Analysis of phonon dynamics based on a linearized Boltzmann transport equation is widely used for thermal analysis of solid thin films, but couplings among various phonon modes appear in some situations. We propose a direct simulation Monte Carlo (DSMC) scheme to simulate the phonon gas starting without the conventional linearization approximation. This requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes. A prototype code based on a simple phonon model was developed, and energy flux was evaluated for thin films of various thickness as a test calculation.
Issue Section:
Research Papers
References
1.
Cahill
, D. G.
, Ford
, W. K.
, Goodson
, K. E.
, Mahan
, G. D.
, Majumdar, A., Maris
, H. J.
, Merlin, R., and Phillpot
, S. R.
, 2003, “Nanoscale Thermal Transport
,” J. Appl. Phys.
, 93
, pp. 793
–818
.2.
Chen
, G.
, 2005, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons
, Oxford University Press
, Oxford
.3.
Kittel
, C.
, 2005, Introduction to Solid State Physics
, 8th ed., Wiley
, Hoboken, NJ
.4.
Casimir
, H. B. G.
, 1938, “Note on the Conduction of Heat in Crystals
,” Physica
, 5
, pp. 495
–500
.5.
Majumdar
, A.
, 1993, “Microscale Heat Conduction in Dielectric Thin Films
,” J. Heat Transfer
, 115
, pp. 7
–16
.6.
Joshi
, A. A.
, and Majumdar
, A.
, 1993, “Transient Ballistic and Diffusive Phonon Heat Transport in Thin Films
,” J. Appl. Phys.
, 74
, pp. 31
–39
.7.
Ziman
, J. M.
, 1960, Electrons and Phonons
, Oxford University Press
, Oxford
, Chaps 3 and 8.8.
Narumanchi
, S. V. J
, Murthy
, J. Y.
, and Amon
, C. H.
, 2004, “Submicron Heat Transport Model in Silicon Accounting for Phonon Dispersion and Polarization
,” J. Heat Trans.
, 126
, pp. 946
–955
.9.
Narumanchi
, S. V. J
, Murthy
, J. Y.
, and Amon
, C. H.
, 2005, “Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-Insulator Transistors
,” J. Heat Transfer
, 127
, pp. 713
–723
.10.
Chen
, G.
, and Neagu
, M.
, 1997, “Thermal Conductivity and Heat Transfer in Superlattices
,” Appl. Phys. Lett.
, 71
, pp. 2761
–2763
.11.
Sverdrup
, P. G.
, Ju
, Y. S.
, and Goodson
, K. E.
, 2001, “Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors
,” J. Heat Transfer
, 123
, pp. 130
–137
.12.
Jin
, J. S.
, and Lee
, J. S.
, 2009, “Electron-Phonon Interaction Model and its Application to Thermal Transport Simulation During Electrostatic Discharge Event in NMOS Transistor
,” J. Heat Transfer
, 131
, p. 092401
.13.
Yang
, R.
, Chen
, G.
, Laroche
, M.
, and Taur
, Y.
, 2005, “Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation
,” J. Heat Transfer
, 127
, pp. 298
–306
.14.
Peterson
, R. B.
, 1994, “Direct Simulation of Phonon-Mediated Heat Transfer in a Debye Crystal
,” J. Heat Transfer
, 116
, pp. 815
–822
.15.
Mazumder
, S.
, and Majumdar
, A.
, 2001, “Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization
,” J. Heat Transfer
, 123
pp. 749
–759
.16.
Lacroix
, D.
, Joulain
, K.
, and Lemonnier
, D.
, 2005, “Monte Carlo Transient Phonon Transport in Silicon and Germanium at Nanoscales
,” Phys. Rev. B
72
, p. 064305
.17.
Lukes
, J. R.
, Li
, D. Y.
, Liang
, X.-G.
, and Tien
, C.-L.
, 2000, “Molecular Dynamics Study of Solid Thin-Film Thermal Conductivity
,” J. Heat Transfer
, 122
, pp. 536
–543
.18.
Matsumoto
, M
, 2008, “How Can Molecular Simulations Contribute to Thermal Engineering? –Topics From Micro Bubbles and Microscale Heat Conduction
,” J. Therm. Sci. Technol.
, 3
, pp. 309
–318
.19.
Volz
, S.
, Saulnier
, J.-B.
, Lallemand
, M.
, Perrin
, B.
, Depondt
, P.
, and Mareschal
, M.
, 1996, “Transient Fourier-Law Deviation by Molecular Dynamics in Solid Argon
,” Phys. Rev. B
54
, pp. 340
–347
.20.
Schelling
, P. K.
, and Phillpot
, S. R.
, 2002, “Phonon Wave-Packet Dynamics at Semiconductor Interfaces by Molecular-Dynamics Simulation
,” Appl. Phys. Lett.
, 80
, pp. 2484
–2486
.21.
Matsumoto
, M.
Kunisawa
, T.
, and Xiao
, P.
, 2008, “Relaxation of Phonons in Classical MD Simulation
,” J. Therm. Sci. Technol.
, 3
, pp. 159
–166
.22.
Masao
, Y.
, Okano
, M.
, and Matsumoto
, M.
, 2011, “DSMC Scheme to Study Phonon Dynamics
,” J. Mechanical Sci. Technol.
, 25
, pp. 21
–26
.23.
Bird
, G. A.
, 1994, Molecular Gas Dynamics and the Direct Simulation of Gas Flows
, Clarendon Press
, Oxford
.24.
Lifshitz
, E. M.
, and Pitaevskii
, L. P.
, 1981, Physical Kinetics (Course of Theoretical Physics, Vol.10)
, Butterworth
, Oxford
, Chap. 7.25.
Lindsay
, L.
, and Broido
, D. A.
, 2008, “Three-Phonon Phase Space and Lattice Thermal Conductivity in Semiconductors
,” J. Phys.: Condens. Matter
, 20
, p. 165209
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
