Environmental Engineering Reference
In-Depth Information
transport properties of GNRs. Such study, however, is of crucial
importantforthedevelopmentoffuturenanoelectronicsbecauseof
the serious heat dissipation in ever-smaller integrated circuits.
It is well known that electronic properties of GNRs are strongly
dependent on their edge shape and ribbon width. Such kind of
knowledge is essential for applications of GNRs. Similarly, the
corresponding information on thermal-transport properties is sig-
nificantnotonlyforimprovingperformanceofGNR-basedelectronic
devices but also for designing GNR-based thermal management or
thermoelectricdevices.Therefore,weinvestigatethermal-transport
propertiesofGNRswithdifferentwidthsandedgeshapes,usingthe
NEGF method. Xu
et al.
[38] provide more details of this study.
It should be stressed that a quantum description of thermal
transport is necessary for systems of short transport lengths
(compared to phonon mean free path) or equivalently at low
temperatures(comparedtotheDebyetemperature).Inthediffusive
region (i.e., the length of the transport system is much larger than
phononmeanfreepath),theNewton'smechanics-basedapproaches
[e.g., the classical molecular dynamics (MD)] and the quantum
mechanics-basedapproaches(e.g.,theNEGFmethod)areequivalent
and both work at this classical limit. While as the system size
becomes comparable or smaller than phonon mean free path, the
Newton'smechanics-basedapproachesfailbecauseofthedominant
quantum effects due to the wave nature of thermal-transport
carriers, which cannot be correctly described in the classical
framework. Alternatively, as the temperature decreases phonon
mean free path increases thus the quantum effects play a more and
more important role in thermal transport. For carbon materials, the
roomtemperaturebelongstothelow-temperatureregionbecauseof
theirextremelyhighDebyetemperature(over2000Kfordiamond).
A full quantum mechanics description is requisite for thermal
transport in graphene around room temperature.
GNRs with width varying from 0.5 nm to 35 nm are considered
for exploring size effects. The influence of edge shape will also
be investigated by comparing thermal-transport properties of two
representative types of GNRs: zigzag GNRs (ZGNRs) and armchair
GNRs (AGNRs) as shown in Fig. 3.7. Following the conventional
notation,
N
a
-AGNR(
N
z
- ZGNR) denotes an AGNR (a ZGNR) with
