Experimental Study on Interfacial Thermal Transport of Multi-Walled Carbon Nanotube

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1 Experimental Study on Interfacial Thermal Transport of Multi-Walled Carbon Nanotube KOJI TAKAHASHI 1, 2, 3), JUN HIROTANI 1), YUTAKA YAMADA 1) 1) Department of Aeronautics and Astronautics 2) JST, CREST 3) International Institute for Carbon-Neutral Energy Research (WPI-I2CNER) Kyushu University Motooka 744, Nishi-ku, Fukuoka, JAPAN Abstract: - Interfacial thermal transport of multi-walled carbon nanotube is explored by using T-type sensor. Reliable signals of heat flow through an individual nanotube were obtained. Estimated thermal boundary resistances between the end of CNT and solid surfaces do not show the clear dependency on material that has been predicted by the diffuse mismatch model treating graphite. This discrepancy is mainly due to the weak van der Waals force at the contact. The heat transfer coefficients of nanotube in gases were also measured by applying the T-type sensor and fin theory. Obtained results show good agreement with the kinetic theory for various gases but a large deviation was found for low pressure regime. Key-Words: - Carbon Nanotube, Thermal Conductivity, Thermal Contact Resistance, Defect, Hot-Film Sensor, MEMS, HRTEM 1 Introduction The outstanding electrical, thermal and mechanical properties of carbon nanotubes (CNTs) make them attractive materials in wide range of areas. In the last two decades, the great efforts of many researchers have unveiled most of their intrinsic properties. For example, the distinguished thermal conductivity is known to come from the strong sp 2 covalent bonds between light-weight carbon atoms and the long phonon mean free path in boundaryfree lattice structures. Experimental techniques also have been improved to obtain the reliable data of thermal conductivity by using individual CNT [1-2]. However, the interfacial thermal phenomena of CNT are still veiled even though the thermal boundary resistance (TBR) at the interfaces might dominate the thermal transport of nanomaterialbased devices, for example, CNT transistors, thermal interface materials using CNTs, and CNT fins. As theoretical approaches, diffuse mismatch model (DMM) and molecular dynamics (MD) simulations are used to calculate the TBR but their reliability is questionable due to their simple modeling of totally unknown interfacial phenomena [3-6]. To follow-up the numerical studies, it is vital to establish a reliable experimental method to obtain the real TBR of nanomaterials but the difficulty of both nanoscale thermal measurement and CNThandling prevent many researchers from successful experiments. So far, a few experimental studies have been conducted on TBR between CNT and solid surface, which uses scanning thermal microscopy, breakdown method, etc, but are inappropriate to obtain reliable quantity [7-9]. The heat transport coefficient (HTC) between CNT and fluid is also important but HTC data also very limited. For example, no successful experiment has been reported for heat transfer of individual CNT surrounded by gases [10-11]. The author s group has been developing experimental technique for thermal characterization of multi-walled (MW) CNTs, which uses a sampleattached T-type sensor employing suspended platinum nano hot-film [2, 12]. This method has the advantages of simplicity and extensibility in comparison with other reliable experimental methods using MEMS sensor/heater on two suspended membranes. In this paper, we report our extensive experiments to measure TBR and HTC of individual MWCNTs. ISBN:

2 MWCNT (a) Edge line of substrate Electrode (Heat sink) can be estimated from its electrical resistance using pre-calibrated temperature coefficient of resistance. The change (shift) of electrical resistance of the hotfilm sensor gives us the quantitative information of additional heat path and enables us to deduce the TBR or HTC. Our hot-film sensor is made from platinum thin film on a silicon substrate micro-fabricated by using electron beam lithography, physical vapor deposition, lift-off technique, and isotropic etching as described previously. Oxygen plasma is used in the final step to make sure of the electrical insulation of substrate surface. The width, length and thickness of our hot-film are ca. 500nm, ca. 10 m, and 40nm, respectively. An individual CNT specimen is picked up after HRTEM observation by using nano manipulator and one of its ends is bonded on the suspended hot-film by using electronbeam induced deposition (EBID). The contact at the junction is carefully checked by FESEM for minimum error due to contact resistance there. HRTEM is used to determine the accurate size of MWCNT and to check the lattice defects and undesirable deposition before measurement. Pt hot film (b) Fig.1 Schematic of T-type sensor for MWCNT probe. MWCNT is set to protrude from the sensor edge. Hotfilm temperature changes in dependent on the amount of heat dissipation through the probe. 2.2 Thermal boundary resistance between MWCNT end and solid surface For interfacial transport, any contamination on surface significantly degrades the reliability of data. SEM is useful to check the contact visually but always accompanies deposition of amorphous carbon on the observed surface. Thus we have replaced the SEM by an optical microscope with a long working-distance 50x lens (Nikon CFI LU Plan 2 Experimental 2.1 T-type nano thermal sensor The basic configuration of our sensor for the present study consists of a platinum hot-film suspended between two heat-sinks/electrodes and a specimen (MWCNT) bonded on the hot-film as shown in Fig.1 (a). By fabricating the hot-film close to the edge of sensor substrate, we can make the MWCNT protrude from the substrate and use it as thermal probe. While the CNT is away from any heat path other than the hot-film, a quadratic temperature distribution is formed along the hot-film. When the CNT contacts with a target surface or is surrounded by gas both of which has the same temperature as the electrodes on substrate, the hot-film temperature shifts to the solid line as listed in Fig.1 (b). It has to be noted that the temperature distribution cannot be obtained but the average temperature of the hot-film Optical microscope (long working-distance 50x lens) Target (Pt, SiO 2 ) Manipulator Vacuum chamber Peltier stage CNT V V Standard resistance Fig.2 Schematic of experimental setup. An optical microscope with a long working-distance 50 lens is used for monitoring the relative distance between a CNT end and a target surface and the target can be moved by a manipulator. ISBN:

3 Recent Advances in Circuits, Communications and Signal Processing by kleindiek MM3A-EM and both sensor and target are kept same temperature by using Peltier stage. Measurement principle is explained by Fig.3. When a CNT end contacts with target surface, a portion of the Joule heat in the hot film goes through the CNT into the target, which depends on the sum of three thermal resistances, the thermal resistance of the CNT itself, RCNT, the contact resistance at the CNT/hot-film junction, Rj, and that between the end of a CNT and target surface, Re. The current and the voltage of the hot-film are measured by a four-probe method with a current source (Advantest R6243) and two voltmeters (Keithley 2002). The effect of radiation and convection can be neglected because the temperature increase of the hot film is less than 10 K and experiments are conducted in high vacuum conditions of 10-3 Pa. As shown in Fig.4, the contact test was conducted repeatedly and reliable signals were Fig.3 Heat transfer model to obtain the TBR between CNT end and target surface. (a) Fig.4 Measured electrical resistance change of hot-film when the CNT end contacts with the target (Pt, SiO2). EPI ELWD) for the present contact tests in a chamber of controllable vacuum environment. Our experimental set-up is listed in Fig.2. To investigate the TBR dependence on material, we prepare deposited films on an identical substrate and conduct contact tests. The substrate is manipulated ISBN: Fig.5 TEM image of the CNT end (a). The contact area is assumed to be disk-shaped with a diameter A(32nm), B(26nm) and C(30nm), respectively. AFM images of Pt (b) and SiO2 (c) surfaces. Root-mean-square surface roughness of a target is evaluated from the average of scanning some nm2 areas. 312

4 obtained which are much larger than the resistance fluctuation caused by temperature instability. When the CNT end contacts with a solid surface, resistance shift is almost constant within less than a 5% variation. By using our measured thermal conductivity data of MWCNTs picked-up from the identical bulk containing the current sample as well as our previous report for CNT end Au contact [12], the TBR is obtained as [K/W] for the CNT end Pt contact, [K/W] for the CNT end SiO 2 contact, respectively. To compare our data with other reports, TBR per unit area has to be obtained. We carefully conducted HRTEM observation of employed MWCNT end as shown in Fig. 5 (a). We assume that the contact area on the CNT end is a disk with a diameter of 32nm (A), 26nm (B) or 30nm (C), as indicated by the arrows in Fig.5 (a), corresponding to contact areas of [m 2 ]. AFM investigation of the target surface is also conducted and listed in Fig.5 (a) and (b). The effect of surface roughness is discussed afterwards. as the length and thermal conductivity of the CNT and the electrical resistance shift in each contact. Our TBR value between a CNT and a SiO 2 surface is consistent with the reported data between graphene and a SiO 2 surface, [(m 2 K)/W] [13], which is explained by the analogy between a (a) 2.3 Heat transfer coefficient of individual MWCNT in gases The experiment to determine the heat transfer coefficient needs three steps as explained in Fig. 6. At first, the thermal and electrical properties of hotfilm have to be measured in vacuum condition. Next, a gas is introduced to the chamber then heat transfer from hot-film into air generates, which causes the temperature decrease of the Joule-heated hot-film. We can assess the heat transfer coefficient of Pt hotfilm from these two steps. Finally, CNT is bonded on the hot-film and similar experiment is conducted in the same gas condition. Because the CNT works as a pin fin, the heat transfer coefficient of CNT is calculated using the fin theory from the data of temperature shift between those with and without CNT fin. HRTEM observation of the employed MWCNT is conducted for defect/contamination check and diameter measurement. Obtained electrical resistance change for each step as a function of heating power is listed in Fig. 7. Here we skip the formulation in detail but by comparing them we can determine the heat transfer coefficient between Pt hot film and surrounding air and that between CNT and surrounding air. (b) Fig.6 Measurement principles for obtaining heat ytransfer coefficient of an individual CNT. After calibrating the properties of Pt hot-film (a), the heat flow from the CNT to surrounding gas is measured (b). 3 Discussion TBRs per unit area are calculated and listed in Table.1, which include all of estimation errors, such Fig.7 Electrical resistance change versus supplied power of hot-film measured in a vacuum and air, with and without CNT. ISBN:

5 Table 1 Thermal boundary resistance and root-meansquare surface roughness values found in this work. The TBR value between a CNT end and a gold surface is taken from reference 12. The DMM results for a CNT contacting Pt or Au are calculated by only considering the elastic scattering. The TBR between graphite and SiO 2 is taken from reference 13. Fig.8 Heat transfer coefficients of individual CNTs in air, nitrogen, argon, and helium environments and theoretical estimations. CNT and graphene. Both experiments show lower TBR values than that predicted for SWCNT/SiO 2 by a MD simulation of [(m 2 K)/W] [14], so that the gap between the MD value and ours stems from the differences in the materials and the uncertainties in the potentials used in the MD simulation. In addition, because of the analogy between MWCNT and graphite, we use DMM to calculate the TBR between Graphite and metals (Pt, Au) by only accounting for elastic scattering [4], and also added the estimated TBR value between graphite and SiO 2 [13] in Table.1. In the DMM prediction, the TBR is dependent on the materials. However, our experimental results do not show a clear materialdependence of the TBR and produce much larger value than that from that DMM calculation. Because the DMM method assumes a very strong bond at the interface and only accounts for phonon contributions, it is not always adequate to describe weak bonding at an interface, such as van der Waals forces. The weak interface interaction restricts the transmission of high frequency phonons and low frequency phonons would dominate interfacial heat transport. Heat transfer coefficient is determined for air, nitrogen, argon, and helium and shown in figure 8. The value for air of ca W/m 2 K is consistent with molecular dynamics prediction [15] and the dependence on gas species shows good agreement with kinetic theory for rarefied gas as, h nvcv / 4 where n is number density of molecules, v is velocity, and C v is specific heat per molecule [16]. It is assumed that the molecular accommodation coefficient is set to 1, which means incident Fig.9 Measured heat transfer coefficient versus surrounding air pressure. molecule achieve the thermal equilibrium with the solid surface after collision with the solid surface. The real accommodation coefficient is less than 1. Comparison between our data and this kinetic theory is listed in Fig. 9. Between 1 to 0.1 atm, our results are consistent with kinetic theory. However, at lower pressure, or in molecule flow regime, HTC becomes larger than the theory. Further investigation is required for understanding the interfacial heat transfer of CNT with gas in this regime. 4 Conclusion Interfacial thermal transport of MWCNT was explored by using T-type sensor. Obtained TBRs between the end of CNT and solid surfaces do not show the clear dependency on material that is predicted by the DMM. Our results are the first reliable TBR data for van der Waals force regime and should contribute the future improvement of ISBN:

6 theory on interfacial thermal phenomena. The measured HTCs are also the first data for individual CNT, which show good agreement with the kinetic theory but further study is desired for low pressure regime. Acknowledgement This work was partially supported by JSPS KAKENHI Grant Number , , and Sensor fabrication was partially conducted at the Collabo-Station II of Kyushu University. HRTEM observation was conducted in the Research Laboratory for High Voltage Electron Microscopy, Kyushu University. References: [1] P. Kim, L. Shi, A. Majumdar, P. L. McEuen, Thermal Transport Measurements of Individual Multiwalled Nanotubes, Physical Review Letters, Vol.87, 2001, [2] M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe and T. Shimizu, Measuring the Thermal Conductivity of a Single Carbon Nanotube, Physical Review Letters, Vol. 95, 2005, [3] R. Prasher, Thermal boundary resistance and thermal conductivity of multiwalled carbon nanotubes, Physical Review B Vol. 77, 2008, [4] J. C. Duda, J. L. Smoyer, P. M. Norris, and P. E. Hopkins, Extension of the diffuse mismatch model for thermal boundary conductance between isotropic and anisotropic materials, Applied Physics Letters, Vol. 95, 2009, [5] M. Hu, P. Keblinski, J.-S. Wang, and N. Raravikar, Interfacial thermal conductance between silicon and a vertical carbon nanotube, Journal of Applied Physics, Vol. 104, 2008, [6] C. F. Carlborg, J. Shiomi, and S. Maruyama, Thermal boundary resistance between singlewalled carbon nanotubes and surrounding matrices, Physical Review B, Vol. 78, 2008, [7] L. Shi, J. Zhou, P. Kim, A. Bachtold, A. Majumdar and P. L. McEuen, Thermal probing of energy dissipation in current-carrying carbon nanotubes, Journal of Applied Physics, Vol. 105, 2009, [8] H. Maune, H.-Y. Chiu, and M. Bockrath, Thermal resistance of the nanoscale constrictions between carbon nanotubes and solid substrates, Applied Physics Letters, Vol. 89, 2006, [9] C.-L. Tsai, A. Liao, E. Pop, and M. Shim, Electrical power dissipation in semiconducting carbon nanotubes on single crystal quartz and amorphous SiO 2, Applied Physics Letters, Vol. 99, 2011, [10] I-K. Hsu, M. T. Pettes, M. Aykol, L. Shi, and S. B. Cronin, The effect of gas environment on electrical heating in suspended carbon nanotubes, Journal of Applied Physics, Vol. 108, 2010, [11] I-K. Hsu, M. T. Pettes, M. Aykol, C.-C. Chang, W.-H. Hung, J. Theiss, L. Shi, and S. B. Cronin, Direct observation of heat dissipation in individual suspended carbon nanotubes using a two-laser technique, Journal of Applied Physics Vol. 110, 2011, [12] J. Hirotani, T. Ikuta, T. Nishiyama and K. Takahashi, Thermal Boundary Resistance between the End of an Individual Carbon Nanotube and a Au Surface, Nanotechnology. Vol. 22, 2011, [13] Z. Chen, W. Jang, W. Bao, C. N. Lau, and C. Dames, Thermal contact resistance between graphene and silicon dioxide, Applied Physics Letters, Vol. 95, 2009, [14] Z-Y. Ong and E. Pop, Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and SiO 2, Physical Review B, Vol. 81, 2010, [15] M. Hu, S. Shenogin, P. Keblinski, and N. Raravikar, Thermal energy exchange between carbon nanotube and air, Applied Physics Letters, Vol. 90, 2007, [16] J. Jeans, An introduction to the kinetic theory of gases, Cambridge University Press,1967 ISBN: