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表面低配位原子对声子的散射机制

霍龙桦 谢国锋

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表面低配位原子对声子的散射机制

霍龙桦, 谢国锋

Mechanism of phonon scattering by under-coordinated atoms on surface

Huo Long-Hua, Xie Guo-Feng
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  • 由于纳米结构具有极高的表体比, 声子-表面散射机制对声子的热输运性质起到关键作用. 提出了表面低配位原子对声子的散射机制, 并且结合量子微扰理论与键序理论推导出该机制的散射率. 由于散射率正比于材料的表体比, 这种散射机制对声子输运的重要性随着纳米结构尺寸的减小而增大. 散射率正比于声子频率的4次方, 所以这种散射机制对高频声子的作用远远强于对低频声子的作用. 基于声子玻尔兹曼输运方程, 计算了硅纳米薄膜和硅纳米线的热导率, 发现本文模型比传统的声子-边界散射模型更接近实验值. 此发现不仅有助于理解声子-表面散射的物理机制, 也有助于应用声子表面工程调控纳米结构的热输运性质.
    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.
      通信作者: 谢国锋, xieguofeng@hnust.cn
    • 基金项目: 国家自然科学基金(批准号: 11874145)资助的课题.
      Corresponding author: Xie Guo-Feng, xieguofeng@hnust.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874145).
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    Ju Y S, Goodson K E 1999 Appl. Phys. Lett. 74 3005Google Scholar

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    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 245423Google Scholar

  • 图 1  薄膜和纳米线示意图

    Fig. 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

    Fig. 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

    Fig. 3.  Various scattering rates of phonons as functions of phonon angular frequency at room temperature.

    图 4  R与温度的关系

    Fig. 4.  R as a function of temperature.

  • [1]

    Wang J, Xie F, Cao X H, An S C, Zhou W X, Tang L M, Chen K Q 2017 Sci. Rep. 7 41418Google 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 2114Google 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 012101Google Scholar

    [4]

    Ouyang T, Jiang E L, Tang C, Li J, He C Y, Zhong J X 2018 J. Mater. Chem. A 6 21532Google 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 21Google 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 275701Google 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 15843Google Scholar

    [10]

    Chen X K, Xie Z X, Zhou W X, Tang L M, Chen K Q 2016 Carbon 100 492Google Scholar

    [11]

    Yang N, Xu X, Zhang G, Li B W 2012 AIP Adv. 2 041410Google Scholar

    [12]

    Xie G F, Ding D, Zhang G 2018 Adv. Phys. X 3 1480417Google 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 163Google Scholar

    [15]

    Maldovan M 2015 Nat. Mater. 14 667Google Scholar

    [16]

    Chen X K, Xie Z X, Zhou W X, Tang L M, Chen K Q 2016 Appl. Phys. Lett. 109 023101Google Scholar

    [17]

    Yu J K, Mitrovic S, Tham D, Varghese J, Heath J R 2010 Nat. Nanotech. 5 718Google 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 107Google Scholar

    [19]

    Alaie S, Goettler D F, Su M, Leseman Z C, Reinke C M, El-Kady I 2015 Nat. Commun. 6 7228Google 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 14054Google Scholar

    [21]

    Maire J, Anufriev R, Yanagisawa R, Ramiere A, Volz S, Nomura M 2017 Sci. Adv. 3 e1700027Google 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 5661Google Scholar

    [23]

    Dechaumphai E, Chen R 2012 J. Appl. Phys. 111 073508Google Scholar

    [24]

    Ravichandran N K, Minnich A J 2014 Phys. Rev. B 89 205432Google Scholar

    [25]

    Tesanovic Z, Jaric M V, Maekawa S 1986 Phys. Rev. Lett. 57 2760Google 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 074319Google Scholar

    [27]

    Klemens P G 1955 Proc. Phys. Soc. A 68 1113Google Scholar

    [28]

    Pauling L 1947 J. Am. Chem. Soc. 69 542Google Scholar

    [29]

    Bahn S R, Jacobsen K W 2001 Phys. Rev. Lett. 87 266101Google Scholar

    [30]

    Sun C Q 2007 Prog. Solid State Chem. 35 1Google Scholar

    [31]

    Pan L K, Sun C Q, Li C M 2004 J. Phys. Chem. B 108 3404Google Scholar

    [32]

    McGaughey A J H, Landry E S, Sellan D P, Amon C H 2011 Appl. Phys. Lett. 99 131904Google 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 233901Google 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 14647Google Scholar

    [35]

    Song I H, Peter Y A, Meunier M 2007 J. Micromech. Microeng. 17 1593Google Scholar

    [36]

    Li D Y, Wu Y Y, Kim P, Shi L, Yang P D, Majumdar A 2003 Appl. Phys. Lett. 83 2934Google Scholar

    [37]

    Ju Y S, Goodson K E 1999 Appl. Phys. Lett. 74 3005Google Scholar

    [38]

    Liu W, Asheghi M 2006 J. Heat Transfer 128 75Google 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 245423Google Scholar

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出版历程
  • 收稿日期:  2019-02-12
  • 修回日期:  2019-03-06
  • 上网日期:  2019-04-01
  • 刊出日期:  2019-04-20

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