We have developed a nanofabricated resistance thermometer device to measure the thermal conductivity of graphene monolayers exfoliated onto silicon dioxide. The measurement results show that the thermal conductivity of the supported graphene is approximately at room temperature. While this value is lower than the reported basal plane values for graphite and suspended graphene because of phonon leakage across the graphene-support interface, it is still considerably higher than the values for common thin film electronic materials. Here, we present a detailed discussion of the design and fabrication of the measurement device. Analytical and numerical heat transfer solutions are developed to evaluate the accuracy and uncertainty of this method for thermal conductivity measurement of high-thermal conductivity ultrathin films.
1.
Novoselov
, K. S.
, Geim
, A. K.
, Morozov
, S. V.
, Jiang
, D.
, Zhang
, Y.
, Dubonos
, S. V.
, Grigorieva
, I. V.
, and Firsov
, A. A.
, 2004, “Electric Field Effect in Atomically Thin Carbon Films
,” Science
0036-8075, 306
(5696
), pp. 666
–669
.2.
Bolotin
, K. I.
, Sikes
, K. J.
, Jiang
, Z.
, Klima
, M.
, Fudenberg
, G.
, Hone
, J.
, Kim
, P.
, and Stormer
, H. L.
, 2008, “Ultrahigh Electron Mobility in Suspended Graphene
,” Solid State Commun.
0038-1098, 146
(9–10
), pp. 351
–355
.3.
Lee
, C.
, Wei
, X.
, Kysar
, J. W.
, and Hone
, J.
, 2008, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
,” Science
0036-8075, 321
(5887
), pp. 385
–388
.4.
Balandin
, A. A.
, Ghosh
, S.
, Bao
, W.
, Calizo
, I.
, Teweldebrhan
, D.
, Miao
, F.
, and Lau
, C. N.
, 2008, “Superior Thermal Conductivity of Single-Layer Graphene
,” Nano Lett.
1530-6984, 8
(3
), pp. 902
–907
.5.
Cahill
, D. G.
, and Pohl
, R. O.
, 1987, “Thermal Conductivity of Amorphous Solids Above the Plateau
,” Phys. Rev. B
0556-2805, 35
(8
), pp. 4067
–4073
.6.
Hostetler
, J. L.
, Smith
, A. N.
, and Norris
, P. M.
, 1997, “Thin-Film Thermal Conductivity and Thickness Measurements Using Picosecond Ultrasounds
,” Nanoscale Microscale Thermophys. Eng.
1556-7265, 1
(3
), pp. 237
–244
.7.
Cahill
, D. G.
, 2004, “Analysis of Heat Flow in Layered Structures for Time-Domain Thermoreflectance
,” Rev. Sci. Instrum.
0034-6748, 75
(12
), pp. 5119
–5122
.8.
Stevens
, R. J.
, Smith
, A. N.
, and Norris
, P. M.
, 2005, “Measurement of Thermal Boundary Conductance of a Series of Metal-Dielectric Interfaces by the Transient Thermoreflectance Technique
,” ASME J. Heat Transfer
0022-1481, 127
(3
), pp. 315
–322
.9.
Ju
, Y. S.
, Kurabayashi
, K.
, and Goodson
, K. E.
, 1999, “Thermal Characterization of Anisotropic Thin Dielectric Films Using Harmonic Joule Heating
,” Thin Solid Films
0040-6090, 339
(1–2
), pp. 160
–164
.10.
Jain
, A.
, and Goodson
, K. E.
, 2008, “Measurement of the Thermal Conductivity and Heat Capacity of Freestanding Shape Memory Thin Films Using the 3ω Method
,” ASME J. Heat Transfer
0022-1481, 130
(10
), p. 102402
.11.
Mavrokefalos
, A.
, Pettes
, M. T.
, Zhou
, F.
, and Shi
, L.
, 2007, “Four-Probe Measurements of the In-Plane Thermoelectric Properties of Nanofilms
,” Rev. Sci. Instrum.
0034-6748, 78
(3
), p. 034901
.12.
Zink
, B. L.
, Revaz
, B.
, Cherry
, J. J.
, and Hellman
, F.
, 2005, “Measurement of Thermal Conductivity of Thin Films With a Si-N Membrane-Based Microcalorimeter
,” Rev. Sci. Instrum.
0034-6748, 76
(2
), p. 024901
.13.
Nair
, R. R.
, Blake
, P.
, Grigorenko
, A. N.
, Novoselov
, K. S.
, Booth
, T. J.
, Stauber
, T.
, Peres
, N. M. R.
, and Geim
, A. K.
, 2008, “Fine Structure Constant Defines Visual Transparency of Graphene
,” Science
0036-8075, 320
(5881
), pp. 1308
.14.
Faugeras
, C.
, Faugeras
, B.
, Orlita
, M.
, Potemski
, M.
, Nair
, R. R.
, and Geim
, A. K.
, 2010, “Thermal Conductivity of Graphene in Corbino Membrane Geometry
,” ACS Nano
1936-0851, 4
(4
), pp. 1889
–1892
.15.
Cai
, W.
, Moore
, A. L.
, Zhu
, Y.
, Li
, X.
, Chen
, S.
, Shi
, L.
, and Ruoff
, R. S.
, 2010, “Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition
,” Nano Lett.
1530-6984, 10
(5
), pp. 1645
–1651
.16.
Klemens
, P. G.
, 2001, “Theory of Thermal Conduction in Thin Ceramic Films
,” Int. J. Thermophys.
0195-928X, 22
(1
), pp. 265
–275
.17.
Prasher
, R.
, 2007, “Thermal Conductance of Single-Walled Carbon Nanotube Embedded in an Elastic Half-Space
,” Appl. Phys. Lett.
0003-6951, 90
(14
), p. 143110
.18.
Seol
, J. H.
, Jo
, I.
, Moore
, A. L.
, Lindsay
, L.
, Aitken
, Z. H.
, Pettes
, M. T.
, Li
, X.
, Yao
, Z.
, Huang
, R.
, Broido
, D.
, Mingo
, N.
, Ruoff
, R. S.
, and Shi
, L.
, 2010, “Two-Dimensional Phonon Transport in Supported Graphene
,” Science
0036-8075, 328
(5975
), pp. 213
–216
.19.
Blake
, P.
, Hill
, E. W.
, Castro Neto
, A. H.
, Novoselov
, K. S.
, Jiang
, D.
, Yang
, R.
, Booth
, T. J.
, and Geim
, A. K.
, 2007, “Making Graphene Visible
,” Appl. Phys. Lett.
0003-6951, 91
(6
), p. 063124
.20.
Abergel
, D. S. L.
, Russell
, A.
, and Fal’ko
, V. I.
, 2007, “Visibility of Graphene Flakes on a Dielectric Substrate
,” Appl. Phys. Lett.
0003-6951, 91
(6
), p. 063125
.21.
Ferrari
, A. C.
, and Robertson
, J.
, 2000, “Interpretation of Raman Spectra of Disordered and Amorphous Carbon
,” Phys. Rev. B
0556-2805, 61
(20
), pp. 14095
–14107
.22.
Incropera
, F. P.
, DeWitt
, P. D.
, Bergman
, T. L.
, and Lavine
, A. L.
, 2007, Fundamentals of Heat and Mass Transfer
, Wiley
, Hoboken, NJ
.23.
Schmidt
, A. J.
, Chen
, X.
, and Chen
, G.
, 2008, “Pulse Accumulation, Radial Heat Conduction, and Anisotropic Thermal Conductivity in Pump-Probe Transient Thermoreflectance
,” Rev. Sci. Instrum.
0034-6748, 79
(11
), p. 114902
.24.
Li
, Q. W.
, Liu
, C. H.
, and Fan
, S. S.
, 2009, “Thermal Boundary Resistances of Carbon Nanotubes in Contact With Metals and Polymers
,” Nano Lett.
1530-6984, 9
(11
), pp. 3805
–3809
.25.
Persson
, A. I.
, Koh
, Y. K.
, Cahill
, D. G.
, Samuelson
, L.
, and Linke
, H.
, 2009, “Thermal Conductance of InAs Nanowire Composites
,” Nano Lett.
1530-6984, 9
(12
), pp. 4484
–4488
.26.
Chen
, Z.
, Jang
, W.
, Bao
, W.
, Lau
, C. N.
, and Dames
, C.
, 2009, “Thermal Contact Resistance Between Graphene and Silicon Dioxide
,” Appl. Phys. Lett.
0003-6951, 95
(16
), p. 161910
.27.
Ashcroft
, N. W.
, and Mermin
, N. D.
, 1976, Solid State Physics
, Saunders College Publishing
, Fort Worth, TX
.28.
Cahill
, D. G.
, 1990, “Thermal Conductivity Measurement From 30 to 750 K: The 3ω Method
,” Rev. Sci. Instrum.
0034-6748, 61
(2
), pp. 802
–808
.29.
Al-Jishi
, R.
, and Dresselhaus
, G.
, 1982, “Lattice-Dynamical Model for Graphite
,” Phys. Rev. B
0556-2805, 26
(8
), pp. 4514
–4522
.30.
Zhang
, Q. G.
, Cao
, B. Y.
, Zhang
, X.
, Fujii
, M.
, and Takahashi
, K.
, 2006, “Size Effects on the Thermal Conductivity of Polycrystalline Platinum Nanofilms
,” J. Phys.: Condens. Matter
0953-8984, 18
, pp. 7937
–7950
.31.
Zhang
, X.
, Xie
, H.
, Fujii
, M.
, Ago
, H.
, Takahashi
, K.
, Ikuta
, T.
, Abe
, H.
, and Shimizu
, T.
, 2005, “Thermal and Electrical Conductivity of a Suspended Platinum Nanofilm
,” Appl. Phys. Lett.
0003-6951, 86
, p. 171912
.32.
Slack
, G. A.
, 1962, “Anisotropic Thermal Conductivity of Pyrolytic Graphite
,” Phys. Rev.
0031-899X, 127
(3
), pp. 694
–701
.33.
Nath
, P.
, and Chopra
, K. L.
, 1974, “Thermal Conductivity of Copper Films
,” Thin Solid Films
0040-6090, 20
(1
), pp. 53
–62
.34.
Ju
, Y. S.
, and Goodson
, K. E.
, 1999, “Phonon Scattering in Silicon Films With Thickness of Order 100 nm
,” Appl. Phys. Lett.
0003-6951, 74
(20
), pp. 3005
–3007
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