A Monte Carlo Based Method Simulating Both Particle and Wave Behaviours of Phonon Transport

In recent years, the decreased accessible length scale in fabricating micro/nano structure materials have raised a challenging task for understanding and modeling the submicron thermal transport, especially for nanoscale superlattices and composites. Currently, heat transport in small scale is either modeled at the atomic level using, for example, molecular dynamics or lattice dynamics, which have a limitation on the problem size that can be handled; or investigated through transport of phonons, which are treated as classical particles governed by Boltzmann transport equation. However, in the pure particle picture of phonons, the phase information carried by phonon waves is ignored. Hence such an approach is only valid in the incoherent regime. However, the coherent phonon transport, due to the interference of phonons scattered from the interfaces, is known to exist and has been demonstrated experimentally [1]. Thereby, over a considerable range, both coherent and incoherent phonon transport are likely to be important, and hence a mesoscopic method that can simulate both two effects would be highly desirable and expected to provide a way to manage the thermal transport or design composite materials by manipulating the phonon wave. Inspired by the work in which the motion of wave packets was simulated using a particle approach and the interference effect was considered by superposing the amplitudes of phonons based on phase information instead of energy [2], a new Monte Carlo (MC) method has been developed to simulate both particle and wave behaviours of phonons. In this approach, phonon is still modeled as a particle, but carries its amplitude and phase information. When a phonon collides with an interface and coherent interference occurs, it preserves its phase information. When the phonon undergoes anharmonic scattering process as it does in the conventional MC, its phase information is destroyed and randomly reset. Additionally, an associated interface model has been constructed to facilitate the simulation of phonon transport across an interface, which involves both coherent transport and anharmonic interfacial scattering. Our studies have been conducted in the superlattice structure consists of two materials, silicon and its heavy isotope. It has been shown that in the diffusion limit, where wave effect is covered, the new method and the conventional MC produce the same temperature and heat flux as expected; while in the wave regime, the results obtained from the two methods are vastly different with those obtained from our new method being more closed to the experimentally observed trend, that is, the thermal conductivity of superlattice increases with the increased number of periods [1]. Meanwhile, it has also been found that larger mass mismatch of the two material lead to weaker wave interference effect when all the other interface conditions keep the same. Furthermore, for non-periodic superlattice structures with layer thickness variation, a highly reduced thermal conductivity compared with it of periodic structure is obtained, where the wave effect is shown to be destructive.