Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations
Abstract
Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but are widely believed to break down when the characteristic length scale is similar or less than the phonon mean-free-path. Building on our prior work, we demonstrate how well-known diffusion equations, namely, the hyperbolic heat equation and the Cattaneo equation, can be used to model ballistic phonon effects in frequency-dependent periodic steady-state thermal transport. Our analytical solutions are found to compare excellently to rigorous numerical results of the phonon Boltzmann transport equation. The correct physical boundary conditions can be different from those traditionally used and are paramount for accurately capturing ballistic effects. To illustrate the technique, we consider a simple model problem using two different, commonly used heating conditions. We demonstrate how this framework can easily handle detailed material properties, by considering the case of bulk silicon using a full phonon dispersion and mean-free-path distribution. This physically transparent approach provides clear insights into the nonequilibrium physics of quasi-ballistic phonon transport and its impact on thermal transport properties.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 01, 2016
- Source ID
- 10.1063/1.4942836
Entities
People
- Jesse Maassen
- Mark S. Lundstrom
Organizations
- Dalhousie University
- Defense Advanced Research Projects Agency
- National Science Foundation
- Purdue University
- Semiconductor Research Corporation