Abstract
Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.
Date of this Version
2015
Published in:
J. Appl. Phys. 117, 135102 (2015)
Comments
Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Appl. Phys. 117, 135102 (2015) and may be found at http://dx.doi.org/10.1063/1.4916245. The following article has been submitted to/accepted by Journal of Applied Physics. Copyright (2015) Jesse Maassen & Mark Lundstrom. This article is distributed under a Creative Commons Attribution 3.0 Unported License.