Environmental Engineering Reference
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conductance of narrow GNRs is mostly dominated by phonons,
since all sub-10 nm GNRs are semiconducting as shown by recent
experiment [56]. In our NEGF calculations, we neglect the complex
many-body interactions (i.e., phonon-phonon and electron-phonon
interactions), which induce very few phonon scatterings because
of the extremely long phonon mean free path in graphene (around
775 nm at room temperature [30]), much longer than the length
of the central part of our calculated transport systems. With
such approximation that does not affect our final results, the
quantum thermal-transport problem can be solved exactly by the
NEGF method. We calculated the phonon Hamiltonian (i.e., force
constant matrix) by the second-generation reactive empirical bond
order potential [39], which has been demonstrated to be able to
predict accurate phonon structures for graphene-based systems
[40]. Phonon transmission and phonon local density of states
(LDOS) are givenby theNEGFcalculations. Thermal conductanceas
a function of temperature is computed by the Landauer formula.
3.4.3.1 Contact geometry
Connecting two GNRs together can form various single-interface
graphene junctions that could be used for basic device building
blocks (Fig. 3.12) [52]. Electronic transport in such junctions is well
known to be strongly dependent on the geometrical structure in
the contact region. Here we study effects of contact geometry on
thermal transport, by considering various single-interface junctions
that share the same composed GNRs but have different structure
close to the interface. Though contact geometries are distinctly
different, their thermal conductance only shows slight variances.
Thermaltransportisinsensitivetothechangesincontactgeometry,
in contrast to electronic transport, which shows strong dependence
on contact geometry. The distinct feature of electronic and thermal
transport can be explained from two aspects: (1) the typical length
scales (e.g., wavelength and mean free path) of phonons and
electrons are different; and (2) only electrons near the Fermi level
contribute to electronic conductance, while all phonon modes that
are populated (or excited) contribute to thermal conductance. Since
different contact geometries give rise to negligible difference in
