Research Papers: Experimental Techniques

Four-Probe Measurement of Thermal Transport in Suspended Few-Layer Graphene With Polymer Residue

[+] Author and Article Information
Eric Ou

Department of Mechanical Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: eric.ou@utexas.edu

Xun Li

Department of Mechanical Engineering and
Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: xul34@pitt.edu

Sangyeop Lee

Department of Mechanical Engineering and
Materials Science,
Department of Physics and Astronomy,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: sylee@pitt.edu

Kenji Watanabe

Research Center for Functional Materials,
National Institute of Materials Science,
1-1 Namiki,
Tsukuba 305-0044, Japan
e-mail: WATANABE.Kenji.AML@nims.go.jp

Takashi Taniguchi

Research Center for Functional Materials,
National Institute of Materials Science,
1-1 Namiki,
Tsukuba 305-0044, Japan
e-mail: TANIGUCHI.Takashi@nims.go.jp

Li Shi

Department of Mechanical Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: lishi@mail.utexas.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 2, 2018; final manuscript received March 7, 2019; published online April 17, 2019. Assoc. Editor: Evelyn Wang.

J. Heat Transfer 141(6), 061601 (Apr 17, 2019) (5 pages) Paper No: HT-18-1644; doi: 10.1115/1.4043167 History: Received October 02, 2018; Revised March 07, 2019

The presence of unknown thermal contact thermal resistance has limited prior two-probe thermal transport measurements of suspended graphene samples. Here, we report four-probe thermal transport measurements of suspended seven-layer graphene. By isolating the thermal contact resistance, we are able to attribute the observed reduced thermal conductivity primarily to polymeric residue on the sample instead of the contact thermal resistance, which resulted in ambiguity in the prior experimental studies of the effect of polymer reside. The extrinsic scattering rate due to the polymer residue is extracted from the measurement results based on a solution of the Peierls-Boltzmann phonon transport equation.

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Grahic Jump Location
Fig. 1

(a) Optical and (b) scanning electron micrographs of a 3.8 μm wide, seven-layer thick patterned FLG sample assembled across four suspended Pd/SiNx beams, each of which acts as a resistance thermometer (RT). Additional Pd pads were deposited on top of the FLG sample to clamp the graphene sample onto the thermometer lines. The black dots left on the sample and metal lines are polymeric dirt particles. (c) Thermal resistance circuit of the measurement device when the first thermometer line is Joule heated with power (IV)1. Rb,j is the thermal resistance of the jth RT beam. Rc,j represents the thermal contact resistance between the sample and the jth RT. R1, R2, and R3 represent the intrinsic thermal resistances of the three suspended sample segments. θc,j,i is the jth RT temperature rise at the contact point with the sample when the ith line is heated. θ0 is the temperature rise at the point where the suspended RT lines terminate into the bulk substrate. Qj,i is the heat flow from the jth line to the sample when the ith line is heated.

Grahic Jump Location
Fig. 2

Atomic force microscope scan of the seven-layer graphene sample before patterning. The thickness of the sample was determined by averaging the step height measured at multiple points on the right edge of the scan.

Grahic Jump Location
Fig. 3

Measured electrical resistance change of the thermometer lines as a function of the heating current through the first thermometer line

Grahic Jump Location
Fig. 4

Measured electrical resistances of the four thermometer lines at a low bias current as a function of the stage temperature

Grahic Jump Location
Fig. 5

Measured thermal resistances of the sample and the average thermal resistance of the thermometer lines. The random uncertainty of the values does not exceed the marker size.

Grahic Jump Location
Fig. 6

Measured thermal conductivity of the FLG as a function of temperature for the as-transferred (circles), 1 h annealed (unfilled up triangles), and 9 h annealed sample (squares). Shown for comparison is the highest basal-plane thermal conductivity reported for bulk highly oriented pyrolytic graphite (down triangles) in Touloukian et al. [23], and the theoretical thermal conductivity (diamonds) of a defect-free single layer graphene sample with the same lateral dimension as the measured FLG. The lines are the fitting of the experimental data by using the calculated phonon dispersion of seven-layer graphene and a frequency-dependent scattering rate.

Grahic Jump Location
Fig. 7

Raman spectrum of the middle suspended segment of the sample. The background slope is indicative of the presence of polymer residue.



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