We investigate the size and edge roughness dependence on thermal conductivity of monolayer MoS 2 (MLMoS 2 ) by phonon Boltzmann transport equation combined with relaxation time approximation. The relative contribution of spectral phonons to thermal conductivity is explored, and we compared the characteristics of phonon transport with those in single layer graphene (SLG), which is a representative two-dimensional material. Quite different from SLG, because of the ultra-short intrinsic phonon mean free path, the thermal conductivity of MLMoS 2 ribbons is size and roughness insensitive. The LA phonons have the major contribution to thermal conductivity of MLMoS 2 , and the ZA phonons in MLMoS 2 have high relative contribution to thermal conductivity. The relative contribution to thermal conductivity from both high frequency and low frequency phonons in MLMoS 2 is lower than that in SLG. The underlying mechanism of these distinct characteristics results from the different phonon dispersions and anharmonic characteristic between MLMoS 2 and SLG. Very recently, the thermal conductivity of monolayer MoS 2 (MLMoS 2 ), one of the most stable layered transition metal dichalcogenides (TMD), has attracted numerous interest.1-7 Unlike graphene, MLMoS 2 is a semiconductor with a large bandgap, and hence, MLMoS 2 is regarded as a promising candidate for field effect transistor and optoelectronics device applications. 8,9 In electronic and energy device applications, highly efficient heat dissipation is critical for the device reliability and performance. On the other side, the large Seebeck coefficient 10 suggests potential applications of 2D MoS 2 as thermal energy harvesting and thermoelectric cooling. In thermoelectric application, low thermal conductivity is preferred. Although high power factor is also observed in graphene, the ultra-high thermal conductivity of graphene 11 offsets its advantages and limits application of graphene as efficient 2D thermoelectric materials. In contrast to the superior thermal conductivity of graphene, 11-14 the thermal conductivity of MLMoS 2 is low, which has been presented by theoretical analysis 1-4 and experimental measurements. 7While a number of studies have been performed, the knowledge of thermal conductivity of MoS 2 is still not enough and largely obscure. For instance, systematic investigations on various effects on thermal conductivity of graphene have been done, including impacts of isotopic doping, folding, grain boundary, vacancy, defects, surface functionalization, etc.14 In monolayer 2D sheet, there are three acoustic phonon polarization branches, which are transverseacoustic (TA), longitudinal-acoustic (LA), and out-of-plane acoustic (ZA) phonons. The frequency dependent contribution of different acoustic phonon modes to thermal conductivity of graphene has been widely addressed.12-14 The phonon mean free path (MFP) and the relative contribution of spectral phonons to thermal conductivity are crucial towards understanding and engineering the thermal conductivity of nanostru...

We theoretically investigate the phonon scattering by vacancies, including the impacts of missing mass and linkages () and the variation of the force constant of bonds associated with vacancies () by the bond-order-length-strength correlation mechanism. We find that in bulk crystals, the phonon scattering rate due to change of force constant is about three orders of magnitude lower than that due to missing mass and linkages . In contrast to the negligible in bulk materials, in two-dimensional materials can be 3–10 folds larger than . Incorporating this phonon scattering mechanism to the Boltzmann transport equation derives that the thermal conductivity of vacancy defective graphene is severely reduced even for very low vacancy density. High-frequency phonon contribution to thermal conductivity reduces substantially. Our findings are helpful not only to understand the severe suppression of thermal conductivity by vacancies, but also to manipulate thermal conductivity in two-dimensional materials by phononic engineering.

Although graphene holds great promise in thermal applications owing to its superior thermal conductivity, an intriguing question remains as to which polarizations and frequencies are dominant in its heat conduction. In this work, by incorporating the direction-dependent phonon-boundary scattering and the special selection rule for three-phonon scattering into the linearized phonon Boltzmann transport equation, we systematically investigate the relative contributions from longitudinal-acoustic, transverse-acoustic, and out-of-plane acoustic (ZA) branches to the thermal conductivity of graphene ribbons, focusing on the effects of their size and temperature. We find that the relative contribution from ZA branch to heat conduction increases with decreasing the size, specularity parameter, and temperature of graphene ribbons. Our analysis reveals that this change arises from the huge difference in the phonon dispersion and in the phonon mean free path of Umklapp process between in-plane and out-of-plane branches.

By incorporating the phonon-phonon scattering, phonon-boundary scattering and phonon-vacancy scattering into the linearized Boltzmann transport equation, we theoretically investigate the effects of size and edge roughness on thermal conductivity of single vacancy-defective graphene ribbons. Due to the severe suppression of high-frequency phonons by phonon-vacancy scattering which includes the impacts of missing mass and linkages, as well as the variation of the force constant of bonds associated with vacancies, the low-frequency ballistic phonons have a higher contribution to the thermal conductivity, which results in the stronger length, weaker width and weaker edge roughness dependence on thermal conductivity of vacancy-defective graphene ribbons than that of pristine ones. Our findings are helpful to understand and manipulate thermal conductivity of graphene by phononic engineering.

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