A hybrid phonon Monte Carlo-diffusion method for ballistic-diffusive heat conduction in nano- and micro- structures

Abstract

The existing phonon Monte Carlo (MC) for ballistic-diffusive heat conduction are limited to small and simple structures owing to the huge time cost following with the increasing scale. This article presents a new hybrid phonon Monte Carlo-diffusion method for ballistic-diffusive heat conduction, which successfully characterizes the ballistic effect with significantly reducing the computational cost. Based on the idea that the phonon-boundary scattering mainly affects the regions adjacent to the boundaries when the system is considerably large, the whole system is divided into three zones: the boundary MC zone and the middle diffusion zone, between which is the overlap zone. By using an alternating method and setting virtual phonon bath or specular reflection as the boundary condition for the MC zones, the results of the phonon tracing MC and diffusion equation can be coupled and converge at the overlap zone. To verify, the cross-plane and in-plane film heat conduction, where slip boundary conditions are the major characteristics of the ballistic-diffusive regime, are simulated by the hybrid method as well as standard phonon tracing MC which works as a benchmark. It is found that the hybrid method can accurately predict the distributions of temperature and heat flux in the system with nearly the same precision as the phonon tracing MC while the computation time can reduce up to 90%, validating its potential use for larger and more complex structures.