An efficient two-step Monte Carlo method for heat conduction in nanostructures

Research on the heat conduction in nanostructures has drawn much attention due to their potential applications in thermoelectric devices. Although the phonon tracing Monte Carlo (MC) technique, where the trajectories of individual phonons are simulated independently, has been extensively used for simulating the heat conduction in nanomaterials, it cannot efficiently simulate the phonon transport in the large area periodic nanostructures yet, due to the demand of absorbing boundaries. In the present work, we develop a two-step phonon tracing MC method to solve this problem. At the first step, the initial phonon transmittance and the phonon emission distributions at the internal virtual boundary are obtained by simulating phonon transport in the initial simulation unit that is directly in contact with the phonon bath. At the second step, the internal phonon transmittance is calculated for the internal simulation units according to the internal boundary phonon emission distributions. Since the whole structure can be simplified as a one-dimensional phonon transport system, the total phonon transmittance can be readily calculated via the combination of initial and internal phonon transmittances, and the effective thermal conductivity is then derived. Furthermore, for verification, we calculate the effective thermal conductivities of three typical nanostructures, that is, the cross-plane and in-plane nanofilms and the periodic nanoporous structures, by using the theoretical models, the standard and the two-step MC simulations, respectively. The two-step MC method well predicts the results calculated by the standard MC simulations and the theoretical models. More importantly, the computation time of the two-step MC simulation is at least one order of magnitude less than that of the standard MC simulation, while its under-prediction can be less than 10% even 5%.