Mesoscopic thermal and thermoelectric measurements of individual carbon nanotubes

Solid State Communications 127 (2003) 181–186 www.elsevier.com/locate/ssc

Mesoscopic thermal and thermoelectric measurements of individual carbon nanotubes Joshua P. Smalla, Li Shib, Philip Kima,* a

Department of Physics, Columbia University, 538 West 120th Street, New York, NY 10027, USA b Department of Mechanical Engineering, University of Texas, Austin, TX 78712, USA Received 25 March 2003

Abstract We discuss the mesoscopic experimental measurements of electron energy dissipation, phonon thermal transport, and thermoelectric phenomena in individual carbon nanotubes. The temperature distributions in electrically heated individual multiwalled carbon nanotubes have been measured with a scanning thermal microscope. The temperature profiles along the tube axis in nanotubes indicate the bulk dissipation of electronic energy to phonons. In addition, thermal conductivity of an individual multiwalled nanotube has been measured using a microfabricated suspended device. The observed thermal conductivity is two orders of magnitude higher than the estimation from previous experiments that used macroscopic mat samples. Finally, we present thermoelectric power (TEP) of individual single walled carbon nanotubes using a novel mesoscopic device. A strong modulation of TEP as a function of the gate electrode was observed. q 2003 Elsevier Science Ltd. All rights reserved. PACS: 61.46.tw; 63.22.tm; 65.80.tn Keywords: A. Nanotube; D. Thermal conductivity; D. Thermopower

1. Introduction The intriguing 1-dimensional (1D) nature of electrons and phonons in carbon nanotubes have attracted considerable amount of theoretical and experimental work [1]. One of the fundamental issues that are also important for the device applications is how electrons and phonons transport through the nanotubes, i.e. how charges and energy are transported through these materials. Recent electrical transport experiments suggest that metallic single walled nanotubes (SWNTs) are remarkably good ballistic conductors [2 – 4] due to the strong suppression of back scatterings in the special symmetric 1D band [5]. In contrast, most of multiwalled nanotubes (MWNTs) experiments indicate diffusive electron transport [6 – 8], although others under a different experimental condition show * Corresponding author. Tel.: þ1-212-854-0102; fax: þ 1-212854-3379. E-mail address: [email protected] (P. Kim).

ballistic transport [9]. These interesting electron transport characteristics are often related to the energy dissipation and disturbance of local quasi equilibrium. Therefore, local temperature profile along the current-carrying nanotubes elucidates the characteristics of electron transport mechanism in these 1D materials. In addition to unusual electronic properties, carbon nanotubes are expected to have high thermal conductivity [10] and can conduct heat efficiently, thus preventing structure damage while used as current-carrying wires in micro/nano devices. Previous electronic transport measurements at high electric field regime [11,12] suggested that carbon nanotubes can carry substantial amounts of current before their structural failure. To investigate these intriguing electrical and thermal properties, mesoscopic experimental methods at a single nanotube level are desirable. On small length scales, however, the thermal transport quantities are more difficult to measure than their electrical counterparts, and thus have attracted less attention. There have been a number of experimental efforts to measure

0038-1098/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0038-1098(03)00341-7

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thermal transport properties such as thermal conductivity and thermoelectric power (TEP) of nanotubes using macroscopic ‘mat’ samples [13 – 20]. However, these macroscopic scale measurements inherently include artifacts resulting from numerous unknown tube– tube junctions in the sample. In addition, the ensemble average over different tube species blurs the intrinsic properties of individual nanotubes. Therefore, the mesoscopic scale thermal transport measurements are necessary to investigate the intrinsic thermal properties of carbon nanotubes. In this paper, we will discuss our recent mesoscopic experimental efforts to study electron energy dissipation, phonon thermal transport, and thermoelectric phenomena in individual carbon nanotubes.

2. Energy dissipation in MWNTs Electron transport in mesoscopic conductors is closely related to the energy dissipation mechanism, and is often correlated with the temperature distribution along them. Recent transport studies of SWNTs [11,12] and MWNTs [21] under a high bias voltage regime have suggested that the energy dissipation is largely due to the increased coupling of these energetic electrons to optical and zone boundary phonons, and hence the increase of lattice temperature should be expected. We have demonstrated the local temperature measurements of carbon nanotubes under electron transport [22]. By using a microscopic thermocouple junction at the end of an atomic force microscope (AFM) tip, the local temperature of the nanotube has been probed, which elucidate the energy dissipation mechanism in these materials. Thermal probe AFM tips have been fabricated and characterized as described in detail elsewhere [23]. The micropatterned Pt and Cr lines form a junction at the apex of the AFM tip that has a lateral spatial resolution ,30 nm (Fig. 1). It is known from the previous study [24] that the measured local temperature, Tm ðrÞ; in ambient condition is given by the convolution of the local temperature at surface Ð TðrÞ : Tm ðrÞ ¼ Kðr; r0 ÞTðr0 Þdr0 ; where the integration is over the surface and Kðr; r0 Þ is heat transfer function, contains the contribution of heat conduction through air and water meniscus as well as the direct solid to solid conduction. Phenomenologically, we found that Kðr; r0 Þ , 2  where rtip , 50 nm: If the radius of a exp½2lr 2 r0 l2 =rtip nanotube, rtube ; is smaller than rtip ; the above convolution yields the temperature of the nanotube, Tt ; to be: DTt < ðrtube =rtip ÞDTm ; where D indicates the changes from the ambient temperature. It is worth noting that the probe measures ‘phonon’ temperatures because a thin oxide layer formed on the outer Cr layer of the thermal probe prevent direct electronic coupling between the probe and a sample. Shown in Fig. 2(a) and (b) is the simultaneously taken topographic and corresponding thermal signal, DTm ; on a

Fig. 1. SEM image of the microfabricated scanning thermal probe. Patterned platinum and chrome lines, respectively, form the Pt–Cr thermocouple junctions at the end of the pyramidal shape tip. The inset shows an enlarged view of the end of the tip.

14 nm diameter MWNT device fabricated on 1 mm silicon oxide/silicon surface. Clearly, DTm is higher near the MWNT with the estimated tube temperature increase ,30 K at its highest position. The total electronic power dissipated in this device was 22 mW along the length of the tube. This dissipated energy eventually transferred to the substrate. Since the heat flow through the silicon oxide substrate is proportional to the temperature gradient, the power dissipation through the substrate, Q; can be estimated from the temperature profile. The estimated Q of the above image is 8.5 mW where the tube length L , 4 mm: From this value, the junction thermal conductance per unit length of

Fig. 2. (a) Topographic image of a MWNT device. Scale bar represent 1 mm. (b) The corresponding thermal signal simultaneously taken with (a). The applied bias voltage on the MWNT was 1 V and the current was 22 mA. (c) The temperature profile along the tube axis.

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tube could be computed: Kj ¼ Q=LðTt 2 Ts Þ , 0:08 W=m K where Ts is the substrate temperature underneath of the tube. Fig. 2(c) shows the temperature map along the tube axis. This temperature profile exhibits clearly a negative curvature. This temperature profile is indeed expected for a classical Ohmic conductor that has a finite bulk dissipation P inside the conductor. We also found that the tube temperature at the middle of the MWNT increases quadratically as a function of the bias voltage V (data not shown here). Since P ¼ V 2 =R for a dissipative Ohmic conductor where R is the resistance, these observations therefore suggest that MWNTs are energy dissipative in the electron transport and thus a diffusive conductor [8].

3. Thermal transport in MWNTs The thermal conductivity of carbon nanotubes have been measured by several groups using a millimeter sized mat sample [13 – 16]. Although these studies demonstrated qualitative understanding of the low dimensional nature of these materials, it is difficult to extract absolute values of thermal conductivity in a mat sample due to the presence of numerous uncertain tube– tube junctions that might be the dominant barriers to the thermal transport through the sample. We have recently developed a mesoscopic device which hybrids nanotubes to microelectromechanical systems (MEMS) and used it for thermal property measurement of an individual MWNT [25]. Fig. 3 shows the scanning electron microscope (SEM) image of the device, which is a suspended structure consisting of two adjacent 10 mm £ 10 mm silicon nitride membranes or islands suspended with three 200 mm long and 2 mm wide silicon nitride beams. One 30 nm thick, 200 nm wide, and 150 mm

Fig. 3. SEM image of the suspended device to measure the thermal conductivity of an individual carbon nanotube. Inset represents angled detail view of the central part of the device. A MWNT with the diameter of 14 nm bridges two suspended islands.

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long platinum (Pt) heater/thermometer coil was built on each island. A mechanical manipulation similar to that used for the fabrication of nanotube scanning probe microscopy tip was used to place MWNTs on the desired part of the device. This approach routinely produces a nanotube device that can be used to measure the thermal conductivity of the bridging nanotube segment. In particular, Fig. 3 inset shows an example of such a device. An individual MWNT with the diameter of 14 nm forms a thermal path between two suspended islands otherwise thermally isolated from each other. A bias voltage applied to one of the resistors, Rh ; creates Joule heat, P; and increases the temperature, Th ; of the heater island from the thermal bath temperature T0 : In a steady state, there is a heat transfer to the other island through the nanotubes, and thus also the temperature, Ts ; of the resistor Rs rises. From the relation between Th and Ts to P; we can estimate the thermal conductance of the MWNT. Fig. 4 shows the temperature dependent thermal conductivity kðTÞ; of isolated MWNT in Fig. 3. This result shows remarkable differences from the previous ‘bulk’ measurements as described below. First, the room temperature value of kðTÞ is over 3000 W/m K, whereas the previous ‘bulk’ measurement on a MWNT mat using the 3v method estimates only 20 W/m K [14]. Note that our observed value is also an order of magnitude higher than that of aligned SWNT sample (250 W/m K) [16] but comparable to the theoretical expectation, 6000 W/m K [10]. This large difference between single-tube and ‘bulk’ measurements suggests that numerous highly resistive thermal junctions between the tubes largely dominate the

Fig. 4. The thermal conductivity of an individual MWNT of a diameter 14 nm. The solid lines represent linear fits of the data in a logarithmic scale at different temperature ranges. The slopes of the line fits are 2.5 and 2.0, respectively.

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thermal transport in mat samples. Second, kðTÞ shows interesting temperature dependent behavior that was absent in bulk measurements. As shown in this log – log plot, kðTÞ has two distinctively different temperature regimes where kðTÞ , T 2:5 ðT , 50 KÞ and kðTÞ , T 2 ð50 , T , 150 KÞ before the Umklapp scattering process sets in. From this cross-over behavior, it was also possible to extract out-ofplane Debye temperature u , 50 K in this sample [25].

4. Mesoscopic thermoelectricpower measurements There have been a number of experimental efforts to measure TEP of single walled [26,27], and mutliwalled nanotubes [17] using macroscopic ‘mat’ samples. These studies showed interesting unique thermoelectric phenomena, such as, sign change of TEP upon absorption and desorption of gas molecules on the sample and a logarithmic temperature dependence of TEP. However, mesoscopic measurements of single nanotubes are required to understand the intrinsic TEP of nanotube materials as we already discussed. In the previous section for thermal transport measurement, a suspended structure was required to isolated energy flow to the underlying substrate. However, for a TEP measurement, the tight control of energy flow in the device is not necessary. A temperature gradient along the length of the nanotube provided by local heating of the substrate is sufficient to facilitate the TEP measurement at mesoscopic scales. Fig. 5 shows a SEM image of a typical device for TEP measurement and its schematics. A SWNT was grown on a silicon oxide/silicon substrate using chemical vapor deposition [28]. After the SWNT growth, electrodes separated by , 2 mm were fabricated by electron beam lithography and following thermal evaporation of Cr (5 nm) and Au (30 nm) metal layers, contacting both ends of the SWNT. A microheater was fabricated adjacent to one of the nanotube– electrode contacts. The bias voltage applied to this heater line produces joule heating and raises the temperature locally around the adjacent contact area. The heat generated by the local heater initially propagates through the silicon oxide layer (1 mm thick), which has a relatively lower thermal conductivity (,0.5 W/m K), creating a temperature gradient across the SWNT and the surface of the substrate to which it is thermally anchored. The heat dissipates quickly, once it reaches the underlying silicon substrate, which has higher thermal conductivity (150 W/m K). The temperature of the SWNT-electrode junctions was monitored by the resistance changes of the thin electrodes by the four-probe method. These resistance changes were mapped to the temperature changes of junction electrodes later by measuring resistance changes of electrodes at different temperatures at equilibrium. The resulting temperature gradient across the SWNT was 0.1– 0.5 K/mm, while typical

Fig. 5. A SEM image (top) and a schematic (bottom) of a device for TEP measurement. Tow four-probe measuring thin metal lines serve as thermometer to probe the nanotube-junction temperature and electrodes to measure thermoelectric voltage.

power consumption in the microheater was less than 100 mW. The thermoelectric voltage across the SWNT can be readily measured with the electrode contacts with a high input impedance voltage preamplifier. Fig. 6 shows comparison of measured TEP and electronic conductance in a metallic SWNT device. We have measured the TEP of SWNTs over a large range of the gate voltages at lower temperatures. According to Mott’s formula, the electron diffusion component of TEP, Sd ; should be related to the change of electrical conductance, GðEÞ; as a function of the Fermi level Ef of the sample [29]:  2p2 kB2 T 1 dG  Sd ¼ 3lel G dE Ef Indeed, our TEP measurement (Fig. 6) clearly indicates the above relation between Sd and G holds qualitatively. Further investigation on these interesting mesoscopic phenomena is underway.

5. Prospect The TEP, thermal and electrical conductivity of the materials are of interest for thermoelectric device applications, such as heat pumps and power generators [30]. The

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transmission coefficient due to the resonant defect scattering [33,34] or the curvature induced small gap [35]. If we carefully choose the gate voltage near the sharp peaks in G; where dG=dVgate is large, we may be able to create a giant TEP (.200 mV/K), while the electrical conductance is not far from the quantum conductance. The phonon conduction will be limited by its quantum conductance in this regime. Achieving high ZT values in the quantum transport regime will not only be interesting for the research of fundamental transport phenomena, but also will have a tremendous impact in low temperature thermoelectric applications.

Acknowledgements The authors wish to thank A. Majumdar and P.L. McEuen for helpful discussion. This work is supported primarily by the Nanoscale Science and Engineering Initiative of the National Science Foundation under NSF Award Number CHE-011752.

Fig. 6. The electric conductance and thermopower of a SWNT at different gate voltages. The dotted lines represent the measurements at T ¼ 100 K and the solid lines represent measurement results at T ¼ 50 K:

performance of a thermoelectric device is quantified by a figure of merit, ZT ¼ S2 GT=k: ZT is a dimensionless number which measures the thermoelectric efficiency of thermoelectric energy conversion. Higher value correspond higher thermoelectric energy conversion efficiency. Recent work on superlattice semiconducting device demonstrated ZT , 2:5 at room temperature, breaking the long-standing limit of ZT , 1 for most of best known thermoelectric materials [31]. The key improvement in this work was to enhance the transport of current-carrying electrons while inhibiting transport of heat-carrying phonons. In 1D nanoscale systems, the increase of ZT might be further enhanced by the quantum confining of electrons and phonons in low dimensions [32]. It will be particularly interesting to consider ZT when both the electrical and thermal transports are in the quantum limit. In this regime, it might be possible to attain high ZT: SWNTs are an interesting material to test this idea. The conductance of CVD grown SWNTs with good contacts often approaches the ideal quantum conductance in the two ballistic channel. It is also believed that the phonon quantum transport regime should be achieved at relatively high temperature (. 30 K). Since only the four lowest acoustic phonon modes in SWNTs are available in this regime, S , 200 mV=K would be sufficient to have ZT . 1 for SWNTs below 30 K. In our initial effort, it was shown that the TEP can be tuned by the gate potential (Fig. 6). The large variations of G of SWNTs in the ballistic regime have been reported and interpreted as the change of the electron

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