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

Journal Article · Thu May 07 00:00:00 EDT 2015 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.4919432· OSTI ID:22403011

Hua, Chengyun

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.

• OSTI ID: 22403011
• Journal Information: Journal of Applied Physics, Vol. 117, Issue 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

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