Environmental Engineering Reference
In-Depth Information
Figure 5.4
Basic algorithm of Green-Kubo MDsimulations.
B
ij
is a function of the number of neighboring atoms, bond angles,
and bond lengths. The detailed expressions of Tersoff potential
functions and the parameters for silicon, nitrogen, and hydrogen
atomsarereportedbyDeBritoMota
et al.
[48].Tersoffpotentialhas
beensuccessfullyappliedtocalculatethermalconductivityofSiNWs
[13, 17] and SiGe NWs[28].
Figure 5.4 shows the basic algorithm of the EMD method. After
a NVT (constant particle number
N
, volume
V
, and temperature
T
) equilibration, NVE (constant
N
,
V
, and total energy
E
)MD
simulationsarecarriedouttoobtainheatcurrent
J
(
t
)whichisgiven
by
d
dt
J
(
t
)
=
(
r
i
E
i
),
(5.2)
i
where
r
i
and
E
i
are the time-dependent atomic position vector and
the microscopic total energy of atom
i
, respectively. The thermal
conductivity along the
z
-axial direction is then calculated with the
Green-Kubo formula [49],
Vk
B
T
2
∞
1
0
κ
z
=
J
z
(0)
J
z
(
t
)
dt
,
(5.3)