  Accurate measurements and physical understanding of thermal boundary
resistance (R) of two-dimensional (2D) materials are imperative for effective
thermal management of 2D electronics and photonics. In previous studies, heat
dissipation from 2D material devices was presumed to be dominated by phonon
transport across the interfaces. In this study, we find that in addition to
phonon transport, thermal resistance between non-equilibrium phonons in the 2D
materials could play a critical role too when the 2D material devices are
internally self-heated, either optically or electrically. We accurately measure
R of oxide/MoS2/oxide and oxide/graphene/oxide interfaces for three oxides
(SiO2, HfO2, Al2O3) by differential time-domain thermoreflectance (TDTR). Our
measurements of R across these interfaces with external heating are 2-to-4
times lower than previously reported R of the similar interfaces measured by
Raman thermometry with internal self-heating. Using a simple model, we show
that the observed discrepancy can be explained by an additional internal
thermal resistance (Rint) between non-equilibrium phonons present during Raman
measurements. We subsequently estimate that for MoS2 and graphene, Rint is
about 31 and 22 m2 K/GW, respectively. The values are comparable to the thermal
resistance due to finite phonon transmission across interfaces of 2D materials
and thus cannot be ignored in the design of 2D material devices. Moreover, the
non-equilibrium phonons also lead to a different temperature dependence than
that by phonon transport. As such, our work provides important insights into
physical understanding of heat dissipation in 2D material devices.
