Profiling Nanowire Thermal Resistance with a Spatial Resolution ofNanometersDan Liu,†,‡,§ Rongguo Xie,†,‡ Nuo Yang,∥ Baowen Li,*,†,§,∥ and John T. L. Thong*,‡,§

†Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546,Republic of Singapore‡Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Republic of Singapore§NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117456, Republic ofSingapore∥Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai,People’s Republic of China

*S Supporting Information

ABSTRACT: We report a new technique to profile the thermal resistance alonga nanowire with a spatial resolution of better than 20 nm. Using this technique,we mapped the thermal conductivity along a Si0.7Ge0.3/NiSi0.7Ge0.3 hetero-structured nanowire. We also measured the interfacial thermal resistance (ITR)across the Si/NiSi2 interface embedded in Si/NiSi2 heterostructured nanowires.The ITR does not change even for adjacent interfaces as close as ∼50 atomiclayers.

KEYWORDS: Thermal conductance, nanowires, nanostructures, thermal measurement, electron beam heating,nanoscale thermal transport

Thermal transport in nanowires differs significantly fromthat in bulk materials as phonon boundary scattering can

play a significant or even dominant role when nanowirediameters approach the phonon mean free path. At evensmaller diameters approaching the phonon wavelength, phononconfinement effects come into play.1 The prospect ofenhancing the thermoelectric performance of semiconductorsin the form of nanowires has triggered a spate of theoretical andexperimental works.2−12

Because of the microscopic sample dimensions and the smallheat flows involved, measuring thermal conductivity ofnanowires is technically challenging. Currently the mostpopular technique is the thermal bridge method, which utilizestwo thermally isolated microfabricated islands with resistanceloops, one of which acts as a heater and the other as a passivetemperature sensor, to which the ends of a nanowire areattached.13 The nanowire’s thermal conductance is calculatedfrom the heat flow through the nanowire and the temperaturedifference between its ends. Since its invention, experimentalstudies using this technique have generated many excitingresults and inspired further theoretical work. However, by itsvery nature, the thermal bridge method only yields the totalthermal resistance of the nanowire connection between the twoislands. This leads to two major limitations. First, the measuredthermal resistance includes the parasitic contact resistancebetween the nanowire and the heat source/sink which couldpresent a significant source of systematic error, particularly in

cases where the conductance of the nanowire is large. Forexample, the thermal contact resistance can account for asmuch as 50% of the measured thermal resistance of amultiwalled carbon nanotube.14 Previous approaches toaccount for the contact resistance include extrapolating thelength-dependent measurements of thermal resistance14 or byusing the thermoelectric voltage drop across the contacts.15

Second, the measurement does not discriminate inhomogene-ities along the nanowire. For example, in heterostructurednanowires, not only would the thermal conductivity vary withmaterial composition along the wire, but each interface wouldalso give rise to interfacial thermal resistance (ITR). The lack ofan experimental technique to probe heat flow at the nanoscalelimits our ability to examine and understand thermal transportin nanowire systems.Here we present a new approach using a focused electron

beam as a noncontact localized heat source to carry outspatially resolved thermal resistance and ITR measurements.We had previously introduced the technique to measure thethermal contact resistance between the sample and the heater/sensor islands in a thermal-bridge setup.7,13 In this paper, wepresent the electron beam heating technique in detail, addressissues and limitations associated with the technique, and show

Received: November 8, 2013Revised: December 20, 2013Published: January 1, 2014

Letter

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that with the improvements made we are able to spatiallyresolve the thermal resistance of a heterostructured nanowire,including the ITR of each vertical interface embedded in thenanowire. Two nanoscale material systems of technologicalimportance are studied. First, we use a silicon−germanium(Si0.7Ge0.3) nanowire embedded with nickel germanosilicidesegments to show how the thermal conductance of bothSi0.7Ge0.3 and germanosilicide segments are measured and howthis technique circumvents the issue of thermal contactresistance inherent in the thermal bridge approach. Second,we demonstrate how the ITR across each silicon/nickel−silicide interface can be directly measured in epitaxial Si/NiSi2heterostructured nanowires. This nanowire material systempresents nearly abrupt interfaces at the atomic scale andrepresents a semiconductor−metal contact system that iswidely used in modern CMOS electronic devices. Making useof the sharp heterointerface, we show that the spatial resolutionof our technique can reach better than 20 nm. The techniqueallows us to probe the ITR of multiple interfaces along thenanowire. Measurements on adjacent interfaces at progressivelysmaller separations down to ∼50 atomic layers show the sameresults as those with larger separations.The technique is described in the following few paragraphs.

In a configuration that is similar to that used for thermal bridgemeasurements, the nanowire to be measured is suspendedbetween two silicon nitride platforms with integral platinum(Pt) resistance loops. These islands are part of a micro-electrothermal system (METS) device fabricated using standardsilicon MEMS processes and are each suspended from thesilicon substrate (thermal reservoir) via six long suspensionbeams for thermal isolation.7,13 However, unlike the thermalbridge setup, where one island is heated and the other acts as atemperature sensor, in the present arrangement the Pt loops onboth islands are configured as thermometers to sense thetemperature of the left and right islands. Figure 1a shows aschematic of the setup where a nanowire, with a segment ofdifferent material in the middle, is anchored at its ends to thetwo islands. A focused electron beam is positioned along thenanowire and acts as a localized heat source wherein part of theenergy of the electron beam is absorbed by the nanowirethrough electron beam−material interactions. This raises thelocal temperature above that of the substrate and causes heat toflow through both sides of the nanowire to their respectiveislands and finally through the suspension beams to the thermalreservoir. In a typical measurement, the electron beam isscanned along the length of the nanowire, as the temperaturesof the left and right islands are measured, corresponding to theheat flux flowing out through the ends of the nanowire.Assuming that the nanowire is long and thin, and the heatingvolume is uniform over the cross-section of the nanowire, theheat flow is essentially one-dimensional in nature.Figure 1b shows the equivalent thermal resistance circuit. RCL

and RCR represent the contact thermal resistance between thenanowire ends and the left and right islands, respectively. In theabsence of electron beam irradiation, there is no other heatsource, and the entire system is at thermal equilibrium with thesubstrate, which is assumed to be an infinite heatsink atconstant temperature T0. The electron beam is positioned atdistance x along the nanowire from the left island and raises thelocal temperature by ΔTi(x). ΔTL and ΔTR are the measuredtemperature rises of the left and right islands, respectively.Consider the heat flux from the heating spot to the left islandat a steady state, the heat flux from the heating spot to the left

island has to be equal to the heat flux from the island to thesubstrate through the six beams, hence:

Δ − Δ=

ΔT x TR x

TR

( )( )

i L

i

L

b (1)

where Ri(x) is the cumulative thermal resistance from the leftisland to the heating spot, and Rb is the equivalent thermalresistance of the six suspension beams connecting the left (orthe right) island to the environment; Rb is measured by thethermal bridge method.7,13

Likewise, if we consider the heat flux from the heating spot tothe right island, we have:

Δ − Δ−

=ΔT x T

R R xT

R( )

( )i R

T i

R

b (2)

RT, the total resistance of the nanowire plus the two contacts(RCL and RCR), is measured by the traditional thermal bridgemethod, that is, by electrically heating the left island to raise itstemperature by ΔTL0, and measuring the temperature rise of

Figure 1. Experimental setup for electron beam heating technique. (a)Schematic of the microelectro-thermal system device, showing the leftand right platinum resistance sensor islands. A focused electron beam(purple cone) is used as a heat source. (b) Equivalent thermalresistance circuit, showing Ri, the cumulative thermal resistance fromthe left island to the heating spot, and the temperature rise of left andright sensors (ΔTL and ΔTR). (c) Electrical circuit showing the offsetcompensation arrangement, where the nominal resistance of the Ptloop is compensated by the variable resistors (Rf), so as to increase thesensitivity of the thermometry.

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the right island ΔTR0. From eqs 1 and 2, Ri(x) can be writtenas:

α αα

=−−

⎧⎨⎩⎫⎬⎭R x R

xx

( )( )

1 ( )i b0 i

i (3)

where αi = ΔTL/ΔTR and α0 = ΔTL0/ΔTR0.Underlying eqs 1 and 2 is the assumption that the thermal

transport along the nanowire obeys Fourier’s law. The thermalresistance of the entire nanowire can then be considered as thatof the left and right nanowire segments in series and is constantirrespective of the heat source position. Since Ri is a function ofposition x, by scanning the electron beam along the nanowirefrom the left to the right island and recording thecorresponding temperature rises ΔTL and ΔTR, we obtain aspatially resolved thermal resistance profile of the nanowire.The spatial resolution is limited by the heating volume within

the nanowire, rather than by the electron beam spot size.Although the latter can be as small as 1 nm, the extent of theheating volume is typically much larger, with the lower boundset by the electron beam−specimen interaction volume. Thelatter is primarily determined by the energy of the electronbeam, the diameter of the nanowire, and the local atomiccomposition. In general, thin wires and low atomic numbercomposition favor a small interaction volume. However, for agiven sample, the parameter to consider is the electron beamenergy. In the case of a nanowire, the electron beam is mainlytransmitted, and hence the forward-scattering profile definesthe shape of the electron beam−specimen interaction volume.Here, a higher energy beam is desirable to reduce the extent offorward scattering within the nanowire, but the trade-off is thatless of the incident electron energy is absorbed at very highbeam energies. The choice of beam energy is then a balancebetween energy absorption, which depends on the nanowirediameter and its composition, and the spatial resolution.Additionally, in the case of a semiconductor, the electron beamcreates electron−hole pairs (EHPs) which diffuse along the

nanowire and recombine, with part of the energy being releasedas heat. In a nanowire, surface recombination is likely todominate and the carrier diffusion length would then be muchsmaller compared to that of the bulk material.16 Nevertheless,this phenomenon will enlarge the heating volume. Indeed, it isdifficult to define the spatial resolution, which depends on howlong a distance it takes before thermal equilibrium conditionsare established in the material after it is locally perturbed by thehigh energy electron beam. Besides the EHP diffusion, therelaxation rate of hot carriers (which depends on the electron−phonon coupling strength) should also be considered. Hencethe spatial resolution of this technique depends on the materialproperties, with a lower bound set by the electron-beamspecimen interaction volume.We carried out the experiment in a scanning electron

microscope (SEM) chamber at high vacuum where heat lossthrough convection may be neglected. The focused electronbeam is rapidly and repetitively scanned across the diameter ofthe nanowire, effectively creating a line heating source that isperpendicular to the wire axis. This heating source is thenmoved from the left to the right along the nanowire at rate witha corresponding time constant that is much longer than thethermal time constant of the METS device (<10 ms) such thatthe thermal system is at steady state at every data collectionpoint. Doubling of the scanning time gave rise to no observabledifferences within the bounds of noise. A Faraday cup beneaththe device prevents backscattered and secondary electrons fromstriking the SiNx islands, which would otherwise induce bothunwanted heating and parallel conduction paths among the Ptloops as a result of electron-beam induced conductivity. Thesensitivity of the resistance thermometry measurement set up isenhanced by adopting a differential circuit configuration tooffset the nominal resistance of the Pt loop, as shown in Figure1c, which allows us to use a more sensitive range of the lock-inamplifier. In conjunction with other techniques (see Supporting

Figure 2. Spatially resolved measurement of thermal resistance. (a) TEM image of a Si0.7Ge0.3/NiSi0.7Ge0.3 interface. Scale bar: 50 nm. (b) High-resolution transmission electron microscope (HRTEM) image of the Si0.7Ge0.3/NiSi0.7Ge0.3 interface. The dark portion is NiSi0.7Ge0.3, and the brightportion is Si0.7Ge0.3. Scale bar: 5 nm. (c) SEM image of a heterostructured nanowire. Scale bar: 500 nm. (d) Upper: Temperature rise of left and rightsensors (ΔTL and ΔTR) as a function of heating spot position (x). Lower: Cumulative thermal resistance (Ri) as function of distance from the leftsensor. Thermal resistivity 1/κ = (dRi/dx)A, where A is the cross sectional area of the nanowire. κ(Si0.7Ge0.3) = 1.9 ± 0.3 W/m·K and κ(NiSi0.7Ge0.3)= 13.4 ± 1.3 W/m·K.

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Information S1), we achieved a measurement sensitivity ofbetter than 0.4 mK, which is necessary for this technique.To highlight pertinent features of the spatially resolved

thermal conductivity measurement, we carried out a measure-ment on heterostructured Si0.7Ge0.3/NiSi0.7Ge0.3 nanowires.The two material systems stand in contrast in terms of theirelectron energy absorption and thermal conductivity, the nickelgermanosilicide being larger in both aspects compared to thesilicon−germanium.Such nanowires were synthesized by first depositing a thin

nickel film on Si0.7Ge0.3 nanowires.17 Upon annealing, thenickel film agglomerates and reacts with the underlyingSi0.7Ge0.3 nanowire to form NiSi0.7Ge0.3 segments. Thesesegments alternate with Si0.7Ge0.3 segments with a typicalpitch of 0.3−0.4 μm, as shown in Figure 2c. Figure 2b shows alattice resolved transmission electron microscope (TEM)image: the bright portion is Si0.7Ge0.3, and the dark portion isNiSi0.7Ge0.3, interpreted from the lattice spacings (seeSupporting Information S2.1). The interface is not exactlyperpendicular to the heat flow direction, as seen from Figure 2c,and it also undulates over a range of ∼15 nm (Figure 2a). Onesuch nanowire was picked up by a nanomanipulator and fixedon the METS device by electron-beam-induced deposition ofPt (the configuration is illustrated in the SupportingInformation S2.1). An 18 keV electron beam was scannedalong the nanowire from left to right.The upper part of Figure 2d shows the measured

temperature rise of the left and right islands (ΔTL and ΔTR).Since the power has to flow through both islands, the absorbedpower is P(x) = (ΔTL + ΔTR)/Rb. ΔTL and ΔTR are higherwhen the electron beam scans along a NiSi0.7Ge0.3 segmentbecause compared to Si0.7Ge0.3 the denser NiSi0.7Ge0.3 absorbsmore power from the electron beam.The red line in Figure 2d is the cumulative thermal resistance

Ri, calculated from eq 3. Note that in spite of the irregular ΔTL

and ΔTR curves arising from variable heat absorption, Riincreases monotonically from left to right, since Ri is derivedfrom the ratio of the power flows toward the left and the right,(ΔTL/ΔTR), irrespective of the absorbed power. The linearincrease in Ri within the same material segment is expected asthe segment is uniform both in terms of its structure andthermal conductivity. If we compare the two materials, Riincreases at a lower rate in NiSi0.7Ge0.3 segments (of brighterappearance in the SEM image) compared to the Si0.7Ge0.3segments. The thermal conductivity of Si0.7Ge0.3 andNiSi0.7Ge0.3 is calculated from the slope of Ri(x) of therespective material segments, from which

κ =·R x A

1(d /d )i

where A = πd2/4, d representing the diameter of the nanowire.From the measured data we obtain κ(Si0.7Ge0.3) = 1.9 W/m·K,which is comparable to values reported in the literature18 andκ(NiSi0.7Ge0.3) = 13.4 W/m·K, which is much higher than thatof the Si0.7Ge0.3 portion. Apart from being able to resolveheterogeneous nanowires, since κ is calculated from dRi/dx, thisapproach to measuring nanowire thermal conductivity avoidsthe uncertainty due to unknown thermal contact resistance(RCL and RCR) in a conventional thermal bridge measurement.As the Si0.7Ge0.3/NiSi0.7Ge0.3 interface is neither straight nor

perfectly perpendicular to the 1D heat flow direction along thenanowire, the interfacial thermal resistance (ITR) could not beextracted unambiguously. In comparison, Si/NiSi2 heterostruc-tured nanowires provide nearly abrupt epitaxial interfaces,which allows us to evaluate the spatial resolution of thetechnique as well as study the ITR.These nanowires were prepared by placing silicon nanowires

in partial contact with nickel islands on a substrate. Upon hightemperature annealing at 730 °C, Ni diffuses through the

Figure 3. NiSi2 fillet embedded in Si nanowire. (a) TEM image showing the Si/NiSi2 interface is perpendicular to the Si nanowire axis. Dark portion:NiSi2; bright portion: Si. Scale bar: 20 nm. Upper right inset: selected area electron diffraction (SAED) pattern of the Si portion. Lower left inset:SAED pattern with the electron spot enclosing the NiSi2 fillet. Both Si and NiSi2 SAED patterns can be seen here, and the pattern for NiSi2 ishighlighted by the yellow line. The growth direction of NiSi2 is [111], which is the same as that for Si. The zone axis for both Si and NiSi2 is [11 ̅0].(b) HRTEM image of the Si/NiSi2 interface, showing that it is nearly abrupt but with minor lattice disorder. Scale bar: 5 nm.

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nanowire, and at locations where there is a change in thesurface energy (e.g., where there is a nanoparticle attached onthe surface), NiSi2 starts to nucleate and grow, forming a single-crystal fillet within the Si nanowire. The NiSi2 fillet isperpendicular to the Si nanowire growth direction, as shownby Figure 3a. The selected area electron diffraction (SAED)pattern in the inset of Figure 3a shows that the fillet grows inthe [111] direction, which is the same as that of the Sinanowire. In the particular case shown, the zone axis for Si andNiSi2 are both in the [1 1 ̅ 0] direction. The detail of the Si/NiSi2 interface is shown in the lattice-resolved TEM image(Figure 3b). The interface is perpendicular to the nanowiregrowth direction, and nearly abrupt but with minor latticedisorders, for example, dislocations, lattice misfits, within a spanof ∼5 nm at the interface (more details provided in theSupporting Information S2.2).Such nanowire samples were fixed onto the METS device

using the same procedure as that for the previous Si0.7Ge0.3/NiSi0.7Ge0.3 heterostructured nanowire. A 29 keV electronbeam was used to scan along the nanowire (Figure 4). Figure

4c shows the profile of the power absorbed by the nanowirefrom the electron beam in the vicinity of an interface. SinceNiSi2 is denser and better in stopping the electron beam thanSi, a larger fraction of the incident beam power is absorbed inthe NiSi2 portion. As a result, the absorbed power P increasesrapidly as the electron beam traverses the interface. Based onthe full-width-at-half-maximum (fwhm) of the differential

absorbed power (dP/dx), the spatial extent of the energyabsorption volume is determined to be ∼11.7 nm, with theportion in silicon (∼4.5 nm) being smaller than that in NiSi2(∼7.2 nm). This is in agreement with the Monte Carlosimulation results of absorbed energy volume in Si and NiSi2(insets of Figure 4c).Ri was calculated using eq 3 and is plotted as a red solid line

in Figure 5a. The through-hole in our METS device allows usto carry out TEM imaging of the same sample, so that we canobtain the sample dimensions with nanometer precision, asshown superimposed in the background of Figure 5. Weobtained dRi/dx by carrying out a linear fitting of Ri for Si andNiSi2 portions individually and extracted the nanowire diameterfrom the corresponding TEM image, from which the thermalconductivity of both portions is calculated as κ(Si) = 53 W/m·K and κ(NiSi2) = 33 W/m·K, respectively, for the sampleshown in Figure 4a. Measurements on different samples yieldedvery similar thermal conductivities because the nanowires are ofnearly the same diameter (150 nm) and are all grown in the[111] direction. The electron contribution to the thermalconductivity of metallic NiSi2 phase at room temperature (300K) is calculated by Wiedemann−Franz law: κe = σLT, where Lis the Lorenz number (2.44 × 10−8 W·Ω·K2), and σ is theelectrical conductivity of NiSi2. The electrical resistivity hasbeen reported as ∼35 × 10−8 Ω·m for polycrystalline NiSi2films19−21 and ∼30 × 10−8 Ω·m for NiSi2 nanowiressynthesized by chemical vapor deposition,22 the latter beinglower because the NiSi2 nanowire is single crystalline anddefect-free. From this, κe is ∼21−24.4 W/m·K, and the rest(∼10 W/m·K) could be attributed to the lattice contribution.There is a step change in Ri at the Si/NiSi2 interface, which

represents intuitively the ITR. As the electron beam traversesthe interface between two materials with different energyabsorption properties, dP(x)/dx peaks (Figure 4c). Theposition of the material interface is close to but not exactly atthis peak, but the offset is small, typically less than 1 nm, asshown in the Monte Carlo simulation in SupportingInformation S3. We observe that the span where Ri increasesrapidly is mainly on the Si side. The reason for this could bedue to the EHPs generated in the Si portion, which diffuse andrecombine, especially at the interface, thereby altering the shapeof heating volume. This is further discussed in SupportingInformation S4. On the other hand, in the metallic NiSi2portion, the Ri profile is seen to correspond to the energyabsorption profile shown in Figure 4, with the transition in P(x)taking place over a distance of <20 nm, showing the inherentspatial resolution of the technique.To determine the ITR, we carried out a linear fitting of Ri in

both Si and NiSi2 portions using data sufficiently far away fromthe interface (see Supporting Information S4) and extrapolatedthe two fitted lines to intersect with the interface. Thedifference between the values at the two intersects is taken asthe ITR (denoted as RINT). The interfacial thermal conductance(denoted as hINT) is then calculated as hINT = 1/(RINTA), whichis a geometrically independent parameter. hINT was determinedfor several interfaces and plotted in Figure 6, as data pointsinside the red dotted circle. The average value is higher thanthat of the metal−semiconductor interface measured byHopkins and Duda et al.23,24 employing the time-domainthermoreflectance (TDTR) technique, for a number of reasons.First, compared to metals, a metal silicide has a better acousticmatch with Si. Second, the interface for their TDTRmeasurement was formed by thermal evaporating metal on a

Figure 4. Energy absorption at the interface between Si and NiSi2. (a)SEM image of a Si/NiSi2 heterostructured nanowire bridging the leftand right sensor islands. Dark portion: NiSi2; bright portion: Si. Thegap between left and right islands is 5 μm. (b) Enlarged SEM imageshowing the embedded NiSi2. Scale bar: 100 nm. (c) The absorbedpower P(x) measured as the electron beam is scanned across theinterface in the region enclosed by the orange dashed rectangle in b.The actual interface is close to the peak of dP(x)/dx. Full-width-at-half-maximum (fwhm) of dP(x)/dx. Monte Carlo simulation ofabsorbed energy volume in both Si (left inset) and NiSi2 (right inset).

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silicon surface, whereas in our material system, the bondingbetween Si and NiSi2 is covalent in nature. Better acousticmatch and stronger bonds result in higher interfacial thermalconductance.To understand the underlying physics, we numerically

calculate the interfacial thermal conductance (hINT) from thediffuse mismatch model (DMM)25 (more details of calculationcan be found in Supporting Information S5) which gives rise tothe value of hINT of 325 MW/m2·K. Our experimental value(∼500 MW/m2·K) is larger than the value from DMM. Thediscrepancy may be qualitatively explained by considering thefollowing. On the one hand, in our DMM calculations, theDOS of the bulk material is used instead of the DOS ofnanowire as this is not available. This may give rise to error in

the DMM calculations. On the other hand, the largerexperimental conductance values might be caused by the so-called phonon bridging effect induced by a diffused interface.Recently, Zhou et al.26 have studied the effect of interfacestructure on the interfacial thermal conductance. They foundthat when the interface is changed from a very sharp one to adiffused one (in which the atoms of two materials inter-penetrate around the interface), the temperature drop at theinterface is reduced when the same heat flux is applied, whichleads to the enhancement of interfacial thermal conductance inthe diffused case as we observed in our experiment. Indeed, ifwe examine Figure 3b, we can see this kind of diffused interface.The ∼5 nm layer with disorder and dislocations at the interfaceserves as a buffer layer that bridges phonon transmission fromSi to NiSi2. The overlapping density of states (DOS) betweenthe buffer layer/Si and buffer layer/NiSi2 is larger than thatbetween Si and NiSi2 without an intervening layer, therebyproviding more elastic scattering channels for phonons totransport across the interface. This phonon bridging effect hasbeen fully investigated via nonequilibrium molecular dynam-ics.27,28 However, more detailed numerical calculations andexperimental work need to be done to get a quantitativecomparison.As the electron beam heating technique makes it possible to

directly measure the thermal resistance of individual interfaces,this opens up the possibility of investigating what happenswhen two interfaces are very close to each other, at separationsthat are comparable to the phonon mean free path. Weconducted a series of experiments with progressively thinnerNiSi2 fillets, which brings the two Si/NiSi2 interfaces into closeproximity to each other, as shown in Figure 5. The thinnestfillet we could find is 16 nm (inset of Figure 5c). This thicknessis comparable to the electron beam−specimen interactionvolume, so the two steps in Ri arising from the two interfacescould not be individually resolved, making it impossible tocalculate the RINT of each interface. To manage this, we carriedout linear fits to Ri of the two Si portions away from thejunction, as before. The two fitted lines are parallel to eachother but separated by the jump in Ri across the NiSi2 fillet(denoted as Rstep). Rstep comprises the resistance of the NiSi2(denoted as Rfillet), and 2RINT represents the two Si/NiSi2interfaces. The ITR of a single interface is then:

Figure 5. Measurement of interfacial thermal resistance across Si/NiSi2 interfaces. (a) Ri(x) as the electron beam is scanned across the NiSi2 fillet.RINT is calculated by linear fitting the Ri(x) curve for both Si and NiSi2 portions, extrapolating it across the interface and taking the step. TEM imageof the measured sample is superimposed. The dark portion is NiSi2, and the bright portion is Si. One embedded NiSi2 fillet creates two Si/NiSi2interfaces. (b) Similar measurement for thinner fillet with closer interfaces. (c) A very thin NiSi2 fillet creating two interfaces separated by 16 nm(equivalent to ∼50 NiSi2 (111) atomic layers). This distance is comparable to the extent of the energy absorption volume in NiSi2, so the two RINTmerge.

Figure 6. Interfacial thermal conductance:hINT = 1/(RINTA). Eachblack square marker is the measured interfacial thermal conductancefor one Si/NiSi2 interface. Samples 1−4 are from the samples shown inFigure 5a and b, while samples 5−8 are from other nanowires (whichare not shown in this paper). The error bars are calculated from errorpropagation. The last black square marker is calculated as 1/(RstepA),where Rstep is calculated by linear fitting the Ri(x) curve for the two Siportions in Figure 5c, extrapolating it across the center of the NiSi2fillet and taking the step. The red diamond is the inferred hBd, in whichRINT = (Rstep − Rfillet)/2, where Rfillet is the thermal resistance of the 16nm NiSi2 fillet.

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=−

RR R

2INTstep fillet

where Rfillet = L/κ(NiSi2)A, L = 16 nm, and A is the cross-sectional area. We assume κ(NiSi2) =30 W/m·K, based on themeasured values for the samples shown in Figure 5a and b.However, the exact value of κ (NiSi2) has a marginal effect onthe value of RINT obtained because of the small L. hINT iscalculated in the same way as for previous samples, and its valueis indicated by the red diamond in Figure 6. From this figure wecan see that the hINT of an interface separated by 16 nmdistance (which is equivalent to ∼50 NiSi2 (111) atomic layers)from another is the same as that of an isolated interface.In this paper, we reported a new thermal measurement

technique that is capable of profiling the thermal resistance ofan individual nanowire with a spatial resolution better than 20nm. In this technique, a focused electron beam is employed as alocalized heat source to establish a temperature gradient alongthe nanowire. The heat fluxes from the two ends of thenanowire are measured using platinum resistor loops on twosuspended thermally isolated islands. With improvements tothe electrical measurement setup, a sensitivity of 0.4 mK,limited by quantization noise of lock-in amplifier could beachieved.This electron beam heating technique was demonstrated on

two material systems: Si0.7Ge0.3/NiSi0.7Ge0.3 and Si/NiSi2heterostructured nanowires. We show that, by scanning theelectron beam along a heterostructured nanowire, we are ableto measure the local thermal conductivities that varied with thematerial composition of the nanowire. Moreover, with the highspatial resolution and high sensitivity, we are also able tomeasure the interfacial thermal resistance (ITR) of a single Si/NiSi2 interface. Last but not least, we measured the ITR of twoadjacent Si/NiSi2 interfaces with separations as small as 16 nm.We found that the ITR does not change even when there areonly ∼50 atomic NiSi2 layers in between two interfaces.In summary, the electron beam heating technique is able to

spatially resolve the thermal conductivity of an individualnanowire and also addresses the long-standing problem of ill-defined thermal contact resistance between the nanowire andthe two islands, which is a serious drawback in the conventionalthermal bridge method. Moreover, its capability of directly andseparately measuring the ITR of multiple interfaces renders it apowerful tool to study how heat flows across interfaces at thenanometer scale. This technique is also extendable to lowtemperature measurement and probing how heat flows incomplex networks.

■ ASSOCIATED CONTENT

*S Supporting InformationImprovement on measurement sensitivity, sample preparationand characterization, Monte Carlo simulation showing theposition of interface, obtaining the ITR, and numericalcalculation of ITR between Si/NiSi2 interface. This materialis available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Author ContributionsD.L. and R.X. contributed equally to this work.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank Yee-Kan Koh, Xiangfan Xu and Sha Liu for helpfuldiscussions and Hao Gong and Chunhua Tang for assistance incharacterization of the nanowires. This work is funded by grantMOE2011-T2-1-052 from the Ministry of Education, Singa-pore, and grants R-144-000-284-646and R-263-000-626-646from NUS. N.Y. and B.L. are also supported from NSF Chinathrough Grant 11334007.

■ REFERENCES(1) Cahill, D. G.; Ford, W. K.; Goodson, K. E.; Mahan, G. D.;Majumdar, A.; Maris, H. J.; Merlin, R.; Phillpot, S. R. J. Appl. Phys.2003, 93, 793.(2) Li, D.; Wu, Y.; Kim, P.; Shi, L.; Yang, P.; Majumdar, A. Appl. Phys.Lett. 2003, 83, 2934.(3) Shi, L.; Hao, Q.; Yu, C.; Mingo, N.; Kong, X.; Wang, Z. L. Appl.Phys. Lett. 2004, 84, 2638.(4) Hochbaum, A. I.; Chen, R.; Delgado, R. D.; Liang, W.; Garnett, E.C.; Najarian, M.; Majumdar, A.; Yang, P. Nature 2008, 451, 163−7.(5) Chen, R.; Hochbaum, A. I.; Murphy, P.; Moore, J.; Yang, P.;Majumdar, A. Phys. Rev. Lett. 2008, 101, 10.(6) Lim, J.; Hippalgaonkar, K.; Andrews, S. C.; Majumdar, A.; Yang,P. Nano Lett. 2012, 12, 2475−82.(7) Bui, C. T.; Xie, R.; Zheng, M.; Zhang, Q.; Sow, C. H.; Li, B.;Thong, J. T. Small 2012, 8, 738−45.(8) Ghossoub, M. G.; Valavala, K. V.; Seong, M.; Azeredo, B.; Hsu,K.; Sadhu, J. S.; Singh, P. K.; Sinha, S. Nano Lett. 2013, 13, 1564−71.(9) Chen, J.; Zhang, G.; Li, B. J. Chem. Phys. 2011, 135, 104508.(10) Wingert, M. C.; Chen, Z. C.; Dechaumphai, E.; Moon, J.; Kim,J.-H.; Xiang, J.; Chen, R. Nano Lett. 2011, 11, 5507−5513.(11) Hu, M.; Poulikakos, D. Nano Lett. 2012, 12, 5487−94.(12) Chen, J.; Zhang, G.; Li, B. Nano Lett. 2012, 12, 2826−32.(13) Wang, Z.; Xie, R.; Bui, C. T.; Liu, D.; Ni, X.; Li, B.; Thong, J. T.Nano Lett. 2010, 11, 113−118.(14) Yang, J.; Yang, Y.; Waltermire, S. W.; Gutu, T.; Zinn, A. A.; Xu,T. T.; Chen, Y.; Li, D. Small 2011, 7, 2334−40.(15) Mavrokefalos, A.; Pettes, M. T.; Zhou, F.; Shi, L. Rev. Sci.Instrum. 2007, 78, 034901.(16) Allen, J. E.; Hemesath, E. R.; Perea, D. E.; Lensch-Falk, J. L.; Li,Z. Y.; Yin, F.; Gass, M. H.; Wang, P.; Bleloch, A. L.; Palmer, R. E.;Lauhon, L. J. Nat. Nanotechnol. 2008, 3, 168−73.(17) Whang, S.; Lee, S.; Yang, W.; Cho, B.; Kwong, D. Appl. Phys.Lett. 2007, 91, 072105.(18) Lee, E. K.; Yin, L.; Lee, Y.; Lee, J. W.; Lee, S. J.; Lee, J.; Cha, S.N.; Whang, D.; Hwang, G. S.; Hippalgaonkar, K.; Majumdar, A.; Yu,C.; Choi, B. L.; Kim, J. M.; Kim, K. Nano Lett. 2012, 12, 2918−23.(19) Hensel, J. C.; Tung, R. T.; Poate, J. M.; Unterwald, F. C. Appl.Phys. Lett. 1984, 44, 913.(20) Chen, L. J.; Tu, K. N. Mater. Sci. Rep. 1991, 6, 53−140.(21) Gambino, J. P.; Colgan, E. G. Mater. Chem. Phys. 1998, 52, 99−146.(22) Lee, C.-Y.; Lu, M.-P.; Liao, K.-F.; Lee, W.-F.; Huang, C.-T.;Chen, S.-Y.; Chen, L.-J. J. Phys. Chem. C 2009, 113, 2286−2289.(23) Hopkins, P. E.; Duda, J. C.; Petz, C. W.; Floro, J. A. Phys. Rev. B2011, 84, 035438.(24) Duda, J. C.; Hopkins, P. E. Appl. Phys. Lett. 2012, 100, 111602.(25) Swartz, E.; Pohl, R. Rev. Mod. Phys. 1989, 61, 605−668.(26) Zhou, X. W.; Jones, R. E.; Kimmer, C. J.; Duda, J. C.; Hopkins,P. E. Phys. Rev. B 2013, 87, 094303.(27) Liang, Z.; Tsai, H. L. J. Phys.: Condens. Matter 2011, 23, 495303.(28) English, T. S.; Duda, J. C.; Smoyer, J. L.; Jordan, D. A.; Norris,P. M.; Zhigilei, L. V. Phys. Rev. B 2012, 85, 035438.

Nano Letters Letter

dx.doi.org/10.1021/nl4041516 | Nano Lett. 2014, 14, 806−812812