SCIENCE CHINA Information Sciences, Volume 64 , Issue 4 : 140401(2021) https://doi.org/10.1007/s11432-020-3151-5

Filling the gap: thermal properties and device applications of graphene

More info
  • ReceivedNov 10, 2020
  • AcceptedDec 28, 2020
  • PublishedMar 2, 2021



This work was supported in part by China Electronics Technology Group Corporation, Institute of Information Science (Grant No. H1125), National Natural Science Foundation of China (Grant Nos. 62022047, 61874065, 51861145202), National Key RD Program (Grant No. 2016YFA0200400), Research Fund from Beijing Innovation Center for Future Chip and the Independent Research Program of Tsinghua University (Grant No. 20193080047), Young Elite Scientists Sponsorship Program by CAST (Grant No. 2018QNRC001), and Fok Ying-Tong Education Foundation (Grant No. 171051).


[1] Novoselov K S. Electric Field Effect in Atomically Thin Carbon Films. Science, 2004, 306: 666-669 CrossRef ADS arXiv Google Scholar

[2] Balandin A A, Ghosh S, Bao W. Superior Thermal Conductivity of Single-Layer Graphene. Nano Lett, 2008, 8: 902-907 CrossRef ADS Google Scholar

[3] Balandin A A. Thermal properties of graphene and nanostructured carbon materials. Nat Mater, 2011, 10: 569-581 CrossRef ADS arXiv Google Scholar

[4] Zhang Z, Ouyang Y, Cheng Y. Size-dependent phononic thermal transport in low-dimensional nanomaterials. Phys Rep, 2020, 860: 1-26 CrossRef ADS Google Scholar

[5] Nakazawa H. Energy Flow in Harmonic Linear Chain. Prog Theor Phys, 1968, 39: 236-238 CrossRef ADS Google Scholar

[6] Rieder Z, Lebowitz J L, Lieb E. Properties of a Harmonic Crystal in a Stationary Nonequilibrium State. J Math Phys, 1967, 8: 1073-1078 CrossRef ADS Google Scholar

[7] Lepri S, Livi R, Politi A. Heat Conduction in Chains of Nonlinear Oscillators. Phys Rev Lett, 1997, 78: 1896-1899 CrossRef ADS Google Scholar

[8] Lepri S, Livi R, Politi A. On the anomalous thermal conductivity of one-dimensional lattices. Europhys Lett, 1998, 43: 271-276 CrossRef ADS arXiv Google Scholar

[9] Grassberger P, Nadler W, Yang L. Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas. Phys Rev Lett, 2002, 89: 180601 CrossRef ADS arXiv Google Scholar

[10] Hatano K. Error analysis for scaling coefficients and wavelet coefficients that are derived from the trapezoidal rule. Surikaisekikenkyusho Kokyuroku, 1999, 1084: 1--15. Google Scholar

[11] Lepri S. Relaxation of classical many-body Hamiltonians in one dimension. Phys Rev E, 1998, 58: 7165-7171 CrossRef ADS arXiv Google Scholar

[12] Narayan O, Ramaswamy S. Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems. Phys Rev Lett, 2002, 89: 200601 CrossRef ADS arXiv Google Scholar

[13] Pereverzev A. Phys Rev E, 2003, 68: 056124 CrossRef ADS arXiv Google Scholar

[14] Ghosh S, Calizo I, Teweldebrhan D. Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits. Appl Phys Lett, 2008, 92: 151911 CrossRef ADS Google Scholar

[15] Xie G, Ding D, Zhang G. Phonon coherence and its effect on thermal conductivity of nanostructures. Adv Phys-X, 2018, 3: 1480417 CrossRef ADS arXiv Google Scholar

[16] Zhang G, Duan W H. Thermal properties of low-dimensional nanoscale materials (in Chinese). Physics, 2020, 49: 668--678. Google Scholar

[17] Klemens, P.G., Thermal Conductivity and Lattice Vibrational Modes. Solid State Physics, 1958. 7: 1-98 DOI: 10.1016/S0081-1947(08)60551-2. Google Scholar

[18] Callaway J. Model for Lattice Thermal Conductivity at Low Temperatures. Phys Rev, 1959, 113: 1046-1051 CrossRef ADS Google Scholar

[19] New Books. Phys Today, 1977, 30: 60-63 CrossRef ADS Google Scholar

[20] Schelling P K, Phillpot S R, Keblinski P. Comparison of atomic-level simulation methods for computing thermal conductivity. Phys Rev B, 2002, 65: 144306 CrossRef ADS Google Scholar

[21] Lindsay L, Broido D A, Mingo N. Flexural phonons and thermal transport in graphene. Phys Rev B, 2010, 82: 115427 CrossRef ADS Google Scholar

[22] Khadem M H, Wemhoff A P. Molecular dynamics predictions of the influence of graphite stacking arrangement on the thermal conductivity tensor. Chem Phys Lett, 2013, 574: 78-82 CrossRef ADS Google Scholar

[23] Nika D L, Pokatilov E P, Askerov A S. Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering. Phys Rev B, 2009, 79: 155413 CrossRef ADS Google Scholar

[24] Evans W J, Hu L, Keblinski P. Thermal conductivity of graphene ribbons from equilibrium molecular dynamics: Effect of ribbon width, edge roughness, and hydrogen termination. Appl Phys Lett, 2010, 96: 203112 CrossRef ADS Google Scholar

[25] Adamyan V, Zavalniuk V. Phonons in graphene with point defects. J Phys-Condens Matter, 2011, 23: 015402 CrossRef ADS arXiv Google Scholar

[26] Adamyan V, Zavalniuk V. Lattice thermal conductivity of graphene with conventionally isotopic defects. J Phys-Condens Matter, 2012, 24: 415401 CrossRef ADS arXiv Google Scholar

[27] Srivastava G P, Kresin V. The Physics of Phonons. Phys Today, 1991, 44: 75-76 CrossRef ADS Google Scholar

[28] Omini M, Sparavigna A. An iterative approach to the phonon Boltzmann equation in the theory of thermal conductivity. Physica B-Condensed Matter, 1995, 212: 101-112 CrossRef Google Scholar

[29] Broido D A, Ward A, Mingo N. Lattice thermal conductivity of silicon from empirical interatomic potentials. Phys Rev B, 2005, 72: 014308 CrossRef ADS Google Scholar

[30] Lindsay L, Broido D A, Mingo N. Lattice thermal conductivity of single-walled carbon nanotubes: Beyond the relaxation time approximation and phonon-phonon scattering selection rules. Phys Rev B, 2009, 80: 125407 CrossRef ADS Google Scholar

[31] Wang Y, Vallabhaneni A K, Qiu B. Two-Dimensional Thermal Transport in Graphene: A Review of Numerical Modeling Studies. Nanoscale Microscale ThermoPhys Eng, 2014, 18: 155-182 CrossRef ADS Google Scholar

[32] Wang J S, Agarwalla B K, Li H. Nonequilibrium Green's function method for quantum thermal transport. Front Phys, 2014, 9: 673-697 CrossRef ADS arXiv Google Scholar

[33] Zhang W, Fisher T S, Mingo N. The Atomistic Green's Function Method: An Efficient Simulation Approach for Nanoscale Phonon Transport. Numer Heat Transfer Part B-Fundamentals, 2007, 51: 333-349 CrossRef ADS Google Scholar

[34] Gu X, Yang R. PHONON TRANSPORT AND THERMAL CONDUCTIVITY IN TWO-DIMENSIONAL MATERIALS. Annu Rev Heat Transfer, 2016, 19: 1-65 CrossRef Google Scholar

[35] Kaviani M. Heat Transfer Physics. 2nd ed. Cambridge: Cambridge University Press, 2014. Google Scholar

[36] Chou F C, Lukes J R, Liang X G. MOLECULAR DYNAMICS IN MICROSCALE THERMOPHYSICAL ENGINEERING. Annu Rev Heat Transfer, 1999, 10: 141-176 CrossRef Google Scholar

[37] Evans D J. Homogeneous NEMD algorithm for thermal conductivity-Application of non-canonical linear response theory. Phys Lett A, 1982, 91: 457-460 CrossRef Google Scholar

[38] Ikeshoji T, Hafskjold B. Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface. Mol Phys, 1994, 81: 251-261 CrossRef ADS Google Scholar

[39] Müller-Plathe F. A simple nonequilibrium molecular dynamics method for calculating the thermal conductivity. J Chem Phys, 1997, 106: 6082-6085 CrossRef ADS Google Scholar

[40] Ren X X, Kang W, Cheng Z F. Temperature-Dependent Debye Temperature and Specific Capacity of Graphene. Chin Phys Lett, 2016, 33: 126501 CrossRef ADS Google Scholar

[41] Rapaport D C. Molecular dynamics simulation. Comput Sci Eng, 1999, 1: 70--71. Google Scholar

[42] Chen X K, Xie Z X, Zhou W X. Phonon wave interference in graphene and boron nitride superlattice. Appl Phys Lett, 2016, 109: 023101 CrossRef ADS Google Scholar

[43] Hollcroft T R. The October meeting in New York. Bull Amer Math Soc, 1943, 49: 24-29 CrossRef Google Scholar

[44] Clough R W. The Finite Element Method in Plane Stress Analysis. In: Proceedings of Asce Conference on Electronic Computation, 1960. Google Scholar

[45] Mortazavi B, Benzerara O, Meyer H. Combined molecular dynamics-finite element multiscale modeling of thermal conduction in graphene epoxy nanocomposites. Carbon, 2013, 60: 356-365 CrossRef Google Scholar

[46] Cahill D G. Thermal conductivity measurement from 30 to 750 K: the 3ω method. Rev Sci Instruments, 1990, 61: 802-808 CrossRef ADS Google Scholar

[47] Fu Y, Hansson J, Liu Y. Graphene related materials for thermal management. 2D Mater, 2020, 7: 012001 CrossRef ADS Google Scholar

[48] Ghosh S, Nika D L, Pokatilov E P. Heat conduction in graphene: experimental study and theoretical interpretation. New J Phys, 2009, 11: 095012 CrossRef ADS Google Scholar

[49] Jauregui L A, Yue Y, Sidorov A N. Thermal Transport in Graphene Nanostructures: Experiments and Simulations. ECS Trans, 2010, 28: 73-83 CrossRef ADS Google Scholar

[50] Cai W, Moore A L, Zhu Y. Thermal Transport in Suspended and Supported Monolayer Graphene Grown by Chemical Vapor Deposition. Nano Lett, 2010, 10: 1645-1651 CrossRef ADS Google Scholar

[51] Chen Z, Jang W Y, Bao W Z, et al. Heat transfer in encased graphene. In: Proceedings of ASME 2009 Heat Transfer Summer Conference Collocated with the InterPACK09 and 3rd Energy Sustainability Conferences, 2009. Google Scholar

[52] Jang W, Chen Z, Bao W. Thickness-Dependent Thermal Conductivity of Encased Graphene and Ultrathin Graphite. Nano Lett, 2010, 10: 3909-3913 CrossRef ADS Google Scholar

[53] Seol J H, Jo I, Moore A L. Two-Dimensional Phonon Transport in Supported Graphene. Science, 2010, 328: 213-216 CrossRef ADS Google Scholar

[54] Renteria J D, Ramirez S, Malekpour H. Strongly Anisotropic Thermal Conductivity of Free-Standing Reduced Graphene Oxide Films Annealed at High Temperature. Adv Funct Mater, 2015, 25: 4664-4672 CrossRef Google Scholar

[55] Yang J, Ziade E, Maragliano C. Thermal conductance imaging of graphene contacts. J Appl Phys, 2014, 116: 023515 CrossRef ADS Google Scholar

[56] Faugeras C, Faugeras B, Orlita M. Thermal Conductivity of Graphene in Corbino Membrane Geometry. ACS Nano, 2010, 4: 1889-1892 CrossRef Google Scholar

[57] Sledzinska M, Graczykowski B, Placidi M. Thermal conductivity of MoS$_{2}$ polycrystalline nanomembranes. 2D Mater, 2016, 3: 035016 CrossRef ADS arXiv Google Scholar

[58] Xu X, Pereira L F C, Wang Y. Length-dependent thermal conductivity in suspended single-layer graphene. Nat Commun, 2014, 5: 3689 CrossRef ADS arXiv Google Scholar

[59] Cahill D G, Ford W K, Goodson K E. Nanoscale thermal transport. J Appl Phys, 2003, 93: 793-818 CrossRef ADS Google Scholar

[60] Fukushima H, Drzal L T, Rook B P. Thermal conductivity of exfoliated graphite nanocomposites. J Therm Anal Calorim, 2006, 85: 235-238 CrossRef Google Scholar

[61] Wei L, Wu F, Shi D. Spontaneous intercalation of long-chain alkyl ammonium into edge-selectively oxidized graphite to efficiently produce high-quality graphene. Sci Rep, 2013, 3: 2636 CrossRef ADS Google Scholar

[62] Chen X K, Zeng Y J, Chen K Q. Thermal Transport in Two-Dimensional Heterostructures. Front Mater, 2020, 7: 578791 CrossRef Google Scholar

[63] Liu X, Zhang G, Zhang Y W. Graphene-based thermal modulators. Nano Res, 2015, 8: 2755-2762 CrossRef Google Scholar

[64] Xu W, Zhang G, Li B. Interfacial thermal resistance and thermal rectification between suspended and encased single layer graphene. J Appl Phys, 2014, 116: 134303 CrossRef ADS Google Scholar

[65] Nandanapalli K R, Mudusu D, Lee S. Functionalization of graphene layers and advancements in device applications. Carbon, 2019, 152: 954-985 CrossRef Google Scholar

[66] Zeng Y J, Wu D, Cao X H. Nanoscale Organic Thermoelectric Materials: Measurement, Theoretical Models, and Optimization Strategies. Adv Funct Mater, 2020, 30: 1903873 CrossRef Google Scholar

[67] Ju Y S, Goodson K E. Phonon scattering in silicon films with thickness of order 100 nm. Appl Phys Lett, 1999, 74: 3005-3007 CrossRef ADS Google Scholar

[68] Yang Y, Liu W, Asheghi M. Thermal and electrical characterization of Cu/CoFe superlattices. Appl Phys Lett, 2004, 84: 3121-3123 CrossRef ADS Google Scholar

[69] Subrina S, Kotchetkov D, Balandin A A. Heat Removal in Silicon-on-Insulator Integrated Circuits With Graphene Lateral Heat Spreaders. IEEE Electron Device Lett, 2009, 30: 1281-1283 CrossRef ADS Google Scholar

[70] Zhang Y, Edwards M, Samani M K. Characterization and simulation of liquid phase exfoliated graphene-based films for heat spreading applications. Carbon, 2016, 106: 195-201 CrossRef Google Scholar

[71] Gao, Z.L., et al., Graphene Heat Spreader for Thermal Management of Hot Spots in Electronic Packaging. 2012. Google Scholar

[72] Gao Z, Zhang Y, Fu Y. Thermal chemical vapor deposition grown graphene heat spreader for thermal management of hot spots. Carbon, 2013, 61: 342-348 CrossRef Google Scholar

[73] Shih M H, Li L J, Yang Y C. Efficient Heat Dissipation of Photonic Crystal Microcavity by Monolayer Graphene. ACS Nano, 2013, 7: 10818-10824 CrossRef Google Scholar

[74] Zhang Y, Han H, Wang N. Improved Heat Spreading Performance of Functionalized Graphene in Microelectronic Device Application. Adv Funct Mater, 2015, 25: 4430-4435 CrossRef Google Scholar

[75] Han N, Viet Cuong T, Han M. Improved heat dissipation in gallium nitride light-emitting diodes with embedded graphene oxide pattern. Nat Commun, 2013, 4: 1452 CrossRef ADS Google Scholar

[76] Huang, S., et al., Graphene based heat spreader for high power chip cooling using flip-chip technology. 2013 DOI: 10.1109/EPTC.2013.6745740. Google Scholar

[77] Bae S H, Shabani R, Lee J B. Graphene-Based Heat Spreader for Flexible Electronic Devices. IEEE Trans Electron Devices, 2014, 61: 4171-4175 CrossRef ADS Google Scholar

[78] Lee P H, Tu W M, Tseng H C. Graphene Heat Spreaders for Thermal Management of InGaP/GaAs Collector-Up HBTs. IEEE Trans Electron Devices, 2018, 65: 352-355 CrossRef ADS Google Scholar

[79] Thermal Conductivity of Graphene-Polymer Composites: Mechanisms, Properties, and Applications. Polymers, 2017, 9: 437 CrossRef Google Scholar

[80] Shahil K M F, Balandin A A. Graphene-Multilayer Graphene Nanocomposites as Highly Efficient Thermal Interface Materials. Nano Lett, 2012, 12: 861-867 CrossRef ADS arXiv Google Scholar

[81] Shen X, Wang Z, Wu Y. Multilayer Graphene Enables Higher Efficiency in Improving Thermal Conductivities of Graphene/Epoxy Composites. Nano Lett, 2016, 16: 3585-3593 CrossRef ADS Google Scholar

[82] Shtein M, Nadiv R, Buzaglo M. Thermally Conductive Graphene-Polymer Composites: Size, Percolation, and Synergy Effects. Chem Mater, 2015, 27: 2100-2106 CrossRef Google Scholar

[83] Yavari F, Fard H R, Pashayi K. Enhanced Thermal Conductivity in a Nanostructured Phase Change Composite due to Low Concentration Graphene Additives. J Phys Chem C, 2011, 115: 8753-8758 CrossRef Google Scholar

[84] Ji H, Sellan D P, Pettes M T. Enhanced thermal conductivity of phase change materials with ultrathin-graphite foams for thermal energy storage. Energy Environ Sci, 2014, 7: 1185-1192 CrossRef Google Scholar

[85] Mehrali M, Latibari S T, Mehrali M. Shape-stabilized phase change materials with high thermal conductivity based on paraffin/graphene oxide composite. Energy Convers Manage, 2013, 67: 275-282 CrossRef Google Scholar

[86] Norley J, Tzeng J-W, Klug J. Graphite-based heat sink. Google Patents, 2003. Google Scholar

[87] Hsieh C T, Chen Y F, Lee C E. Heat transport enhancement of heat sinks using Cu-coated graphene composites. Mater Chem Phys, 2017, 197: 105-112 CrossRef Google Scholar

[88] Hu J, Xu J, Zhu C. Significant enhancement of metal heat dissipation from mechanically exfoliated graphene nanosheets through thermal radiation effect. AIP Adv, 2017, 7: 055315 CrossRef ADS Google Scholar

[89] Chu K, Li W, Dong H. Role of graphene waviness on the thermal conductivity of graphene composites. Appl Phys A, 2013, 111: 221-225 CrossRef ADS Google Scholar

[90] Chen X K, Chen K Q. Thermal transport of carbon nanomaterials. J Phys-Condens Matter, 2020, 32: 153002 CrossRef ADS Google Scholar

[91] Liu X, Zhang G, Zhang Y W. Thermal Conduction Across Graphene Cross-Linkers. J Phys Chem C, 2014, 118: 12541-12547 CrossRef Google Scholar

[92] Ong Z Y, Zhang G, Zhang Y W. Controlling the thermal conductance of graphene/h -BN lateral interface with strain and structure engineering. Phys Rev B, 2016, 93: 075406 CrossRef ADS Google Scholar

[93] Ci H, Chang H, Wang R. Enhancement of Heat Dissipation in Ultraviolet Light?Emitting Diodes by a Vertically Oriented Graphene Nanowall Buffer Layer. Adv Mater, 2019, 31: 1901624 CrossRef Google Scholar

[94] Xu S, Wang S, Chen Z. Electric?Field?Assisted Growth of Vertical Graphene Arrays and the Application in Thermal Interface Materials. Adv Funct Mater, 2020, 30: 2003302 CrossRef Google Scholar

[95] Liang Q, Yao X, Wang W. A Three-Dimensional Vertically Aligned Functionalized Multilayer Graphene Architecture: An Approach for Graphene-Based Thermal Interfacial Materials. ACS Nano, 2011, 5: 2392-2401 CrossRef Google Scholar

[96] Loeblein M, Tsang S H, Pawlik M. High-Density 3D-Boron Nitride and 3D-Graphene for High-Performance Nano-Thermal Interface Material. ACS Nano, 2017, 11: 2033-2044 CrossRef Google Scholar

[97] Zhamu A, Jang B Z. Chemical-free production of 3D graphene-carbon hybrid foam. Google Patents, 2017. Google Scholar

[98] Moniruzzaman M, Winey K I. Polymer Nanocomposites Containing Carbon Nanotubes. Macromolecules, 2006, 39: 5194-5205 CrossRef ADS Google Scholar

[99] Prasher R S, Matayabas J C. Thermal contact resistance of cured gel polymeric thermal interface material. IEEE Trans Compon Packag Tech, 2004, 27: 702--709. Google Scholar

[100] Jiang X. Broadband absorption of graphene from magnetic dipole resonances in hybrid nanostructure. J Semicond, 2019, 40: 062006 CrossRef ADS Google Scholar

[101] Wang X, Zhou P. Special Focus on Two-Dimensional Materials and Device Applications. Sci China Inf Sci, 2019, 62: 220400 CrossRef Google Scholar

  • Figure 1

    (Color online) Schematic of theory & modeling, experiment and device application of graphene. Gaps exist between theories of different scales and between experimental results and actual effect.

  • Figure 2

    (Color online) Methods used for measurement of thermal conductivity of 2D materials [47].

  • Figure 3

    (Color online) Schematic of the experiment showing the excitation laser light focused on a graphene layer suspended across a trench. The focused laser light creates a local hot spot and generates a heat wave inside SLG propagating toward heat sinks [2].

  • Figure 4

    (Color online) Schematic of the “heat spreader method" to measure the in-plane $\kappa$ of graphene encased in a film of ${\rm~SiO}_2$ [51,52].

  • Figure 5

    (Color online) Schematic of our FDTR micro-scope. A digitally modulated pump laser heats the sample while a probe beam monitors the surface reflectivity. A balanced photodetector is used to improve the signal to noise ratio. A piezo stage is used to scan the sample for imaging [55].

  • Figure 6

    (Color online) (a) Schematic of the simulation structure. The thicknesses are not to scale [69]. (b) Temperature distribution obtained by finite element simulation. (c)–(e) Hot spot temperature before and after graphene is transferred onto the chip with the data from [70,71].

  • Figure 7

    (Color online) (a) Demonstration of principle of TIM [80]@Copyright 2020 the American Chemical Society. protectłinebreak (b) Composites' TC with different graphene layers, with data from [81].

  • Figure 8

    (Color online) Simulation models of vertical graphene (a) nanowalls [93]and (b) arrays [94].

  • Table 1  

    Table 1Summary of computational results of $\kappa$ of graphene at room temperature (RT)

    $\kappa$ (W$\cdot~{\rm~m}^{-1}\cdot~{\rm~K}^{-1}$ Method Comment Ref.
    $\sim$2350 BTE $L=10~{\mu}$m [21]
    480–850 GK-MD $\kappa$ depends on stacking order [22]
    2000–5000 Valence force field, BTE Strong width dependence [23]
    8000–10000 MD, Tersoff Square graphene sheet [24]
  • Table 2  

    Table 2Summary of TC of graphene in experiments

    $\kappa~({\rm~W}\cdot~{\rm~m}^{-1}\cdot~{\rm~K}^{-1})$MethodMaterial type Ref.
    Optothermal Raman spectroscopy technique
    Suspended exfoliated single-layer graphene (SLG), room temperature (RT)
    1[1]*$\sim$ 3000–5300
    Suspended exfoliated SLG, RT
    1[1]*$\sim$ 3080–5150
    Suspended exfoliated SLG, RT
    2[2]*$\sim$ 1500–5000
    Optothermal Raman spectroscopy technique $+$ electrical burning
    Suspended chemical vapor deposition (CVD) graphene, RT
    Optothermal Raman spectroscopy technique
    Suspended CVD graphene, 350 K
    Suspended CVD graphene, 500 K
    Graphene membrane, 600 K
    2[2]*below 160
    Heat spreader method ($3\omega$ method)
    Exfoliated SLG encased within silicon dioxide, RT
    $\sim~7000$ (crude estimate)
    All electrical, $3\omega$ method
    Substrate-supported CVD graphene, RT
    Thermal bridge
    SLG exfoliated on a silicon dioxide support
    Laser heating
    Exfoliated graphene supported on ${\rm~SiO}_2$, RT