Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films
- Creators
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Hua, Chengyun
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Minnich, Austin J.
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.
Additional Information
© 2015 AIP Publishing LLC. Received 4 March 2015; accepted 18 April 2015; published online 5 May 2015. This work was sponsored in part by the National Science Foundation under Grant No. CBET CAREER 1254213, and by Boeing under the Boeing-Caltech Strategic Research and Development Relationship Agreement.Attached Files
Published - 1.4919432.pdf
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Additional details
- Eprint ID
- 57400
- Resolver ID
- CaltechAUTHORS:20150511-075225662
- NSF
- CBET 1254213
- Boeing-Caltech Strategic Research & Development Relationship Agreement
- Created
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2015-05-11Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field