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Title: Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

Abstract

Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. 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 the 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 straightforward physical understanding of cross-plane heat conduction in thin films.

Authors:
;  [1]
  1. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125 (United States)
Publication Date:
OSTI Identifier:
22403011
Resource Type:
Journal Article
Journal Name:
Journal of Applied Physics
Additional Journal Information:
Journal Volume: 117; Journal Issue: 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 77 NANOSCIENCE AND NANOTECHNOLOGY; ANALYTICAL SOLUTION; BOLTZMANN EQUATION; COMPARATIVE EVALUATIONS; FREQUENCY DEPENDENCE; LASERS; LIGHT EMITTING DIODES; MEAN FREE PATH; PHONONS; QUANTUM WELLS; THERMAL CONDUCTION; THERMAL CONDUCTIVITY; THICKNESS; THIN FILMS; TRANSIENTS

Citation Formats

Hua, Chengyun, and Minnich, Austin J., E-mail: aminnich@caltech.edu. Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films. United States: N. p., 2015. Web. doi:10.1063/1.4919432.
Hua, Chengyun, & Minnich, Austin J., E-mail: aminnich@caltech.edu. Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films. United States. doi:10.1063/1.4919432.
Hua, Chengyun, and Minnich, Austin J., E-mail: aminnich@caltech.edu. Thu . "Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films". United States. doi:10.1063/1.4919432.
@article{osti_22403011,
title = {Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films},
author = {Hua, Chengyun and Minnich, Austin J., E-mail: aminnich@caltech.edu},
abstractNote = {Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. 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 the 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 straightforward physical understanding of cross-plane heat conduction in thin films.},
doi = {10.1063/1.4919432},
journal = {Journal of Applied Physics},
issn = {0021-8979},
number = 17,
volume = 117,
place = {United States},
year = {2015},
month = {5}
}