2014/10/10 by Chengyun Hua, Hua, Chengyun, Austin J. Minnich +1
Engineering · Materials Science · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #FOS: Physical sciences #Heat Transfer and Optimization #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Thermal properties of materials #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.1410.2845
arxiv created 2014/10/10 · openalex publication_date 2014/10/10 · arxiv updated 2014/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cross-plane heat transport in thin films with thickness comparable to the phonon mean free paths is of both fundamental and practical interest. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a more accurate understanding of heat conduction in thin films.