Thermal conductivity of bulk and monolayer MoS2

We show that the lattice contribution to the thermal conductivity of MoS2 strongly dominates the carrier contribution in a broad temperature range from 300 to 800K. Since theoretical insight into the lattice contribution is largely missing, though it would be essential for materials design, we solve the Boltzmann transport equation for the phonons self-consistently in order to evaluate the phonon lifetimes. In addition, the length scale for transition between diffusive and ballistic transport is determined. The low out-of-plane thermal conductivity of bulk MoS2 (2.3Wm−1K−1 at 300K) is useful for thermoelectric applications. On the other hand, the thermal conductivity of monolayer MoS2 (131Wm −1K−1 at 300K) is comparable to that of Si. Copyright c © EPLA, 2016 Introduction. – Traditionally molybdenum disulphide (MoS2) is used in photovoltaics [1,2], solid lubrication [3–5], catalysis [6,7], and for improving the performance of Li-ion batteries [8–13]. Analogous to the interlayer bonding in graphite [14], the coupling between H-stacks (further on referred to as monolayers) in 2H-MoS2 is due to weak van der Waals interaction, paving the way to obtaining monolayer MoS2 by exfoliation [15–20]. While in the bulk form 2H-MoS2 is an indirect band gap semiconductor [21], the material becomes a direct band gap semiconductor as monolayer [22] due to quantum confinement [23]. Along with a decent electron mobility (∼ 200 cm2V−1s−1) and a high current on/off ratio (∼ 10) at room temperature [24] this makes monolayer MoS2 a promising material for nanoelectronics, optoelectronics, photodetection, nanophotonics, light-emitting diodes, gas sensing, and transistors [20,25–28]. Both bulk and monolayer MoS2 show high thermoelectric power due to the large band gap. For example, at room temperature for p-type bulk MoS2 a value of 700μVK−1 (hole concentration of 1.5 × 10 cm−3) [29] was found and for n-type monolayer MoS2 a value of −400μVK−1 [30]. Using ab initio calculations, refs. [31] and [32] have evaluated only the electronic contribution to the thermoelectric properties, while ref. [33] has included the in-plane thermal conductivity reported in ref. [34]. Exact knowledge of the thermal conductivity, however, is crucial to describe the heat dissipation. Since in electronic devices the heat must be removed as soon as possible to avoid overheating, a large thermal conductivity is required. On the contrary, a low thermal conductivity yields a high thermoelectric figure of merit [35]. Experimentally, the out-of-plane thermal conductivity of bulk MoS2 at 300K is 1.05Wm−1K−1 [36]. While Sahoo and coworkers have extracted a thermal conductivity of 52Wm−1K−1 for 11-layer MoS2 from Raman data [37], direct measurements found for 4-layer and 7-layer MoS2 values of 44Wm−1K−1 and 48Wm−1K−1, respectively [38]. Raman measurements for monolayer MoS2 resulted in a value of 34.5Wm−1K−1 [39]. Theoretically, the heat conduction in MoS2 has been investigated by molecular dynamics [34,40,41] and ab initio methods [42,43]. For the in-plane and outof-plane thermal conductivities of bulk MoS2 values of 18.06 and 4.17Wm−1K−1, respectively, have been reported [34]. Contradictory values of 1.35Wm−1K−1 and 5.8Wm−1K−1 have been obtained in refs. [12] and [41] for monolayer MoS2, which may be due to differences in the parametrisation of the interatomic potentials. Upper limits have been estimated for armchair nanoribbons (674Wm−1K−1) and zigzag nanoribbons (841Wm−1K−1) [44]. Furthermore, ab initio approaches employing the relaxation time approximation [45] have found for monolayer MoS2 at 300K a lower limit of 83Wm−1K−1 [42] and a value of 23.2Wm−1K−1 [43], which constitutes a large discrepancy. As compared to the relaxation time approximation, more accurate results can be achieved by solving the Boltzmann transport equation