Environmental Engineering Reference
In-Depth Information
of processes: one is geometric scattering and the other is many-
body scattering, Geometric scattering concerns phonon scatterings
caused by structural imperfections, such as boundary scattering,
interface scattering, defect scattering, impurity scattering, and so
on.Additionally,theinhomogeneousdistributionofatomicmasscan
also induce phonon scattering, such as isotope effects. In contrast
to the weak temperature-dependence of geometric scattering,
the strength of many-body scattering significantly varies as the
temperature changes. The many-body scattering arises due to the
coupling of phonons with other quasi-particles (e.g., electrons) and
with collective excitations (e.g., photons), as well as with phonons
themselves. Phonon-phonon scatterings are caused by anharmonic
interactions. They can be categorized into normal scatterings
(N-processes) and Umklapp (U) processes. Both are important
for establishing local thermal equilibrium, but only U-processes
contributetothermalresistance.Themany-bodyscatteringsrequire
theconservationofenergyandquasi-momentum.Thesatisfactionof
theseconditions,however,becomesdi
cultinlowdimensionalsys-
temslikegrapheneorgraphenenanoribbons(GNRs).Consequently,
many-body scatterings become less important in systems of lower
dimension.
According to kinetic theory of gases, there exists a rela-
tion between (average) phonon mean free path and thermal
conductivity
κ
:
κ
=
cvl
/
D
,
(3.3)
where
c
is the heat capacity per volume,
v
is the average group
velocity of phonons and
D
is the dimensionality of the transport
system. The relation is generally used for estimating (average)
phonon mean free path.
When the system size becomes comparable or smaller than
phonon mean free path, quantum effects becomes important. The
graphene-like structures have very long phonon mean free path,
as we will show. Theoretically studying such systems requires
incorporating quantum effects into thermal transport. The non-
equilibrium Green's function (NEGF) method, based on quantum
mechanics, isthe method of choice.
