Environmental Engineering Reference
In-Depth Information
ballisticthermalrectificationinasimilarthree-terminalmesoscopic
dielectric system at low temperature is analytically obtained based
on the Landauer transport theorem, and the rectifying e
ciency
can be e
ciently tuned by changing the structural asymmetry or
adjusting the central probe [92]. These results indicate that three-
terminal mesoscopic junctions have an important application in
nanodevices, such as mode splitter, thermal rectifier, andso on.
4.3.3
Properties of Ballistic Thermal Transport in 3D
Quantum Structures
It is worthy noting that these previous studies mainly focused
on the ballistic thermal transport in the quantum structures with
inhomogeneities, where it is assumed that the thickness of each
regionisverysmallwithrespecttotheotherdimensionsandalsoto
the elastic phonon wavelength. In fact, the out-of-plane dynamics is
ignored and only the 2D geometries are considered. By developing
the 2D model technique, Li
et al.
[47] first calculated the ballistic
thermal conductance in a 3D quantum structure with an abrupt
junction, and predicted that the thermal conductance is lower than
the universal unit
π
2
k
B
T
/
3
h
and is strongly influenced by the
abrupt junction structure in the low temperature limit. Recently,
Peng
et al.
presented a numerical study of the low temperature
thermal conductance in a 3D quantum wire with a stub structure
undertwodifferentboundaryconditions[56].TheresultsinFig.4.6
show that when stress-free boundary conditions are applied, the
thermal conductance
vs.
temperature displays similar behavior
as that in 2D model. In the low temperature limit, the thermal
conductanceapproachesthequantumvalue
π
2
k
B
T
/
3
h
regardlessof
the geometric structure, which agrees with the results by 2D model,
and also agrees with the experimental results. However, when hard
wall boundary conditions are applied, the thermal conductance
vs.
temperature displays different behavior from that for 2D models.
More recently, Xie
et al.
investigated the ballistic phonon transport
and thermal conductance in a 3D double-bend quantum structure
[60]. These studies reveal that the thermal conductance in 3D
model is much larger than that in 2D model for the same structural
