Environmental Engineering Reference
In-Depth Information
thickness is achievable with atomistic layer deposition technology,
this MD-based study indicates a practical approach that can be
realized to tune thermal conductivity.
It is worth to point out the critical coating thickness depends
on the diameter of the NW before coating. To see this dependence
more clearly, the normalized thermal conductivity versus coating
thickness for GeNWs with different diameters was plotted in Fig.
1.13c. Thermal conductivity of GeNW is used as reference at each
D
Ge
. According to the abovementioned two competing effects, the
maximum reduction of thermal conductivity occurs at the optimal
coating thickness of about 0.5-1 nm. Further increase of coating
thickness will result in the increase of thermal conductivity, but the
increase trend becomes slower at larger diameters. The dashed line
in Fig. 1.13c draws the unity for reference, and the arrows point
thecriticalcoatingthicknessbelowwhichcoatingiseffectiveforthe
purpose of thermal conductivity reduction.
Figure 1.13d shows the dependence of critical coating thickness
D
critical
on the NW diameter: it monotonically increases with NW
diameter, with a linear slope of about 0.34. These MD simulation
results suggest that coating is a quite effective method for
thermoelectric applications and ismore robust at larger diameter.
1.6 Equilibrium Molecular Dynamics
1.6.1
Green-Kubo Formula
Equilibrium molecular dynamics (EMD) simulation is based on the
Green-Kuboformula(GKF)derivedfromthefluctuation-dissipation
theorem [28] and linear response theory, which relates thermal
conductivity with heat current autocorrelation function (HCACF)
[52-54]. In GKF, the entire dynamics of the systems is expressed
through the time correlation function in thermal equilibrium,
which invokes little assumption about the physical property of
the material. EMD simulation has been applied to study thermal
properties ofvarious materials [55-58].
Several derivations of GKF exist in literature [59]. Here we
follow the derivation by Kubo
et al.
[60], with emphasis on some
