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Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation

机译：纳米结构的热导率预测：声子色散近似的影响

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摘要

In this study, the influence of phonon dispersion approximation on the prediction of in-plane and out-of-plane thermal conductivity of thin films and nanowires is shown. Results obtained using the famous Holland dispersion approximation and the Brillouin zone boundary condition (BZBC) dispersion curves are compared. For (in-plane and out-of-plane) thermal conductivity predictions based on BZBC dispersion curves, new relaxation time parameters fitted from experimental data of bulk silicon thermal conductivity are reported. The in-plane thermal conductivity of nanostructures (films of thicknesses 20 nm, 100 nm, and 420 nm and nanowires of widths 22 nm, 37 nm, and 100 nm) in the temperature range 20-1000 K is calculated from the modified bulk thermal conductivity model by scaling the bulk phonon mean free path (MFP) by the Fuch-Sondheimer factor of boundary scattering developed for nanostructures with rectangular cross-section. The pseudo out-of-plane thermal conductivity of films of thicknesses 20 nm, 100 nm, and 420 nm and in the temperature range 150-1000 K is calculated from the solution of the Boltzmann transport equation (BTE) for phonons by using the Discrete ordinate method (DOM), and the Monte Carlo (MC) simulation. In order to confirm the current results, the calculated in-plane thermal conductivity of silicon thin films and silicon nanowires are compared with existing experimental data. Moreover, due to lack of experimental and theoretical data of out-of-plane thermal conductivity of thin films, comparison of the DOM and MC simulation is performed. The current work shows that a drastic simplification of dispersion curves can lead to wrong prediction of both in-plane and out-of-plane thermal conductivities of nanostructures, especially for ultra thin nanostructures and/or at high temperatures. Comparison with experimental data of in-plane thermal conductivity of silicon thin films and silicon nanowires proves that more refined dispersion approximation such as the BZBC is well adequate for phonon transport calculations when confinement has negligible effect. Moreover, the comparison between the thermal conductivity in the out-of-plane direction and that in the in-plane direction enables one to quantify the anisotropy of thermal conductivity of the film.
机译：在这项研究中，显示了声子色散近似对薄膜和纳米线的面内和面外热导率预测的影响。比较了使用著名的荷兰色散逼近和布里渊区边界条件（BZBC）色散曲线获得的结果。对于基于BZBC色散曲线的（平面内和平面外）热导率预测，报告了根据体硅热导率实验数据拟合的新弛豫时间参数。由修正的体热计算得出在20-1000 K温度范围内的纳米结构（厚度为20 nm，100 nm和420 nm的薄膜以及宽度为22 nm，37 nm和100 nm的纳米线）的面内导热率。电导率模型是通过为矩形截面的纳米结构开发的边界散射的Fuch-Sondheimer因子来缩放体声子平均自由程（MFP）。根据离散声子的玻尔兹曼输运方程（BTE）的解，可以计算出厚度为20 nm，100 nm和420 nm且温度范围为150-1000 K的薄膜的拟平面外热导率坐标法（DOM）和蒙特卡洛（MC）模拟。为了确认当前结果，将计算出的硅薄膜和硅纳米线的面内导热率与现有实验数据进行了比较。此外，由于缺乏薄膜的平面外热导率的实验和理论数据，因此进行了DOM和MC模拟的比较。当前的工作表明，色散曲线的极大简化会导致对纳米结构的平面内和平面外导热率的错误预测，尤其是对于超薄纳米结构和/或高温。与硅薄膜和硅纳米线的平面内热导率的实验数据进行比较证明，当约束作用可忽略时，诸如BZBC之类的更精细的色散逼近非常适合进行声子传输计算。而且，通过将面外方向的热传导率与面内方向的热传导率进行比较，可以量化膜的热传导率的各向异性。

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  • 来源
    《International Journal of Heat and Mass Transfer》 |2009年第12期|2516-2527|共12页
  • 作者

    D. Baillis; J. Randrianalisoa;

  • 作者单位

    CETHIL UMR5008, CNRS, INSA-Lyon, Universite Lyon 1, F-69621 Villeurbanne, France;

    CETHIL UMR5008, CNRS, INSA-Lyon, Universite Lyon 1, F-69621 Villeurbanne, France;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
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