Environmental Engineering Reference
In-Depth Information
in detecting it in a nanowire consisting of silicon nitride below
0.6 K using a sophisticated fabrication technique [5]. Figure 2.2a
shows the experimental setup used to measure the quantum
κ
0
.
The small square at the center is a silicon nitride (SiN) membrane.
The membrane is heated by two C-shaped heaters made by a gold
thin film and acts as a heat reservoir. Since this membrane is
suspended by four SiN bridges in vacuum, the heat reservoir and
the four bridges are thermally isolated from the environment and
the heat flows from the membrane into 4 SiN nanowire without
heat dissipation. The perfect phonon transmission was realized by
constructing smooth connections between the membrane and the
SiN nanowires, as shown in Fig.2.2b.
Figure 2.2c shows the temperature dependence of the phonon-
derived thermal conductance of SiN nanowires normalized by
16
κ
0
. The total thermal conductance of the device in Fig. 2.2a is
expected to be 16
κ
0
because each of the four acoustic modes in
each of the four bridges carries the quantum
κ
0
.Atanextremely
low temperature, below a threshold temperature of
∼
0.6 K, the
normalized thermal conductance is one or lower, as we expect.
Above the threshold temperature, the thermal conductance curve
increases because the optical phonon modes begin to contribute to
the thermal transport.
As well as in SiN nanowires, quantization of the thermal
conductance has also been observed in carbon nanotubes [11] just
after its theoretical prediction [12].
2.2.3
Non-equilibrium Green's Function Method for
Phonon Transport
The Landauer formula in Eq. 2.7 tells us that the thermal
conductance is determined by the phonon transmission function
ζ
(
ω
). Except for the ideal case of perfect transmission for all
modes, it is di
cult to calculate analytically the transmission
ζ
(
ω
)
for nanoscale objects with complex atomic structures. One of the
powerful numerical techniques to calculate
) for nanomaterials
is the non-equilibrium Green's function (NEGF) method [13-15].
According to the scattering theory using the NEGF technique, the
ζ
(
ω
