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

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
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 117; Journal Issue: 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
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