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Thermal properties of graphene and nanostructured carbon materials

Nature Materials volume 10, pages 569–581 (2011)Cite this article

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Abstract

Recent years have seen a rapid growth of interest by the scientific and engineering communities in the thermal properties of materials. Heat removal has become a crucial issue for continuing progress in the electronic industry, and thermal conduction in low-dimensional structures has revealed truly intriguing features. Carbon allotropes and their derivatives occupy a unique place in terms of their ability to conduct heat. The room-temperature thermal conductivity of carbon materials span an extraordinary large range — of over five orders of magnitude — from the lowest in amorphous carbons to the highest in graphene and carbon nanotubes. Here, I review the thermal properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder. Special attention is given to the unusual size dependence of heat conduction in two-dimensional crystals and, specifically, in graphene. I also describe the prospects of applications of graphene and carbon materials for thermal management of electronics.

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Figure 1: Thermal properties of carbon allotropes and their derivatives.
Figure 2: Thermal conductivity of disordered and nanostructured carbon materials.
Figure 3: Thermal conductivity of quasi-2D carbon materials: intrinsic versus extrinsic effects.
Figure 4: Thermal properties of low-dimensional carbon materials.

References

  1. Balandin, A. A. Better computing through CPU cooling. IEEE Spectrum 29–33 (October, 2009).

  2. Ioffe, A. F. Semiconductor Thermoelements and Thermal Cooling (Nauka, 1956).

    Google Scholar 

  3. Borca-Tasciuc, T. et al. Thermal conductivity of InAs/AlSb superlattices. Microscale Thermophys. Eng. 5, 225–231 (2001).

    CAS  Google Scholar 

  4. Balandin, A. & Wang, K. L. Significant decrease of the lattice thermal conductivity due to phonon confinement in a free-standing semiconductor quantum well. Phys. Rev. B. 58, 1544–1549 (1998).

    CAS  Google Scholar 

  5. Lepri, S., Livi, R. & Politi, A. Thermal conduction in classical low-dimensional lattices. Phys. Rep. 377, 1–80 (2003).

    CAS  Google Scholar 

  6. Basile, G., Bernardin, C. & Olla, S. Momentum conversion model with anomalous thermal conductivity in low dimensional system. Phys. Rev. Lett. 96, 204303–204304 (2006).

    Google Scholar 

  7. Chang, C. W., Okawa, D., Garcia, H., Majumdar, A. & Zettl, A. Breakdown of Fourier's law in nanotube thermal conductors. Phys. Rev. Lett. 101, 075903–075904 (2008).

    CAS  Google Scholar 

  8. Narayan, O. & Ramaswamy, S. Anomalous heat conduction in one dimensional momentum-conserving systems. Phys. Rev. Lett. 89, 200601–200604 (2002).

    Google Scholar 

  9. Dresselhaus, M. S., Dresselhaus, G. & Eklund, P. C. Science of Fullerenes and Carbon Nanotubes (Academic Press, 1996).

    Google Scholar 

  10. Kim, P., Shi, L., Majumdar, A. & Mc Euen, P. L. Thermal transport measurement of individual multiwalled nanotubes. Phys. Rev. Lett. 87, 215502 (2001).

    CAS  Google Scholar 

  11. Pop, E., Mann, D., Wang, Q., Goodson, K. & Dai, H. Thermal conductance of an individual single-wall carbon nanotube above room temperature. Nano Lett. 6, 96–100 (2006).

    CAS  Google Scholar 

  12. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    CAS  Google Scholar 

  13. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007).

    CAS  Google Scholar 

  14. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    CAS  Google Scholar 

  15. Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005).

    CAS  Google Scholar 

  16. Balandin, A. A. et al. Superior thermal conductivity of single layer graphene. Nano Lett. 8, 902–907 (2008).

    CAS  Google Scholar 

  17. Ghosh, S. et al. Extremely high thermal conductivity in graphene: Prospects for thermal management application in nanoelectronic circuits. Appl. Phys. Lett. 92, 151911 (2008).

    Google Scholar 

  18. Calizo, I., Balandin, A. A., Bao, W., Miao, F. & Lau, C. N. Temperature dependence of the Raman spectra of graphene and graphene multilayers. Nano Lett. 7, 2645–2649 (2007).

    CAS  Google Scholar 

  19. Ghosh, S. et al. Thermal properties of polycrystalline graphene films and reduced graphene-oxide films. MRS Proc. S6.2, 198 (2010).

    Google Scholar 

  20. Bhandari, C. M. & Rowe, D. M. Thermal Conduction in Semiconductors (Wiley & Sons, 1988).

    Google Scholar 

  21. Cahill, D. G. Thermal conductivity measurement from 30 to 750 K: the 3ω method. Rev. Sci. Instrum. 61, 802–808 (1990).

    CAS  Google Scholar 

  22. Klemens, P. G. Solid State Physics Vol. 7 (eds Seitz, F. & Turnbull, D.) 1–98 (Academic, 1958).

    Google Scholar 

  23. Klemens, P. G. Theory of the A-plane thermal conductivity of graphite. J. Wide Bandgap Mater. 7, 332–339 (2000).

    CAS  Google Scholar 

  24. Pierson, H. O. Handbook of Carbon, Graphite, Diamonds and Fullerenes: Processing, Properties and Applications (Noyes Publications, 2010).

    Google Scholar 

  25. Callaway, J. Model for lattice thermal conductivity at low temperatures. Phys. Rev. 113, 1046–1051 (1959).

    CAS  Google Scholar 

  26. Parrott, J. E. & Stuckes, A. D. Thermal Conductivity of Solids (Methuen, 1975).

    Google Scholar 

  27. Ziman, J. M. Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford Univ. Press, 2001).

    Google Scholar 

  28. Balandin, A. & Wang, K. L. Effect of phonon confinement on the thermoelectric figure of merit of quantum wells. J. Appl. Phys. 84, 6149–6153 (1998).

    CAS  Google Scholar 

  29. Ho, C. Y., Powell, R. W. & Liley, P. E. Thermal conductivity of the elements: a comprehensive review. J. Phys. Chem. Ref. Data 3 (suppl. 1), 1–30 (1974).

    Google Scholar 

  30. Woodcraft, A. L. et al. Thermal conductivity measurements of pitch-bonded at millikelvin temperatures: finding a replacement for AGOT graphite. Cryogenics 49, 159–164 (2009).

    CAS  Google Scholar 

  31. Nelson, F. J. et al. Optical properties of large-area polycrystalline chemical vapour deposited graphene by spectroscopic ellipsometry. Appl. Phys. Lett. 97, 253110 (2010).

    Google Scholar 

  32. Park, S. & Ruoff, R. S. Chemical methods for the production of graphenes. Nature Nanotech. 4, 217–224 (2009).

    CAS  Google Scholar 

  33. Klemens, P. G. & Pedraza, D. F. Thermal conductivity of graphite in basal plane. Carbon 32, 735–741 (1994).

    CAS  Google Scholar 

  34. Cahill, D. G. & Pohl, R. O. Heat flow and lattice vibrations in glasses. Solid State Commun. 70, 927–930 (1989).

    Google Scholar 

  35. Robertson, J. Diamond like amorphous carbon. Mater. Sci. Eng. R37, 129–281 (2002).

    CAS  Google Scholar 

  36. Morath, C. J. et al. Picosecond optical studies of amorphous diamond and diamond-like carbon: Thermal conductivity and longitudinal sound velocity. J. Appl. Phys. 76, 2636–2640 (1994).

    CAS  Google Scholar 

  37. Hurler, W., Pietralla, M. & Hammerschmidt, A. Determination of thermal properties of hydrogenated amorphous carbon thin films via mirage effect measurement. Diam. Relat. Mater. 4, 954–957 (1995).

    CAS  Google Scholar 

  38. Zhang, Z. J., Fan, S., Huang, J. & Lieber, C. M. Diamond-like properties in single phase carbon nitride solid. Appl. Phys. Lett. 68, 2639–2641 (1996).

    CAS  Google Scholar 

  39. Bullen, A. J., O'Hara, K. E., Cahill, D. G., Monteiro, O. & von Keudell, A. Thermal conductivity of amorphous carbon thin films. J. Appl. Phys. 88, 6317–6320 (2000).

    CAS  Google Scholar 

  40. Chen, G., Hui, P. & Xu, S. Thermal conduction in metalized tetrahedral amorphous carbon (ta-C) films on silicon. Thin Solid Films 366, 95–99 (2000).

    CAS  Google Scholar 

  41. Shamsa, M. et al. Thermal conductivity of diamond like carbon films. Appl. Phys. Lett. 89, 161921 (2006).

    Google Scholar 

  42. Balandin, A. A., Shamsa, M., Liu, W. L., Casiraghi, C. & Ferrari, A. C. Thermal conductivity of ultrathin tetrahedral amorphous carbon. Appl. Phys. Lett. 93, 043115 (2008).

    Google Scholar 

  43. Butler, J. E. & Sumant, A. V. The CVD of nanodiamond materials. Chem. Vapor Depos. 14, 145–160 (2008).

    CAS  Google Scholar 

  44. Auciello, O. & Sumant, A. V. Status review of the science and technology of devices. Diam. Relat. Mater. 19, 699–718 (2010).

    CAS  Google Scholar 

  45. Gruen, D. M., Liu, S., Krauss, A. R. & Pan, X. Buckyball microwave plasmas: Fragmentation and diamond-film growth. J. Appl. Phys. 75, 1758–1763 (1994).

    CAS  Google Scholar 

  46. Hartmann, J., Voigt, P. & Reichling, M. Measuring local thermal conductivity in polycrystalline diamond with a high resolution photothermal microscope. J. Appl. Phys. 81, 2966–2972 (1997).

    CAS  Google Scholar 

  47. Reichling, M., Klotzbucher, T. & Hartmann, J. Local variation of room-temperature thermal conductivity in high-quality polycrystalline diamond. Appl. Phys. Lett. 73, 756–758 (1998).

    CAS  Google Scholar 

  48. Philip, J. et al. Elastic, mechanical and thermal properties of nanocrystalline diamond films. J. Appl. Phys. 93, 2164–2171 (2003).

    CAS  Google Scholar 

  49. Angadi, M. A. et al. Thermal transport and grain boundary conductance in ultrananocrystalline diamond thin films. J. Appl. Phys. 99, 114301 (2006).

    Google Scholar 

  50. Liu, W. L. et al. Thermal conduction in nanocrystalline diamond thin films: Effect of grain boundary scattering and nitrogen doping. Appl. Phys. Lett. 89, 171915 (2006).

    Google Scholar 

  51. Shamsa, M. et al. Thermal conductivity of nitrogened ultrananocrystalline diamond films on silicon. J. Appl. Phys. 103, 083538 (2008).

    Google Scholar 

  52. Khitun, A., Balandin, A., Liu, J. L. & Wang, K. L. In-plane lattice thermal conductivity of quantum-dot superlattice. J. Appl. Phys. 88, 696–699 (2000).

    CAS  Google Scholar 

  53. Braginsky, L., Shklover, V., Hofmann, H. & Bowen, P. High-temperature thermal conductivity of porous Al2O3 nanostructures. Phys. Rev. B 70, 134201 (2004).

    Google Scholar 

  54. Ferrari, A. C. & Robertson, J. Origin of the 1,150 cm-1 Raman mode in nanocrystalline diamond. Phys. Rev. B 63, 121405 (2001).

    Google Scholar 

  55. Goyal, V., Subrina, S., Nika, D. L. & Balandin, A. A. Reduced thermal resistance of the silicon-synthetic diamond composite substrate at elevated temperatures. Appl. Phys. Lett. 97, 031904 (2010).

    Google Scholar 

  56. Saito, K. & Dhar, A. Heat conduction in a three dimensional anharmonic crystal. Phys. Rev. Lett. 104, 040601 (2010).

    Google Scholar 

  57. Lippi, A. & Livi, R. Heat conduction in two-dimensional nonlinear lattices. J. Stat. Phys. 100, 1147–1172 (2000).

    Google Scholar 

  58. Yang, L. Finite heat conduction in a 2D disorder lattice. Phys. Rev. Lett. 88, 094301 (2002).

    Google Scholar 

  59. Dhar, A. Heat conduction in the disordered harmonic chain revisited. Phys. Rev. Lett. 86, 5882–5885 (2001).

    CAS  Google Scholar 

  60. Casher, A. & Lebowitz, J. L. Heat flow in regular and disordered harmonic chains. J. Math. Phys. 12, 1701–1711 (1971).

    Google Scholar 

  61. Klemens, P. G. Theory of thermal conduction in the ceramic films. Int. J. Thermophys. 22, 265–275 (2001).

    CAS  Google Scholar 

  62. Nika, D. L., Ghosh, S., Pokatilov, E. P. & Balandin, A. A. Lattice thermal conductivity of graphene flakes: Comparison and bulk graphite. Appl. Phys. Lett. 94, 203103 (2009).

    Google Scholar 

  63. Hone, J., Whitney, M., Piskoti, C. & Zettl, A. Thermal conductivity of single-walled carbon nanotubes. Phys. Rev. B 59, R2514–R2516 (1999).

    CAS  Google Scholar 

  64. Yu, C. H., Shi, L., Yao, Z., Li, D. Y. & Majumdar, A. Thermal conductance and thermopower of an single-wall carbon nanotubes. Nano Lett. 5, 1842–1846 (2005).

    CAS  Google Scholar 

  65. Fujii, M. et al. Measuring thermal conductivity of a single carbon nanotube. Phys. Rev. Lett. 95, 065502 (2005).

    Google Scholar 

  66. Berber, S., Kwon, Y-K. & Tomanek, D. Unusually high thermal conductivity of carbon nanotubes. Phys. Rev. Lett. 84, 4613–4616 (2000).

    CAS  Google Scholar 

  67. Che, J., Cagin, T. & Goddard, W. A. III Thermal conductivity of carbon nanotubes. Nanotechnology 11, 65–69 (2000).

    CAS  Google Scholar 

  68. Osman, M. A. & Srivastava, D. Temperature dependence of thermal conductivity of single-wall carbon nanotubes. Nanotechnology 12, 21–24 (2001).

    CAS  Google Scholar 

  69. Lindsay, L., Broido, D. A. & Mingo, N. Diameter dependence of carbon nanotube thermal conductivity and extension to the graphene limit. Phys. Rev. B 82, 161402 (2010).

    Google Scholar 

  70. Donadio, D. & Galli, G. Thermal conductivity of isolated and interacting carbon nanotubes: Comparing results from molecular dynamics and the Boltzmann transport equation. Phys. Rev. Lett. 99, 255502 (2007).

    Google Scholar 

  71. Chang, C. W. et al. Isotope effect on the thermal conductivity of boron nitride nanotubes. Phys. Rev. Lett. 97, 085901 (2006).

    CAS  Google Scholar 

  72. Rego, L. C. G. & Kirczenow, G. Fractional exclusion statistics and the universal quantum of thermal conductance: A unifying approach. Phys. Rev. B 59, 13080–13086 (1999).

    CAS  Google Scholar 

  73. Ghosh, S., Nika, D. L., Pokatilov, E. P. & Balandin, A. A. Heat conduction in graphene: Experimental study and theoretical interpretation. New J. Phys. 11, 095012 (2009).

    Google Scholar 

  74. Ghosh, S. et al. Dimensional crossover of thermal transport in few-layer graphene. Nature Mater. 9, 555–558 (2010).

    CAS  Google Scholar 

  75. Cai, W. et al. Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition. Nano Lett. 10, 1645–1651 (2010).

    CAS  Google Scholar 

  76. Faugeras, C. et al. Thermal conductivity of graphene in Corbino membrane geometry. ACS Nano 4, 1889–1892 (2010).

    CAS  Google Scholar 

  77. Jauregui, L. A. et al. Thermal transport in graphene nanostructures: Experiments and simulations. ECS Trans. 28, 73–83 (2010).

    CAS  Google Scholar 

  78. Seol, J. H. et al. Two-dimensional phonon transport in supported graphene. Science 328, 213–216 (2010).

    CAS  Google Scholar 

  79. Murali, R., Yang, Y., Brenner, K., Beck, T. & Meindl, J. D. Breakdown current density of graphene nanoribbons. Appl. Phys. Lett. 94, 243114 (2009).

    Google Scholar 

  80. Zhong, W. R., Zhang, M. P., Ai, B. Q. & Zheng, D. Q. Chirality and thickness-dependent thermal conductivity of few-layer graphene: A molecular dynamics study. Appl. Phys. Lett. 98, 113107 (2011).

    Google Scholar 

  81. Singh, D., Murthy, J. Y. & Fisher, T. S. Mechanism of thermal conductivity reduction in few-layer graphene. Preprint at http://arxiv.org/abs/1104.4964 (2011).

  82. Jang, W., Chen, Z., Bao, W., Lau, C. N. & Dames, C. Thickness-dependent thermal conductivity of encased graphene and ultrathin graphite. Nano Lett. 10, 3909–3913 (2010).

    CAS  Google Scholar 

  83. Nika, D. L., Pokatilov, E. P., Askerov, A. S. & Balandin, A. A. Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering. Phys. Rev. B 79, 155413 (2009).

    Google Scholar 

  84. Evans, W. J., Hu, L. & Keblinsky, P. Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: Effect of ribbon width, edge roughness, and hydrogen termination. Appl. Phys. Lett. 96, 203112 (2010).

    Google Scholar 

  85. Lindsay, L., Broido, D. A. & Mingo, N. Flexural phonons and thermal transport in graphene. Phys. Rev. B 82, 115427 (2010).

    Google Scholar 

  86. Munoz, E., Lu, J. & Yakobson, B. I. Ballistic thermal conductance of graphene ribbons. Nano Lett. 10, 1652–1656 (2010).

    CAS  Google Scholar 

  87. Savin, A. V., Kivshar, Y. S. & Hu, B. Suppression of thermal conductivity in graphene nanoribbons with rough edges. Phys. Rev. B 82, 195422 (2010).

    Google Scholar 

  88. Jiang, J-W., Wang, J-S. & Li, B. Thermal conductance of graphite and dimerite. Phys. Rev. B 79, 205418 (2009).

    Google Scholar 

  89. Huang, Z., Fisher, T. S. & Murthy, J. Y. Simulation of phonon transmission through graphene and graphene nanoribbons with a green's function method. J. Appl. Phys. 108, 094319 (2010).

    Google Scholar 

  90. Hu, J., Ruan, X. & Chen, Y. P. Thermal conductivity and thermal rectification in graphene nanoribbons: A molecular dynamic study. Nano Lett. 9, 2730–2735 (2009).

    CAS  Google Scholar 

  91. Guo, Z., Zhang, D. & Gong, X-G. Thermal conductivity of graphene nanoribbons. Appl. Phys. Lett. 95, 163103 (2009).

    Google Scholar 

  92. Chen, S. et al. Raman measurement of thermal transport in suspended monolayer graphene of variable sizes in vacuum and gaseous environments. ACS Nano 5, 321–328 (2011).

    Google Scholar 

  93. Lee, J. U., Yoon, D., Kim, H., Lee, S. W. & Cheong, H. Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy. Phys. Rev. B 83, 081419 (2011).

    Google Scholar 

  94. Mak, K. F., Shan, J. & Heinz, T. F. Seeing many-body effects in single and few layer graphene: observation of two-dimensional saddle point excitons. Phys. Rev. Lett. 106, 046401 (2011).

    Google Scholar 

  95. Huang, Y., Wu, J. & Hwang, K. C. Thickness of graphene and single-wall carbon nanotubes. Phys. Rev. B 74, 245413 (2006).

    Google Scholar 

  96. Odegard, G. M., Gates, T. S., Nicholson, L. M. & Wise, K. E. Continuum model for the vibration of multilayered graphene sheets. Compos. Sci. Technol. 62, 1869 (2002).

    CAS  Google Scholar 

  97. Kapitza, P. L. Collected Papers of P. L. Kapitza Vol. II (ed. ter Haar, D.) 581 (Pergamon Press, 1967).

    Google Scholar 

  98. Freitag, M. et al. Energy dissipation in graphene field effect transistors. Nano Lett. 9, 1883–1888 (2009).

    CAS  Google Scholar 

  99. Chen, Z., Jang, W., Bao, W., Lau, C. N. & Dames, C. Thermal contact resistance between graphene and silicon dioxide. Appl. Phys. Lett. 95, 161910 (2009).

    Google Scholar 

  100. Mak, K. F., Liu, C. H. & Heinz, T. F. Thermal conductance at the graphene-SiO2 interface measured by optical pump-probe spectroscopy. Preprint at http://arxiv.org/abs/1009.0231 (2010).

  101. Koh, Y. K., Bae, M-H., Cahill, D. G. & Pop, E. Heat conduction across monolayer and few-layer graphenes. Nano Lett. 10, 4363–4368 (2010).

    CAS  Google Scholar 

  102. Schmidt, A. J., Collins, K. C., Minnich, A. J. & Chen, G. Thermal conductance and phonon transmissivity of metal-graphite interfaces. J. Appl. Phys. 107, 104907 (2010).

    Google Scholar 

  103. Persson, B. N. J. & Ueba, H. Heat transfer between weakly coupled systems: Graphene on a-SiO2 . Europhys. Lett. 91, 56001 (2010).

    Google Scholar 

  104. Konatham, D. & Striolo, A. Thermal boundary resistance at the graphene-oil interface. Appl. Phys. Lett. 95, 163105 (2009).

    Google Scholar 

  105. Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E. & Grulke, E. A. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett. 79, 2252–2254 (2001).

    CAS  Google Scholar 

  106. Biercuk, M. J. et al. Carbon nanotube composite for thermal management. Appl. Phys. Lett. 80, 2767–2769 (2002).

    CAS  Google Scholar 

  107. Konatham, D. & Striolo, A. Thermal boundary resistance at the graphene-oil interface. Mol. Phys. 109, 97–111 (2011).

    CAS  Google Scholar 

  108. Yu, A., Itkis, M. E., Bekyarova, E & Haddon, R. C. Effect of single-walled carbon nanotube purity on the thermal conductivity of carbon nanotube-based composite. Appl. Phys. Lett. 89, 133102 (2006).

    Google Scholar 

  109. Yu, A., Ramesh, P., Itkis, M. E., Bekyarova, E. & Haddon, R. C. Graphite nanoplatelet- epoxy composite thermal interface materials. J. Phys. Chem. Lett. 111, 7565–7569 (2007).

    CAS  Google Scholar 

  110. Yu, W., Xie, H. & Chen, W. Experimental investigation on thermal conductivity of nanofluids containing graphene oxide nanosheets. J. Appl. Phys. 107, 094317 (2010).

    Google Scholar 

  111. Wang, S., Tambraparni, M., Qiu, J., Tipton, J. & Dean, D. Thermal expansion of graphene composites. Macromolecules 42, 5251–5255 (2009).

    CAS  Google Scholar 

  112. Shahil, K. M. F., Goyal, V. & Balandin, A. A. Thermal properties of graphene: Applications in thermal interface materials. ECS Trans. 35, 193–195 (2011).

    CAS  Google Scholar 

  113. Zhang, K., Chai, Y., Yuen, M. M. F., Xiao, D. G. W. & Chan, P. C. H. Carbon nanotube thermal interface material for high-brightness light-emitting-diode cooling. Nanotechnology 19, 215706 (2008).

    CAS  Google Scholar 

  114. Veca, L. M. et al. Carbon nanosheets for polymeric nanocomposites with high thermal conductivity. Adv. Mater. 21, 2088–2092 (2009).

    CAS  Google Scholar 

  115. Kim, K. et al. High-temperature stability of suspended single-layer graphene. Phys. Status Solidi 11, 302–304 (2010).

    Google Scholar 

  116. Lotya, M., King, P. J., Khan, U., De, S. & Coleman, J. N. Liquid phase production of graphene by exfoliation of graphite in surfactant/water solutions. ACS Nano. 4, 3155–3162 (2010).

    CAS  Google Scholar 

  117. Segal, M. Selling graphene by the ton. Nature Nanotech. 4, 612–614 (2009).

    CAS  Google Scholar 

  118. Zuev, Y. M., Chang, W. & Kim, P. Thermoelectric and magneto-thermoelectric transport measurements of graphene. Phys. Rev. Lett. 102, 096807 (2009).

    Google Scholar 

  119. Wei, P., Bao, W., Pu, Y., Lau, C. N. & Shi, J. Anomalous thermoelectric transport of Dirac particles in graphene. Phys. Rev. Lett. 102, 166808 (2009).

    Google Scholar 

  120. Checkelsky, J. G. & Ong, N. P. Thermopower and Nernst effect in graphene in a magnetic field. Phys. Rev. B 80, 081413 (2009).

    Google Scholar 

  121. Hwang, E. H., Rossi, E. & Das Sarma, S. Theory of carrier transport in bilayer graphene. Phys. Rev. B 80, 235415 (2009).

    Google Scholar 

  122. Bao, W. S., Liu, S. Y. & Lei, X. L. Nonlinear d.c. transport in graphene. J. Phys. Condens. Mat. 22, 315502 (2010).

    CAS  Google Scholar 

  123. Kubakaddi, S. S. & Bhargavi, K. S. Enhancement of phonon-drag thermopower in bilayer graphene. Phys. Rev. B 82, 155410 (2010).

    Google Scholar 

  124. Hu, J., Schiffli, S., Vallabhaneni, A., Ruan, X. & Chen, Y. P. Tuning the thermal conductivity of graphene nanoribbons by edge passivation and isotope engineering: A molecular dynamics study. Appl. Phys. Lett. 97, 133107 (2010).

    Google Scholar 

  125. Makeev, M. A. & Srivastava, D. Silicon carbide nanowires under external loads: An atomistic simulation study. Appl. Phys. Lett. 95, 181908 (2009).

    Google Scholar 

  126. Sevincli, H. & Cuniberti, G. Enhanced thermoelectric figure of merit in edge-disordered zigzag graphene nanoribbons. Phys. Rev. B 81, 113401 (2010).

    Google Scholar 

  127. Teweldebrhan, D. & Balandin, A. A. Modification of graphene properties due to electron-beam irradiation. Appl. Phys. Lett. 94, 013101 (2009).

    Google Scholar 

  128. Wang, D. & Shi, J. Effect of charged impurities on the thermoelectric power of graphene near the Dirac point. Phys. Rev. B. 83, 113403 (2011).

    Google Scholar 

  129. Subrina, S., Kotchetkov, D. & Balandin, A. A. Heat removal in silicon-on-insulator integrated circuits with graphene lateral heat spreaders. IEEE Electr. Device Lett. 30, 1281 (2009).

    CAS  Google Scholar 

  130. Kim, K. S. et al. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457, 706–710 (2009).

    CAS  Google Scholar 

  131. Reina, A. et al. Large area few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano Lett. 9, 30–35 (2009).

    CAS  Google Scholar 

  132. Li, X. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324, 1312–1313 (2009).

    CAS  Google Scholar 

  133. Yan, Z., Liu, G., Subrina, S. & Balandin, A. A. Experimental demonstration of efficient thermal management of high-power GaN/AlGaN transistors with graphene lateral heat spreaders. MRS Proc. Y3.5 (2011).

  134. Zou J. & Balandin, A. A. Phonon heat conduction in a semiconductor nanowire, J. Appl. Phys. 89, 2932–2938 (2001).

    CAS  Google Scholar 

  135. Zakharchenko, K. V., Los, J. H., Katsnelson, M. I. & Fasolino, A. Atomistic simulations of structural and thermodynamic properties of bilayer graphene. Phys. Rev. B 81, 235439 (2010).

    Google Scholar 

  136. Mounet, N. & Marzari, N. First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives. Phys. Rev. B 71, 205214 (2005).

    Google Scholar 

  137. Michel, K. H. & Verberck, B. Theory of the evolution of phonon spectra and elastic constants from graphene to graphite. Phys. Rev. B 78, 085424 (2008).

    Google Scholar 

  138. Shelling, P. K. & Keblinski, P. Thermal expansion of carbon structures. Phys. Rev. B 68, 035425 (2003).

    Google Scholar 

  139. Pereira, V. M. & Castro-Neto, A. H. Strain engineering of graphene's electronic structure. Phys. Rev. Lett. 103, 046801 (2009).

    Google Scholar 

  140. Xu, X. et al. Phonon transport in suspended single layer graphene. Preprint at http://arxiv.org/abs/1012.2937 (2010).

  141. Wang, Z. et al. Thermal transport in suspended and supported few-layer graphene. Nano Lett. 11, 113–118 (2011).

    Google Scholar 

  142. Pettes, M. T., Jo, I., Yao, Z. & Shi, L. Influence of polymeric residue on the thermal conductivity of suspended bilayer graphene. Nano Lett. 11, 1195–1200 (2011).

    CAS  Google Scholar 

  143. Pettes, M. T. & Shi, L. Thermal and structural characterization of individual single-, double- and multi-walled carbon nanotubes. Adv. Funct. Mater. 19, 3918–3925 (2009).

    CAS  Google Scholar 

  144. Hsu, I. K. et al. Optical measurement of thermal transport in suspended carbon nanotubes. Appl. Phys. Lett. 92, 063119 (2008).

    Google Scholar 

  145. Capinski, W. S. et al. Thermal conductivity of isotopically enriched Si. Appl. Phys. Lett. 71, 2109–2111 (1997).

    CAS  Google Scholar 

  146. Inyushkin, A. V., Taldenkov, A. N., Gibin, A. M., Gusev, A. V. & Pohl, H. J. Ab initio theory of the lattice thermal conductivity in diamond. Phys. Status Solidi 1, 2995–2998 (2004).

    CAS  Google Scholar 

  147. Zhang, H. et al. Isotope effect on the thermal conductivity of graphene. J. Nanomater. 2010, 537657 (2010).

    Google Scholar 

  148. Wei, D., Song, Y. & Wang, F. A. A simple molecular mechanics potential for mm scale graphene simulations from the adaptive force matching method. J. Chem. Phys. 134, 184704 (2011).

    Google Scholar 

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Acknowledgements

I am indebted to K. Saito, L. Lindsay, N. Mingo, C. Dames, R. S. Ruoff, L. Shi, N. Mounet, N. Marzari, B. Q. Ai and T. Heinz for providing figure files. I thank E. P. Pokatilov, D. Nika, C. Dames, L. Shi, D. Cahill, N. Mingo, R. S. Ruoff, P. Kim, J. Shi, M. Dresselhaus, A. Geim and K. Novoselov for useful discussions. This work was supported by the Office of Naval Research (ONR) through award N00014-10-1-0224, Semiconductor Research Corporation (SRC) and Defense Advanced Research Projects Agency (DARPA) through Focus Center Research Program (FCRP) Center on Functional Engineered Nano Architectonics (FENA), and DARPA Defense Microelectronics Activity (DMEA) under agreement H94003-10-2-1003. Past funding from US Air Force Office of Scientific Research (AFOSR) through contract A9550-08-1-0100 is also acknowledged.

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  1. Department of Electrical Engineering and Materials Science and Engineering Program, Bourns College of Engineering, University of California, Riverside, 92521, California, USA

    Alexander A. Balandin

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Balandin, A. Thermal properties of graphene and nanostructured carbon materials. Nature Mater 10, 569–581 (2011). https://doi.org/10.1038/nmat3064

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