DSMC for Phonon Transport in Solid Thin Films

As the scale of electronic devices decreases, heat transfer analysis and thermal design becomes more important. In particular, heat transfer through various solid thin films is strongly affected by thickness dependence of thermal conductivity and interfacial thermal resistance. Analysis of phonon dynamics based on a linearized Boltzmann transport equation, or the so-called relaxation time approximation, has been widely used, but detailed analysis using molecular dynamics simulation reveals that couplings among various phonon modes can affect the energy transfer. In this study, we propose a DSMC scheme to simulate phonon dynamics starting from the original Boltzmann transport equation. In contrast to the linearized model, this scheme requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes, although we have to assume some appropriate model of phonon-phonon collisions. As a test calculation, energy flux was evaluated for model thin films of various thicknesses, and a phenomenon similar to the Casimir limit was retrieved. This scheme will enable us to include other factors, such as phonon-electron couplings.