Effect of surface roughness on thermal conductivity of VLS-grown rough Si<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> nanowires

The recent demonstration of thermal conductivity of rough electrolessly etched Si nanowire (Hochbaum et al., Nature, 451:163, 2008) attracted a lot of interest, because it could not be explained by the existing theory; thermal conductivity of rough Si nanowires falls below the boundary scattering of the thermal conductivity. However, nanoscale pores presented in the nanowires (Hochbaum et al., Nano Letters, 9:3550–3554, 2009) hinder one to be fully convinced that the surface roughness solely made a contribution to the significant reduction in thermal conductivity. In this study, we synthesized vapor–liquid–solid (VLS) grown rough Si_1−x Ge _x nanowire and measured and theoretically simulated thermal conductivity of the nanowire. The thermal conductivity of rough Si_0.96Ge_0.04 nanowire is an order of magnitude lower than that of bulk Si_0.96Ge_0.04 and around a factor of four times lower than that of smooth Si_0.96Ge_0.04 nanowire. This significant reduction could be explained by the fact that the surface roughness scatters medium-wavelength phonons, whereas the long-wavelength phonons are scattered by phonon boundary scattering, and the short-wavelength phonons are scattered by alloy scattering.     

The effect of surface roughness on lattice thermal conductivity of silicon nanowires

A theoretic model is presented to take into account the roughness effects on phonon transport in Si nanowires (NWs). Based on the roughness model, an indirect Monte Carlo (MC) simulation is carried out to predict the lattice thermal conductivities of the NWs with different surface qualities. Through fitting the experimental data with the MC predictions, the scattering strength on phonons from the boundary, umklapp phonon-phonon processes and impurities can be estimated. It is found that the scattering on phonons by the roughness cell boundaries in a rough nanowire can reduce the phonon mean free path to be smaller than the nanowire diameter, the Casimir limit of the phonon mean free path in a flat nanowire for phonons engaged in completely diffused boundary scattering processes.     

Low-temperature anisotropy of the thermal conductivity of single-crystal nanofilms and nanowires

The effect of phonon focusing on the phonon transport in single-crystal nanofilms and nanowires is studied in the boundary scattering regime. The dependences of the thermal conductivity and the free path of phonons on the geometric parameters of nanostructures with various elastic energy anisotropies are analyzed for diffuse phonon scattering by boundaries. It is shown that the anisotropies of thermal conductivity for nanostructures made of cubic crystals with positive (LiF, GaAs, Ge, Si, diamond, YAG) and negative (CaF₂, NaCl, YIG) anisotropies of the second-order elastic moduli are qualitatively different for both nanofilms and nanowires. The single-crystal film plane orientations and the heat flow directions that ensure the maximum or minimum thermal conductivity in a film plane are determined for the crystals of both types. The thermal conductivity of nanowires with a square cross section mainly depends on a heat flow direction, and the thermal conductivity of sufficiently wide nanofilms is substantially determined by a film plane orientation.     

表面低配位原子对声子的散射机制

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.     

考虑界面散射的金属纳米线热导率修正

理论分析了声子和电子输运对Cu, Ag金属纳米线热导率的贡献. 采用镶嵌原子作用势模型描述纳米尺寸下金属原子间的相互作用, 应用平衡分子动力学方法和Green-Kubo函数模拟了金属纳米线的声子热导率; 采用玻尔兹曼输运理论和Wiedemann-Franz定律计算电子热导率; 并通过散射失配模型和Mayadas-Shatzkes模型引入晶界散射的影响. 在此基础上, 考察分析了纳米线尺度和温度的影响. 研究结果表明: Cu, Ag纳米线热导率的变化规律相似; 电子输运对金属纳米线的导热占主导地位, 而声子热导率的贡献也不容忽视; 晶界散射导致热导率减小, 尤其对电子热导率作用显著; 纳米线总热导率随着温度的升高而降低; 随着截面尺寸减小而减小, 但声子热导率所占份额有所增加. 关键词： 纳米线 热导率 表面散射 晶界散射     

表面共振圆环结构对Si纳米线热传导的调控

利用声子的波动性,在纳米线表面引入共振结构,可以有效阻碍声子输运.为进一步优化共振结构,本文基于平衡态分子动力学(EMD)方法,研究表面共振圆环结构的高度和宽度对Si纳米线热输运性质的影响.结果表明：随着共振圆环高度的增加,Si纳米线的热导率逐渐减小,最大减幅可达61.9%.当高度达到2nm以后,热导率基本不再变化.共振圆环宽度则对热导率的影响较小.声子色散关系中出现的平带,证实了共振圆环引起的声子共振效应;最低共振频率的变化说明了共振圆环中的声子波长决定了共振圆环高度对纳米线热导率的最大影响程度.研究进一步发现,随着共振圆环高度的增加,声学支声子对热导率贡献的比重变小.本文研究结果对高效热电材料和隔热材料的微纳结构设计提供了一种新的思路.     

The effect of the electron-phonon coupling on the thermal conductivity of silicon nanowires

The thermal conductivity of free-standing silicon nanowires (SiNWs) with diameters from 1-3?nm has been studied by using the one-dimensional Boltzmann's transport equation. Our model explicitly accounts for the Umklapp scattering process and electron-phonon coupling effects in the calculation of the phonon scattering rates. The role of the electron-phonon coupling in the heat transport is relatively small for large silicon nanowires. It is found that the effect of the electron-phonon coupling on the thermal conduction is enhanced as the diameter of the silicon nanowires decreases. Electrons in the conduction band scatter low-energy phonons effectively where surface modes dominate, resulting in a smaller thermal conductivity. Neglecting the electron-phonon coupling leads to overestimation of the thermal transport for ultra-thin SiNWs. The detailed study of the phonon density of states from the surface atoms and central atoms shows a better understanding of the nontrivial size dependence of the heat transport in silicon nanowire.     

Shape,size and phonon scattering effect on the thermal conductivity of nanostructures

A phenomological model is described here to study the effect of size, shape and phonon scattering on the thermal conductivity of nanostructures. Using the classical model proposed by Guisbiers et al (Phys. Chem. Chem. Phys. 12, 7203 (2010), J. Phys. Chem. C 112, 4097 (2008)) in terms of the melting temperature of nanostructures, the expression for variation of thermal conductivity is obtained in terms of shape and size parameter. An additional term is included in the expression of thermal conductivity to consider the impact of phonon scattering due to the surface roughness with a decrease in size. The expression of thermal conductivity is obtained for spherical nanosolids, nanowires and nanofilms. The thermal conductivity is found to decrease in nanostructures in comparison with the counterpart bulk material. The values of thermal conductivity obtained from the present model are found to be close to the available experimental data for different values of roughness parameter which verifies the suitability of the model.     

Tuning Thermal Conductivity in Si Nanowires with Patterned Structures

Tuning the thermal conductivity of silicon nanowires(Si-NWs)is essential for realization of future thermoelectric devices.The corresponding management of thermal transport is strongly related to the scattering of phonons,which are the primary heat carriers in Si-NWs.Using the molecular dynamics method,we find that the scattering of phonons from internal body defects is stronger than that from surface structures in the low-porosity range.Based on our simulations,we propose the concept of an exponential decay in thermal conductivity with porosity,specifically in the low-porosity range.In contrast,the thermal conductivity of Si-NWs with a higher porosity approaches the amorphous limit,and is insensitive to specific phonon scattering processes.Our findings contribute to a better understanding of the tuning of thermal conductivity in Si-NWs by means of patterned nanostructures,and may provide valuable insights into the optimal design of one-dimensional thermoelectric materials.     

Lattice thermal conductivity crossovers in semiconductor nanowires

For binary compound semiconductor nanowires, we find a striking relationship between the nanowire's thermal conductivity kappa(nwire), the bulk material's thermal conductivity kappa(bulk), and the mass ratio of the material's constituent atoms, r, as kappa(bulk)/kappa(nwire) (alpha) (1+1/r)(-3/2). A significant consequence is the presence of crossovers in which a material with higher bulk thermal conductivity than the rest is no longer the best nanowire thermal conductor. We show that this behavior stems from a change in the dominant phonon scattering mechanism with decreasing nanowire size. The results have important implications for nanoscale heat dissipation, thermoelectricity, and thermal conductivity of nanocomposites.     

表面粗糙度对薄膜面向热导率的影响研究

通过求解声子辐射输运方程(EPRT)计算得到了薄膜的面向晶格热导率.在薄膜界面采用与声子波长相关的镜反射率模型,考虑了薄膜的厚度、温度和表面粗糙度等对其热导率的影响.结果表明,界面粗糙度对薄膜热导率的影响很大.减小界面粗糙度,会使得薄膜热导率大大增加.另外,薄膜厚度减小使得热导率峰值对应的温度增加.     

Anisotropy and temperature dependences of thermal conductivity for silicon nanowires

The anisotropy and temperature dependences of thermal conductivity for silicon nanowires with diameters higher than 50 nm is investigated using the Callaway three-mode model. Contributions to the thermal conductivity from the boundary and bulk mechanisms of phonon scattering are calculated at room temperature. The relationship between the thermal conductivity and nanowire diameter is analyzed in symmetrical directions and at room temperature.     

Nanoscale thermal cloaking by in-situ annealing silicon membrane

With the advent of thermal metamaterials, many new thermal functionalities have been proposed, like thermal cloaking, concentrating, etc. However, these thermal functionalities are based on the transformation thermotics or scattering cancellation technique, which, derived from Fourier's law, cannot apply to the micro-/nanoscale counterparts. In this paper, we design a nanoscale thermal cloak based on a crystalline silicon (Si) membrane and investigate the in-plane phonon transport via non-equilibrium molecular dynamics (NEMD) simulation by in-situ tuning the thermal conductivity of the thermal cloak from crystalline Si to amorphous Si. The two-dimensional temperature profile is obtained, and the thermal cloaking effect is evaluated by the ratio of heat flux. By analyzing the phonon density of state (PDOS) and the mode participation ratio (MPR), the mechanism can be attributed to the phonon localization in the annealed cloaking region. The proposed nanoscale thermal cloak by in-situ tuned thermal conductivity, may trigger the development of nanoscale thermal functionalities and open avenues for and thermal management for nano-photonics and nano-electronics.     

Reduction of phonon mean free path: From low-temperature physics to room temperature applications in thermoelectricity

It has been proposed for a long time now that the reduction of the thermal conductivity by reducing the phonon mean free path is one of the best way to improve the current performance of thermoelectrics. By measuring the thermal conductance and thermal conductivity of nanowires and thin films, we show different ways of increasing the phonon scattering from low-temperature up to room-temperature experiments. It is shown that playing with the geometry (constriction, periodic structures, nano-inclusions), from the ballistic to the diffusive limit, the phonon thermal transport can be severely altered in single crystalline semiconducting structures; the phonon mean free path is in consequence reduced. The diverse implications on thermoelectric properties will be eventually discussed.     

Measurements of roughness noise

Experiments have been performed on the roughness noise produced by a two-dimensional turbulent wall jet boundary layer flowing over short fetches of sandpaper roughness. A range of rough surface sizes were studied from hydrodynamically smooth through fully rough. Velocity measurements were made to document the form of the wall jet boundary layer and the influence of the roughness upon it. Acoustic measurements showed background noise levels to be very low so that the sound produced by the rough surfaces could be clearly detected with signal to noise ratios as large as 20 dB. Even hydrodynamically smooth roughness was found to produce noise, conclusively indicating the presence of scattering as a source mechanism. Variations of the roughness noise spectra with flow speed and roughness size are found to be inconsistent with any simple parameter scaling. Boundary layer wall pressure fluctuation measurements made within the roughness fetches reveal a spectral form quite different than the roughness noise, and fluctuation levels some 50-70 dB higher. Despite these differences the wall pressure and roughness noise are found to be very simply related, at least at lower frequencies (<6 kHz). The roughness noise spectrum varies closely as the product of the wall pressure spectrum, the frequency squared, and the mean-square roughness height. This is the scaling predicted by scattering theory and implies a major simplification to the problem of roughness noise prediction for stochastic surfaces.     

Thermal and kinetic surface roughening studied by scanning tunneling microscopy and atomic force microscopy

Recent studies of thermal roughening on Si surfaces and kinetic roughening of some growing films, copper and tungsten, by using scanning tunneling microscopy and atomic force microscopy are reviewed. A logarithmic divergence of the surface height fluctuations of Si(111) vicinal surfaces is confirmed, in agreement with the theoretical prediction of rough surface in thermal equilibrium. For the kinetically formed rough surfaces, power law dependences of the interface width on the system size are clearly observed. Furthermore, the tungsten films show a short-range scaling regime and a long-range “smooth” regime. The roughness exponents α are compared with theoretical predictions: for the typical Cu electrode position condition (α=1/2), the exponent appears to be close to that found for local growth models, and for tungsten films (0.7～0.8), it is consistent with recent predictions for growth where surface diffusion is predominant.     

Anomalous Heat and Momentum Transport Arising from Surface Roughness in a Normal <Superscript>3</Superscript>He Slab

I discuss heat and momentum transport in a mesoscopic film of ³He, confined by rough walls in the normal Fermi liquid state. Inelastic binary quasiparticle scattering mediated by elastic scattering from the surface roughness gives rise to a coherent “mixed” scattering channel that drives anomalous transport over a range of temperature. I calculate the thermal conductivity and viscosity of the film in this regime and derive these in terms of the film thickness and autocorrelation function of the surface roughness, which enters the formulation as an independent input. This calculation can be useful in understanding and isolating the effects of confinement and surface roughness, especially in the context of exploring the superfluid state in the film.     

Thermal transport in graphene

The recent advances in graphene isolation and synthesis methods have enabled potential applications of graphene in nanoelectronics and thermal management, and have offered a unique opportunity for investigation of phonon transport in two-dimensional materials. In this review, current understanding of phonon transport in graphene is discussed along with associated experimental and theoretical investigation techniques. Several theories and experiments have suggested that the absence of interlayer phonon scattering in suspended monolayer graphene can result in higher intrinsic basal plane thermal conductivity than that for graphite. However, accurate experimental thermal conductivity data of clean suspended graphene at different temperatures are still lacking. It is now known that contact of graphene with an amorphous solid or organic matrix can suppress phonon transport in graphene, although further efforts are needed to better quantify the relative roles of interface roughness scattering and phonon leakage across the interface and to examine the effects of other support materials. Moreover, opportunities remain to verify competing theories regarding mode specific scattering mechanisms and contributions to the total thermal conductivity of suspended and supported graphene, especially regarding the contribution from the flexural phonons. Several measurements have yielded consistent interface thermal conductance values between graphene and different dielectrics and metals. A challenge has remained in establishing a comprehensive theoretical model of coupled phonon and electron transport across the highly anisotropic and dissimilar interface.     

Influence of surface scattering on the thermal properties of spatially confined GaN nanofilm

Gallium nitride(GaN), the notable representative of third generation semiconductors, has been widely applied to optoelectronic and microelectronic devices due to its excellent physical and chemical properties. In this paper, we investigate the surface scattering effect on the thermal properties of GaN nanofilms. The contribution of surface scattering to phonon transport is involved in solving a Boltzmann transport equation(BTE). The confined phonon properties of GaN nanofilms are calculated based on the elastic model. The theoretical results show that the surface scattering effect can modify the cross-plane phonon thermal conductivity of GaN nanostructures completely, resulting in the significant change of size effect on the conductivity in GaN nanofilm. Compared with the quantum confinement effect, the surface scattering leads to the order-of-magnitude reduction of the cross-plane thermal conductivity in GaN nanofilm. This work could be helpful for controlling the thermal properties of Ga N nanostructures in nanoelectronic devices through surface engineering.     

Phonon thermal transport in InAs nanowires with different size and growth directions

We investigate the phonon thermal transport properties in InAs nanowires with different size and growth directions by using nonequilibrium molecular dynamics methods. The results show a remarkable anisotropy for the thermal conductivity in InAs nanowire. It is found that the thermal conductivity along [110] growth direction is about three times larger than that along [100] or [111] direction. With the increase of temperature, the thermal conductivity along [110] direction decreases significantly. However, the thermal conductivity along other two directions is not sensitive to temperature. Moreover, we find a crossover from ballistic to ballistic-diffusive thermal transport for a certain length of InAs nanowire. A brief physical analysis of these results is given. It is suggested that the anisotropy of thermal conductivity is common for nanowires with zinc blende structures.