A Monte Carlo rejection technique for numerically solving the complete, nonlinear phonon Boltzmann transport equation (BTE) is presented in this work, including three particles interactions. The technique has been developed to explicitly model population-dependent scattering within a full-band cellular Monte Carlo (CMC) framework, to simulate phonon transport in semiconductors, while ensuring conservation of energy and momentum for each scattering event within gridding error. The scattering algorithm directly solves the many-body problem accounting for the instantaneous distribution of the phonons. Our general approach is capable of simulating any nonequilibrium phase space distribution of phonons using the full phonon dispersion without the need of approximations used in previous Monte Carlo simulations. In particular, no assumptions are made on the dominant modes responsible for anharmonic decay, while normal and umklapp scattering are treated on the same footing. In this work, we discuss details of the algorithmic implementation of both the three-particle scattering for the treatment of the anharmonic interactions between phonons, as well as treating isotope and impurity scattering within the same framework. The simulation code was validated by comparison with both analytical and experimental results; in particular, the simulation results show close agreement with a wide range of experimental data such as thermal conductivity as function of the isotopic composition, the temperature, and the thin-film thickness.
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March 2017
Research-Article
Simulation of Phonon Transport in Semiconductors Using a Population-Dependent Many-Body Cellular Monte Carlo Approach
Flavio F. M. Sabatti,
Flavio F. M. Sabatti
School of Electrical, Computer and
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: fsabatti@asu.edu
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: fsabatti@asu.edu
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Stephen M. Goodnick,
Stephen M. Goodnick
School of Electrical, Computer and
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: stephen.goodnick@asu.edu
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: stephen.goodnick@asu.edu
Search for other works by this author on:
Marco Saraniti
Marco Saraniti
School of Electrical, Computer and
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: marco.saraniti@asu.edu
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: marco.saraniti@asu.edu
Search for other works by this author on:
Flavio F. M. Sabatti
School of Electrical, Computer and
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: fsabatti@asu.edu
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: fsabatti@asu.edu
Stephen M. Goodnick
School of Electrical, Computer and
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: stephen.goodnick@asu.edu
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: stephen.goodnick@asu.edu
Marco Saraniti
School of Electrical, Computer and
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: marco.saraniti@asu.edu
Energy Engineering,
Arizona State University,
Tempe, AZ 85287-5706
e-mail: marco.saraniti@asu.edu
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 6, 2016; final manuscript received October 18, 2016; published online December 28, 2016. Assoc. Editor: Alan McGaughey.
J. Heat Transfer. Mar 2017, 139(3): 032002 (10 pages)
Published Online: December 28, 2016
Article history
Received:
June 6, 2016
Revised:
October 18, 2016
Citation
Sabatti, F. F. M., Goodnick, S. M., and Saraniti, M. (December 28, 2016). "Simulation of Phonon Transport in Semiconductors Using a Population-Dependent Many-Body Cellular Monte Carlo Approach." ASME. J. Heat Transfer. March 2017; 139(3): 032002. https://doi.org/10.1115/1.4035042
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