  Electrical and thermal properties of atomically thin two-dimensional (2D)
materials are affected by their environment, e.g. through remote phonon
scattering or dielectric screening. However, while it is known that mobility
and thermal conductivity (TC) of graphene are reduced on a substrate, these
effects are much less explored in 2D semiconductors such as MoS$_2$. Here, we
use molecular dynamics to understand TC changes in monolayer (1L) and bilayer
(2L) MoS$_2$ by comparing suspended, supported, and encased structures. The TC
of monolayer MoS$_2$ is reduced from ~117 Wm$^{-1}$K$^{-1}$ when suspended, to
~31 Wm$^{-1}$K$^{-1}$ when supported by SiO$_2$, at 300 K. Encasing 1L MoS$_2$
in SiO$_2$ further reduces its TC down to ~22 Wm$^{-1}$K$^{-1}$. In contrast,
the TC of 2L MoS$_2$ is not as drastically reduced, being >50% higher than 1L
both when supported and encased. These effects are due to phonon scattering
with remote vibrational modes of the substrate, which are partly screened in 2L
MoS$_2$. We also examine the TC of 1L MoS$_2$ across a wide range of
temperatures (300 to 700 K) and defect densities (up to 5$\times$10$^{13}$
cm$^{-2}$), finding that the substrate reduces the dependence of TC on these
factors. Taken together, these are important findings for all applications
which will use 2D semiconductors supported or encased by insulators, instead of
freely suspended.
