A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

Journal Article · Tue Apr 07 04:00:00 EDT 2015 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.4916245· OSTI ID:22399402

Maassen, Jesse; Lundstrom, Mark ^[1]

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1. Network for Computational Nanotechnology, School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States)

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.

• OSTI ID: 22399402
• Journal Information: Journal of Applied Physics, Journal Name: Journal of Applied Physics Journal Issue: 13 Vol. 117; ISSN JAPIAU; ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOLTZMANN EQUATION
BOUNDARY CONDITIONS
COMPARATIVE EVALUATIONS
ELECTRONS
ENERGY DEPENDENCE
MEAN FREE PATH
PHONONS
TEMPERATURE DEPENDENCE
TEMPERATURE GRADIENTS
THERMAL CONDUCTION
TRANSIENTS