Environmental Engineering Reference
In-Depth Information
of graphene is
∼
4.2 nW/K/nm
2
at room temperature. The two
approaches give essentially the same result. The slight difference
in the predicted thermal conductance arises from the fact that the
energy potential of graphene is described by different approaches:
the former calculation uses first-principles method and the latter
uses empirical potential.
The two separated calculations consistently predict that the
scaled ballistic thermal conductance is
∼
4nW/K/nm
2
at room
temperature, consistent with previous study [41]. As a comparison,
the scaled room temperature ballistic thermal conductance of
pristine silicon nanowires (SiNWs) is
∼
1nW/K/nm
2
[43], of the
sameorderasthatofgraphene.Thiscannotexplainthethreeorders
of magnitude difference in their thermal conductivity measured by
experiments.Ourresultsdemonstratethatitistheverylongphonon
mean free path, instead of the extremely high ballistic thermal
conductance, that gives rise to the extraordinary high thermal
conductivity of graphene.
3.4.2.2 Long phonon mean free path in graphene
In last subsection, we theoretically demonstrate that the extra-
ordinary high thermal conductivity of graphene comes from its
superiorly long phonon mean free path. Thermal measurements
using a noncontact technique based on micro-Raman spectroscopy
estimate that the phonon mean free path of graphene is around
775 nm at room temperature [30]. An estimation of thermal
conductivity, employing the Eq. 3.68 using the calculated ballistic
thermal conductance and the experimental phonon mean free
path, gives a value about 3000 W/m/K, consistent with previous
experimental measurements.
What is the underlying mechanism of the long phonon mean
free path in graphene? First, the many body interactions (electron-
phononandphonon-phononinteractions)areweakerin2Dsystems
than 3D systems, because the requirement of simultaneously
satisfying boththe momentum and energy conservation laws exerts
stronger restrictions on scattering events in systems of lower
dimensions. Second, structural distortion has minor effects on
thermal transport in graphene. Our recent study finds that even
