparticles are of wide interest in nanotechnology due totheir potential use in the fabrication of nanoscale electricaldevices, such as transistors and resistors [5,22]. In addition,nanoparticles exhibit mechanical properties distinct from theirbulk counterparts owing to their small volumes. Mook et al. [38]and Chrobak et al. [13] observed length scale effects on themodulus andhardness of Si andTi nanoparticles.Mook et al. [39]and Lahouij et al. [26] conducted compression experiments onAu and MoS2 nanoparticles, respectively, where they were ableto capture the stepwise deformation of these nanomaterials.Wang et al. [57] and Yin et al. [64] performed indentationexperiments on arrays of Ni and hollow silica nanoparticles.More details on the nanoindentation studies of single nano-particles and their arrays are discussed below.

As an example, the compression behavior of gold nano-particles (“nanodots”) with nominal diameters of 340 nm and

heights of 270 nm deposited on a silicon wafer has beeninvestigated by Mook et al. [39]. The experiments wereconducted on ananoindenter system installed inside a scanningelectron microscope (SEM) to allow in situ imaging of the

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compression process. The tip used in the experiments was adiamondmilledwith a focused ion beam (FIB) tool to create a flatpunch geometry. SEM images of the nanoparticle before andafter compression with a nanoindenter tip are shown in Fig. 2a.The spherical particle was flattened after the indentation, andnewsurface areawas created, as evidenced by the appearance of

vertical light-colored areas on the sidewall of the goldnanoparticle.

Load–displacement profiles are shown in Fig. 2b, whichshows details of the elastic (top), burst (middle) and reloading(bottom) behavior of a Au nanodot for an indentation experi-ment under displacement control. During the burst event, thefeedback loop is not in control of the tip displacement for 0.1 s(steps 2–3), after which it recovers control (steps 4–5). Thenanodot then deforms elastically (step 6), after which, itplastically deforms and load drops attributed to dislocationprocesses or cracking are observed (step 7). The compression ofAu nanodots is an example of deformation of a freestandingstructure with little to no mobile defects available before yield,unlike the bulk material. While the collapse of the nanoparticleis not considered as fracture, it is a sudden event that takesplace with a small amount of plasticity beforehand [39].

In a study by Chrobak et al. [13], compression experimentswere performed on silicon nanoparticles on a sapphire sub-strate with radii ranging from 19 to 169 nm using an indenta-tion system with a blunt diamond tip and placed in atransmission electron microscope (TEM) for in situ imaging.The observed load–displacement curves exhibited the behaviorshown in Fig. 3a, where small nanospheres (radius of less than57 nm) display a pop-in (PI) in the loading portion of the curve,while larger nanospheres show a combination of a PI duringloading and a push-out (or pop-out, PO) upon unloading. The PIevent during loading signals the initiation of plastic deforma-tion, where phase transformation of silicon from a diamondcubic into a body-centered tetragonal occurs. Bulk silicon showsPO during unloading, where the area under the indenterundergoes a crystalline to amorphous phase transformation[11,25,62,66,67].

Molecular dynamics (MD) simulations are conducted toobtain theoretical basis on the deformation mechanism ofaggregates of atoms. MD simulationswere performed on siliconnanoparticles, where it was found that the maximum contactpressure attained in the nanoparticles (21.3–23.5 GPa) is nearlytwice as that of bulk silicon (~12 GPa) [13]. The pressure dropsshown in Fig. 3b are attributed to the pop-in events, which isdue to the onset of plasticity in defect-free crystals. Fig. 3cshows MD simulation on the distribution of the hydrostaticpressure (σh) for the compression of the nanoparticle(deconfined case) and the elastic nanoscale deformation ofbulk silicon (confined case) at the same strain level. In thesilicon nanoparticle, the stress is spread on the atoms through-out the volume of the particle. This is a stark contrast with bulksilicon, which is highly stressed only at the volume directlyunder the tip. The MD simulations have also shown that in the

Fig. 3 – (a) Load–displacement schematics showing theoccurrence of characteristic push-out (PO) and pop-in (PI)events from nanoindentation of bulk silicon andnanocompression of silicon nanospheres. (b) Contact pressure(pc) as a function of strain showing that themaximum pc in thenanoparticles is almost twice the hardness of the bulkmaterial. (c) Simulation of the hydrostatic pressuredistribution in the silicon nanosphere (top) and bulk silicon(bottom), both subjected to an elastic strain of 0.0725.Adapted from Chrobak et al. [13].

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nanoparticles, plastic deformation initiates with perfect dislo-cations joined by stacking fault regions. This is unique tonanoparticles since simulations for bulk silicon have shownthat plastic deformation initiation does not involve disloca-tions, but instead, a multi-phase amorphous zone forms wherethe coordination numbers of the atoms range from 1 to 5[12,13,31].

Arrays of nanoparticles, also referred to as nanodot-patterned surfaces (NDPSs) were investigated by Wang et al.[57] due to their potential applications in electronics, optoelec-tronics and magnetic storage devices. In this study, 70 nm tallNi nanodot arrays with a 100 nm dot-to-dot spacing weredeposited on a silicon substrate as shown in Fig. 4a. Theresulting surface was indented with a sphero-conical tip togenerate load–displacement data such as those shown inFig. 4b. Plastic deformation was observed from the indentationconditions, which was confirmed by post-indent imaging. TheSEM image in Fig. 4c shows the highlighted area which waslower than its surrounding, i.e., the areaof contactwhereplasticdeformation occurred. This area was corrected to exclude theareas between nanodots, and the result was used in thehardness calculation. The hardness and contact area variationas a function of load is summarized in Fig. 4d. The hardnessvalue calculated was comparable to that of nanocrystalline Ni,andmuchhigher thanmicrocrystallineNi. This implies that thenanodots in the array have much fewer defects relative tomicrocrystalline Ni owing to their smaller size.

Fig. 4 – (a) SEM images of the nickel nanodot patterned surface (NDNDPS with the indented area highlighted. (d) Hardness and contAdapted from Wang et al. [57].

3. Nanoindentation ofMicro/nanopillar Structures

Micro/nanopillar structures represent another geometry ofnanomaterials that can be utilized as components for variousMEMS/NEMS technologies [41,43,50]. Similar to nanoparticles,these structures have very small material volumes. As a result,the mechanical deformation of micro/nanopillars differs fromtheir bulk counterparts.

Uchic et al. [55] first reported the use of the focused ion beam(FIB) microscope to prepare metallic micropillar samples,followed by a uniaxial compression experiment using a nano-indenter. Greer et al. [19] and Nix et al. [43] investigated thedeformation of goldmicropillars, where they proposed that theobserved significant hardening at this length scale is due todislocation starvation, where dislocations leave the crystalfaster than its rate of proliferation. They postulate that thisphenomenon is different from the indentation size effect (ISE)attributed to the presence of strain gradients typically observedat the micrometer scale [42]. San Juan et al. [50] and Korte et al.[24] studied the compression of superalloy micropillarsunder ambient and high temperature conditions, respectively.Niederberger et al. [41] and Maeder et al. [32] studied thecompression of GaAs micropillars using indentation in con-junction with the electron backscatter diffraction (EBSD)technique. Beaber et al. [2] and Howie et al. [20] induced fracture

PS). (b) Load–displacement curves of the NDPS. (c) SEM of theact area as a function of load.

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on various brittle micropillars. More detailed examples ofcompression and nanoindentation studies of the elastic, plasticand fracture properties of micro/nanopillars are discussed asfollows.

San Juan et al. [50] performed compression studies on metalsuperalloy pillars composed of Cu–Al–Ni and with a diameter of900 nm fabricated by focused ion beam (FIB) micromachining.Shapememory alloys are of scientific and technological interestas they can transform between the austenite phase andmartensite phases reversibly. The submicron diameter pillarsuch as the one shown in Fig. 5a was subjected to cycliccompression using a diamond sphero-conical tip. Two load–displacement curves taken after ten compression cycles areshown in Fig. 5b. At a load of about 95 μN, an abrupt burst indisplacement is observed as a result of the stress-inducedmartensitic transformation. During unloading, the reversetransformation is observed at an ~45 μN load, and continuesgradually until a load of ~22 μN is attained. The compression iscompletely elastic as no residual deformation was observed. Inthis study, a size effect was observed, such that the martensitephase has improved stability relative to its bulk form due torelaxation effects at the free surface. As a consequence, the

Fig. 5 – (a) SEM image of a submicrometer pillar composed ofCu–Al–Ni alloy. (b) Load–displacement curves from twoconsecutive nanocompression experiments.Adapted from San Juan et al. [50].

reverse transformation takes place onlywhen very low values ofthe stress are attained during the unloading. This is manifestedby the large hysteresis seen in the load–displacement curve priorto elastic recovery.

The compression of superalloy micropillars at elevatedtemperatures of up to 630 °C and in vacuum was carried outby Korte et al. [24] using a sapphire flat punch tip. The fullstress–strain curves obtained at ambient temperature (25 °C),300 °C and 630 °C are shown in Fig. 6a. The low strain areaof thecurve ismagnified in Fig. 6b, with offsets applied to the elevatedtemperature data to separate those from the 25 °C curves. Theelastic modulus was calculated from the linear loading portionof the curves, which agreedwithmacroscalemodulus data. Theplastic deformation was evaluated in terms of the yield stress,where it was found to be comparable to macroscale yield stressreported in the literature. In addition, the hardness (specifically,H/3)was related to the stress at several percent of strain (chosento be 5%) using the Tabor approximation [53]. It was found thatthe stress at 5% strain was consistent with the literature valuesof H/3 [24].

The electron backscatter diffraction (EBSD) technique, alsoknown as backscatter Kikuchi diffraction (BKD), is an experi-ment that has been demonstrated to monitor changes in thecrystal orientation during the compression of single crystalGaAs micropillars in situ [41]. This experiment requires a SEMequipped with an EBSD detector, and a built-in indentationcapability. Fig. 7 shows the data from compression experimentsconducted on the GaAs micropillar using a diamond tip thatwas milled using a focused ion beam to obtain a flat punchgeometry. As shown in the load–displacement curves (Fig. 7a),themicropillar was loaded twice. The first load cycle is denotedby steps 1–3, while the second load cycle is at points 3–5. EBSDmaps are shown in Fig. 7b to g, where the base and tip of thepillar are on the left and right sides, respectively, on each of themaps. Fig. 7b to d corresponds to the crystal orientation before,during andafter the first compression cycle,while the images inFig. 7e to g are data for the second cycle. The crystal orientationis uniform before loading, as shown in Fig. 7b and e. While loadis being applied to themicropillar, the crystal orientation at thebase remains the same, but a gradient is observed along thelength pillar, as seen in Fig. 7c and f. Uponunloading, the crystalorientation reverts to being uniform, implying that themicropillar deformed elastically during the first compressioncycle. However, in the second cycle, the EBSD maps showedirreversible change, indicating the occurrence of plastic defor-mation [41].

Beaber et al. [2] investigated the indentation-induced fractureof nanopillars (“nanotowers”) composed of a silicon core andcoatedwith a SiC shell. The core had diameters ranging from400to 500 nm, while the SiC coating was 250–350 nm thick. Thestructures were subjected to FIB processing to expose the Si coreat the top surface of the towers. Indents weremade at the top ofthe nanopillars using a sharp cube corner indenter. Examples ofthe load–displacement curves and the corresponding post-indent SEM images are shown in Fig. 8 for maximum displace-ments of 75 nm (Fig. 8a and b) and 125 nm (Fig. 8c and d).Fracture was not observed in the 75 nm indent, as seen in theabsence of load drops in the load–displacement curve or visiblecracks in the SEM image. However, plastic pile up occurred, asseen in the white areas surrounding the indent. Meanwhile,

Fig. 6 – (a) Stress–strain curves taken on a single crystal nickel superalloy micropillars in vacuum at 25 °C, 300 °C and 630 °C.The arrows in the bottom part of the unloading portion of the data are hold segments at 10% of the maximum load used for thedetermination of instrument drift. (b) Low strain area of the curve in (a) with the data for higher temperatures offset from theambient temperature data.Adapted from Korte et al. [24].

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cracking was observed in the tower indented up to 125 nm, andis seen to readily propagate into the SiC shell. Due to thecoefficient of thermal expansion (CTE)mismatch between the Sicore and SiC shell materials, the former is under compressionwhile the latter is in tension. The compression inhibits crackgrowth in Si, while the residual tensile stress in the shell isresponsible for crack propagation in SiC. For indents wherecracking was observed, the fracture toughness was calculatedusing [27]:

K Ic ¼ αEH

� �1=2 Pc3=2

� �ð1Þ

where α is a indenter tip geometry dependent factor, E is themodulus,H is thehardness, P is themaximumindentation load,and c is the crack length as measured from the center of theindent.

Compression tests onmicropillars were performed by Howieet al. [20] to induce fracture along the length of the structure. An

Fig. 7 – (a) Load–displacement curve for the compression of a GaAsmapswere taken, and the arrowsdenote the initiationof bending. (bduring and after loading). (e)–(g) EBSD maps taken from the second

example is shown in Fig. 9a, for a Si pillarwith an initial diameterof 320 nm, where an axial splitting crack was produced aftercompression with a diamond flat punch. Different modes offracture were observed on other materials. Crack growth on theupper portion of the pillar and on the side surface was seen onInAsmicropillars (side splittingmode), while an array of parallelcracks on the apex surface was observed on GaAs and MgOmicropillars (top surface splitting mode).

It was postulated that the axial splitting cracks are producedwhen two opposite slip planes that intersect are activated,leading to dislocation pile-up at a certain distance below the topof the pillar. In the side-splitting mode, a single slip plane isactivated, and no intersection with another plane takes place.The top surface splitting mode due to duplex slip takes place,which leads to an increase in the dimensions of the bulk of thepillar relative to the top layer. Upon unloading of the indentertip, the top layer strains to conform to the bulk of the pillar,leading to the formation of parallel cracks on the top.

micropillar. The numbers indicate the points when the EBSD)–(d) EBSDmaps taken from the first loading experiment (before,loading experiment (before, during and after loading) [41].

Fig. 8 – Load–displacement data (a,c) and post-indent SEM images (b,d) of Si–SiC composite nanopillars. Top and bottom dataare for maximum displacements of 75 nm (a,b) and 125 nm (c,d), respectively [2].

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Experimental data from the variousmicropillar materials areplotted in Fig. 9b, where the x-axis is the pillar diameter (d) andthe y-axis is the square of the parameter (KIc/ksβσy). KIc is thefracture toughness, ks is a constant related to the Schmid factoron the slip plane and the angle between the slip plane normaland the axis of compression, β is a geometrical constant, and σy

is the yield strength of the material. The parameter (KIc/ksβσy)corresponds to the square root of the critical pillar diameter (dcrit)belowwhich, axial splitting cannot occur. This can be expressedas follows [20]:

dcrit ¼1ksβ

K Ic

σy

� �2ð2Þ

In Fig. 9b, open symbols are for micropillars where axialsplitting cracks were observed, while the solid symbols are formicropillars where no cracking occurred. The solid line denotesthe transition between the two possible outcomes as predictedby Eq. (2). This parameter is useful because the combination ofthe presence of intersecting slip bands (which will depend onthe dimensions of the material) and the yield stress willdetermine the splitting mode of the micropillar.

4. Nanoindentation of Microbeamsand Micro/nanofibers

Micro/nanobeams are structures commonly found in sensorand actuator devices. Quasi-one-dimensional materials, suchas nanotubes and nanowires and their arrays, have generatedintense interest among researchers due to their electrical andmechanical properties, and their potential for integration inmicrolectronics and biomedical applications [5,6]. Li et al. [30],Wei et al. [60] and Palacio et al. [47] performed bendingexperiments on microbeams. Li et al. [28], Yang et al. [63],McAllister et al. [35] and Wang et al. [59] indented individualfibers. Kaul et al. [21], Maschmann et al. [34] and Qiu et al. [48]indented nanofiber arrays. Examples of nanoindentationstudies on these types of materials are discussed below.

4.1. Microbeams

The deformation of metallic micro beams was characterized byLi et al. [30]. Fig. 10a shows the SEM images, load–displacementcurve and FEM stress contour for a notched Ni–P cantilevermicrobeam that was bent to failure with a Berkovich tip. In this

Fig. 9 – (a) Compressed Si micropillar with an axial splittingcrack. (b) Plot predicting the occurrence of axial split crackson a micropillar, where the solid line is the transition fromthe absence to the presence of axial splitting. Open symbolsdenote pillars where axial splitting occurred, while solidsymbols are for pillars that deformed without any axialsplitting.Adapted from Howie et al. [20].

Fig. 10 – (a) Image of the undeformed Ni–P cantilevermicrobeam and load–displacement data (top), images of thebrokenmicrobeam (middle) and stress distribution from FEM(bottom). (b) Image of the undeformed Au bridge microbeamand load–displacement data (top) and image of the deformedmicrobeam and stress distribution from FEM (bottom).Adapted from Li et al. [30].

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microbeam, the distance between the loading position and thefixed end is 40 μm.The 3 μmdeepnotch is 10 μmfrom the fixedend. This notched beam showed linear behavior followed byabrupt failure. This suggests that flaws like notches on thebeam surface can greatly affect its deformation behavior, andthat in the fabrication of micro/nanostructures, more attentionneeds to be given to the effect of surface flaws and roughness.Even small flaws could change the design properties since theratio of flaw size to beam dimension could be much larger inmicro/nanostructures. Examination of the FEM stress contourshows that there is a higher stress concentration at the notchtip. The maximum tensile stress σm at the notch tip can beanalyzed by using Griffith fracture theory as follows [27,30]:

σm ¼ 2σocρ

� �1=2

ð3Þ

where σo is the average applied tensile stress on the beam, c isthe crack length, and ρ is the crack tip radius. Therefore, elastic–plastic deformation will first occur locally at the end of thenotch tip, followed by abrupt fracture failure after the σm

reaches the ultimate tensile strength of Ni–P, even though therest of the beam is still in the elastic regime. The SEM image ofthe fracture surface shows that the fracture started right from

Fig. 11 – (a) Load–displacement curves for the normal beambending of polymer beams composed of PPMA, PMMA, PS and PS/Clay(left), where SEM images (right) correspond to the beams subjected to 3 mN load. (b) Lateral force plotted as a function of thedisplacement (left) for the lateral bending of PS and PS/Clay cantilever beams,where the arrows indicate the onset of yield for bothPS and PS/Clay, cracking for PS and breaking for PS/Clay. SEM images (middle and right) indicate the bending direction and thelocation of the cracks.Adapted from Palacio et al. [47].

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Fig. 12 – (a) SEM image of ZnS nanobelts. (b) Load–displacement curves for two nanobelt thicknesses, where the plot on theright shows pop-in behavior indicative of crack initiation. (c) AFM image of an indentation-induced crack on a nanobelt.Adapted from Yang et al. [63].

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the notch tip with plastic deformation characteristic, indicatingthat although local plastic deformation occurred at thenotch tiparea, the whole beam failed catastrophically. This shows thatFEM simulation can predict well the stress concentration, and

help in understanding the failure mechanisms of the notchedbeams.

Fig. 10b shows the SEM images, load–displacement curveand FEM stress contour for the Au bridge microbeam that was

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deformed by nanoindentation. The recession gap between thebeam and substrate is about 7 μm, which is not large enough tobreak the beam at the load applied. The beam experienced

Fig. 13 – (a) Image of a carbon nanotube turf with amagnification of a portion of the side and top surfaces (inset).(b) Load–displacement curves showing the variation of theadhesive force as a function of unloading rate. Amagnificationof the initial loading and final unloading points is shown onthe inset. (c) Plot showing the variation of the load and currentwith the displacement held constant over a period of time.Adapted from Qiu et al. [48].

elastic–plastic deformation based on the load–displacementprofile. The FEM stress contour shows that the maximumtensile stress is locatedat the fixedends,whereas theminimumcompressive stress is located around the center of the beam.The SEM image shows that the beam has been permanentlydeformed.No crackwas found on the beamsurface. This showsthat Au structures can be mechanically formed into variousdesired shapes, which could help in the fabrication of function-ally complex smart micro/nanodevices that require conductorsfor power supply and input/output signals [30].

Nanoindentation studies focused on polymer microbeamsdesigned for the BioMEMS device known as a cell force sensorwere conducted by Palacio et al. [47], where the materialsinvestigated were poly(propyl methacrylate), poly(methyl meth-acrylate), poly(styrene) and a poly(styrene)–nanoclay composite(abbreviated as PPMA, PMMA, PS and PS/Clay, respectively). Forthis application, nanoindentation was used for conductingbending experiments in the normal and lateral directions witha sphero-conical diamond tip. These experiments provideinformation on the elastic modulus, yield strength and breakingstrength of these materials. This example illustrates hownanoindentation can be used beyond the more traditionalexperiments carried out on bulk materials and thin films.

Bending experiments were performed by Palacio et al. [47]with applied loads in the millinewton range in order toinvestigate the behavior of polymer beams beyond the elasticdeformation regime. Fig. 11a shows normal load–displacementprofiles at nominal maximum imposed loads of 0.5, 1.5 and3.0 mN (actual attained load is lower) applied on three differentbeams in one wafer sample. For PPMA, PMMA and PS, theloadingportionoverlaps, indicating uniformbeamquality. Slightvariability in the loading profile is observed in the PS/Claycomposite, which is attributed to variable interfacial adhesionbetween the filler and the matrix and inhomogeneities in thedispersion of the clay particles.

The first inflection in the load–displacement profiles impliesthe onset of yield, where the locations are indicated by arrows.The three unfilled polymers (PPMA, PMMA and PS) exhibitductility, as seen in the SEM images for the beams tested withan applied load of 3 mN. The beams stretch at the ends andunderneath their centers. These correspond to regions subjectedtomaximumtensile stress. The beamsdeformed symmetrically,indicating that the load was applied equidistant from theclamping points. The PS/Clay nanocomposite beam exhibitedslight yielding, followed by breaking, as indicated by an arrow inthe load–displacement profile. After breaking, the load contin-ued to increase because a pre-defined load is imposed by thenanoindenter. The corresponding SEM image for PS/Clay showsa flat fracture surface, indicating that the crack propagatedperpendicular to the direction of the applied stress [47].

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From the load–displacement curves, the yield strength canbe evaluated by using [47,65]:

σ ¼ 34

Fl

bh2ð4Þ

where F is the load corresponding to yield of the beam (asindicated by arrows in the load–displacement profile), l, b andh are the beam's length, width and height, respectively. It isassumed that the beam-ends are clamped.

Fig. 11b presents the results of the lateral bending experi-ments on PS and PS/Clay cantilever beams. On the left columnare the plots for the lateral force recorded as a function of thelateral displacement. From the linear elastic regime (as indicat-ed by the straight line drawn over the data points), themoduluscan be evaluated. For a cantilever beamwith one end clamped,it is expressed as [47,65]:

E ¼ l3

3Im ð5Þ

where l is the beam length, I is the area moment of inertia forthe beam cross section andm is the slope of the linear region ofthe force–displacement curve.

From the load–displacement curves, the yield strength canbe evaluated by using [47,65]:

σ ¼ 6Fl

bh2ð6Þ

where F, l, b and h are defined similarly as in Eq. (4). The forceused for calculating the yield strength is taken at the point

Fig. 14 – (a) Load–displacement plots for the radial indentation ofplotted as functions of the displacement (middle) and the squareexpanding cavity model as applied to a fiber, where the principaAdapted from McAllister et al. [35].

where a change in slope was observed (as indicated by thearrows on the left in Fig. 11b).

For PS, a steady decrease in the lateral load was observed at160 mm, while for the PS/Clay beam, the drop at 80 mm wasabrupt (as indicated by the arrows on the right). SEM imagesreveal that for PS, this corresponds to crack formation at thebase of the beam that did not run throughout the entirethickness of the beam. However for PS/Clay, the beam broke,which implies that the addition of the nanoclay filler inducesembrittlement of the beam.

4.2. Micro/nanofibers

Nanobelts are nanostructures with a high width to height (orthickness) ratio, where the thickness is on the order of tens ofnanometers. Yang et al. [63] studied the nanomechanicaldeformation of ZnS nanobelts using a Berkovich tip. Fig. 12a isa SEM image of these nanomaterials, illustrating the unifor-mity of the feature width (on the order of ~1 μm) along theentire length of the material. It was found that at lowindentation loads, the contact stiffness is independent of thenanobelt thickness, such that there is no apparent size effecton the elastic deformation of these nanomaterials. Examplesof load–displacement curves for 65 nm and 110 nm-thick ZnSnanobelts are shown in Fig. 12b at a load level where plasticdeformation is observed. The loading portion of the indenta-tion curve of the thicker nanobelt exhibits pop-in behavior at~160 μN, which is indicative of the initiation of a surfacecrack. An atomic force microscope (AFM) image of an indent

a 10 μm radius glass fiber (left) and slope of the loading curveroot of the displacement (right). (b) Schematic of thel stress contours are overlaid on the fiber cross-section.

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performed with a higher applied load (350 μN) is shown inFig. 12c, where the surface cracks initiated at the indent edgepropagates along the surface [63].

The data from the indentation of these nanomaterialsshould be usedmore qualitatively, and if E and H are reported,it should be interpreted carefully. In a study by Shu et al. [52],numerical modeling and finite element analysis have shownthat the E and H obtained using the Oliver–Pharr methodwithout any corrections could be underestimated, such that amodified model that takes into account the geometry of thenanomaterial would yield more accurate results.

Qiu et al. [48] investigated the time-dependence of thecontact between the diamond Berkovich indenter tip and acarbon nanotube array (or CNT “turf”). An image of the CNT turfis shown in Fig. 13a, where the array is 100 μm tall with adiameter of 200 μm. Indents were performed where theunloading ratewas varied from100 μm/s to 100 nm/s toobservethe rate dependence of the adhesion between the indenter tipand the sample surface. The load–displacement data for

Fig. 15 – Load–displacement plots of indentations made at 0.1 anvarious glass fibers.Adapted from Li et al. [28].

displacement-controlled indentations shown in Fig. 13b showtwo manifestations of adhesion. First is the appearance of thepull-off force, the negative load necessary to separate the tipfrom the surface. The other feature is the presence of contactbetween the tip and CNT at a distance of about 100 nm abovethe surface of the zero point (inset of Fig. 13b). The highestpull-off force was observed at the fastest unloading rate.

The results of another notable experiment conducted toassess the carbon nanotube array–indenter tip interaction areshown in Fig. 13c, where electrical contact resistance (ECR) wasused to monitor the current resulting from the application of afixed voltage between thenanotube and the diamondBerkovichtip in conjunction with the standard load and displacementdata obtained in an indentation experiment. In the initialsegment, the sample is penetrated, such that the contact areaincreases aswell as the amountof theCNT–tip contacts, leadingto an observed increase in the current. During thehold segment,the displacementwasheld constant and the load relaxeswithina few seconds, but the current remains constant. This implies

d 5 mN peak indentation loads on the cross-sections of

15M A T E R I A L S C H A R A C T E R I Z A T I O N 7 8 ( 2 0 1 3 ) 1 – 2 0

that the number of CNT–tip contacts does not change signifi-cantly during the indentation, and the load relaxation is not dueto a reduction of the amount of contacts [48].

In another study, McAllister et al. [35] investigated thedeformation of glass fibers using a sphero-conical diamondtip, where they accounted for sources of compliance in theindentation of fibers in the radial direction (i.e., the curvedsurface). Fig. 14a shows the load–displacement data (left),showing the typical hysteresis between the loading andunloading portions as a result of elastic–plastic response. Theloading portion was further analyzed and its slope (dP/dh) as afunction of the depth and the square root of depth are shown inthemiddle and right plots, respectively on Fig. 14a. In bothplots,data below h=60 nm is affected by the surface roughness anddoes not represent bulk material deformation. Beyond thisroughness-affected depth, the initial portion of the dP/dh vs. hplot is concave down, indicating elastic contact. The profilethen changes to a linear relationship as plastic deformationtakes place. Meanwhile, the dP/dh vs. h1/2 plot is initially linear,as it is under spherical contact and shows elastic behaviorwhere the load is proportional to h3/2. Afterwards, the profilechanges to a concave up shape due to the onset of plasticity,where the load is proportional to h2 [35].

A physical model of the deformation of the glass fiber isshown in Fig. 14b, where the stress contours shown are thosepredicted by the expanding cavity model. It should be notedthat the stress distribution illustrated by the contours is for anideal flat surface, and does not describe the distribution for afiber indented along the radial direction. For the fiber, thestress contours tend to be elongated towards the fiber bulkand shear stresses are higher at the fiber surface. Theseconditions facilitate easier elastic and plastic deformationrelative to a non-curved surface [35].

Load–displacement curves are shown in Fig. 15 for glassfibers, which are used as reinforcements innumerousmaterialsincluding plastic, rubber, cement as well as heat insulationmaterials [28]. The indents were made on polished cross-sections of the fibers using a Berkovich tip. Fibers C, Q and Sare all 16 μm diameter fibers, each with different formulations.The load–displacement plots of indentations made at 0.1 mNpeak loads on all fibers exhibit several displacement disconti-nuities of pop-in marks during the first and second loadingsteps of the indentation, as denoted by the arrows in Fig. 15.Pop-in marks in the loading curves result from suddenpenetrations of the tip into the sample. Fiber S exhibits thesmallest pop-in marks, followed by fibers Q and C, suggestingthat Fiber S has the highest resistance to plastic deformation aswell as crack formation and crack propagation.

Fig. 16 – (a) Image of the WS2 nanotubes.(b) Load–displacement plots of the SWCNT/epoxy andWS2/epoxy nanocomposites.Adapted from Tehrani et al. [54].

5. Nanoindentation of Nanocomposites

Various types of nanocomposites are being developed asnext-generation nanomaterials that possess the durability,flexibility, electrical and/or optical properties required fornovel device applications. Palacio et al. [47], McCumiskey et al.[36], dos Santos et al. [15], Seena et al. [51], and Tehrani et al.[54] studied the effects of adding nanoclay, CdSe quantumdots, carbon nanotubes, carbon black andWS2 respectively, asfillers on composites with a polymer matrix. Ni et al. [40]

performed nanoindentation on composites with polymers asfillers on a porous silicon matrix. In all cases, the modulationof the mechanical and fracture properties was observed,which depended on the relative amounts of the filler andmatrix materials. Below are a few examples of the resultsfrom nanoindentation studies on nanocomposites consistingof different types of matrix and filler materials.

Inorganic andorganicnanotubes are currently being exploredas components in composites. Tungsten disulfide (WS2) is anexample of an inorganic material that has generated consider-able interest in its nanostructured forms due to its potential inlubricants, catalysts, and coatings applications, among others.Tehrani et al. [54] compared the mechanical properties ofcomposites consisting of WS2 nanotubes dispersed in epoxy tothat of single walled carbon nanotubes (SWCNT)–epoxy com-posites. Fig. 16a shows that theWS2nanotubesused in this studywere typically several micrometers long and had an averagediameter of 60 nm. Fig. 16b shows load–displacement data forthe composites obtainedwith a sphero-conical diamond indent-er tip, where it is observed that the WS2–epoxy composite hashigher elastic modulus and hardness (4 GPa and 190 MPa,respectively) than the SWCNT–epoxy composite (3 GPa and170 MPa, respectively), and that the former has a two-foldimprovement in the mechanical properties relative to unfilledepoxy. Comparing the two filler materials, SWCNT has superiorstrength andmechanical properties relative toWS2, but thiswasnot manifested in their polymer composites. The observedproperties were attributed to the state of dispersion of thenanotubes on the polymer matrix. It was proposed that theWS2

16 M A T E R I A L S C H A R A C T E R I Z A T I O N 7 8 ( 2 0 1 3 ) 1 – 2 0

nanotubes are better dispersed while SWCNTs tend to agglom-erate when mixed with the epoxy matrix, which led to thesuperiormechanical properties of the inorganic nanotube-basedcomposite material [54].

Quantum dots are nanoscale particles with tunable opticaland electrical properties. These materials are being studiedfor applications such as solar cells, flexible electronics andsensors. A method being explored to utilize quantum dots isto incorporate these nanostructures into a polymer device.McCumiskey et al. [36] prepared and characterized compos-ites consisting of CdSe quantum dots dispersed in poly[2-methoxy-5-(2′-ethylhexyloxy)-p-phenylene vinylene] (ab-breviated as MEH-PPV). Fig. 17a shows TEM images of a 50%(by weight) CdSe dispersion in MEH-PPV at two magnificationlevels. The nanocomposite solutions were then deposited onglass substrates to form solid films. The modulus andhardness data obtained by nanoindentation with a Berkovichtip are shown in Fig. 17b, where an increase in the mechanicalproperties is seen at shallower depths due to an indentationsize effect (ISE). An improvement in the properties was seenwith the increased fraction of the CdSe quantum dots in thenanocomposite. The stability of the pure CdSe quantum dotfilm was attributed to the formation of a solid nanocrystallinefilm as a result of sintering.

In a study by Ni et al. [40], porous silicon was filled witheither the polymer MEH-PPV or poly(p-phenenylene vinylene)

Fig. 17 – (a) TEM images of the CdSe quantum dot dispersion on t(right) as a function of contact depth for the nanocomposites, puAdapted from McCumiskey et al. [36].

(PPV) to form a nanocomposite with “bamboo-like” morphol-ogy and properties. This nanocomposite was developed in anattempt to fabricate light emitting diode (LED) materials,where the presence of nanoscale polymers in the silicon poresis expected to tune the optical properties of the resultingmaterial. Load–displacement data using a Berkovich tip forthe nanocomposites with Si(100) and porous silicon (PS) asreference are shown in Fig. 18a. The nanocomposites haveinferior mechanical properties compared to Si(100) and theporous silicon, with the MEH-PPV nanocomposite being betterthan the PPV nanocomposite. However, the nanocompositeshave superior fracture properties as determined using theVickers indentation test, where it was found that MEH-PPVhas double the fracture toughness of PS. This is accounted forwith a mechanism represented by the schematic in Fig. 18b,where the presence of polymer in the cavities of the poroussilicon is thought to arrest crack propagation.

6. Nanoindentation of Membranes andMonolayer Films

Nanoindentation is routinely used to characterize the deforma-tion properties of submicron thin films deposited on a substrate[8]. It has been shown that nanoindentation can be used tocharacterize freestanding films as well. However, the contact

he polymer MEH-PPV. (b) Elastic modulus (left) and hardnessre CdSe and pure MEH-PPV.

Fig. 18 – (a) Load–displacement plots of indentationsmade onSi(100), porous silicon (PS) and two polymer-filled siliconcomposites (MEH-PPV and PPV polymers). (b) Schematicshowing the crack propagation path on the single crystal Si(top) and the polymer–porous silicon composite (bottom).Adapted from Ni et al. [40].

Fig. 19 – (a) Schematic of indentation on a freestanding Cumembrane. (b) Load–deflection curves for five differentapplied loads. (c) Schematic of the deformation mechanismof the membrane, starting from single-point bending (top),yield during stretching (middle) and the formation of plasticdeformation zones after unloading (bottom).Adapted from Wang et al. [58].

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area-dependent load–displacement relationships used to de-scribe themechanical response of thin films and bulkmaterialsare not applicable to freestanding films because the geometry ofthe contact and the mode of deformation mode are different.Constitutive equations based on the mechanics of membranedeformation are used instead [3,23]. Maner et al. [33]characterized the deformation of poly(methyl methacrylate)and poly(2,6-dimethyl-1,4-phenylene ether) freestanding filmswith thicknesses ranging from 350 to 750 nm. Wang et al. [58]studied 50 nm thick Cu films sputtered on a 5 nm carbon layer.

More recently, nanoindentation has also been utilized in thestudy of multi-layered films deposited on a substrate, such asfilms deposited using the atomic layer deposition (ALD)technique. ALD has been gaining interest among researchersdue to its ability to form metal and metal oxide thin films withprecise control of film thickness at the monolayer level [18].

Dafinone et al. [14] and Riley et al. [49] used nanoindentation tostudy the effect of depositing a few monolayers (4–15) of Al2O3

films on ceramic/polymer and polymer composite substrates,respectively. In both studies, a significant improvement in themechanical properties was observed. These applications ofnanoindentation on the study of membranes and monolayerfilms will be discussed below.

6.1. Membranes

As an example of a study of freestanding film deformation,Wang et al. [58] characterized the deformation of a Cu

18 M A T E R I A L S C H A R A C T E R I Z A T I O N 7 8 ( 2 0 1 3 ) 1 – 2 0

membrane that is approximately 50 nm thick. Cu wasdeposited using ion beam sputtering on a 5 nm thick carbonfilm to create the membrane. A schematic of the indentationprocedure is shown in Fig. 19a, where the membrane isclamped at a distance of 10 μm from edge to edge and theBerkovich tip is in contact with the freestanding portion of thematerial. As shown in the load-deflection data in Fig. 19b, fivemaximum loads were selected, and the profile of the curveschanges as the load is increased. At the two lowest loads, theloading profile was linear and a small hysteresis is observedupon unloading. However, at higher loads, an inflection isobserved at around 100 μN, upon which the slope of theloading curve increases sharply. Upon unloading, this slopechange is observed at about 70 μN (from high to low contactstiffness), and a large elastic recovery takes place.

A three-stage mechanism has been proposed to account forthe load–displacement behavior of themembranes, as shown inFig. 19c [58]. At shallow indentation displacements (low loads),membrane bending takes place at a single point as shown onthe top schematic in Fig. 19c. Then, the Cumembrane begins toexperience plastic deformation, which corresponded to theinflection point at 100 μN in Fig. 19b. This is the transition fromsingle-point bending to surface stretching, as illustrated in themiddle schematic in Fig. 19c. Upon unloading, elastic recoverytakes place on areas not contacted by the indenter, and some

Fig. 20 – (a) Load–displacement plots for films prepared with varydisplacement for the various ALD films. (d) Summary of the modAdapted from Dafinone et al. [14].

plastic deformation exists on the area directly underneath theindenter, as shown in the bottom schematic in Fig. 19c. Neckingzones are thought to form on the center and the edges of theindented area.

6.2. Monolayer Films

In a study on monolayer films, Dafinone et al. [14] investigat-ed the mechanical properties of Al2O3 films prepared by ALD,deposited on TiO2/SiO2 layer-by-layer (LbL) films, which inturn, are on a polycarbonate substrate. This material combi-nation was developed to create a mechanically reinforcedantireflective surface. Fig. 20 is a summary of the mechanicalproperties of the ALD films. The indentation data (shown inFig. 20a) was obtained using the continuous stiffness method,where a small oscillating load (applied by a Berkovich tip) isused to measure the contact stiffness at all depths. Thisenabled the point-by-point determination of the modulus andhardness, which are summarized in Fig. 20b and c, respec-tively. As the number of ALD cycles increased from zero to 15,the number of monolayers of deposited Al2O3 also increased,leading to increases in both the modulus and hardness. Thistrend is also shown in Fig. 20d, where the modulus wasobtained from the plateau values of the data in Fig. 20b andthe hardness was taken from the data at ~10% film thickness.

ing ALD cycles. (b) Modulus and (c) hardness as a function ofulus and hardness as a function of the number of ALD cycles.

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However, it should be noted that the properties measured inthis particular experiment are the E and H of the entiresystem, i.e., the composite value for the ALD films andthe underlying LbL film, and with some substrate effectmanifesting as well. These properties cannot be ascribed toeither the film or to the substrate owing to the very lowthickness of the ALD film. Overall, the concept beingdemonstrated here is that the deposition of the Al2O3 thinfilms using the ALD method can effectively modulate themechanical properties of this material system, and a me-chanical reinforcement effect is apparent.

7. Conclusion

As shown in the studies discussed in this article, thedeformation of a wide range of material configurations, suchas nanoparticles, micro/nanopillars, microbeams, micro/nanofibers, nanocomposites, as well as membranes andmonolayer films can be characterized by nanoindentation.The development of advanced instrumentation methods hasenabled the nanoindentation of micro/nanostructures inconjunction with electron microscopy, diffraction and electri-cal measurement studies. This capability for in situ deforma-tion and characterization has led to a better understanding ofmechanical deformation events such as plasticity and frac-ture at the nanoscale. From these studies, micro/nanostruc-tures have been found to exhibit unique deformation andfracture mechanisms that may not be observed in the bulkmaterial due to their ultrasmall dimensions. Understandingthese nanoscale properties impacts how nanomaterials andmicro/nanostructures are integrated in nanotechnologicaldevices. Nanoindentation is an appropriate characterizationtechnique for probing the mechanical deformation ofnanomaterials, and will continue to be indispensable in thedevelopment of novel structures and devices for emergingnanotechnology applications.

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