Thermal conductivity of silicene calculated using an optimized Stillinger-Weber potential

Silicene, the silicon-based counterpart of graphene with a two-dimensional honeycomb lattice, has attracted tremendous interest both theoretically and experimentally due to its significant potential industrial applications. From the aspect of theoretical study, the widely used classical molecular dynamics simulation is an appropriate way to investigate the transport phenomena and mechanisms in nanostructures such as silicene. Unfortunately, no available interatomic potential can precisely characterize the unique features of silicene. Here, we optimized the Stillinger-Weber potential parameters specifically for a single-layer Si sheet, which can accurately reproduce the low buckling structure of silicene and the full phonon dispersion curves obtained from ab initio calculations. By performing equilibrium and nonequilibrium molecular dynamics simulations and anharmonic lattice dynamics calculations with the new potential, we reveal that the three methods consistently yield an extremely low thermal conductivity of silicene and a short phonon mean-free path, suggesting silicene as a potential candidate for high-efficiency thermoelectric materials. Moreover, by qualifying the relative contributions of lattice vibrations in different directions, we found that the longitudinal phonon modes dominate the thermal transport in silicene, which is fundamentally different from graphene, despite the similarity of their two-dimensional honeycomb lattices.

Figure 1

Comparison of the crystal structures between graphene and silicene. (a) Top view and (b) side view of graphene. (c) Top view and (d) side view of silicene. The graphene has perfect planar structure, while silicene has a low buckling in out-of-plane direction (buckling distance indicated by $h$).

Figure 2

Full phonon dispersion curves of silicene in the Brillouin zone. The solid black and blue lines are calculated by the optimized SW1 and optimized SW2 parameters, respectively. The red triangles are the results from ab initio calculations.

Figure 3

The thermal conductivity of silicene as a function of sample size. The left/bottom and right/top axes correspond to the result calculated by EMD and NEMD simulations, respectively. All results correspond to the real system temperature of 230 K after quantum correction. The black solid and dotted lines are the ALD results at the same temperature for the optimized SW1 and optimized SW2 parameters, respectively. The red dash-dotted lines are the curves fitting to Eq. (8).

Figure 4

The percentage contribution to thermal conductivity as a function of phonon MFP for the optimized SW1 and optimized SW2 parameters at 230 and 300 K.

Figure 5

Relative contribution (percentage) of lattice vibrations in the $x$ (transverse), $y$ (longitudinal), and $z$ (out-of-plane) directions to total heat flux in the NEMD simulation. Inset: atomic displacements of a typical out-of-plane acoustic (ZA) phonon mode in silicene at the $M$-point of the first Brillouin zone.