Experimental Study on Interfacial Thermal Transport of Multi-Walled

Carbon Nanotube

KOJI TAKAHASHI1, 2, 3), JUN HIROTANI1), YUTAKA YAMADA1) 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 takahashi@aero.kyushu-u.ac.jp

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 sp2 covalent bonds between light-weight carbon atoms and the long phonon mean free path in boundary-free 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 nanomaterial-based 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 CNT-handling 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 sample-attached 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.

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(a)

MWCNT

Edge line of substrate

Pt hot film

Electrode(Heat sink)

(b)

Fig.1 Schematic of T-type sensor for MWCNT probe.MWCNT is set to protrude from the sensor edge. Hot-film temperature changes in dependent on the amountof heat dissipation through the probe.

Manipulator

Peltier stage

Target (Pt, SiO2)

CNT

Optical microscope(long working-distance

50x lens)

V

VStandard resistance

Vacuumchamber

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.

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

can be estimated from its electrical resistance using pre-calibrated temperature coefficient of resistance. The change (shift) of electrical resistance of the hot-film 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. 10m, 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 electron-beam 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. 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

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Fig.3 Heat transfer model to obtain the TBR betweenCNT end and target surface.

Fig.4 Measured electrical resistance change of hot-filmwhen the CNT end contacts with the target (Pt, SiO2).

(a)

Fig.5 TEM image of the CNT end (a). The contact areais 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 surfaceroughness of a target is evaluated from the average ofscanning some 30×30 nm2 areas.

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

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

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(a)

(b)

Fig.6 Measurement principles for obtaining heatytransfer coefficient of an individual CNT. Aftercalibrating the properties of Pt hot-film (a), the heatflow from the CNT to surrounding gas is measured (b).

Fig.7 Electrical resistance change versus suppliedpower of hot-film measured in a vacuum and air, withand without CNT.

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 7.10-10.1 ×106 [K/W] for the CNT end – Pt contact, 12.5-15.3 ×106 [K/W] for the CNT end – SiO2 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 5.2-8.2 ×10-16 [m2]. 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.

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 hot-film 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 hot-film 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.

3 Discussion TBRs per unit area are calculated and listed in

Table.1, which include all of estimation errors, such

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 SiO2 surface is consistent with the reported data between graphene and a SiO2 surface, 5.6-12×10-9 [(m2K)/W] [13], which is explained by the analogy between a

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Table 1 Thermal boundary resistance and root-mean-square surface roughness values found in this work.The TBR value between a CNT end and a gold surfaceis taken from reference 12. The DMM results for aCNT contacting Pt or Au are calculated by onlyconsidering the elastic scattering. The TBR betweengraphite and SiO2 is taken from reference 13.

Fig.8 Heat transfer coefficients of individual CNTs in air,nitrogen, argon, and helium environments and theoreticalestimations.

Fig.9 Measured heat transfer coefficient versussurrounding air pressure.

CNT and graphene. Both experiments show lower TBR values than that predicted for SWCNT/SiO2 by a MD simulation of 17×10-9 [(m2K)/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 SiO2 [13] in Table.1. In the DMM prediction, the TBR is dependent on the materials. However, our experimental results do not show a clear material-

dependence 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. 9 104 W/m2K is consistent with molecular dynamics prediction [15] and the dependence on gas species shows good agreement with kinetic theory for rarefied gas as,

4/nvCh v where n is number density of molecules, v is velocity, and Cv is specific heat per molecule [16]. It is assumed that the molecular accommodation coefficient is set to 1, which means incident

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

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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 23360101, 23656153, 23760191 and 24560237. 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,

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[16] J. Jeans, An introduction to the kinetic theory of gases, Cambridge University Press,1967

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