The temperature distribution due to the ballistic-diffusive phonon transport

When the size of a solid material is comparable to or smaller than the mean free path of thermal carriers, temperature jumps and nonlinearity are often observed near the boundaries. Usually they are attributed to the ballistic behavior of thermal carriers. In this work, phonons are of interest and these phenomena are explored numerically based on a spectral deviational Monte Carlo simulation. Theoretical models for predictions, which take the direct as well as indirect phonon ballistic contribution into consideration, are proposed. A detailed energy balance is assumed and so is the existence of the so-called spectral temperature. Both the numerical spectral heat flux and spectral temperature distributions are examined to confirm the assumptions and, together with the model predictions, used to explore the significance and influence of the phonon ballistic transport. (C) 2019 Elsevier Ltd. All rights reserved.