Graphene versus MoS₂: A short review

Abstract

Graphene and MoS₂ are two well-known quasi two-dimensional materials. This review presents a comparative survey of the complementary lattice dynamical and mechanical properties of graphene and MoS₂, which facilitates the study of graphene/MoS₂ heterostructures. These hybrid heterostructures are expected to mitigate the negative properties of each individual constituent and have attracted intense academic and industrial research interest.

Graphical abstract

Keywords

graphene / molybdenum disulphide / lattice dynamics / mechanical properties

References

[1] A. K. Geim and K. S. Novoselov, The rise of graphene, Nat. Mater.6(3), 183 (2007)

[2] A. H. C. Neto and K. Novoselov, New directions in science and technology: Two-dimensional crystals, Rep. Prog. Phys.74(8), 082501 (2011)

[3] C. Lee, X. Wei, J. W. Kysar, and J. Hone, Measurement of the elastic properties and intrinsic strength of mono-layer graphene, Science321(5887), 385 (2008)

[4] R. C. Cooper, C. Lee, C. A. Marianetti, X. Wei, J. Hone, and J. W. Kysar, Nonlinear elastic behavior of two-dimensional molybdenum disulfide, Phys. Rev. B87(3), 035423 (2013)

[5] Z. C. Ouyang, Z. B. Su, and C. L. Wang, Coil formation in multishell carbon nanotubes: Competition between curvature elasticity and interlayer adhesion, Phys. Rev. Lett.78(21), 4055 (1997)

[6] Z. C. Tu and Z. C. Ou-Yang, Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective Young’s moduli dependent on layer number, Phys. Rev. B65(23), 233407 (2002)

[7] M. Arroyo and T. Belytschko, An atomistic-based nite defor-mation membrane for single layer crystalline films, J. Mech. Phys. Solids50(9), 1941 (2002)

[8] Q. Lu, M. Arroyo, and R. Huang, Elastic bending modulus of monolayer graphene, J. Phys. D: Appl. Phys.42(10), 102002 (2009)

[9] J. W. Jiang, Z. Qi, H. S. Park, and T. Rabczuk, Elastic bending modulus of single-layer molybdenum disul-phide (MoS₂): Finite thickness effect, Nanotechnology24(43), 435705 (2013)

[10] J. W. Jiang and H. S. Park, Negative Poisson’s ratio in single-layer black phosphorus, Nat. Commun.5, 4727 (2014)

[11] A. C. Ferrari, Raman spectroscopy of graphene and graphite: Disorder, electron-phonon coupling, doping and nonadiabatic effects, Solid State Commun.143(1-2), 47 (2007)

[12] A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys.81(1), 109 (2009)

[13] A. K. Geim, Graphene: Status and prospects, Science324(5934), 1530 (2009)

[14] L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dressel-haus, Raman spectroscopy in graphene, Physics Reports473, 51 (2009)

[15] C. N. R. Rao, A. K. Sood, K. S. Subrahmanyam, and A. Govin-daraj, Graphene: The new two-dimensional nanomaterial, Angew. Chem. Int. Ed.48(42), 7752 (2009)

[16] M. J. Allen, V. C. Tung, and R. B. Kaner, Honeycomb carbon: A review of graphene, Chem. Rev.110(1), 132 (2010)

[17] F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, Graphene photonics and optoelectronics, Nat. Photonics4(9), 611 (2010)

[18] F. Schwierz, Graphene transistors, Nat. Nanotechnol.5(7), 487 (2010)

[19] A. A. Balandin, Thermal properties of graphene and nanostructured carbon materials, Nat. Mater.10(8), 569 (2011)

[20] Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Electronics and optoelectronics of twodimensional transition metal dichalcogenides, Nat. Nanotechnol.7(11), 699 (2012)

[21] M. Chhowalla, H. S. Shin, G. Eda, L. Li, K. P. Loh, and H. Zhang, The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets, Nat. Chem.5(4), 263 (2013)

[22] M. Xu, T. Liang, M. Shi, and H. Chen, Graphene-like twodimensional materials, Chem. Rev.113(5), 3766 (2013)

[23] S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutiérrez, T. F. Heinz, S. S. Hong, J. Huang, A. F. Ismach, E. Johnston-Halperin, M. Kuno, V. V. Plashnitsa, R. D. Robinson, R. S. Ruoff, S. Salahuddin, J. Shan, L. Shi, M. G. Spencer, M. Terrones, W. Windl, and J. E. Goldberger, Progress, challenges, and opportunities in two-dimensional materials beyond graphene, ACS Nano7(4), 2898 (2013)

[24] X. Huang, Z. Zeng, and H. Zhang, Metal dichalcogenide nanosheets: Preparation, properties and applications, Chem. Soc. Rev.42(5), 1934 (2013)

[25] L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y. J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. C.Neto, and K. S. Novoselov, Strong light-matter interactions in heterostructures of atomically thin films, Science340(6138), 1311 (2013)

[26] R. Zan, Q. M. Ramasse, R. Jalil, T. Georgiou, U. Bangert, and K. S. Novoselov, Control of radiation damage in MoS₂ by graphene encapsulation, ACS Nano7(11), 10167 (2013)

[27] R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes, London: Imperial College, 1998

[28] J. W. Jiang, H. S. Park, and T. Rabczuk, Molecular dynamics simulations of single-layer molybdenum disulphide (MoS₂): Stillinger–Weber parametrization, mechanical properties, and thermal conductivity, J. Appl. Phys.114(6), 064307 (2013)

[29] A. Molina-Sánchez and L. Wirtz, Phonons in single-layer and few-layer MoS₂ and WS₂, Phys. Rev. B84(15), 155413 (2011)

[30] N. Wakabayashi, H. G. Smith, and R. M. Nicklow, Lattice dynamics of hexagonal MoS₂ studied by neutron scattering, Phys. Rev. B12(2), 659 (1975)

[31] G. Kresse and J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B54(16), 11169 (1996)

[32] J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Jun-quera, P. Ordejon, and D. Sánchez-Portal, The siesta method for ab initio ordern materials simulation, J. Phys.: Condens. Matter14(11), 2745 (2002) (Code available from http://www.icmab.es/dmmis/leem/siesta/.)

[33] D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys.: Condens. Matter14(4), 783 (2002)

[34] J. Tersoff, Empirical interatomic potential for carbon, with applications to amorphous carbon, Phys. Rev. Lett.61(25), 2879 (1988)

[35] F. H. Stillinger and T. A. Weber, Computer simulation of local order in condensed phases of silicon, Phys. Rev. B31(8), 5262 (1985)

[36] F. F. Abraham and I. P. Batra, Theoretical interpretation of atomic force microscope images of graphite, Surf. Sci.209(1-2), L125 (1989)

[37] T. Aizawa, R. Souda, S. Otani, Y. Ishizawa, and C. Oshima, Bond softening in monolayer graphite formed on transitionmetal carbide surfaces, Phys. Rev. B42(18), 11469 (1990)

[38] T. Liang, S. R. Phillpot, and S. B. Sinnott, Parametrization of a reactive many-body potential for Mo-S systems, Phys. Rev. B79(24), 245110 (2009)

[39] J. A. Stewart and D. E. Spearot, Atomistic simulations of nanoindentation on the basal plane of crystalline molyb-denum disulfide (MoS₂), Model. Simul. Mater. Sci. Eng.21(4), 045003 (2013)

[40] J. D. Gale, Gulp: A computer program for the symmetryadapted simulation of solids, J. Chem. Soc., Faraday Trans.93(4), 629 (1997) (Code available from https://projects.ivec.org/gulp/.)

[41] Lammps, http://www.cs.sandia.gov/~sjplimp/lammps.html (2012)

[42] S. Jiménez Sandoval, D. Yang, R. F. Frindt, and J. C. Irwin, Raman study and lattice dynamics of single molecular layers of MoS₂, Phys. Rev. B44(8), 3955 (1991)

[43] E. Dobardžić, I. Milosevic, B. Dakic, and M. Damnjanovic, Raman and infrared-active modes inMS₂ nanotubes (M=Mo,W), Phys. Rev. B74(3), 033403 (2006)

[44] M. Damnjanovic, E. Dobardzic, I. Miloeevic, M. Virsek, and M. Remskar, Phonons in MoS₂ and WS₂ nanotubes, Mater. Manuf. Process.23(6), 579 (2008)

[45] H. Wang, Y. Wang, X. Cao, M. Feng, and G. Lan, Vibrational properties of graphene and graphene layers, Journal of Raman Spectroscopy40(12), 1791 (2009)

[46] X. Zhang, W. Han, J. Wu, S. Milana, Y. Lu, Q. Li, A. Ferrari, and P. Tan, Raman spectroscopy of shear and layer breathing modes in multilayer MoS₂, Phys. Rev. B87, 115413 (2013)

[47] J. W. Jiang, H. S. Park, and T. Rabczuk, MoS₂ nanoresonators: Intrinsically better than graphene? Nanoscale6(7), 3618 (2014)

[48] F. Liu, P. Ming, and J. Li, Ab initio calculation of ideal strength and phonon instability of graphene under tension, Phys. Rev. B76(6), 064120 (2007)

[49] F. Hao, D. Fang, and Z. Xu, Mechanical and thermal transport properties of graphene with defects, Appl. Phys. Lett.99(4), 041901 (2011)

[50] Z. Ni, H. Bu, M. Zou, H. Yi, K. Bi, and Y. Chen, Anisotropic mechanical properties of graphene sheets from molecular dynamics, Physica B405(5), 1301 (2010)

[51] Y. Gao and P. Hao, Mechanical properties of mono-layer graphene under tensile and compressive loading, Physica E41(8), 1561 (2009)

[52] Y. Guo, L. Jiang, and W. Guo, Opening carbon nanotubes into zigzag graphene nanoribbons by energy-optimum oxidation, Phys. Rev. B82(11), 115440 (2010)

[53] Y. Zheng, N. Wei, Z. Fan, L. Xu, and Z. Huang, Mechanical properties of grafold: A demonstration of strengthened graphene, Nanotechnology22(40), 405701 (2011)

[54] Y. Wei, J. Wu, H. Yin, X. Shi, R. Yang, and M. Dresselhaus, The nature of strength enhancement and weakening by pentagonheptagon defects in graphene, Nat. Mater.11(9), 759 (2012)

[55] Y. Zhang and C. Pan, Measurements of mechanical properties and number of layers of graphene from nano-indentation, Diamond Related Materials24, 1 (2012)

[56] Q. Yue, J. Kang, Z. Shao, X. Zhang, S. Chang, G. Wang, S. Qin, and J. Li, Mechanical and electronic properties of monolayer MoS₂ under elastic strain, Phys. Lett. A376(12-13), 1166 (2012)

[57] Y. Huang, J. Wu, and K. C. Hwang, Thickness of graphene and single-wall carbon nanotubes, Phys. Rev. B74(24), 245413 (2006)

[58] L. Shen, H. S. Shen, and C. L. Zhang, Temperaturedependent elastic properties of single layer graphene sheets, Mater. Des.31(9), 4445 (2010)

[59] T. Han, P. He, Y. Luo, and X. Zhang, Research progress in the mechanical properties of graphene, Advances in Mechanics41(3), 279 (2011)

[60] L. Xu, N. Wei, Y. Zheng, Z. Fan, H. Q. Wang, and J. C. Zheng, Graphene-nanotube 3d networks: Intriguing thermal and mechanical properties, J. Mater. Chem.22(4), 1435 (2011)

[61] J. W. Jiang, J. S. Wang, and B. Li, Elastic and nonlinear stiffness of graphene: A simple approach, Phys. Rev. B81(7), 073405 (2010)

[62] S. Bertolazzi, J. Brivio, and A. Kis, Stretching and breaking of ultrathin MoS₂, ACS Nano5(12), 9703 (2011)

[63] R. C. Cooper, C. Lee, C. A. Marianetti, X. Wei, J. Hone, and J. W. Kysar, Erratum: Nonlinear elastic behavior of twodimensional molybdenum disulfide [Phys. Rev. B 87, 035423 (2013)], Phys. Rev. B87(7), 079901 (2013)

[64] K. Liu, Q. Yan, M. Chen, W. Fan, Y. Sun, J. Suh, D. Y. Fu, S. Lee, J. Zhou, S. Tongay, J. Ji, J. B. Neaton, and J. Q. Wu, Elastic properties of chemical-vapor-deposited monolayer MoS₂, WS₂, and their bilayer heterostructures, arXiv: 1407.2669 (2014)

[65] A. Castellanos-Gomez, M. Poot, G. A. Steele, H. S. J. van der Zant, N. Agrait, and G. Rubio-Bollinger, Elastic properties of freely suspended MoS₂ nano sheets, Adv. Mater.24(6), 772 (2012)

[66] E. Cadelano, P. L. Palla, S. Giordano, and L. Colombo, Nonlinear elasticity of monolayer graphene, Phys. Rev. Lett.102(23), 235502 (2009)

[67] C. D. Reddy, S. Rajendran, and K. M. Liew, Equilibrium configuration and continuum elastic properties of finite sized graphene, Nanotechnology17(3), 864 (2006)

[68] H. Zhao, K. Min, and N. R. Aluru, Size and chirality dependent elastic properties of graphene nanoribbons under uniaxial tension, Nano Lett.9(8), 3012 (2009)

[69] P. Tao, H. Guo, T. Yang, and Z. Zhang, Strain-induced magnetism in MoS2 monolayer with defects, J. Appl. Phys.115(5), 054305 (2014)

[70] Y. C. Lin, D. O. Dumcenco, Y. S. Huang, and K. Suenaga, Atomic mechanism of the semiconducting-to-metallic phase transition in single-layered MoS₂, Nat. Nanotechnol.9(5), 391 (2014)

[71] J. W. Jiang, Phonon bandgap engineering of strained monolayer MoS₂, Nanoscale6(14), 8326 (2014)

[72] M. Kan, J. Y. Wang, X. W. Li, S. H. Zhang, Y. W. Li, Y. Kawazoe, Q. Sun, and P. Jena, Structures and phase transition of a MoS₂ monolayer, J. Phys. Chem. C118(3), 1515 (2014)

[73] K. Q. Dang, J. P. Simpson, and D. E. Spearot, Phase transformation in monolayer molybdenum disulphide (MoS2) under tension predicted by molecular dynamics simulations, Scr. Mater.76, 41 (2014)

[74] Y. Wei, B. Wang, J. Wu, R. Yang, and M. L. Dunn, Bending rigidity and gaussian bending stiffness of single-layered graphene, Nano Lett.13(1), 26 (2013)

[75] X. Zhou, J. J. Zhou, and Z. C. Ou-Yang, Strain energy and Young’s modulus of single-wall carbon nanotubes calculated from electronic energy-band theory, Phys. Rev. B62(20), 13692 (2000)

[76] T. Ma, B. Li, and T. Chang, Chirality- and curvaturedependent bending stiffness of single layer graphene, Appl. Phys. Lett.99(20), 201901 (2011)

[77] Y. Shen and H. Wu, Interlayer shear effect on multilayer graphene subjected to bending, Appl. Phys. Lett.100(10), 101909 (2012)

[78] X. Shi, B. Peng, N. M. Pugno, and H. Gao, Stretch-induced softening of bending rigidity in graphene, Appl. Phys. Lett.100(19), 191913 (2012)

[79] M. Arroyo and T. Belytschko, Finite crystal elasticity of carbon nanotubes based on the exponential cauchy-born rule, Phys. Rev. B69(11), 115415 (2004)

[80] Y. Wang, R. Yang, Z. Shi, L. Zhang, D. Shi, E. Wang, and G. Zhang, Super-elastic graphene ripples for flexible strain sensors, ACS Nano5(5), 3645 (2011)

[81] J. Zhang, J. Xiao, X. Meng, C. Monroe, Y. Huang, and J. M. Zuo, Free folding of suspended graphene sheets by random mechanical stimulation, Phys. Rev. Lett.104(16), 166805 (2010)

[82] J. X. Shi, Q. Q. Ni, X. W. Lei, and T. Natsuki, Nonlocal elasticity theory for the buckling of double-layer graphene nanoribbons based on a continuum model, Comput. Mater. Sci.50(11), 3085 (2011)

[83] C. Wang, L. Lan, and H. Tan, The physics of wrinkling in graphene membranes under local tension, Phys. Chem. Chem. Phys.15(8), 2764 (2013)

[84] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd Ed., New York: McGraw-Hill, 1987

[85] J. W. Jiang, The buckling of single-layer MoS₂ under uniaxial compression, Nanotechnology25(35), 355402 (2014)

[86] M. Zhou, Y. Zhai, and S. Dong, Electrochemical sensing and biosensing platform based on chemically reduced graphene oxide, Anal. Chem.81(14), 5603 (2009)

[87] Y. Xu, C. Chen, V. V. Deshpande, F. A. DiRenno, A. Gondarenko, D. B. Heinz, S. Liu, P. Kim, and J. Hone, Radio frequency electrical transduction of graphene mechanical resonators, Appl. Phys. Lett.97(24), 243111 (2010)

[88] X. Q. He, S. Kitipornchai, and K. M. Liew, Resonance analysis of multi-layered graphene sheets used as nanoscale resonators, Nanotechnology16(10), 2086 (2005)

[89] Y. Liu, Z. Xu, and Q. Zheng, The interlayer shear effect on graphene multilayer resonators, J. Mech. Phys. Solids59(8), 1613 (2011)

[90] J. Wang, X. He, S. Kitipornchai, and H. Zhang, Geometrical nonlinear free vibration of multi-layered graphene sheets, J. Phys. D: Appl. Phys.44(13), 135401 (2011)

[91] Y. Xu, S. Yan, Z. Jin, and Y. Wang, Quantum-squeezing effects of strained multilayer graphene nems, Nanoscale Res. Lett.6(1), 355 (2011)

[92] F. Gu, J. H. Zhang, L. J. Yang, and B. Gu, Molecular dynamics simulation of resonance properties of strain graphene nanoribbons, Acta Phys. Sin.60(5), 056103 (2011)

[93] Z. B. Shen, H. L. Tang, D. K. Li, and G. J. Tang, Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory, Comput. Mater. Sci.61, 200 (2012)

[94] S. M. Zhou, L. P. Sheng, and Z. B. Shen, Transverse vibration of circular graphene sheet-based mass sensor via nonlocal Kirchhoff plate theory, Comput. Mater. Sci.86, 73 (2014)

[95] K. L. Ekinci and M. L. Roukes, Nanoelectromechanical systems, Rev. Sci. Instrum.76(6), 061101 (2005)

[96] A. M. Zande, R. A. Barton, J. S. Alden, C. S. Ruiz-Vargas, W. S. Whitney, P. H. Q. Pham, J. Park, J. M. Parpia, H. G. Craighead, and P. L. McEuen, Large-scale arrays of singlelayer graphene resonators, Nano Lett.10(12), 4869 (2010)

[97] C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L. Stormer, T. F. Heinz, and J. Hone, Performance of monolayer graphene nanomechanical resonators with electrical read-out, Nat. Nanotechnol.4(12), 861 (2009)

[98] J. W. Jiang, B. S. Wang, H. S. Park, and T. Rabczuk, Adsorbate migration effects on continuous and discontinuous temperature-dependent transitions in the quality factors of graphene nanoresonators, Nanotechnology25(2), 025501 (2014)

[99] C. Edblom and A. Isacsson, Diffusion-induced dissipation and mode coupling in nanomechanical resonators, arXiv: 1406.1365v1 (2014)

[100] A. Eichler, J. Moser, J. Chaste, M. Zdrojek, I. Wilson- Rae, and A. Bachtold, Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene, Nat. Nanotechnol.6(6), 339 (2011)

[101] A. Castellanos-Gomez, R. van Leeuwen, M. Buscema, H. S. J. van der Zant, G. A. Steele, and W. J. Venstra, Singlelayer MoS₂ mechanical resonators, Adv. Mater.25(46), 6719 (2013)

[102] J. Lee, Z. Wang, K. He, J. Shan, and P. X. L. Feng, High frequency MoS2 nanomechanical resonators, ACS Nano7(7), 6086 (2013)

[103] A. A. Balandin, Low-frequency 1/f noise in graphene devices, Nat. Nanotechnol.8(8), 549 (2013)

[104] Y. M. Lin and P. Avouris, Strong suppression of electrical noise in bilayer graphene nanodevices, Nano Lett.8(8), 2119 (2008)

[105] A. N. Pal and A. Ghosh, Resistance noise in electrically biased bilayer graphene, Phys. Rev. Lett.102(12), 126805 (2009)

[106] Z. Cheng, Q. Li, Z. Li, Q. Zhou, and Y. Fang, Suspended graphene sensors with improved signal and reduced noise, Nano Lett.10(5), 1864 (2010)

[107] S. Rumyantsev, G. Liu, W. Stillman, M. Shur, and A. A. Balandin, Electrical and noise characteristics of graphene fieldeffect transistors: Ambient effects, noise sources and physical mechanisms, J. Phys.: Condens. Matter22(39), 395302 (2010)

[108] G. Liu, S. Rumyantsev, M. Shur, and A. A. Balandin, Graphene thickness-graded transistors with reduced electronic noise, Appl. Phys. Lett.100(3), 033103 (2012)

[109] M. Z. Hossain, S. L. Roumiantsev, M. Shur, and A. A. Balandin, Reduction of 1/f noise in graphene after electronbeam irradiation, Appl. Phys. Lett.102(15), 153512 (2013)

[110] K. Saito, J. Nakamura, and A. Natori, Ballistic thermal conductance of a graphene sheet, Phys. Rev. B76(11), 115409 (2007)

[111] S. Yien, V. Tayari, J. O. Island, J. M. Porter, and A. R. Champagne, Electronic thermal conductivity measurements in intrinsic graphene, Phys. Rev. B87(24), 241411 (2013)

[112] J. S. Wang, J. Wang, and J. T. Lü, Quantum thermal transport in nanostructures, Eur. Phys. J. B62(4), 381 (2008)

[113] J. S. Wang, B. K. Agarwalla, H. Li, and J. Thingna, Nonequilibrium greens function method for quantum thermal transport, Front. Phys.9(6), 673 (2013)

[114] S. Chen, Q. Wu, C. Mishra, J. Kang, H. Zhang, K. Cho, W. Cai, A. A. Balandin, and R. S. Ruoff, Thermal conductivity of isotopically modified graphene, Nat. Mater.11(3), 203 (2012)

[115] Z. Guo, D. Zhang, and X. G. Gong, Thermal conductivity of graphene nanoribbons, Appl. Phys. Lett.95(16), 163103 (2009)

[116] Y. Xu, X. Chen, B. L. Gu, and W. Duan, Intrinsic anisotropy of thermal conductance in graphene nanoribbons, Appl. Phys. Lett.95(23), 233116 (2009)

[117] S. Chen, A. L. Moore, W. Cai, J. W. Suk, J. An, C. Mishra, C. Amos, C. W. Magnuson, J. Kang, L. Shi, and R. S. Ruoff, Raman measurements of thermal transport in suspended monolayer graphene of variable sizes in vacuum and gaseous environments, ACS Nano5(1), 321 (2011)

[118] N. Wei, L. Xu, H. Q. Wang, and J. C. Zheng, Strain engineering of thermal conductivity in graphene sheets and nanoribbons: A demonstration of magic flexibility, Nanotechnology22(10), 105705 (2011)

[119] Z. Wei, Z. Ni, K. Bi, M. Chen, and Y. Chen, In-plane lattice thermal conductivities of multilayer graphene films, Carbon49(8), 2653 (2011)

[120] Z. X. Xie, K. Q. Chen, and W. Duan, Thermal transport by phonons in zigzag graphene nanoribbons with structural defects, J. Phys.: Condens. Matter23(31), 315302 (2011)

[121] X. Zhai and G. Jin, Stretching-enhanced ballistic thermal conductance in graphene nanoribbons, Europhys. Lett.96(1), 16002 (2011)

[122] X. F. Peng, X. J. Wang, Z. Q. Gong, and K. Q. Chen, Ballistic thermal conductance in graphene nanoribbon with double-cavity structure, Appl. Phys. Lett.99(23), 233105 (2011)

[123] F. Ma, H. B. Zheng, Y. J. Sun, D. Yang, K. W. Xu, and P. K. Chu, Strain effect on lattice vibration, heat capacity, and thermal conductivity of graphene, Appl. Phys. Lett.101(11), 111904 (2012)

[124] Z. X. Guo, J. W. Ding, and X. G. Gong, Substrate effects on the thermal conductivity of epitaxial graphene nanoribbons, Phys. Rev. B85(23), 235429 (2012)

[125] N. Mingo and D. A. Broido, Carbon nanotube ballistic thermal conductance and its limits, Phys. Rev. Lett.95(9), 096105 (2005)

[126] N. Mingo and D. A. Broido, Length dependence of carbon nanotube thermal conductivity and the “problem of long waves”, Nano Lett.5(7), 1221 (2005)

[127] D. L. Nika, E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, Phonon thermal conduction in graphene: Role of umklapp and edge roughness scattering, Phys. Rev. B79(15), 155413 (2009)

[128] D. L. Nika, A. S. Askerov, and A. A. Balandin, Anomalous size dependence of the thermal conductivity of graphene ribbons, Nano Lett.12(6), 3238 (2012)

[129] X. Xu, L. F. Pereira, Y. Wang, J. Wu, K. Zhang, X. Zhao, S. Bae, C. Tinh Bui, R. Xie, J. T. L. Thong, B. H. Hong, K. P. Loh, D. Donadio, B. Li, and B. Özyilmaz, Lengthdependent thermal conductivity in suspended single-layer graphene, Nat. Commun.5, 3689 (2014)

[130] D. L. Nika, E. P. Pokatilov, and A. A. Balandin, Theoretical description of thermal transport in graphene: The issues of phonon cut-off frequencies and polarization branches, Phys. Status Solidi B248(11), 2609 (2011)

[131] J. Wang, X. M. Wang, Y. F. Chen, and J. S. Wang, Dimensional crossover of thermal conductance in graphene nanoribbons: A first-principles approach, J. Phys.: Condens. Matter24(29), 295403 (2012)

[132] D. L. Nika and A. A. Balandin, Two-dimensional phonon transport in graphene, J. Phys.: Condens. Matter24(23), 233203 (2012)

[133] N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, and B. Li, Phononics: Manipulating heat flow with electronic analogs and beyond, Rev. Mod. Phys.84(3), 1045 (2012)

[134] J. W. Jiang, J. Lan, J. S. Wang, and B. Li, Iso-topic effects on the thermal conductivity of graphene nanoribbons: Localization mechanism, J. Appl. Phys.107(5), 054314 (2010)

[135] W. Cai, A. L. Moore, Y. Zhu, X. Li, S. Chen, L. Shi, and R. S. Ruoff, Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition, Nano Lett.10(5), 1645 (2010)

[136] A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Superior thermal conductivity of single-layer graphene, Nano Lett.8(3), 902 (2008)

[137] S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L. Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits, Appl. Phys. Lett.92(15), 151911 (2008)

[138] L. Lindsay, D. A. Broido, and N. Mingo, Flexural phonons and thermal transport in multilayer graphene and graphite, Phys. Rev. B83(23), 235428 (2011)

[139] Z. Aksamija and I. Knezevic, Lattice thermal conductivity of graphene nanoribbons: Anisotropy and edge roughness scattering, Appl. Phys. Lett.98(14), 141919 (2011)

[140] L. Chen and S. Kumar, Thermal transport in graphene supported on copper, J. Appl. Phys.112(4), 043502 (2012)

[141] Z. Wei, J. Yang, K. Bi, and Y. Chen, Mode dependent lattice thermal conductivity of single layer graphene, J. Appl. Phys.116(15), 153503 (2014)

[142] S. Ghosh, W. Bao, D. L. Nika, S. Subrina, E. P. Pokatilov, C. N. Lau, and A. A. Balandin, Dimensional crossover of thermal transport in few-layer graphene, Nat. Mater.9(7), 555 (2010)

[143] D. Singh, J. Y. Murthy, and T. S. Fisher, Mechanism of thermal conductivity reduction in few-layer graphene, J. Appl. Phys.110(4), 044317 (2011)

[144] G. Zhang and H. Zhang, Thermal conduction and rectification in few-layer graphene y junctions, Nanoscale3(11), 4604 (2011)

[145] W.R. Zhong, M.P. Zhang, B.Q. Ai, and D.Q. Zheng, Chirality and thickness-dependent thermal conductivity of fewlayer graphene: A molecular dynamics study, Appl. Phys. Lett.98(11), 113107 (2011)

[146] W. R. Zhong, W. H. Huang, X. R. Deng, and B. Q. Ai, Thermal rectification in thickness-asymmetric graphene nanoribbons, Appl. Phys. Lett.99(19), 193104 (2011)

[147] A. Rajabpour and S. M. Vaez Allaei, Tuning thermal conductivity of bilayer graphene by inter-layer sp3 bonding: A molecular dynamics study, Appl. Phys. Lett.101(5), 053115 (2012)

[148] H. Y. Cao, Z. X. Guo, H. Xiang, and X. G. Gong, Layer and size dependence of thermal conductivity in multilayer graphene nanoribbons, Phys. Lett. A376(4), 525 (2012)

[149] T. Sun, J. Wang, and W. Kang, Van der waals interactiontuned heat transfer in nanostructures, Nanoscale5(1), 128 (2012)

[150] S. Sahoo, A. P. S. Gaur, M. Ahmadi, M. J. F. Guinel, and R. S. Katiyar, Temperature dependent raman studies and thermal conductivity of few layer MoS₂, J. Phys. Chem. C117(17), 9042 (2013)

[151] V. Varshney, S. S. Patnaik, C. Muratore, A. K. Roy, A. A. Voevodin, and B. L. Farmer, Md simulations of molybdenum disulphide (MoS₂): Force-field parameterization and thermal transport behavior, Comput. Mater. Sci.48(1), 101 (2010)

[152] W. Huang, H. Da, and G. Liang, Thermoelectric performance of MX₂ (M=Mo, W; X=S, Se) monolayers, J. Appl. Phys.113(10), 104304 (2013)

[153] J. W. Jiang, X. Y. Zhuang, and T. Rabczuk, Orientation dependent thermal conductance in single-layer MoS₂, Scientific Reports3, 2209 (2013)

[154] J. W. Jiang, J. S. Wang, and B. Li, Thermal conductance of graphene and dimerite, Phys. Rev. B79(20), 205418 (2009)

[155] X. Liu, G. Zhang, Q. X. Pei, and Y. W. Zhang, Phonon thermal conductivity of monolayer MoS₂ sheet and nanoribbons, Appl. Phys. Lett.103(13), 133113 (2013)

[156] Z. Yan, G. Liu, J. M. Khan, and A. A. Balandin, Graphene quilts for thermal management of high-power gan transistors, Nat. Commun.3, 827 (2012)

[157] V. Goyal and A. A. Balandin, Thermal properties of the hybrid graphene-metal nano-micro-composites: Applications in thermal interface materials, Appl. Phys. Lett.100(7), 073113 (2012)

[158] K. M. F. Shahil and A. A. Balandin, Graphenemultilayer graphene nanocomposites as highly efficient thermal interface materials, Nano Lett.12(2), 861 (2012)

[159] P. Goli, S. Legedza, A. Dhar, R. Salgado, J. Renteria, and A. A. Balandin, Graphene-enhanced hybrid phase change materials for thermal management of Li-ion batteries, J. Power Sources248(15), 37 (2014)

[160] H. Malekpour, K. H. Chang, J. C. Chen, C. Y. Lu, D. L. Nika, K. S. Novoselov, and A. A. Balandin, Thermal conductivity of graphene laminate, Nano Lett.14(9), 5155 (2014)

[161] P. Song, Z. Cao, Y. Cai, L. Zhao, Z. Fang, and S. Fu, Fabrication of exfoliated graphene-based polypropy-lene nanocomposites with enhanced mechanical and thermal properties, Polymer52(18), 4001 (2011)

[162] W. Yu, H. Xie, and D. Bao, Enhanced thermal conductivities of nanofluids containing graphene oxide nanosheets, Nanotechnology21(5), 055705 (2010)

[163] W. Yu, H. Xie, and W. Chen, Experimental investigation on thermal conductivity of nanofluids containing graphene oxide nanosheets, J. Appl. Phys.107(9), 094317 (2010)

[164] W. Yu, H. Xie, X. Wang, and X. Wang, Significant thermal conductivity enhancement for nanofluids containing graphene nanosheets, Phys. Lett. A375(10), 1323 (2011)

[165] Y. Wang, Z. Shi, Y. Huang, Y. Ma, C. Wang, M. Chen, , Supercapacitor devices based on graphene materials, J. Phys. Chem. C113, 131030 (2009)

[166] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature438(7065), 197 (2005)

[167] S. Y. Zhou, G. H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru, R. D. Diehl, Y. Kopelevich, D.H. Lee, S. G. Louie, and A. Lanzara, First direct observation of Dirac fermions in graphite, Nat. Phys.2(9), 595 (2006)

[168] B. Partoens and F. M. Peeters, Normal and dirac fermions in graphene multilayers: Tight-binding description of the electronic structure, Phys. Rev. B75(19), 193402 (2007)

[169] J. Hass, F. Varchon, J. E. Millan-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. First, L. Magaud, and E. Conrad, Why multi-layer graphene on 4h-sic 000ī behaves like a single sheet of graphene, Phys. Rev. Lett.100(12), 125504 (2008)

[170] S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejon, Tightbinding description of graphene, Phys. Rev. B66(3), 035412 (2002)

[171] V. Pereira, A. Castro Neto, and N. Peres, Tight-binding approach to uniaxial strain in graphene, Phys. Rev. B80(4), 045401 (2009)

[172] F. Guinea, M. I. Katsnelson, and A. K. Geim, Energy gaps and a zero-field quantum hall effect in graphene by strain engineering, Nat. Phys.6(1), 30 (2010)

[173] K. Nakada, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Edge state in graphene ribbons: Nanometer size effect and edge shape dependence, Phys. Rev. B54(24), 17954 (1996)

[174] K. K. Kam and B. A. Parkinson, Detailed photocurrent spectroscopy of the semiconducting group vi transition metal dichalcogenides, J. Phys. Chem.86(4), 463 (1982)

[175] T. Eknapakul, P. D. C. King, M. Asakawa, P. Buaphet, R. H. He, S. K. Mo, H. Takagi, K. M. Shen, F. Baumberger, T. Sasagawa, S. Jungthawan, and W. Meevasana, Electronic structure of a quasi-freestanding MoS₂ monolayer, Nano Lett.14(3), 1312 (2014)

[176] Y. Li, Z. Zhou, S. Zhang, and Z. Chen, MoS₂ nanorib-bons: High stability and unusual electronic and magnetic properties, J. Am. Chem. Soc.130(49), 16739 (2008)

[177] P. Lu, X. Wu, W. Guo, and X. C. Zeng, Strain-dependent electronic and magnetic properties of MoS₂ monolayer, bilayer, nanoribbons and nanotubes, Phys. Chem. Chem. Phys.14(37), 13035 (2012)

[178] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, Single-layer MoS₂ transistors, Nat. Nanotechnol.6(3), 147 (2011)

[179] V. K. Sangwan, H. N. Arnold, D. Jariwala, T. J. Marks, L. J. Lauhon, and M. C. Hersam, Low-frequency electronic noise in single-layer MoS₂ transistors, Nano Lett.13(9), 4351 (2013)

[180] E. Scalise, M. Houssa, G. Pourtois, V. Afanasev, and A. Stesmans, Strain-induced semiconductor to metal transition in the two-dimensional honeycomb structure of MoS₂, Nano Research5(1), 43 (2012)

[181] H. J. Conley, B. Wang, J. I. Ziegler, R. F. Jr Haglund, S. T. Pantelides, and K. I. Bolotin, Bandgap engineering of strained monolayer and bilayer MoS₂, Nano Lett.13(8), 3626 (2013)

[182] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS₂: A new direct-gap semiconductor, Phys. Rev. Lett.105(13), 136805 (2010)

[183] R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, Fine structure constant defines visual transparency of graphene, Science320(5881), 1308 (2008)

[184] F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, Ultrafast graphene photodetector, Nat. Nanotechnol.4(12), 839 (2009)

[185] O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Raden-ovic, and A. Kis, Ultrasensitive photodetectors based on monolayer MoS₂, Nat. Nanotechnol.8(7), 497 (2013)

[186] C. H. Lui, A. J. Frenzel, D. V. Pilon, Y. H. Lee, X. Ling, G. M. Akselrod, , Trion induced negative photoconductivity in monolayer MoS₂, arXiv: 1406.5100 (2014)

[187] K. Roy, M. Padmanabhan, S. Goswami, T. P. Sai, S. Kaushal, and A. Ghosh, Optically active heterostructures of graphene and ultrathin MoS₂, Solid State Commun.175-176, 35 (2013)

[188] G. Algara-Siller, S. Kurasch, M. Sedighi, O. Lehtinen, and U. Kaiser, The pristine atomic structure of MoS₂ monolayer protected from electron radiation damage by graphene, Appl. Phys. Lett.103(20), 203107 (2013)

[189] N. Myoung, K. Seo, S. J. Lee, and G. Ihm, Large current modulation and spin-dependent tunneling of vertical graphene/MoS₂ heterostructures, ACS Nano7(8), 7021 (2013)

[190] S. Bertolazzi, D. Krasnozhon, and A. Kis, Nonvolatile memory cells based on MoS₂/graphene heterostructures, Nano Lett.7(4), 3246 (2013)

[191] S. Larentis, J. R. Tolsma, B. Fallahazad, D. C. Dillen, K. Kim, A. H. MacDonald, and E. Tutuc, Band offset and negative compressibility in graphene- MoS₂ heterostructures, Nano Lett.14(4), 2039 (2014)

[192] W. Zhang, C. P. Chuu, J. K. Huang, C. H. Chen, M. L. Tsai, Y. H. Chang, , Ultrahigh-gain photodetectors based on atomically thin graphene-MoS2 heterostructures, Scientific Reports4, 3826 (2014)

[193] F. Xia, X. Hu, Y. Sun, W. Luo, and Y. Huang, Layer-bylayer assembled MoO₂ graphene thin film as a high-capacity and binder-free anode for lithium-ion batteries, Nanoscale4(15), 4707 (2012)

[194] W. Zhang, C. P. Chuu, J. K. Huang, C. H. Chen, M. L. Tsai, Y. H. Chang, , Ultrahigh-gain photodetectors based on atomically thin graphene-MoS₂ heterostructures, Scientific Reports4, 3826 (2013)

[195] H. Xu, D. He, M. Fu, W. Wang, H. Wu, and Y. Wang, Optical identification of MoS₂/graphene heterostructure on SiO₂/Si substrate, Opt. Express22(13), 15969 (2014)

[196] L. F. Wang, T. B. Ma, Y. Z. Hu, Q. Zheng, H. Wang, and J. Luo, Superlubricity of two-dimensional fluorographene/ MoS₂ heterostructure: A first-principles study, Nanotechnology25(38), 385701 (2014)

[197] Y. Ma, Y. Dai, M. Guo, C. Niu, and B. Huang, Graphene adhesion on MoS₂ monolayer: An ab initio study, Nanoscale3(9), 3883 (2011)

[198] L. Yu, Y. H. Lee, X. Ling, E. J. G. Santos, Y. C. Shin, Y. Lin, M. Dubey, E. Kaxiras, J. Kong, H. Wang, and T. Palacios, Graphene/MoS₂ hybrid technology for large-scale two-dimensional electronics, Nano Lett.14(6), 3055 (2014)

[199] R. H. Miwa and W. L. Scopel, Lithium incorporation at the MoS₂/graphene interface: An ab initio investigation, J. Phys.: Condens. Matter25(44), 445301 (2013)

[200] J. W. Jiang and H. S. Park, Mechanical properties of MoS₂/graphene heterostructures, Appl. Phys. Lett.105(3), 033108 (2014)

[201] K. K. Karkkainen, A. H. Sihvola, and K. I. Nikoskinen, Effective permittivity of mixtures: Numerical validation by the FDTD method, IEEE Trans. Geosci. Rem. Sens.38(3), 1303 (2000)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg