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Because of high surface-to-volume ratio (SVR), the most prominent size effect limiting thermal transport originates from the phonon-surface scattering in nanostructures. Here in this work, we propose the mechanism of phonon scattering by the under-coordinated atoms on surface, and derive the phonon scattering rate of this mechanism by quantum perturbation theory combined with bond order theory. The scattering rate of this mechanism is proportional to SVR, therefore the effect of this mechanism on phonon transport increases with the feature-size of nanostructures decreasing. Due to the ω4 dependence of scattering rate for this mechanism, the high-frequency phonons suffer a much stronger scattering than the low-frequency phonons from the under-coordinated atoms on surface. By incorporating this phonon-surface scattering mechanism into the phonon Boltzmann transport equation, we calculate the thermal conductivity of silicon thin films and silicon nanowires. It is found that the calculated results obtained with our model are closer to the experimental data than those with the classical phonon-boundary scattering model. Furthermore, we demonstrate that the influence of this phonon-surface scattering mechanism on thermal transport is not important at a very low temperature due to the Bose-Einstein distribution of phonons. However, with the increase of the temperature, more and more phonons occupy the high-frequency states, and the influence of this scattering mechanism on phonon transport increases. It is astonished that the phonon scattering induced by the under-coordinated atoms on surface is the dominant mechanism in governing phonon heat transport in silicon nanostructures at room temperature. Our findings are helpful not only in understanding the mechanism of phonon-surface scattering, but also in manipulating thermal transport in nanostructures for surface engineering.
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Keywords:
- phonon-surface scattering mechanism /
- under-coordinated atom /
- nanostructures /
- thermal conductivity
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图 1 薄膜和纳米线示意图
Figure 1. Schematic illustration of thin film and nanowire.
图 2 硅纳米结构热导率计算值与实验值的比较 (a)纳米线; (b)薄膜
Figure 2. Comparison of thermal conductivities between models and experimental data for silicon nanostructures: (a) Nanowire; (b) thin film.
图 3 室温下声子各种散射率与角频率的关系
Figure 3. Various scattering rates of phonons as functions of phonon angular frequency at room temperature.
图 4 R与温度的关系
Figure 4. R as a function of temperature.
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[1] Wang J, Xie F, Cao X H, An S C, Zhou W X, Tang L M, Chen K Q 2017 Sci. Rep. 7 41418
Google Scholar
[2] Ding Z D, An M, Mo S Q, Yu X X, Jin Z L, Liao Y X, Esfarjani K, Lü J T, Shiomi J, Yang N 2019 J. Mater. Chem. A 7 2114
Google Scholar
[3] Tang L P, Tang L M, Geng H, Yi Y P, Wei Z M, Chen K Q, Deng H X 2018 Appl. Phys. Lett. 112 012101
Google Scholar
[4] Ouyang T, Jiang E L, Tang C, Li J, He C Y, Zhong J X 2018 J. Mater. Chem. A 6 21532
Google Scholar
[5] Xie G F, Ju Z F, Zhou K K, Wei X L, Guo Z X, Cai Y Q, Zhang G 2018 npj Comput. Mater. 4 21
Google Scholar
[6] Liu Y Y, Zeng Y J, Jia P Z, Cao X H, Jiang X W, Chen K Q 2018 J. Phys.: Condens. Matter 30 275701
Google Scholar
[7] Hu S Q, Zhang Z W, Wang Z T, Zeng K Y, Cheng Y, Chen J, Zhang G 2018 ES Energy Environ 1 74
[8] Liu C Q, Chen M, Yu W, He Y 2018 ES Energy Environ 2 31
[9] Wang H, Hu S, Takahashi K, Zhang X, Takamatsu H, Chen J 2017 Nat. Commun. 8 15843
Google Scholar
[10] Chen X K, Xie Z X, Zhou W X, Tang L M, Chen K Q 2016 Carbon 100 492
Google Scholar
[11] Yang N, Xu X, Zhang G, Li B W 2012 AIP Adv. 2 041410
Google Scholar
[12] Xie G F, Ding D, Zhang G 2018 Adv. Phys. X 3 1480417
Google Scholar
[13] Ziman J M 1962 Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford: Clarendon) p168
[14] Hochbaum A I, Chen R, Delgado R D, Liang W J, Garnett E C, Najarian M, Majumdar A, Yang P D 2008 Nature 451 163
Google Scholar
[15] Maldovan M 2015 Nat. Mater. 14 667
Google Scholar
[16] Chen X K, Xie Z X, Zhou W X, Tang L M, Chen K Q 2016 Appl. Phys. Lett. 109 023101
Google Scholar
[17] Yu J K, Mitrovic S, Tham D, Varghese J, Heath J R 2010 Nat. Nanotech. 5 718
Google Scholar
[18] Hopkins P E, Reinke C M, Su M F, Olsson III R H, Shaner E A, Leseman Z C, Serrano J R, Phinney L M, El-Kady I 2010 Nano Lett. 11 107
Google Scholar
[19] Alaie S, Goettler D F, Su M, Leseman Z C, Reinke C M, El-Kady I 2015 Nat. Commun. 6 7228
Google Scholar
[20] Lee J, Lee W, Wehmeyer G, Dhuey S, Olynick D L, Cabrini S, Dames C, Urban J J, Yang P D 2017 Nat. Commun. 8 14054
Google Scholar
[21] Maire J, Anufriev R, Yanagisawa R, Ramiere A, Volz S, Nomura M 2017 Sci. Adv. 3 e1700027
Google Scholar
[22] Wagner M R, Graczykowski B, Reparaz J S, El Sachat A, Sledzinska M, Alzina F, Sotomayor Torres C M 2016 Nano Lett. 16 5661
Google Scholar
[23] Dechaumphai E, Chen R 2012 J. Appl. Phys. 111 073508
Google Scholar
[24] Ravichandran N K, Minnich A J 2014 Phys. Rev. B 89 205432
Google Scholar
[25] Tesanovic Z, Jaric M V, Maekawa S 1986 Phys. Rev. Lett. 57 2760
Google Scholar
[26] Liu X J, Zhou Z F, Yang L W, Li J W, Xie G F, Fu S Y, Sun C Q 2011 J. Appl. Phys. 109 074319
Google Scholar
[27] Klemens P G 1955 Proc. Phys. Soc. A 68 1113
Google Scholar
[28] Pauling L 1947 J. Am. Chem. Soc. 69 542
Google Scholar
[29] Bahn S R, Jacobsen K W 2001 Phys. Rev. Lett. 87 266101
Google Scholar
[30] Sun C Q 2007 Prog. Solid State Chem. 35 1
Google Scholar
[31] Pan L K, Sun C Q, Li C M 2004 J. Phys. Chem. B 108 3404
Google Scholar
[32] McGaughey A J H, Landry E S, Sellan D P, Amon C H 2011 Appl. Phys. Lett. 99 131904
Google Scholar
[33] Xie G F, Guo Y, Wei X L, Zhang K W, Sun L Z, Zhong J X, Zhang G, Zhang Y W 2014 Appl. Phys. Lett. 104 233901
Google Scholar
[34] Xie G F, Guo Y, Li B H, Yang L W, Zhang K W, Tang M H, Zhang G 2013 Phys. Chem. Chem. Phys. 15 14647
Google Scholar
[35] Song I H, Peter Y A, Meunier M 2007 J. Micromech. Microeng. 17 1593
Google Scholar
[36] Li D Y, Wu Y Y, Kim P, Shi L, Yang P D, Majumdar A 2003 Appl. Phys. Lett. 83 2934
Google Scholar
[37] Ju Y S, Goodson K E 1999 Appl. Phys. Lett. 74 3005
Google Scholar
[38] Liu W, Asheghi M 2006 J. Heat Transfer 128 75
Google Scholar
[39] Cuffe J, Eliason J K, Maznev A A, Collins K C, Johnson J A, Shchepetov A, Prunnila M, Ahopelto J, Torres C M S, Chen G, Nelson K A 2015 Phys. Rev. B 91 245423
Google Scholar
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