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The thermal properties of two-dimensional (2D) materials, like MoS$_2$, areknown to be affected by interactions with their environment, but this hasprimarily been studied only with SiO$_2$ substrates. Here, we compare thethermal conductivity (TC) and thermal boundary conductance (TBC) of monolayerMoS$_2$ on amorphous (a-) and crystalline (c-) SiO$_2$, AlN, Al$_2$O$_3$, and$\textit{h}$-BN monolayers using molecular dynamics. The room temperature TC ofMoS$_2$ is ~38 Wm$^{-1}$K$^{-1}$ on amorphous substrates and up to ~68Wm$^{-1}$K$^{-1}$ on crystalline substrates, with most of the difference due tosubstrate interactions with long-wavelength MoS$_2$ phonons (< 2 THz). An$\textit{h}$-BN monolayer used as a buffer between MoS$_2$ and the substratecauses the MoS$_2$ TC to increase by up to 50%. Length-dependent calculationsreveal TC size effects below ~2 $\mu$m and show that the MoS$_2$ TC is size-but not substrate-limited below ~100 nm. We also find that the TBC of MoS$_2$with c-Al$_2$O$_3$ is over twice that with c-AlN despite a similar MoS$_2$ TCon both, indicating that the TC and TBC could be tuned independently. Finally,we compare the thermal resistance of MoS$_2$ transistors on all substrates toshow that MoS$_2$ TBC is the most important parameter for heat removal forlong-channel (> 150 nm) devices, while TBC and TC are equally important forshort channels. This work provides important insights for electro-thermalapplications of 2D materials on various substrates.

Substrate-Dependence of Monolayer MoS$_2$ Thermal Conductivity and Thermal Boundary Conductance