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The phonon conductivity in suspended graphene and in graphene nanoribbons has been studied within the framework of Callaway’s effective relaxation time theory. The conductivity expression has been computed by employing analytical expressions for phonon dispersion relations and vibrational density of states based on the semicontinuum model by Nihira and Iwata. It is found that the Normal-drift contribution to the conductivity, arising from the consideration of the momentum conserving nature of three-phonon Normal processes, is very important for explaining the magnitude as well as the temperature dependence of the experimentally measured results for suspended graphene.

We report on the evolution of thermal properties from graphene to graphite as a function of layer thickness and temperature. The onset of the inter-layer compressional elastic constant C 33 and the shear elastic constant C 44 results in a large difference between the magnitudes and temperature dependencies of the specific heat and in-plane lattice thermal conductivity of bi-layer graphene (BLG) and single-layer graphene. The changes between BLG and few-layer graphene (FLG) decrease with increase in the number of layers. The cross-plane lattice thermal conductivity increases almost linearly with the number of layers in ultra-thin FLG. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4862319] Graphene, in addition to its remarkable electronic properties, 1 is one of the materials with the highest recorded thermal conductivity values. 2,3 It is also remarkable that compared to most layered systems, fabrication of singlelayer graphene (SLG), bi-layer graphene (BLG), and fewlayer graphene (FLG) can be achieved in a controlled manner. 4 This strongly suggests that the FLG systems can be used to understand the fundamental mechanisms and in achieving controlled alteration of thermal conductivity along and perpendicular to the growth direction. In particular, it would be interesting to ascertain the minimum amount of thermal conductivity established when a BLG is formed.Generally, the intrinsic ability of a material to conduct heat is altered as its dimensionality changes from twodimensional (2D) to three-dimensional (3D). Lateral (inplane) thermal conductivity in conventional semiconductors thin films tends to decrease with decreasing thickness. This is due to the domination of the boundary phonon scattering rate. 5 However, an opposite dependence is observed in FLG where the thermal conductivity is reduced as the number of layers increases. [6][7][8] As graphite is composed of multilayer graphene, it is natural to think that studying thermal properties of FLG will elucidate how the thermal conductivity and specific heat of graphene evolve into graphite-like results with increasing number of layers.In this work, specific heat and thermal conductivity of FLG are calculated. We used the semicontinuum model proposed by Komatsu and Nagamiya, 9 and employed the analytical expressions for phonon dispersion relations and vibrational density of states based on the derivations by Nihira and Iwata. 10 The lattice thermal conductivity tensor was calculated within the framework of Callaway's effective relaxation time theory. 11 We consider the FLG and graphite systems as an assembly of equally spaced elastic layers with compressional and shearing couplings between adjacent layers. According to the theory of elasticity, 12 the strength of the inter-layer coupling in layered materials increases as the number of layers increases. Two elastic constants, C 33 and C 44 , are used to describe the compressional and shearing couplings, respectively. These elastic constants are sensitive to the number of graphene layers, and any chan...

We have employed a semicontinuum model to investigate the effect of tensile strain on thermal properties of graphene. Analytical expressions derived by Nihira and Iwata for phonon dispersion relations and vibrational density of states are employed, based on the semicontinuum model proposed by Komatsu and Nagamiya. The thermal conductivity is computed within the framework of Callaway's effective relaxation time theory. It is found that thermal properties of graphene are quite sensitive to tensile strain. In the presence of tensile strain, the specific heat increases but the thermal conductivity decreases.In this work, we elucidate the effect of tensile strain on the specific heat and thermal conductivity of graphene. We apply Callaway's theory in its full form [13] to study the thermal conductivity. Our calculations employ the analytical expressions for the phonon dispersion relations and the vibrational density of states based on the work by Nihira and Iwata [14] within the semicontinuum model developed by Komatsu and Nagamiya [15]. 182

We have studied the thermal conductivity of graphene using Callaway’s effective relax-ation time theory and by employing analytical expressions for phonon dispersion relations and vibrational density of states based on the semicontinuum model by Nihira and Iwata. It is found that consideration of the momentum conserving nature of three-phonon Normal pro-cesses is very important for explaining the magnitude as well as the temperature dependence of the experimentally measured results. At room temperature, the N-drift contribution (the correction term in Callaway’s theory) provides 94% addition to the result obtained from the single-mode relaxation time theory, clearly suggesting that the single-mode relaxation time approach is inadequate for describing the phonon conductivity of graphene.