Modeling effective thermal conductivity enhanced by surface waves using the Boltzmann transport equation

The thermal management of semiconductors at the device level has become a crucial issue owing to the high integration density and miniaturization of microelectronic systems. Because surface phonon polaritons (SPhPs) exhibit long propagation lengths, they are expected to contribute significantly to the heat dissipation in microelectronic systems. This study aims to numerically estimate the heat transfer due to SPhPs in a thin SiO₂ film. The one-dimensional Boltzmann transport equation (BTE) is solved using the estimated propagation length based on the SPhP dispersion curves. The temperature profiles and heat fluxes are predicted and demonstrate the size effect of the film on the effective in-plane thermal conductivity of the SiO₂ film. The results indicate that the temperature distribution was constant regardless of the film length and thickness because the propagation length was much longer than the film length. In addition, the heat flux increased with decreasing film thickness owing to the depth-averaged energy transfer. The effective thermal conductivities predicted using the BTE differed by ~ 16.5% from the values obtained from the analytical expression. The numerical results of this study can provide valuable data when studying the thermal behavior of SPhPs.