Environmental Engineering Reference
In-Depth Information
Figure 4.6
Thermal conductance divided by temperature
K
/
T
,whichis
reduced by the zero-temperature universal value
π
2
k
B
/
3
h
, as a function
of the reduced temperature
k
B
T
/
in a three-dimensional quantum wire
with stub structure. (a1-a3) and (b1-b3) correspond to the stress-free
and hard wall boundary conditions, respectively. Note that the dash-dotted
curve was calculated by the 2Dmodel in (a2) and (b2)[56].
parameters and temperature. Moreover, the dependence of the
thermal conductance on the temperature in 3D model is different
from that in 2D model. However, some interesting physical effects
that appeared in 2D model, such as the universal quantum thermal
conductance, resonant transmission, stop-frequency gap, and so
on, can be also observed in 3D model. So these results indicate
that although there exist some differences of thermal properties
between the 2D and 3D models due to the two transverse boundary
confinement in 3D model but only one in 2D model. The 2D
model can still hold good approximation to describe qualitatively
the phonon transmission and thermal conductance in real 3D
geometry.
