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A Monte Carlo (MC) method is proposed by establishing a new model of phonon scattering processes with random sampling according to a scattering probability function. The MC scheme is used to simulate steady and transient ballistic-diffusive heat conduction in silicon nanofilm. In the MC simulations, we trace the phonon bundles that emit into media from the boundaries, and obtain the temperature profiles through statistics of the distribution of phonon bundles. It is found that the size effect of phonon transport leads to a boundary temperature jump which increases with the Knudsen number increasing. The thermal conductivity of the silicon nanofilm is calculated and the results suggest that nanofilm thermal conductivity increases with film thickness increasing, which is in good agreement with the experimental data as well as the results from the theoretical model. The temperature profiles vary with time in the transient simulations, which shows that the heat wave is related to not only time scale but also spatial scale. When the spatial scale becomes smaller, the ballistic transport is more dominant, which leads to stronger heat waves.
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Keywords:
- nanofilm /
- ballistic-diffusive heat conduction /
- Monte Carlo simulation /
- size effect
[1] Flik M, Choi B I, Goodson K E 1992 J. Heat Trans. T. Asme 114 666
[2] Ziman J M 1968 Electrons and Phonons (Oxford: Oxford University Press) p15
[3] Joshi A A, Majumdar A 1993 J. Appl. Phys. 74 31
[4] Chen G 2000 Phys. Rev. Lett. 86 2297
[5] Alvareza F X, Jou D 2007 Appl. Phys. Lett. 90 083109
[6] Dong Y, Cao B Y, Guo Z Y 2011 J. Appl. Phys. 110 063504
[7] Ye Z Q, Cao B Y, Guo Z Y 2014 Carbon 66 567
[8] Wu G Q, Kong X R, Sun Z W, Wang Y H 2006 Acta Phys. Sin. 55 1 (in Chinese) [吴国强, 孔宪仁, 孙兆伟, 王亚辉 2006 55 1]
[9] Jiaung W S, Ho J R 2008 Phys. Rev. E 77 066710
[10] Klitsner T, van Cleve J E, Fischer H E, Pohl R O 1988 Phys. Rev. B 38 7576
[11] Peterson R B 1994 J. Heat Trans.-T ASME 116 815
[12] Chen Y F, Li D Y, Lukes J R, Majumdar A 2005 J. Heat Trans. T. Asme 127 1129
[13] Wang Z, Zhao R J, Chen Y F 2010 Sci. China Tech. Sci. 53 429
[14] Jeng M S, Yang R G, Song D, Chen G 2008 J. Heat Trans. T. Asme 130 042410
[15] Lacroix D, Joulain K, Lemonnier D 2005 Phys. Rev. B 72 064305
[16] Siegel R, Howell J R 1992 Thermal Radiation Heat Transfer (Washington, D.C.: Hemisphere Publish Corporation)
[17] Cao B Y, Kong J, Xu Y, Yung K L, Cai A 2013 Heat Transfer Eng. 34 2131
[18] Huang K (adapted by Han R Q) 1988 Solid Physics (Beijing: High Education Press) pp122–133 (in Chinese) [黄昆原著, (韩汝琦改编) 1988 固体物理(北京: 高等教育出版社)第122–133页]
[19] Ju Y S, Goodson K E 1999 Appl. Phys. Lett. 74 3005
[20] Liu W, Asheghi M 2004 Appl. Phys. Lett. 84 3819
[21] Asheghi M, Leung Y K, Wong S S, Goodson K E 1997 Appl. Phys. Lett. 71 1798
[22] Ju Y S, Kurabayashi K, Goodson K E 1999 Thin Solid Films 339 160
[23] Majumdar A 1993 J. Heat Trans. T. Asme 115 7
[24] Li B W, Wang J 2003 Phys. Rev. Lett. 91 044301
[25] Yang N, Zhang C, Li B W 2010 Nano Today 5 85
[26] Rieder Z, Lebowitz J L, Lieb E 1967 J. Math. Phys. 8 1073
[27] Bruesch P 1982 Phonons: Theory and Experiment (Vol.3) (Berlin: Springer-Verlag, Berlin Heidelberg)
[28] Körner C, Bergmann H W 1998 Appl. Phys. A 67 397
[29] Naqvi K R, Waldenstrom S 2005 Phys. Rev. Lett. 95 065901
[30] Alvareza F X, Jou D 2010 J. Heat Trans. T. Asme 132 012404
[31] Cao B Y, Guo Z Y 2007 J. Appl. Phys. 102 53503
[32] Ackerman C C, Bertman B, Fairbank H A, Guyer R A 1966 Phys. Rev. Lett. 16 789
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[1] Flik M, Choi B I, Goodson K E 1992 J. Heat Trans. T. Asme 114 666
[2] Ziman J M 1968 Electrons and Phonons (Oxford: Oxford University Press) p15
[3] Joshi A A, Majumdar A 1993 J. Appl. Phys. 74 31
[4] Chen G 2000 Phys. Rev. Lett. 86 2297
[5] Alvareza F X, Jou D 2007 Appl. Phys. Lett. 90 083109
[6] Dong Y, Cao B Y, Guo Z Y 2011 J. Appl. Phys. 110 063504
[7] Ye Z Q, Cao B Y, Guo Z Y 2014 Carbon 66 567
[8] Wu G Q, Kong X R, Sun Z W, Wang Y H 2006 Acta Phys. Sin. 55 1 (in Chinese) [吴国强, 孔宪仁, 孙兆伟, 王亚辉 2006 55 1]
[9] Jiaung W S, Ho J R 2008 Phys. Rev. E 77 066710
[10] Klitsner T, van Cleve J E, Fischer H E, Pohl R O 1988 Phys. Rev. B 38 7576
[11] Peterson R B 1994 J. Heat Trans.-T ASME 116 815
[12] Chen Y F, Li D Y, Lukes J R, Majumdar A 2005 J. Heat Trans. T. Asme 127 1129
[13] Wang Z, Zhao R J, Chen Y F 2010 Sci. China Tech. Sci. 53 429
[14] Jeng M S, Yang R G, Song D, Chen G 2008 J. Heat Trans. T. Asme 130 042410
[15] Lacroix D, Joulain K, Lemonnier D 2005 Phys. Rev. B 72 064305
[16] Siegel R, Howell J R 1992 Thermal Radiation Heat Transfer (Washington, D.C.: Hemisphere Publish Corporation)
[17] Cao B Y, Kong J, Xu Y, Yung K L, Cai A 2013 Heat Transfer Eng. 34 2131
[18] Huang K (adapted by Han R Q) 1988 Solid Physics (Beijing: High Education Press) pp122–133 (in Chinese) [黄昆原著, (韩汝琦改编) 1988 固体物理(北京: 高等教育出版社)第122–133页]
[19] Ju Y S, Goodson K E 1999 Appl. Phys. Lett. 74 3005
[20] Liu W, Asheghi M 2004 Appl. Phys. Lett. 84 3819
[21] Asheghi M, Leung Y K, Wong S S, Goodson K E 1997 Appl. Phys. Lett. 71 1798
[22] Ju Y S, Kurabayashi K, Goodson K E 1999 Thin Solid Films 339 160
[23] Majumdar A 1993 J. Heat Trans. T. Asme 115 7
[24] Li B W, Wang J 2003 Phys. Rev. Lett. 91 044301
[25] Yang N, Zhang C, Li B W 2010 Nano Today 5 85
[26] Rieder Z, Lebowitz J L, Lieb E 1967 J. Math. Phys. 8 1073
[27] Bruesch P 1982 Phonons: Theory and Experiment (Vol.3) (Berlin: Springer-Verlag, Berlin Heidelberg)
[28] Körner C, Bergmann H W 1998 Appl. Phys. A 67 397
[29] Naqvi K R, Waldenstrom S 2005 Phys. Rev. Lett. 95 065901
[30] Alvareza F X, Jou D 2010 J. Heat Trans. T. Asme 132 012404
[31] Cao B Y, Guo Z Y 2007 J. Appl. Phys. 102 53503
[32] Ackerman C C, Bertman B, Fairbank H A, Guyer R A 1966 Phys. Rev. Lett. 16 789
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