Remote Joule heating by a carbon nanotube
LETTERS PUBLISHED ONLINE: 8 APRIL 2012 | DOI: 10.1038/NNANO.2012.39
Remote Joule heating by a carbon nanotube Kamal H. Baloch1, Norvik Voskanian1, Merijntje Bronsgeest2 and John Cumings1 * Minimizing Joule heating remains an important goal in the design of electronic devices1,2. The prevailing model of Joule heating relies on a simple semiclassical picture in which electrons collide with the atoms of a conductor, generating heat locally and only in regions of non-zero current density, and this model has been supported by most experiments. Recently, however, it has been predicted that electric currents in graphene and carbon nanotubes can couple to the vibrational modes of a neighbouring material3,4, heating it remotely5. Here, we use in situ electron thermal microscopy to detect the remote Joule heating of a silicon nitride substrate by a single multiwalled carbon nanotube. At least 84% of the electrical power supplied to the nanotube is dissipated directly into the substrate, rather than in the nanotube itself. Although it has different physical origins, this phenomenon is reminiscent of induction heating or microwave dielectric heating. Such an ability to dissipate waste energy remotely could lead to improved thermal management in electronic devices6. Thermal management in modern digital electronics is typically addressed by engineering transistors and interconnects to minimize electrical resistance and also by incorporating high thermal conductivity heat spreaders to transport heat effectively to a heat sink. However, there is increasing interest in making use of new carbon-based materials such as graphene and carbon nanotubes, which have superlatively high thermal conductivities, for thermal management7–10. In addition to being extraordinary thermal conductors, these materials have been shown to sustain enormous electrical current densities11–13; together, these features suggest that they may have potential in applications as interconnects in microelectronic circuitry. However, many studies have suggested that the thermal performance of these materials is limited by their large interfacial thermal resistance with other materials14–17. Recently, it has been shown that it is possible to tune this thermal contact resistance by manipulating the area of contact between the neighbouring materials16,17. In the following, we present further results showing a greatly enhanced thermal transport between the nanotube and the substrate that occurs only while the nanotube is carrying an electrical current. We conclude that this thermal transport is occurring by the direct transfer of energy from the charge carriers in the nanotube to the vibrational modes of the substrate, thus demonstrating remote Joule heating as the dominating mode of heat dissipation in such systems. The results were obtained using electron thermal microscopy (EThM)18, a novel thermal imaging method that overcomes the spatial resolution limits of thermal microscopy based on infrared imaging techniques. The approach relies on the solid–liquid phase transition of nanometre-scale metallic indium islands thermally evaporated onto the back side of an electron-transparent silicon nitride (SiN) substrate. In EThM, transmission electron microscope (TEM) imaging in dark-field mode shows this phase transition as a change in contrast of the islands. When the indium islands reversibly melt and freeze, there is no overall change in their
shape or morphology, but the different diffraction properties produce a bright/dark contrast for the liquid/solid phases, respectively. This process yields a binary map, showing the temperature of the substrate at the location of each island as either above or below the melting point, 156.6 8C. By operating a current-carrying nanotube at different voltage biases, several binary maps can be built into a thermal map, revealing the heat sources and temperature distributions at the nanoscale. The results for a simple geometry involving a multiwalled carbon nanotube with two electrical contacts are presented in Fig. 1. TEM micrographs showing the device before and after indium deposition are shown in Fig. 1a,b. A finite-element model of this device using traditional Joule heating was used to calculate the melting profile of indium as the voltage bias across the carbon nanotube was increased. As the nanotube resting on the substrate is embedded underneath metallic palladium contacts, the increased area of overlap between the nanotube and the metal compared with that between nanotube and substrate results in a lower thermal contact a
c A 1.6 V
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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.
1
Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20740, USA, 2 Department of Physics, University of Maryland, College Park, Maryland 20740, USA. *e-mail: [email protected]
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resistance16,17,19. Using the thermal contact resistances between palladium and the nanotube (PdRc , 4.2 m.K W21) and between SiN and the nanotube (SiNRc , 250 m.K W21) (both measured earlier and reported elsewhere16), we obtained a simulated finite-element thermal map, as shown in Fig. 1d. Because SiNRc is about two orders of magnitude larger than PdRc , this simulated thermal map shows the SiN substrate under the contacts to be hotter and thus the melting of indium probes in these regions is expected to occur at lower voltages. However, this is inconsistent with the results of our experimental observations, as shown in Fig. 1c. This suggests fundamental inadequacies in the semiclassical Joule heating model used in our simulations. The experimentally obtained thermal map shows clearly that the SiN substrate under the middle segment of the nanotube and between the metallic contacts heats first, contrary to the predictions of the simulations. Clearly, there is more effective thermal transport from the nanotube to the substrate between the contacts than is suggested by the high contact resistance of 250 m.K W21. As this value was determined during previous low-temperature transport studies, it is possible that the nanotube reaches a higher temperature in the present experiment, manifesting a low thermal contact resistance. To test this hypothesis, we carried out a second experiment to probe more directly the temperature of the nanotube when it carries an electrical current. Here, we take advantage of the fact that arc-discharge multiwalled nanotubes have high crystallinity (Supplementary Section S1) and have been shown to exhibit exceptionally high thermal conductivities in several studies (in excess of 1,000 W m21 K21; refs 9,10). From this and the high thermal contact resistances that are known to occur in these geometries16, it is reasonable to expect the relatively low power dissipation being used here to produce only small temperature differences along the length of the nanotube. Thus, a device that incorporates two electrical contacts along one end of a nanotube would reasonably be expected to heat up the nanotube along its entire length, with the ability to conduct heat into a third isolated metal contact at a different location along the nanotube. A TEM image of a nanotube contacted in this manner is shown in Fig. 2a. A finite-element model including traditional Joule heating confirmed these assumptions and is presented in Fig. 2c. From the model, we expect the indium thermal probes under the third metal contact to melt at lower voltages than those near the current-carrying segment of the nanotube due to the effective transport of heat along the nanotube and poor heat sinking near the isolated contact. Figure 2b presents the results of experiments performed on a device with this geometry, and once again we observe that there is substantial disagreement with a simple Joule heating model. Here, we observe that the melting occurs first under the current-carrying segment of the nanotube, and that the isolated contact plays no noticeable role in determining the thermal distribution. This allows us to conclude that the nanotube is not behaving as a conventional resistive heater in this experiment. It appears as though the electrical current flowing through the nanotube is heating up the substrate directly beneath. This conclusion, while contradicting an intuitive understanding of traditional Joule heating, is not entirely unexpected, given contemporary models of electrical transport in carbon nanotubes and other carbon-based nanomaterials. Specifically, theories of the remote scattering of conduction electrons in these materials by surface vibrations in a dielectric have been used to explain the temperature dependence of electrical transport studies of graphene and nanotubes3,4, and this scattering has even been proposed as a possible essential mechanism of thermal transport5. Indeed, we present here direct evidence of this phenomenon as the dominant mechanism of electrical heating. To obtain agreement between the finite-element analysis and the experimental results, the Joule heating model needs to be modified.
a
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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 b ¼ 0.84, 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.
We achieve this by introducing a new ‘remote-heating’ parameter, b, which is the fraction of the applied power being dissipated directly into the substrate underneath the current-carrying segment of the nanotube in our two-dimensional model. Thus, b ¼ 0 implies a standard Joule heating model where all the power is dissipated in the current-carrying nanotube, whereas b ¼ 1 implies that all the power is deposited directly into the substrate beneath. From our data, we extracted a 95% confidence interval for the voltage needed to melt the indium islands underneath the third contact, and from this interval, we find that the smallest value for which the simulations match the experiment is b ¼ 0.84. The results of a finite-element model incorporating this are shown in Fig. 2d. This means that the substrate under the nanotube gains heat because at least 84% of total power is dissipated directly in the substrate and no more than 16% is dissipated within the nanotube itself. Such a novel energy-transfer mechanism should not be completely counterintuitive, as recent experimental studies have shown a similar non-thermal current-induced gas desorption from nanotube samples20. It is worth noting that this value of b ¼ 0.84 was extracted by assuming diffusive, not ballistic, electronic transport in the nanotube, which agrees with previous observations of multiwalled carbon nanotubes21. The current–voltage (I–V) curves of both devices described here are provided in Supplementary Section S2. These I–V plots demonstrate that the multiwalled
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Figure 3 | Quantitative comparison of experiment and simulations. a, Finite-element simulations corresponding to b ¼ 0.84 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 b ¼ 0.84 and blue for b ¼ 0). 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.
nanotubes used are metallic in nature and should exhibit currentinduced power dissipation. A dissipationless ballistic transport model would be even more difficult to reconcile with our observations, as it would place more power dissipation within the contacts, contradicting the experimental observations of Fig. 1c. Both experiments described above were repeated for at least three devices of each kind. The measurements for all devices yielded similar results, supporting the conclusion that the dominant mode of power dissipation is directly into the substrate. Having developed a model to describe remote Joule heating from the results in Fig. 2, we now revisit the experimental results shown in Fig. 1. We find that here, too, simulations match the experimental results only if we assume that the power is being deposited directly into the substrate. A simulation for the case of b ¼ 0.84 is shown in Fig. 3a, and indeed this matches well with the experimental micrograph of Fig. 1c. To demonstrate this agreement in a more quantitative manner, Fig. 3b presents a plot of the melting voltages of the 318
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indium islands along the length of the nanotube versus their distance from its centre, together with results from finite-element modelling with (b ¼ 0.84) and without (b ¼ 0) remote Joule heating. It can be seen in this plot that the experimental data match closely the modelling with b ¼ 0.84, providing an effective explanation for the discrepancy previously discussed for Fig. 1. The agreement of this remote Joule heating model with the experimental results provides support for its veracity; however, identifying its physical origins would help to delineate the scope of the applicability of the effect. The effect would seem to be arising from the near-field electromagnetic fields around the nanotube directly exciting thermal modes within the substrate, which bears some analogy with induction heating and microwave dielectric heating22. However, both of these phenomena originate from the intentional generation of coherent electromagnetic oscillations, whereas the present observations are driven by strictly d.c. currents. More appropriately, these observations can be explained by the near-field remote scattering of hot electrons in carbon nanotubes off surface polaritons of a polar substrate5,23. Surface polaritons are a vibrational mode of the substrate that results from the coupling of its surface optical phonons and its surface electromagnetic polarization. Instead of scattering off the carbon atoms of the nanotube24, the transport electrons couple to the surface polaritons of nearby dielectric materials and thus transfer their energy directly to the substrate. The spatial range of such a phenomenon could be as large as tens of nanometres23, indicating that effective coupling can be significant between hot electrons in a typical multiwalled nanotube (25 nm in diameter) and vibrations in the substrate on which it rests. The model presented above comprises a clear explanation of our results, and we show in the following that an alternative model with a low thermal conductivity for the multiwalled nanotube does not agree with our observations. If we modify the finite-element models by reducing the thermal conductivity of the nanotube, we find that it is not possible to obtain quantitative agreement with the experimental results; however, a qualitative agreement can be obtained by using a nanotube thermal conductivity value below 50 W m21 K21. In such a case, the nanotube would no longer act as an effective heat-spreader in our tested geometries, and it would 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 can be in qualitative agreement with a standard Joule heating model. However, such a low thermal conductivity would not be consistent with many well-accepted observations. Nanotubes with substantial disorder, such as multiwalled nanotubes synthesized by chemical vapour deposition, can have low thermal conductivities in the range of 50–300 W m21 K21 (ref. 17). However, multiwalled nanotubes grown by arc-discharge, as used here, have been reported in many studies to have exceptionally high thermal conductivities, in excess of 1,000 W m21 K21 (refs 9,10). In performing in situ TEM studies, care needs to be taken that the imaging electron beam does not damage the sample25; in our case, we can neglect these effects, as we use low beam currents and blank the beam between imaging exposures. Under comparable imaging conditions, we find that the highly ordered crystalline nature of our multiwalled nanotubes can be confirmed by high-resolution TEM images throughout our studies (as shown in Supplementary Fig. S1), and in situ electrical transport measurements show no measurable reduction in electrical conductivity. Furthermore, our previous results16 have shown that a multiwalled nanotube measured in a similar set-up is highly capable of transporting heat to a distant contact. From the finite-element models used in these previous studies, we conclude that the nanotubes used in our experiments must 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 with traditional Joule heating. Also, studies performed by another
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group26 with a set-up similar to ours show that similar nanotubes retain their high thermal conductivities, even during electronbeam imaging. In conclusion, we present here evidence for a new form of Joule heating, remote from the electrical current density. This is a direct observation of remote scattering as the dominant heat transport mechanism, as has been predicted by recent theories5. In previous studies, it has been observed that individual nanotubes can carry enormous electrical current densities12,13, much greater than can be achieved in standard metals or even in bulk samples comprising many nanotubes27,28. Our results present an explanation for these previous observations, as transport in a single nanotube resting on a polar substrate will actually dissipate its energy remotely over a much larger volume than just the nanotube itself. This provides hope that the mechanism may be exploited in future electronic devices as a new tool for nanoscale thermal management.
Methods Sample fabrication. Samples were prepared by spin-casting multiwalled nanotubes grown by arc-discharge (Sigma Aldrich) from isopropanol suspension onto 50-nmthick free-standing SiN membranes. Electrical connections were then patterned from palladium metal thin films (typically 27 nm) using electron-beam lithography, metal deposition and lift-off. The thickness of the palladium was chosen so that it was always greater than the diameter of the multiwalled nanotube to ensure that the nanotube was embedded completely under the metal. Indium islands, sub-200 nm in diameter, were deposited on the back side of the substrate by means 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 operated under dark-field conditions. Because the nanotube and metal layers were located on the front side of the insulating substrate, the indium film on the back did not interact electrically. The indium islands did not change shape or morphology during the melting or freezing process due to the presence of a robust oxide layer. At each measurement voltage, a single TEM micrograph captured the information about the phase of every indium island. The voltage was increased in 10 mV steps until all the islands in the field of view were melted, and then individual micrographs were compiled into one thermal map. Finite-element modelling. All finite-element modelling was performed using the commercial package Comsol. The ‘remote-heating’ parameter b was extracted by solving D(K∇T) − (DT/Rc ) + b∗ P = 0, where T is the local temperature, DT is the temperature difference between the nanotube and the substrate, K is thermal conductivity, 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 of melting voltages of an ensemble of indium islands around the centre of remote palladium patch. b was varied until agreement was reached between the simulations and experiments. All our simulation models were two-dimensional. Details of the modelling, together with a validation of using two-dimensional instead of threedimensional 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
References 1. Pop, E., Sinha, S. & Goodson, K. E. Heat generation and transport in nanometerscale transistors. Proc. IEEE 94, 1587–1601 (2006). 2. Pop, E. Energy dissipation and transport in nanoscale devices. Nano Res. 3, 147–169 (2010). 3. Chen, J. H., Jang, C., Xiao, S., Ishigami, M. & Fuhrer, M. S. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nature Nanotech. 3, 206–209 (2008). 4. Perebeinos, V., Rotkin, S. V., Petrov, A. G. & Avouris, P. The effects of substrate phonon mode scattering on transport in carbon nanotubes. Nano Lett. 9, 312–316 (2009). 5. Rotkin, S. V., Perebeinos, V., Petrov, A. G. & Avouris, P. An essential mechanism of heat dissipation in carbon nanotube electronics. Nano Lett. 9, 1850–1855 (2009).
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6. Kenny, T. et al. Advanced cooling technologies for microprocessors. Int. J. High Speed Electron. Syst. 16, 301–313 (2006). 7. Balandin, A. A. et al. Superior thermal conductivity of single layer graphene. Nano Lett. 8, 902–907 (2008). 8. Balandin, A. A. Thermal properties of graphene and nanostructured carbon materials. Nature Mater. 10, 569–581 (2011). 9. Kim, P., Shi, L., Majumdar, A. & McEuen, P. L. Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 87, 215502 (2001). 10. Fujii, M. et al. Measuring the thermal conductivity of a single carbon nanotube. Phys. Rev. Lett. 95, 065502 (2005). 11. Murali, R., Yang, Y., Brenner, K., Beck, T. & Meindl, J. D. Breakdown current density of graphene nanoribbons. Appl. Phys. Lett. 94, 243114 (2009). 12. Yao, Z., Kane, C. L. & Dekker, C. High-field electrical transport in single-wall carbon nanotubes. Phys. Rev. Lett. 84, 2941–2944 (2000). 13. Wei, B. Q., Vajtai, R. & Ajayan, P. M. Reliability and current carrying capacity of carbon nanotubes. Appl. Phys. Lett. 79, 1172–1174 (2001). 14. Huxtable, S. T. et al. Interfacial heat flow in carbon nanotube suspensions. Nature 2, 731–734 (2003). 15. Prasher, R. S. et al. Turning carbon nanotubes from exceptional heat conductors into insulators. Phys. Rev. Lett. 102, 105901 (2009). 16. Baloch, K. H., Voskanian, N. & Cumings, J. Controlling the thermal contact resistance of a carbon nanotube heat spreader. Appl. Phys. Lett. 97, 063105 (2010). 17. Pettes, M. T. & Shi, L. Thermal and structural characterizations of individual single-, double-, and multi-walled carbon nanotubes. Adv. Funct. Mater. 19, 3918–3925 (2009). 18. Brintlinger, T., Qi, Y., Baloch, K. H., Goldhaber-Gordon, D. & Cumings, J. Electron thermal microscopy. Nano Lett. 8, 582–585 (2008). 19. Prasher, R. Predicting the thermal resistance of nanosized constrictions. Nano Lett. 5, 2155–2159 (2005). 20. Salehi-Khojin, A., Lin, K. Y., Field, C. R. & Masel, R. I. Nonthermal currentstimulated desorption of gases from carbon nanotubes. Science 329, 1327–1330 (2010). 21. Bachtold, A. et al. Scanned probe microscopy of electronic transport in carbon nanotubes. Phys. Rev. Lett. 84, 6082–6085 (2000). 22. Piyasena, P., Dussault, C., Koutchma, T., Ramaswamy, H. S. & Awuah, G. B. Radio frequency heating of foods: principles, applications and related properties—a review. Crit. Rev. Food Sci. Nutr. 43, 587–606 (2003). 23. Petrov, A. G. & Rotkin, S. V. Energy relaxation of hot carriers in single-wall carbon nanotubes by surface optical phonons of the substrate. J. Exp. Theor. Phys. Lett. 84, 156–160 (2006). 24. Park, J-Y. et al. Electron–phonon scattering in metallic single-walled carbon nanotubes. Nano Lett. 4, 517–520 (2004). 25. Chopra, N. G. et al. Fully collapsed carbon nanotubes. Nature 377, 135–138 (1995). 26. Begtrup, G. E. et al. Probing nanoscale solids at thermal extremes. Phys. Rev. Lett. 99, 155901 (2007). 27. Nihei, M. et al. Electrical properties of carbon nanotube bundles for future via interconnects. Jpn. J. Appl. Phys. 44, 1626–1628 (2005). 28. Ma, J. et al. Effects of surfactants on spinning carbon nanotube fibers by an electrophoretic method. Sci. Tech. Adv. Mater. 11, 065005 (2010).
Acknowledgements This research was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering (award no. DE-FG0210ER46742). N.V. is supported by the US Nuclear Regulatory Commission under a Faculty Development Grant (NRC3809950).
Author contributions K.H.B. and J.C. conceived the experiments. K.H.B. fabricated the devices, performed measurements and carried out the simulations. N.V. assisted K.H.B. in lithography and data acquisition. All authors discussed the results. K.H.B and M.B. developed finite-element models. M.B. and N.V. helped point out and address any alternative explanations. K.H.B. and J.C. co-wrote the paper.
Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper at www.nature.com/naturenanotechnology. Reprints and permission information is available online at http://www.nature.com/reprints. Correspondence and requests for materials should be addressed to J.C.
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Remote Joule heating by a carbon nanotube Kamal 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. 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 nanotube Kamal H. Baloch1, Norvik Voskanian1, Merijntje Bronsgeest2 and John Cumings1 * Minimizing Joule heating remains an important goal in the design of electronic devices1,2. The prevailing model of Joule heating relies on a simple semiclassical picture in which electrons collide with the atoms of a conductor, generating heat locally and only in regions of non-zero current density, and this model has been supported by most experiments. Recently, however, it has been predicted that electric currents in graphene and carbon nanotubes can couple to the vibrational modes of a neighbouring material3,4, heating it remotely5. Here, we use in situ electron thermal microscopy to detect the remote Joule heating of a silicon nitride substrate by a single multiwalled carbon nanotube. At least 84% of the electrical power supplied to the nanotube is dissipated directly into the substrate, rather than in the nanotube itself. Although it has different physical origins, this phenomenon is reminiscent of induction heating or microwave dielectric heating. Such an ability to dissipate waste energy remotely could lead to improved thermal management in electronic devices6. Thermal management in modern digital electronics is typically addressed by engineering transistors and interconnects to minimize electrical resistance and also by incorporating high thermal conductivity heat spreaders to transport heat effectively to a heat sink. However, there is increasing interest in making use of new carbon-based materials such as graphene and carbon nanotubes, which have superlatively high thermal conductivities, for thermal management7–10. In addition to being extraordinary thermal conductors, these materials have been shown to sustain enormous electrical current densities11–13; together, these features suggest that they may have potential in applications as interconnects in microelectronic circuitry. However, many studies have suggested that the thermal performance of these materials is limited by their large interfacial thermal resistance with other materials14–17. Recently, it has been shown that it is possible to tune this thermal contact resistance by manipulating the area of contact between the neighbouring materials16,17. In the following, we present further results showing a greatly enhanced thermal transport between the nanotube and the substrate that occurs only while the nanotube is carrying an electrical current. We conclude that this thermal transport is occurring by the direct transfer of energy from the charge carriers in the nanotube to the vibrational modes of the substrate, thus demonstrating remote Joule heating as the dominating mode of heat dissipation in such systems. The results were obtained using electron thermal microscopy (EThM)18, a novel thermal imaging method that overcomes the spatial resolution limits of thermal microscopy based on infrared imaging techniques. The approach relies on the solid–liquid phase transition of nanometre-scale metallic indium islands thermally evaporated onto the back side of an electron-transparent silicon nitride (SiN) substrate. In EThM, transmission electron microscope (TEM) imaging in dark-field mode shows this phase transition as a change in contrast of the islands. When the indium islands reversibly melt and freeze, there is no overall change in their
shape or morphology, but the different diffraction properties produce a bright/dark contrast for the liquid/solid phases, respectively. This process yields a binary map, showing the temperature of the substrate at the location of each island as either above or below the melting point, 156.6 8C. By operating a current-carrying nanotube at different voltage biases, several binary maps can be built into a thermal map, revealing the heat sources and temperature distributions at the nanoscale. The results for a simple geometry involving a multiwalled carbon nanotube with two electrical contacts are presented in Fig. 1. TEM micrographs showing the device before and after indium deposition are shown in Fig. 1a,b. A finite-element model of this device using traditional Joule heating was used to calculate the melting profile of indium as the voltage bias across the carbon nanotube was increased. As the nanotube resting on the substrate is embedded underneath metallic palladium contacts, the increased area of overlap between the nanotube and the metal compared with that between nanotube and substrate results in a lower thermal contact a
c A 1.6 V
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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.
1
Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20740, USA, 2 Department of Physics, University of Maryland, College Park, Maryland 20740, USA. *e-mail: [email protected]
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resistance16,17,19. Using the thermal contact resistances between palladium and the nanotube (PdRc , 4.2 m.K W21) and between SiN and the nanotube (SiNRc , 250 m.K W21) (both measured earlier and reported elsewhere16), we obtained a simulated finite-element thermal map, as shown in Fig. 1d. Because SiNRc is about two orders of magnitude larger than PdRc , this simulated thermal map shows the SiN substrate under the contacts to be hotter and thus the melting of indium probes in these regions is expected to occur at lower voltages. However, this is inconsistent with the results of our experimental observations, as shown in Fig. 1c. This suggests fundamental inadequacies in the semiclassical Joule heating model used in our simulations. The experimentally obtained thermal map shows clearly that the SiN substrate under the middle segment of the nanotube and between the metallic contacts heats first, contrary to the predictions of the simulations. Clearly, there is more effective thermal transport from the nanotube to the substrate between the contacts than is suggested by the high contact resistance of 250 m.K W21. As this value was determined during previous low-temperature transport studies, it is possible that the nanotube reaches a higher temperature in the present experiment, manifesting a low thermal contact resistance. To test this hypothesis, we carried out a second experiment to probe more directly the temperature of the nanotube when it carries an electrical current. Here, we take advantage of the fact that arc-discharge multiwalled nanotubes have high crystallinity (Supplementary Section S1) and have been shown to exhibit exceptionally high thermal conductivities in several studies (in excess of 1,000 W m21 K21; refs 9,10). From this and the high thermal contact resistances that are known to occur in these geometries16, it is reasonable to expect the relatively low power dissipation being used here to produce only small temperature differences along the length of the nanotube. Thus, a device that incorporates two electrical contacts along one end of a nanotube would reasonably be expected to heat up the nanotube along its entire length, with the ability to conduct heat into a third isolated metal contact at a different location along the nanotube. A TEM image of a nanotube contacted in this manner is shown in Fig. 2a. A finite-element model including traditional Joule heating confirmed these assumptions and is presented in Fig. 2c. From the model, we expect the indium thermal probes under the third metal contact to melt at lower voltages than those near the current-carrying segment of the nanotube due to the effective transport of heat along the nanotube and poor heat sinking near the isolated contact. Figure 2b presents the results of experiments performed on a device with this geometry, and once again we observe that there is substantial disagreement with a simple Joule heating model. Here, we observe that the melting occurs first under the current-carrying segment of the nanotube, and that the isolated contact plays no noticeable role in determining the thermal distribution. This allows us to conclude that the nanotube is not behaving as a conventional resistive heater in this experiment. It appears as though the electrical current flowing through the nanotube is heating up the substrate directly beneath. This conclusion, while contradicting an intuitive understanding of traditional Joule heating, is not entirely unexpected, given contemporary models of electrical transport in carbon nanotubes and other carbon-based nanomaterials. Specifically, theories of the remote scattering of conduction electrons in these materials by surface vibrations in a dielectric have been used to explain the temperature dependence of electrical transport studies of graphene and nanotubes3,4, and this scattering has even been proposed as a possible essential mechanism of thermal transport5. Indeed, we present here direct evidence of this phenomenon as the dominant mechanism of electrical heating. To obtain agreement between the finite-element analysis and the experimental results, the Joule heating model needs to be modified.
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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 b ¼ 0.84, 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.
We achieve this by introducing a new ‘remote-heating’ parameter, b, which is the fraction of the applied power being dissipated directly into the substrate underneath the current-carrying segment of the nanotube in our two-dimensional model. Thus, b ¼ 0 implies a standard Joule heating model where all the power is dissipated in the current-carrying nanotube, whereas b ¼ 1 implies that all the power is deposited directly into the substrate beneath. From our data, we extracted a 95% confidence interval for the voltage needed to melt the indium islands underneath the third contact, and from this interval, we find that the smallest value for which the simulations match the experiment is b ¼ 0.84. The results of a finite-element model incorporating this are shown in Fig. 2d. This means that the substrate under the nanotube gains heat because at least 84% of total power is dissipated directly in the substrate and no more than 16% is dissipated within the nanotube itself. Such a novel energy-transfer mechanism should not be completely counterintuitive, as recent experimental studies have shown a similar non-thermal current-induced gas desorption from nanotube samples20. It is worth noting that this value of b ¼ 0.84 was extracted by assuming diffusive, not ballistic, electronic transport in the nanotube, which agrees with previous observations of multiwalled carbon nanotubes21. The current–voltage (I–V) curves of both devices described here are provided in Supplementary Section S2. These I–V plots demonstrate that the multiwalled
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a 1.6 V
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Figure 3 | Quantitative comparison of experiment and simulations. a, Finite-element simulations corresponding to b ¼ 0.84 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 b ¼ 0.84 and blue for b ¼ 0). 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.
nanotubes used are metallic in nature and should exhibit currentinduced power dissipation. A dissipationless ballistic transport model would be even more difficult to reconcile with our observations, as it would place more power dissipation within the contacts, contradicting the experimental observations of Fig. 1c. Both experiments described above were repeated for at least three devices of each kind. The measurements for all devices yielded similar results, supporting the conclusion that the dominant mode of power dissipation is directly into the substrate. Having developed a model to describe remote Joule heating from the results in Fig. 2, we now revisit the experimental results shown in Fig. 1. We find that here, too, simulations match the experimental results only if we assume that the power is being deposited directly into the substrate. A simulation for the case of b ¼ 0.84 is shown in Fig. 3a, and indeed this matches well with the experimental micrograph of Fig. 1c. To demonstrate this agreement in a more quantitative manner, Fig. 3b presents a plot of the melting voltages of the 318
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indium islands along the length of the nanotube versus their distance from its centre, together with results from finite-element modelling with (b ¼ 0.84) and without (b ¼ 0) remote Joule heating. It can be seen in this plot that the experimental data match closely the modelling with b ¼ 0.84, providing an effective explanation for the discrepancy previously discussed for Fig. 1. The agreement of this remote Joule heating model with the experimental results provides support for its veracity; however, identifying its physical origins would help to delineate the scope of the applicability of the effect. The effect would seem to be arising from the near-field electromagnetic fields around the nanotube directly exciting thermal modes within the substrate, which bears some analogy with induction heating and microwave dielectric heating22. However, both of these phenomena originate from the intentional generation of coherent electromagnetic oscillations, whereas the present observations are driven by strictly d.c. currents. More appropriately, these observations can be explained by the near-field remote scattering of hot electrons in carbon nanotubes off surface polaritons of a polar substrate5,23. Surface polaritons are a vibrational mode of the substrate that results from the coupling of its surface optical phonons and its surface electromagnetic polarization. Instead of scattering off the carbon atoms of the nanotube24, the transport electrons couple to the surface polaritons of nearby dielectric materials and thus transfer their energy directly to the substrate. The spatial range of such a phenomenon could be as large as tens of nanometres23, indicating that effective coupling can be significant between hot electrons in a typical multiwalled nanotube (25 nm in diameter) and vibrations in the substrate on which it rests. The model presented above comprises a clear explanation of our results, and we show in the following that an alternative model with a low thermal conductivity for the multiwalled nanotube does not agree with our observations. If we modify the finite-element models by reducing the thermal conductivity of the nanotube, we find that it is not possible to obtain quantitative agreement with the experimental results; however, a qualitative agreement can be obtained by using a nanotube thermal conductivity value below 50 W m21 K21. In such a case, the nanotube would no longer act as an effective heat-spreader in our tested geometries, and it would 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 can be in qualitative agreement with a standard Joule heating model. However, such a low thermal conductivity would not be consistent with many well-accepted observations. Nanotubes with substantial disorder, such as multiwalled nanotubes synthesized by chemical vapour deposition, can have low thermal conductivities in the range of 50–300 W m21 K21 (ref. 17). However, multiwalled nanotubes grown by arc-discharge, as used here, have been reported in many studies to have exceptionally high thermal conductivities, in excess of 1,000 W m21 K21 (refs 9,10). In performing in situ TEM studies, care needs to be taken that the imaging electron beam does not damage the sample25; in our case, we can neglect these effects, as we use low beam currents and blank the beam between imaging exposures. Under comparable imaging conditions, we find that the highly ordered crystalline nature of our multiwalled nanotubes can be confirmed by high-resolution TEM images throughout our studies (as shown in Supplementary Fig. S1), and in situ electrical transport measurements show no measurable reduction in electrical conductivity. Furthermore, our previous results16 have shown that a multiwalled nanotube measured in a similar set-up is highly capable of transporting heat to a distant contact. From the finite-element models used in these previous studies, we conclude that the nanotubes used in our experiments must 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 with traditional Joule heating. Also, studies performed by another
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group26 with a set-up similar to ours show that similar nanotubes retain their high thermal conductivities, even during electronbeam imaging. In conclusion, we present here evidence for a new form of Joule heating, remote from the electrical current density. This is a direct observation of remote scattering as the dominant heat transport mechanism, as has been predicted by recent theories5. In previous studies, it has been observed that individual nanotubes can carry enormous electrical current densities12,13, much greater than can be achieved in standard metals or even in bulk samples comprising many nanotubes27,28. Our results present an explanation for these previous observations, as transport in a single nanotube resting on a polar substrate will actually dissipate its energy remotely over a much larger volume than just the nanotube itself. This provides hope that the mechanism may be exploited in future electronic devices as a new tool for nanoscale thermal management.
Methods Sample fabrication. Samples were prepared by spin-casting multiwalled nanotubes grown by arc-discharge (Sigma Aldrich) from isopropanol suspension onto 50-nmthick free-standing SiN membranes. Electrical connections were then patterned from palladium metal thin films (typically 27 nm) using electron-beam lithography, metal deposition and lift-off. The thickness of the palladium was chosen so that it was always greater than the diameter of the multiwalled nanotube to ensure that the nanotube was embedded completely under the metal. Indium islands, sub-200 nm in diameter, were deposited on the back side of the substrate by means 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 operated under dark-field conditions. Because the nanotube and metal layers were located on the front side of the insulating substrate, the indium film on the back did not interact electrically. The indium islands did not change shape or morphology during the melting or freezing process due to the presence of a robust oxide layer. At each measurement voltage, a single TEM micrograph captured the information about the phase of every indium island. The voltage was increased in 10 mV steps until all the islands in the field of view were melted, and then individual micrographs were compiled into one thermal map. Finite-element modelling. All finite-element modelling was performed using the commercial package Comsol. The ‘remote-heating’ parameter b was extracted by solving D(K∇T) − (DT/Rc ) + b∗ P = 0, where T is the local temperature, DT is the temperature difference between the nanotube and the substrate, K is thermal conductivity, 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 of melting voltages of an ensemble of indium islands around the centre of remote palladium patch. b was varied until agreement was reached between the simulations and experiments. All our simulation models were two-dimensional. Details of the modelling, together with a validation of using two-dimensional instead of threedimensional 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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Acknowledgements This research was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering (award no. DE-FG0210ER46742). N.V. is supported by the US Nuclear Regulatory Commission under a Faculty Development Grant (NRC3809950).
Author contributions K.H.B. and J.C. conceived the experiments. K.H.B. fabricated the devices, performed measurements and carried out the simulations. N.V. assisted K.H.B. in lithography and data acquisition. All authors discussed the results. K.H.B and M.B. developed finite-element models. M.B. and N.V. helped point out and address any alternative explanations. K.H.B. and J.C. co-wrote the paper.
Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper at www.nature.com/naturenanotechnology. Reprints and permission information is available online at http://www.nature.com/reprints. Correspondence and requests for materials should be addressed to J.C.
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Remote Joule heating by a carbon nanotube Kamal 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. 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.
