Remote Joule heating by a carbon nanotubeKamal H. Baloch1, Norvik Voskanian1, Merijntje Bronsgeest2 and John Cumings1*

Minimizing Joule heating remains an important goal in thedesign of electronic devices1,2. The prevailing model of Jouleheating relies on a simple semiclassical picture in which elec-trons collide with the atoms of a conductor, generating heatlocally and only in regions of non-zero current density, andthis model has been supported by most experiments.Recently, however, it has been predicted that electric currentsin graphene and carbon nanotubes can couple to the vibrationalmodes of a neighbouring material3,4, heating it remotely5. Here,we use in situ electron thermal microscopy to detect the remoteJoule heating of a silicon nitride substrate by a single multi-walled carbon nanotube. At least 84% of the electrical powersupplied to the nanotube is dissipated directly into the sub-strate, rather than in the nanotube itself. Although it has differ-ent physical origins, this phenomenon is reminiscent ofinduction heating or microwave dielectric heating. Such anability to dissipate waste energy remotely could lead toimproved thermal management in electronic devices6.

Thermal management in modern digital electronics is typicallyaddressed by engineering transistors and interconnects to minimizeelectrical resistance and also by incorporating high thermal conduc-tivity heat spreaders to transport heat effectively to a heat sink.However, there is increasing interest in making use of newcarbon-based materials such as graphene and carbon nanotubes,which have superlatively high thermal conductivities, for thermalmanagement7–10. In addition to being extraordinary thermal con-ductors, these materials have been shown to sustain enormous elec-trical current densities11–13; together, these features suggest that theymay have potential in applications as interconnects in microelec-tronic circuitry. However, many studies have suggested that thethermal performance of these materials is limited by their largeinterfacial thermal resistance with other materials14–17. Recently, ithas been shown that it is possible to tune this thermal contact resist-ance by manipulating the area of contact between the neighbouringmaterials16,17. In the following, we present further results showing agreatly enhanced thermal transport between the nanotube and thesubstrate that occurs only while the nanotube is carrying an electri-cal current. We conclude that this thermal transport is occurring bythe direct transfer of energy from the charge carriers in the nano-tube to the vibrational modes of the substrate, thus demonstratingremote Joule heating as the dominating mode of heat dissipationin such systems.

The results were obtained using electron thermal microscopy(EThM)18, a novel thermal imaging method that overcomes thespatial resolution limits of thermal microscopy based on infraredimaging techniques. The approach relies on the solid–liquid phasetransition of nanometre-scale metallic indium islands thermallyevaporated onto the back side of an electron-transparent siliconnitride (SiN) substrate. In EThM, transmission electron microscope(TEM) imaging in dark-field mode shows this phase transition asa change in contrast of the islands. When the indium islandsreversibly melt and freeze, there is no overall change in their

shape or morphology, but the different diffraction propertiesproduce a bright/dark contrast for the liquid/solid phases, respect-ively. This process yields a binary map, showing the temperature ofthe substrate at the location of each island as either above or belowthe melting point, 156.6 8C. By operating a current-carryingnanotube at different voltage biases, several binary maps can bebuilt into a thermal map, revealing the heat sources and temperaturedistributions at the nanoscale.

The results for a simple geometry involving a multiwalled carbonnanotube with two electrical contacts are presented in Fig. 1. TEMmicrographs showing the device before and after indium depositionare shown in Fig. 1a,b. A finite-element model of this device usingtraditional Joule heating was used to calculate the melting profile ofindium as the voltage bias across the carbon nanotube wasincreased. As the nanotube resting on the substrate is embeddedunderneath metallic palladium contacts, the increased area ofoverlap between the nanotube and the metal compared with thatbetween nanotube and substrate results in a lower thermal contact

b

c

d

aA

1.6 V

1.6 V1.1 V

1.1 V

Figure 1 | Thermal imaging of a multiwalled carbon nanotube under bias.

a, TEM micrograph of the nanotube device with circuit overlay before indium

deposition. Scale bar, 1 mm. b, TEM micrograph of the same device after

indium deposition. The indium islands appear as dark islands on a bright

background. When the TEM is operated in dark-field mode, the change in

phase of the indium manifests itself as a change in contrast of these islands.

c, Experimental voltage map obtained by assigning colour to the voltage at

which each indium island melts. An outline of the nanotube and the

palladium electrodes is overlaid on this map. d, Simulations on the same

device geometry using finite-element analysis. This shows that, owing to

reduced thermal contact resistance, the melting of indium at the contacts is

expected to occur at lower applied voltages, which does not agree with the

experimental results in c.

1Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20740, USA, 2Department of Physics, University ofMaryland, College Park, Maryland 20740, USA. *e-mail: cumings@umd.edu

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resistance16,17,19. Using the thermal contact resistances between pal-ladium and the nanotube (PdRc, 4.2 m.K W21) and between SiNand the nanotube (SiNRc, 250 m.K W21) (both measured earlierand reported elsewhere16), we obtained a simulated finite-elementthermal map, as shown in Fig. 1d. Because SiNRc is about twoorders of magnitude larger than PdRc, this simulated thermal mapshows the SiN substrate under the contacts to be hotter and thusthe melting of indium probes in these regions is expected to occurat lower voltages. However, this is inconsistent with the results ofour experimental observations, as shown in Fig. 1c. This suggestsfundamental inadequacies in the semiclassical Joule heating modelused in our simulations. The experimentally obtained thermalmap shows clearly that the SiN substrate under the middlesegment of the nanotube and between the metallic contacts heatsfirst, contrary to the predictions of the simulations. Clearly, thereis more effective thermal transport from the nanotube to the sub-strate between the contacts than is suggested by the high contactresistance of 250 m.K W21. As this value was determined duringprevious low-temperature transport studies, it is possible that thenanotube reaches a higher temperature in the present experiment,manifesting a low thermal contact resistance.

To test this hypothesis, we carried out a second experiment toprobe more directly the temperature of the nanotube when itcarries an electrical current. Here, we take advantage of the factthat arc-discharge multiwalled nanotubes have high crystallinity(Supplementary Section S1) and have been shown to exhibitexceptionally high thermal conductivities in several studies (inexcess of 1,000 W m21 K21; refs 9,10). From this and the highthermal contact resistances that are known to occur in these geo-metries16, it is reasonable to expect the relatively low power dissi-pation being used here to produce only small temperaturedifferences along the length of the nanotube. Thus, a device thatincorporates two electrical contacts along one end of a nanotubewould reasonably be expected to heat up the nanotube along itsentire length, with the ability to conduct heat into a third isolatedmetal contact at a different location along the nanotube. A TEMimage of a nanotube contacted in this manner is shown inFig. 2a. A finite-element model including traditional Jouleheating confirmed these assumptions and is presented in Fig. 2c.From the model, we expect the indium thermal probes underthe third metal contact to melt at lower voltages than those nearthe current-carrying segment of the nanotube due to the effectivetransport of heat along the nanotube and poor heat sinking nearthe isolated contact.

Figure 2b presents the results of experiments performed on adevice with this geometry, and once again we observe that there issubstantial disagreement with a simple Joule heating model. Here,we observe that the melting occurs first under the current-carryingsegment of the nanotube, and that the isolated contact plays nonoticeable role in determining the thermal distribution. Thisallows us to conclude that the nanotube is not behaving as a conven-tional resistive heater in this experiment. It appears as though theelectrical current flowing through the nanotube is heating up thesubstrate directly beneath. This conclusion, while contradicting anintuitive understanding of traditional Joule heating, is not entirelyunexpected, given contemporary models of electrical transport incarbon nanotubes and other carbon-based nanomaterials.Specifically, theories of the remote scattering of conduction elec-trons in these materials by surface vibrations in a dielectric havebeen used to explain the temperature dependence of electrical trans-port studies of graphene and nanotubes3,4, and this scattering haseven been proposed as a possible essential mechanism of thermaltransport5. Indeed, we present here direct evidence of this phenom-enon as the dominant mechanism of electrical heating.

To obtain agreement between the finite-element analysis and theexperimental results, the Joule heating model needs to be modified.

We achieve this by introducing a new ‘remote-heating’ parameter, b,which is the fraction of the applied power being dissipated directlyinto the substrate underneath the current-carrying segment of thenanotube in our two-dimensional model. Thus, b¼ 0 implies astandard Joule heating model where all the power is dissipated inthe current-carrying nanotube, whereas b¼ 1 implies that all thepower is deposited directly into the substrate beneath. From ourdata, we extracted a 95% confidence interval for the voltageneeded to melt the indium islands underneath the third contact,and from this interval, we find that the smallest value for whichthe simulations match the experiment is b¼ 0.84. The results of afinite-element model incorporating this are shown in Fig. 2d. Thismeans that the substrate under the nanotube gains heat because atleast 84% of total power is dissipated directly in the substrate andno more than 16% is dissipated within the nanotube itself. Such anovel energy-transfer mechanism should not be completely coun-terintuitive, as recent experimental studies have shown a similarnon-thermal current-induced gas desorption from nanotubesamples20. It is worth noting that this value of b¼ 0.84 wasextracted by assuming diffusive, not ballistic, electronic transportin the nanotube, which agrees with previous observations of multi-walled carbon nanotubes21. The current–voltage (I–V) curves ofboth devices described here are provided in SupplementarySection S2. These I–V plots demonstrate that the multiwalled

a

1 µm

b

c

d

460 mV 736 mV

A

Figure 2 | Remote Joule heating by a multiwalled carbon nanotube. a, TEM

micrograph (with circuit overlay) of the device designed and fabricated to

estimate the temperature of the nanotube. Arrowheads point to the position

of the nanotube. b, Experimental thermal map for the device shown in a,

overlaid with a TEM image of the completed device, as in Fig. 1b.

c, Simulations show that indium probes under the palladium at the far end of

the nanotube should melt first, at lower voltages. d, Simulations carried out

with b¼0.84, the smallest value for which the finite-element model

quantitatively matches the experimental data. This shows that a traditional

Joule heating model does not predict the observed results, and that remote

Joule heating occurs between the nanotube and the substrate. (The colour

bar applies to b–d.) As in Fig. 1, each colour represents the applied voltage

at which the indium islands in that region melt.

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nanotubes used are metallic in nature and should exhibit current-induced power dissipation. A dissipationless ballistic transportmodel would be even more difficult to reconcile with our obser-vations, as it would place more power dissipation within the con-tacts, contradicting the experimental observations of Fig. 1c. Bothexperiments described above were repeated for at least threedevices of each kind. The measurements for all devices yieldedsimilar results, supporting the conclusion that the dominantmode of power dissipation is directly into the substrate.

Having developed a model to describe remote Joule heating fromthe results in Fig. 2, we now revisit the experimental results shown inFig. 1. We find that here, too, simulations match the experimentalresults only if we assume that the power is being deposited directlyinto the substrate. A simulation for the case of b¼ 0.84 is shown inFig. 3a, and indeed this matches well with the experimental micro-graph of Fig. 1c. To demonstrate this agreement in a more quanti-tative manner, Fig. 3b presents a plot of the melting voltages of the

indium islands along the length of the nanotube versus their dis-tance from its centre, together with results from finite-element mod-elling with (b¼ 0.84) and without (b¼ 0) remote Joule heating. Itcan be seen in this plot that the experimental data match closely themodelling with b¼ 0.84, providing an effective explanation for thediscrepancy previously discussed for Fig. 1. The agreement of thisremote Joule heating model with the experimental results providessupport for its veracity; however, identifying its physical originswould help to delineate the scope of the applicability of the effect.The effect would seem to be arising from the near-field electromag-netic fields around the nanotube directly exciting thermal modeswithin the substrate, which bears some analogy with inductionheating and microwave dielectric heating22. However, both ofthese phenomena originate from the intentional generation ofcoherent electromagnetic oscillations, whereas the present obser-vations are driven by strictly d.c. currents. More appropriately,these observations can be explained by the near-field remote scatter-ing of hot electrons in carbon nanotubes off surface polaritons of apolar substrate5,23. Surface polaritons are a vibrational mode of thesubstrate that results from the coupling of its surface opticalphonons and its surface electromagnetic polarization. Instead ofscattering off the carbon atoms of the nanotube24, the transport elec-trons couple to the surface polaritons of nearby dielectric materialsand thus transfer their energy directly to the substrate. The spatialrange of such a phenomenon could be as large as tens of nano-metres23, indicating that effective coupling can be significantbetween hot electrons in a typical multiwalled nanotube (�25 nmin diameter) and vibrations in the substrate on which it rests.

The model presented above comprises a clear explanation of ourresults, and we show in the following that an alternative model witha low thermal conductivity for the multiwalled nanotube does notagree with our observations. If we modify the finite-elementmodels by reducing the thermal conductivity of the nanotube, wefind that it is not possible to obtain quantitative agreement withthe experimental results; however, a qualitative agreement can beobtained by using a nanotube thermal conductivity value below�50 W m21 K21. In such a case, the nanotube would no longeract as an effective heat-spreader in our tested geometries, and itwould not have the ability to heat electrical contacts as in Fig. 1,or a third isolated contact as in Fig. 2. In this case, our results canbe in qualitative agreement with a standard Joule heating model.However, such a low thermal conductivity would not be consistentwith many well-accepted observations. Nanotubes with substantialdisorder, such as multiwalled nanotubes synthesized by chemicalvapour deposition, can have low thermal conductivities in therange of 50–300 W m21 K21 (ref. 17). However, multiwalled nano-tubes grown by arc-discharge, as used here, have been reported inmany studies to have exceptionally high thermal conductivities, inexcess of 1,000 W m21 K21 (refs 9,10). In performing in situTEM studies, care needs to be taken that the imaging electronbeam does not damage the sample25; in our case, we can neglectthese effects, as we use low beam currents and blank the beambetween imaging exposures. Under comparable imaging conditions,we find that the highly ordered crystalline nature of our multiwallednanotubes can be confirmed by high-resolution TEM imagesthroughout our studies (as shown in Supplementary Fig. S1), andin situ electrical transport measurements show no measurablereduction in electrical conductivity. Furthermore, our previousresults16 have shown that a multiwalled nanotube measured in asimilar set-up is highly capable of transporting heat to a distantcontact. From the finite-element models used in these previousstudies, we conclude that the nanotubes used in our experimentsmust have a thermal conductivity of at least 500 W m21 K21

(95% confidence), and this lower bound is substantially above the�50 W m21 K21 needed to be even qualitatively consistent withtraditional Joule heating. Also, studies performed by another

1.6 V

β = 0β = 0.84

Data

1.5

1.35

1.2

1.1 V

−0.75 0 0.75Melting distance (µm)

1 µm

b

aV

olta

ge a

pplie

d (V

)

Figure 3 | Quantitative comparison of experiment and simulations.

a, Finite-element simulations corresponding to b¼0.84 for the device

presented in Fig. 1. b, Plot of melting voltage for the indium probes along the

length of the nanotube versus melting distances of these islands from the

centre of the nanotube. Red circles represent average experimental melting

voltage, and solid lines represent finite-element simulations (green for b¼0.84

and blue for b¼0). Error bars are standard deviation for 8–12 indium islands

within the vicinity of the nanotube, spanning a perpendicular distance+20%

of the length of the nanotube. The vertical dotted line denotes the geometric

centre of the nanotube. The results show that the remote Joule heating model

is quantitatively consistent with both sets of experimental observations.

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group26 with a set-up similar to ours show that similar nanotubesretain their high thermal conductivities, even during electron-beam imaging.

In conclusion, we present here evidence for a new form of Jouleheating, remote from the electrical current density. This is a directobservation of remote scattering as the dominant heat transportmechanism, as has been predicted by recent theories5. In previousstudies, it has been observed that individual nanotubes can carryenormous electrical current densities12,13, much greater than canbe achieved in standard metals or even in bulk samples comprisingmany nanotubes27,28. Our results present an explanation for theseprevious observations, as transport in a single nanotube resting ona polar substrate will actually dissipate its energy remotely over amuch larger volume than just the nanotube itself. This provideshope that the mechanism may be exploited in future electronicdevices as a new tool for nanoscale thermal management.

MethodsSample fabrication. Samples were prepared by spin-casting multiwalled nanotubesgrown by arc-discharge (Sigma Aldrich) from isopropanol suspension onto 50-nm-thick free-standing SiN membranes. Electrical connections were then patternedfrom palladium metal thin films (typically �27 nm) using electron-beamlithography, metal deposition and lift-off. The thickness of the palladium waschosen so that it was always greater than the diameter of the multiwalled nanotube toensure that the nanotube was embedded completely under the metal. Indiumislands, sub-200 nm in diameter, were deposited on the back side of the substrate bymeans of thermal evaporation.

EThM imaging. In EThM, the thermometry was performed by capturing the solid–liquid phase transition of a discontinuous indium film when the TEM was operatedunder dark-field conditions. Because the nanotube and metal layers were located onthe front side of the insulating substrate, the indium film on the back did not interactelectrically. The indium islands did not change shape or morphology during themelting or freezing process due to the presence of a robust oxide layer. At eachmeasurement voltage, a single TEM micrograph captured the information about thephase of every indium island. The voltage was increased in 10 mV steps until all theislands in the field of view were melted, and then individual micrographs werecompiled into one thermal map.

Finite-element modelling. All finite-element modelling was performed using thecommercial package Comsol. The ‘remote-heating’ parameter b was extracted bysolving D(K∇T) − (DT/Rc) + b∗ P = 0, where T is the local temperature, DT is thetemperature difference between the nanotube and the substrate, K is thermalconductivity, Rc is the thermal contact resistance of the nanotube with the substrate,and P is the applied power. To measure b we extracted a 95% confidence interval ofmelting voltages of an ensemble of indium islands around the centre of remotepalladium patch. b was varied until agreement was reached between the simulationsand experiments. All our simulation models were two-dimensional. Details of themodelling, together with a validation of using two-dimensional instead of three-dimensional models, are given in Supplementary Section S3.

Received 5 January 2012; accepted 27 February 2012;published online 8 April 2012; corrected online 17 April 2012

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AcknowledgementsThis research was supported by the US Department of Energy, Office of Basic EnergySciences, Division of Materials Sciences and Engineering (award no. DE-FG02-10ER46742). N.V. is supported by the US Nuclear Regulatory Commission under a FacultyDevelopment Grant (NRC3809950).

Author contributionsK.H.B. and J.C. conceived the experiments. K.H.B. fabricated the devices, performedmeasurements and carried out the simulations. N.V. assisted K.H.B. in lithography and dataacquisition. All authors discussed the results. K.H.B and M.B. developed finite-elementmodels. M.B. and N.V. helped point out and address any alternative explanations. K.H.B.and J.C. co-wrote the paper.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper at www.nature.com/naturenanotechnology. Reprints andpermission information is available online at http://www.nature.com/reprints. Correspondenceand requests for materials should be addressed to J.C.

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In the version of this Letter originally published online, in the caption of Fig. 3a, the value of β should have been 0.84. This error has been corrected in all versions of the Letter.

Remote Joule heating by a carbon nanotubeKamal H. Baloch, Norvik Voskanian, Merijntje Bronsgeest and John Cumings

Nature Nanotechnology http://dx.doi.org/10.1038/nnano.2012.39 (2012); published online 8 April 2012; corrected online 17 April 2012.

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