Thermal Conductivity of Monolayer Molybdenum Disulfide Obtained from Temperature-Dependent Raman Spectroscopy*

Atomically-thin transition metal dichalcogenides (TMDs) offer potential for an alternative to graphene in advanced devices owing to their unique electronic and optical properties. We report the temperature-dependent Raman spectra of the monolayer TMD molybdenum disulfide (MoS$_{2})$. Mechanical exfoliation of bulk MoS$_{2}$ provides monolayer flakes, which are then transferred to either sapphire substrates (with and without HfO$_{2}$ overcoating) or suspended over holes in a Si/Si$_{3}$N$_{4}$ substrate. The temperature dependence of Raman spectra from (100 to 400) K reveals two strong phonon modes, the planar$ E_{2g}^{1}$ and out-of-plane $A_{1g}$, both of which soften linearly with increasing temperature as a result of anharmonic effects. We extract a linear temperature coefficient for both Raman-active modes. These data, when combined with the first-order coefficients from laser power-dependent measurements, enable extraction of the thermal conductivity. The resulting room-temperature thermal conductivity, $\kappa = $ 35 W m$^{-1}$ K$^{-1}$, agrees well with first-principles lattice dynamics simulations, however, this value is significantly lower than that of graphene. The impact of the dielectric and substrate environment on extraction of $\kappa $ will be discussed. Additionally, we will present preliminary Raman spectra of related TMDs, $e.g$., TaSe$_{2}$.