Entropy Generation in Thin Films Evaluated From Phonon Radiative Transport

Abstract

One of the approaches for micro/nanoscale heat transfer is to use the Boltzmann transport equation, which reduces to the equation of phonon radiative transfer under the relaxation time approximation. Transfer and generation of entropy are processes inherently associated with thermal energy transport, yet little has been done to analyze entropy generation in solids at length scales comparable with or smaller than the mean free path of heat carriers. This work extends the concept of radiation entropy in a participating medium to phonon radiation, thus providing a general theory of entropy generation that is applicable to both large and small length scales. The conventional formula for entropy generation in heat diffusion can be derived under the local equilibrium assumption. Furthermore, the phonon brightness temperature is introduced to describe the nature of nonequilibrium heat conduction. A fundamental understanding of the entropy generation processes will broaden the knowledge of heat transport in solids, which is particularly important for thermal analysis in nanoelectronics.