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Research Papers: Micro/Nanoscale Heat Transfer

# Thermal Properties of Metal-Coated Vertically Aligned Single-Wall Nanotube Arrays

[+] Author and Article Information
M. A. Panzer

Department of Mechanical Engineering,  Stanford University, Room 101, Building 530, 440 Escondido Mall, Stanford, CA 94305mpanzer@stanford.edu

G. Zhang, D. Mann, H. Dai

Department of Chemistry,  Stanford University, Room 125, William Keck Science Building, Stanford, CA 94305

X. Hu

Intel Corporation, 5000 W Chandler Blvd., Chandler, AZ 85226

E. Pop

Department of Electrical and Computer Engineering,  University of Illinois at Urbana-Champaign, Urbana, IL 61801-2918

K. E. Goodson

Department of Mechanical Engineering,  Stanford University, Room 101, Building 530, 440 Escondido Mall, Stanford, CA 94305

J. Heat Transfer 130(5), 052401 (Apr 08, 2008) (9 pages) doi:10.1115/1.2885159 History: Received October 26, 2006; Revised September 17, 2007; Published April 08, 2008

## Abstract

Owing to their high thermal conductivities, carbon nanotubes (CNTs) are promising for use in advanced thermal interface materials. While there has been much previous research on the properties of isolated CNTs, there are few thermal data for aligned films of single wall nanotubes. Furthermore, such data for nanotube films do not separate volume from interface thermal resistances. This paper uses a thermoreflectance technique to measure the volumetric heat capacity and thermal interface resistance and to place a lower bound on the internal volume resistance of a vertically aligned single wall CNT array capped with an aluminum film and palladium adhesion layer. The total thermal resistance of the structure, including volume and interface contributions, is $12m2KMW−1$. The data show that the top and bottom interfaces of the CNT array strongly reduce its effective vertical thermal conductivity. A low measured value for the effective volumetric heat capacity of the CNT array shows that only a small volume fraction of the CNTs participate in thermal transport by bridging the two interfaces. A thermal model of transport in the array exploits the volumetric heat capacity to extract an individual CNT-metal contact resistance of $10m2K1GW−1$ (based on the annular area $Aa=πdb$), which is equivalent to the volume resistance of $14nm$ of thermal $SiO2$. This work strongly indicates that increasing the fraction of CNT-metal contacts can reduce the total thermal resistance below $1m2KMW−1$.

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## Figures

Figure 1

(a) SEM profile of aligned SWNTs grown on Si—the tube length is 28μm. The SWNT diameter ranges between 1nm and 2nm, with an average of approximately 1.3nm. (b) AFM topographic profile of the top of the CNT film, which indicates that the rms surface roughness is ∼60nm. (c) SEM of the top of the metal film after it has been deposited on CNTs. The image shows that the metal film is porous at a scale below 100nm.

Figure 2

(a) Schematic of the thermoreflectance thermometry experimental setup including the optical and signal paths. (b) Schematic of the sample geometry. The initial deposition of a 20nm thick layer of palladium on the SWNT ends forms an adhesion layer with the 160nm thick aluminum film used for thermal reflectance thermometry.

Figure 3

Typical thermal response trace data for a particular measurement (solid) for the 28μm sample along with the best-fit analytical solution evaluated with the average best-fit parameters summarized in Table 1 below (dashed). The data show two characteristic decay time scales during the measurement: the initial rapid decay lasting ∼0.5μs followed by a longer decay lasting ∼4μs.

Figure 4

Schematic illustrating the hypothesis that a subset of the CNTs is in good thermal contact with the porous and discontinuous evaporated film. The data suggest that the overwhelming majority of the heat transport is brought about by longer tubes that fully contact the metal film. We use a thermal circuit model to account for lateral thermal transport in the CNT film. The heat flows into the central tube that is in thermal contact with the metal film and then flow laterally through the intertube coupling resistance to surrounding tubes. We reduce the thermal network to a frequency dependant parallel equivalent RC thermal circuit, which is what is experimentally measured.

Figure 5

(a) Schematic top view of a CNT in a close-pack arrangement grouped into concentric shells of neighboring tubes to calculate the effective impedance of the series of neighboring tubes, as assumed in the model. (b) Block diagram of impedance network modeling the linking of neighboring shells by an intershell thermal resistance.

Figure 6

The effective thermal capacity Cth,eq, and thermal resistance, Req due to intertube coupling effects normalized to that of an individual tube as a function the intertube coupling resistance Ri″

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