Derivation of a hydrodynamic heat equation from the phonon Boltzmann equation for general semiconductors
Sendra Molins, Lluc (Universitat Autònoma de Barcelona. Departament de Física)
Beardo Ricol, Albert (Universitat Autònoma de Barcelona. Departament de Física)
Torres, Pol (Universitat Autònoma de Barcelona. Departament de Física)
Bafaluy Bafaluy, Javier (Universitat Autònoma de Barcelona. Departament de Física)
Àlvarez Calafell, Francesc Xavier (Universitat Autònoma de Barcelona. Departament de Física)
Camacho Castro, Juan (Universitat Autònoma de Barcelona. Departament de Física)

Date:	2021
Description:	6 pàg.
Abstract:	We present a formalism to solve the phonon Boltzmann transport equation (BTE) for finite Knudsen numbers that supplies a hydrodynamic heat transport equation similar to the Navier-Stokes equation for general semiconductors. This generalization of Fourier's law applies in general cases, from systems dominated by momentum-preserving normal collisions, as is well known, to kinetic materials dominated by resistive collisions, where it captures nonlocal effects. The key feature of our framework is that the macrostate is described in terms of the heat flux and its first derivatives. We obtain explicit expressions for the nonequilibrium phonon distribution and for the geometry-independent macroscopic parameters as a function of phonon properties that can be calculated from first principles. Ab initio model predictions are found to agree with a wide range of experiments in silicon. In contrast to approaches directly based on the BTE, the hydrodynamic equation can be solved in arbitrary geometries, thus providing a powerful tool for nanoscale heat modeling at a low computational cost.
Grants:	Agencia Estatal de Investigación RTI2018-097876-B-C22
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Initio molecular-dynamics ; Total-energy calculations ; Thermal-conductivity ; Transport ; Sound ; Model
Published in:	Physical review B, Vol. 103, issue 14 (2021) , art. L140301, ISSN 2469-9969

DOI: 10.1103/PhysRevB.103.L140301

6 p, 574.3 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > Grup de Propietats de Transport a la Nanoescala
Articles > Research articles
Articles > Published articles