Thermal conductivity of silicon bulk and nanowires: Effects of isotopic composition, phonon confinement, and surface roughness
Thermal conductivity of silicon bulk and nanowires: Effects of isotopic composition, phonon confinement, and surface roughness
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DOI：
10.1063/1.3340973
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发表时间：
2010-04-15
影响因子：
3.2
通讯作者：
Royer, P.
中科院分区：
文献类型：
--
作者：
Kazan, M.;Guisbiers, G.;Royer, P.
我们提出了一个严格的分析体硅（Si）和硅纳米线（Si NWs）的热导率，考虑到各种声学和光学声子机制的确切物理性质。以下的玻尔兹曼方程的卡拉威解决方案，其中电阻和非电阻声子机制的歧视，我们推导出的晶格热导率，考虑到声子的入射角的形式主义。声子散射过程由依赖于频率的弛豫时间表示。除了通常认为的声学三声子过程中，光学声子衰减到声学声子的作用进行了详细的分析。这种光学声子衰减机制被认为是作为声学声子产生率部分抵消声学声子散射率。我们已经推导出了描述这种物理机制的解析表达式，它应该包括在一般的形式主义作为一个修正的电阻声子点缺陷和声子边界散射表达式。声子边界散射机制被视为声子频率，入射角和表面粗糙度的函数。所有的机制，我们已经参与了模型的重要性，清楚地证明了与有关的散装硅和硅NW样品中的同位素组成的影响报告的数据。也就是说，我们的模型解释了先前无法解释的实验结果，关于（i）Ruf等人[Solid State Commun. 115，243（2000）]，（ii）Li等人[Appl.Phys.Lett.115，243（2000）]报道的对单个Si NW的kappa（T）的尺寸效应。83，2934（2003）]，和（iii）Hochbaum等人[Nature（伦敦）451，163（2008）]报道的粗糙Si NW的热导率的显著降低。(C)2010年美国物理学会。[doi：10.1063/1.3340973]
We present a rigorous analysis of the thermal conductivity of bulk silicon (Si) and Si nanowires (Si NWs) which takes into account the exact physical nature of the various acoustic and optical phonon mechanisms. Following the Callaway solution for the Boltzmann equation, where resistive and nonresistive phonon mechanisms are discriminated, we derived formalism for the lattice thermal conductivity that takes into account the phonon incidence angles. The phonon scattering processes are represented by frequency-dependent relaxation time. In addition to the commonly considered acoustic three-phonon processes, a detailed analysis of the role of the optical phonon decay into acoustic phonons is performed. This optical phonon decay mechanism is considered to act as acoustic phonon generation rate partially counteracting the acoustic phonon scattering rates. We have derived the analytical expression describing this physical mechanism which should be included in the general formalism as a correction to the resistive phonon-point-defects and phonon-boundary scattering expressions. The phonon-boundary scattering mechanism is taken as a function of the phonon frequency, incidence angles, and surface roughness. The importance of all the mechanisms we have involved in the model is demonstrated clearly with reference to reported data regarding the isotopic composition effect in bulk Si and Si NW samples. Namely, our model accounts for previously unexplained experimental results regarding (i) the isotope composition effect on the thermal conductivity of bulk silicon reported by Ruf et al. [Solid State Commun. 115, 243 (2000)], (ii) the size effect on kappa(T) of individual Si NWs reported by Li et al. [Appl. Phys. Lett. 83, 2934 (2003)], and (iii) the dramatic decrease in the thermal conductivity for rough Si NWs reported by Hochbaum et al. [Nature (London) 451, 163 (2008)]. (C) 2010 American Institute of Physics. [doi:10.1063/1.3340973]