Two-dimensional 1H transition metal dichalcogenides (TMDs) provide a platform, analogous to group IV cubic semiconductor alloys (${\mathrm{Si}}_{1-x}\mathrm{Ge}$), that enables systematic investigations on the effects of alloying in 2D material systems. The existing literature on TMD alloys explores their electrical, magnetic, and optical properties, but lacks a comprehensive analysis of thermal transport in supported and nanostructured systems. Here we employ first-principles-driven phonon Boltzmann transport formalism and a 2D-3D thermal boundary conductance model to systematically study in-plane and cross-plane phonon transport of suspended and ${\mathrm{SiO}}_2$ supported single-layer TMD alloys. We find that the thermal conductivity of alloyed TMDs is dependent on system size up to tens of microns and that the combination of mass-difference and substrate scattering can significantly reduce thermal transport even in large systems ($>500$ nm). Beyond in-plane transport, we find that the thermal boundary conductance displays a qualitatively different trend and significantly weaker modulation with alloy composition as compared to the thermal conductivity. Our results help shed light on the in-plane and cross-plane thermal transport properties of 2D single-layer TMD alloys and further their applications in nanoelectronics, sensing, and energy devices.

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• Lattice thermal conductivity
• Transition metal dichalcogenides
• Boltzmann theory