Anisotropy of the mean free paths of phonons in single-crystal films of germanium,silicon, and diamond at low temperatures

The physical aspects of the influence of the elastic energy anisotropy of crystals on the anisotropy of the mean free paths of phonons in single-crystal films of germanium, silicon, and diamond in the diffuse scattering of phonons at the boundaries of the samples have been considered. It has been shown that, for sufficiently wide films of germanium, silicon, and diamond with the {100} and {111} orientations and the lengths of less than or equal to their width, the phonon mean free paths are isotropic (independent of the direction of the temperature gradient in the plane of the film). The anisotropy of the phonon mean free paths depends primarily on the orientation of the film plane and is determined by the focusing and defocusing of phonon modes. For single-crystal films of germanium, silicon, and diamond with the {100} and {111} orientations and lengths much larger than their width, the phonon mean free paths are anisotropic.     

Influence of Focusing on Phonon Propagation and Thermal Conductivity in Single Crystal Films with Different Types of Anisotropy of Elastic Energy

The influence of the anisotropy of elastic energy on the phonon propagation and phonon transport in single crystal nanofilms with different types of anisotropy of elastic energy in a Knudsen flow of a phonon gas is studied. The angular distribution of phonon mean free paths in the planes of the films and in their cross section is analyzed. The physical reasons leading to the dependence of the thermal conductivity on the orientation of the film planes and the directions of the heat flux relative to the crystal axes are studied. An analysis of the effect of focusing on the phonon propagation made it possible to explain the qualitative difference between the anisotropy of phonon mean free paths in films of cubic nanocrystals of various types having different orientations of the planes.     

Relaxation times and mean free paths of phonons in the boundary scattering regime for silicon single crystals

The phonon focusing in cubic dielectric crystals and its influence on the heat transfer in the boundary phonon scattering regime at low temperatures have been investigated. The mean free paths of phonons of different polarizations in samples of infinite and finite lengths with circular and square cross sections have been calculated in the anisotropic continuum model. For samples of infinite length with circular and square cross sections in the case of the equality of the cross-sectional areas, the angular dependences of the mean free paths normalized by the Casimir length almost completely coincide. It has been shown that the anisotropy of the mean free paths decreases significantly upon changing over from infinite samples to samples of finite length. For silicon crystals, the anisotropy of the phonon mean free paths has been analyzed for each of the branches of the phonon spectrum. It has been found that the mean free paths for phonons of each vibrational mode reach maximum values in the directions of focusing, and, in these directions, they exceed the mean free paths for phonons of the other vibrational modes.     

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.     

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.     

Effect of dispersion on the phonon focusing and anisotropy of thermal conductivity of silicon single crystals in the boundary scattering regime

The effect of dispersion on the focusing of thermal phonons and on the thermal conductivity of silicon single crystals in the boundary scattering regime has been investigated. Analysis of the spectra of acoustic modes obtained for silicon single crystals from inelastic neutron scattering data has demonstrated that, upon transition from long-wavelength phonons to short-wavelength phonons, the directions of their focusing change. With an increase in temperature, this leads to a change in the anisotropy of thermal conductivity of phonons with different polarizations and, consequently, to a change in the anisotropy of the total thermal conductivity. Analysis of the temperature dependence of the thermal conductivity has revealed that the presence of extended flattened sections in the spectrum of short-wavelength transverse phonons indicates anomalously low values of the group velocity and, accordingly, a significant decrease in the contribution from these phonons to the thermal conductivity with increasing temperature. The contribution from longitudinal phonons to the thermal conductivity also significantly increases even at temperatures higher than 110 K and becomes dominant.     

Effect of normal processes on thermal conductivity of germanium,silicon and diamond

The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch — KK-S model and (b) between different phonon branches — KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.      

Temperature dependence of the thermal conductivity for tellurium dioxide

The thermal conductivity of tellurium dioxide is reported as a function of temperature. At 77K, the thermal conductivity is 0.09 W/cm-K and it decreases approximately as the inverse of the temperature to a value of 0.02 W/cm-K at 300K. The anisotropy between the a- and c-axes is less than 20% over the entire experimental temperature range, with the a-axis more conductive than the c-axis. By making some simplifying assumptions, the phonon mean free paths and relaxation times are deduced.     

Ballistic–diffusive phonon transport and size induced anisotropy of thermal conductivity of silicon nanofilms

The effective thermal conductivity of nanofilms is size dependent due to the diffusive–ballistic transport of phonons. In this paper, we investigate the cross-plane phonon transport from the viewpoint of the phonon Boltzmann equation. A predictive model for the size dependent thermal conductivity is proposed and agrees well with the results of molecular dynamics simulation for silicon nanofilms. The ballistic transport has different effects on the heat conduction in the in-plane or cross-plane directions, which causes the anisotropy of thermal conductivity of nanofilms. Such anisotropy is also size dependent and vanishes with the increase of film thickness.     

单晶硅薄膜法向热导率分子动力学研究

采用非平衡分子动力学方法（NEMD）研究了平均温度为 500K、厚度为 2～32nm的单晶硅薄膜的法向热导率。模拟结果表明,薄膜热导率显著低于对应温度下的体硅单晶的实验值,并随膜厚度减小以接近线性的规律减小。用声子气动力论模型的分析结果与NEMD模拟相一致,表明纳米单晶硅薄膜中声子平均自由程显著减小。     

Anisotropy of the thermal conductivity and electrical resistivity of the SiC/Si biomorphic composite based on a white-eucalyptus biocarbon template

The thermal conductivity κ and electrical resistivity ρ of a cellular ecoceramic, namely, the SiC/Si biomorphic composite, are measured in the temperature range 5–300 K. The SiC/Si biomorphic composite is fabricated using a cellular biocarbon template prepared from white eucalyptus wood by pyrolysis in an argon atmosphere with subsequent infiltration of molten silicon into empty through cellular channels of the template. The temperature dependences κ(T) and ρ(T) of the 3C-SiC/Si biomorphic composite at a silicon content of ～30 vol % are measured for samples cut out parallel and perpendicular to the direction of tree growth. Data on the anisotropy of the thermal conductivity κ are presented. The behavior of the dependences κ(T) and ρ(T) of the SiC/Si biomorphic composite at different silicon contents is discussed in terms of the results obtained and data available in the literature.     

The effect of phonon anisotropic scattering on the thermal conductivity of silicon thin films at 300K and 400K

Previous studies have shown that anisotropy in phonon transport exist because of the difference in phonon dispersion relation due to different lattice directions, as observed by a difference in in-plane and cross-plane thermal conductivities. Our current work intends to study the effect of anisotropy scattering on silicon thermal conductivity at 300 K and 400 K. We adopt the Henyey and Greenstein probability density function in our phonon Monte Carlo simulation to investigate the effect of highly forward and backward scattering events. The impact of applying the anisotropy scattering using this approach is discussed in detail. While the forward and backward scattering will increase and decrease thermal conductivity respectively, the extent of the effect is non-linear such that forward scattering has a more obvious effect on thermal conductivity than backward scattering.     

硅功能化石墨烯热导率的分子动力学模拟

采用Tersoff势函数与Lennard-Jones势函数,结合速度形式的Verlet算法和Fourier定律,对单层和两层硅功能化石墨烯沿长度方向的导热性能进行了正向非平衡态分子动力学模拟.通过模拟发现,硅原子的加入改变了石墨烯声子的模式、平均自由程和移动速度,使得单层硅功能化石墨烯模型的热导率随着硅原子数目的增加而急剧地减小.在300 K至1000 K温度变化范围内,单层硅功能化石墨烯的热导率呈下降趋势,具有明显的温度效应.对双层硅功能化石墨烯而言,少量的硅原子嵌入,起到了提高热导率的作用,但当硅原子数目达到一定数量后,材料的导热性能下降.     

The effect of normal phonon-phonon scattering processes on the maximum thermal conductivity of isotopically pure silicon crystals

The effect of normal phonon-phonon scattering processes on the thermal conductivity of silicon crystals with various degrees of isotope disorder is considered. The redistribution of phonon momentum in normal scattering processes is taken into account within each oscillation branch (the Callaway generalized model), as well as between different oscillation branches of the phonon spectrum (the Herring mechanism). The values of the parameters are obtained that determine the phonon momentum relaxation in anharmonic scattering processes. The contributions of the drift motion of longitudinal and transverse phonons to the thermal conductivity are analyzed. It is shown that the momentum redistribution between longitudinal and transverse phonons in the Herring relaxation model represents an efficient mechanism that limits the maximum thermal conductivity in isotopically pure silicon crystals. The dependence of the maximum thermal conductivity on the degree of isotope disorder is calculated. The maximum thermal conductivity of isotopically pure silicon crystals is estimated for two variants of phonon momentum relaxation in normal phonon-phonon scattering processes.     

多约束纳米结构的声子热导率模型研究

纳米技术的快速发展使得对微纳尺度导热机理的深入研究变得至关重要. 理论和实验都表明, 在纳米尺度下声子热导率将表现出尺寸效应. 基于声子玻尔兹曼方程和修正声子平均自由程的方法得到了多约束纳米结构的声子热导率模型, 可以描述多个几何约束共同作用下热导率的尺寸效应. 不同几何约束对声子输运的限制作用可以分开计算, 总体影响则通过马西森定则进行耦合. 对于热流方向的约束, 采用扩散近似的方法求解声子玻尔兹曼方程; 对于侧面边界约束, 采用修正平均自由程的方法计算边界散射对热导率的影响. 得到的模型能够预测纳米薄膜(法向和面向)及有限长度方形纳米线的热导率随相应特征尺寸的变化. 与蒙特卡罗模拟及硅纳米结构热导率实验值的对比验证了模型的正确性.     

Unusually high thermal conductivity of carbon nanotubes

Combining equilibrium and nonequilibrium molecular dynamics simulations with accurate carbon potentials, we determine the thermal conductivity lambda of carbon nanotubes and its dependence on temperature. Our results suggest an unusually high value, lambda approximately 6600 W/m K, for an isolated (10,10) nanotube at room temperature, comparable to the thermal conductivity of a hypothetical isolated graphene monolayer or diamond. Our results suggest that these high values of lambda are associated with the large phonon mean free paths in these systems; substantially lower values are predicted and observed for the basal plane of bulk graphite.     

氢化非晶硅薄膜的热导率研究

采用铂电极为加热电阻,研究了厚度为300—370nm等离子体化学气相沉积(PECVD)工艺制备的氢化非晶硅(a-Si：H)薄膜的热导率随衬底温度的变化规律.用光谱式椭偏仪拟合测量薄膜的厚度,得到了沉积速率随衬底温度变化规律,傅里叶红外(FTIR)表征了在KBr晶片衬底上制备的a-Si：H薄膜的红外光谱特性,SiH原子团键合模的震动对热量的吸收降低了薄膜热导率.从动力学角度分析了薄膜热导率随平均温度升高而增大的原因,并比较了声子传播和自由电子移动在a-Si：H薄膜热导率变化上的作用差异. 关键词： 非晶硅 热导率 薄膜 热能     

A molecular dynamics simulation: the effect of finite size on the thermal conductivity in a single crystal silicon

Non-equilibrium molecular dynamics (NEMD) simulations are performed to calculate thermal conductivity. The environment-dependent interatomic potential (EDIP) potential on crystal silicon is adopted as a model system. The issues are related to nonlinear response, local thermal equilibrium and statistical averaging. The simulation results by non-equilibrium molecular dynamics show that the calculated thermal conductivity decreases almost linearly as the film thickness reduced at the nanometre scale. The effect of size on the thermal conductivity is also obtained by a theoretic analysis of the kinetic theory and formulas of the heat capacity. The analysis reveals that the contributions of phonon mean free path (MFP) and phonon number in a finite cell to thermal conductivity are very important.     

Characterization of single-crystalline GaAs by imaging with ballistic phonons

Ballistic phonon propagation in single-crystalline [001]-oriented gallium arsenide has been studied using low-temperature scanning electron microscopy for imaging. Deviations in the phonon focusing pattern due to dispersion effects were found by comparing the phonon images to theoretical calculations of the long-wavelength limit. The phonon propagation behavior in, samples cut from differently prepared wafers has been investigated. For highly impure crystals we found a pronounced increase of the diffusive signal component at the expense of the ballistic one. Samples with varying dislocation densities also showed a sensitive dependence, of the ballistic phonon propagation on these crystal defects. For focusing calculations considering elastic scattering processes the diffusivity of the phonons could be determined as a function of the mean scattering length. We have found phonon mean free paths of 0.35 mm to 0.80 mm for the various GaAs crystals.