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.     

Normal phonon-phonon scattering processes and the thermal conductivity of germanium crystals with isotope disorder

The influence of the normal phonon-phonon scattering processes on the thermal conductivity was theoretically studied for germanium crystals with various degrees of the isotope disorder. The theory takes into account redistribution of the phonon momentum in the normal scattering processes both inside each oscillation branch (Simons mechanism) and between various phonon oscillation branches (Herring mechanism). Contributions to the thermal conductivity due to the drift mobility of the longitudinal and transverse phonons are analyzed. It is shown that the momentum redistribution between longitudinal and transverse phonons according to the Herring relaxation mechanism leads to a significant suppression of the drift motions (and to the corresponding drop in contribution to the thermal conductivity) of the longitudinal phonons in isotopically pure germanium crystals. The results of the thermal conductivity calculations involving the Herring relaxation mechanism agree well with the experimental data available for germanium crystals with various degrees of the isotope disorder.     

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.      

Normal processes of phonon-phonon scattering and the drag thermopower in germanium crystals with isotopic disorder

A strong dependence of the thermopower of germanium crystals on the isotopic composition is experimentally found. The theory of phonon drag of electrons in semiconductors with nondegenerate statistics of current carriers is developed, which takes into account the special features of the relaxation of phonon momentum in the normal processes of phonon-phonon scattering. The effect of the drift motion of phonons on the drag thermopower in germanium crystals of different isotopic compositions is analyzed for two options of relaxation of phonon momentum in the normal processes of phonon scattering. The phonon relaxation times determined from the data on the thermal conductivity of germanium are used in calculating the thermopower. The importance of the inelasticity of electron-phonon scattering in the drag thermopower in semiconductors is analyzed. A qualitative explanation of the isotope effect in the drag thermopower is provided. It is demonstrated that this effect is associated with the drift motion of phonons, which turns out to be very sensitive to isotopic disorder in germanium crystals.     

Normal quasiparticle scattering and kinetic effects in degenerate semiconductors

The influence of normal processes of electron-electron and phonon-phonon scattering on quasiparticle momentum relaxation in nonequilibrium electron-phonon systems of degenerate semiconductors is investigated. A system of kinetic equations is solved for the electron and phonon distribution functions, and the kinetic coefficients of a semiconductor are calculated in the linear approximation in the degeneracy parameter. The influence of normal scattering of quasiparticles on the electrical conductivity, thermopower, and heat conductivity of a degenerate semiconductor is analyzed. Redistribution of the phonon momentum in N processes within each branch of the vibrational spectrum, as well as among different branches, is taken into account.     

Anomalous layer thickness dependent thermal conductivity of Td-WTe2 through first-principles calculation

The thickness dependent in-plane thermal conductivity of layered Tungsten ditelluride (WTe₂) is investigated by first-principles calculation. With the layer number increasing from one to infinite, the thermal conductivity displays a decrease to increase trend. The underlying mechanism is attributed to the change of the phonon dispersion relations. As the layer number increases, optical phonon branches shift downward, which provide more channels for the Umklapp scattering, and result in the decrease of the thermal conductivity. Furthering increasing the layer number makes those low-frequency optical phonon branches having high group velocity and leads to the increase of the lattice thermal conductivity.     

Thermoelectric properties of SnzCo8Sb24 skutterudites

Sn-filled CoSb₃ skutterudite compounds were synthesized by the induction melting process. Formation of a single δ-phase of the synthesized materials was confirmed by X-ray diffraction analysis. The temperature dependences of the Seebeck coefficient, electrical resistivity and thermal conductivity were examined in the temperature range of 300-700 K. Positive Seebeck and Hall coefficients confirmed p-type conductivity. Electrical resistivity increased with increasing temperature, which shows that the Sn-filled CoSb₃ skutterudite is a degenerate semiconductor. The thermal conductivity was reduced by Sn-filling because the filler atoms acted as phonon scattering centers in the skutterudite lattice. The lowest thermal conductivity was achieved in the composition of Sn_0.25Co₈Sb₂₄.     

基于第一性原理分子动力学的填充方钴矿热输运性质及微观过程的研究

对于重要热电材料之一的填充方钴矿材料,其低热导率的成因存在两种观点:1)填充原子的局域振动引起共振散射降低热导率;2)填充原子的引入加强了三声子倒逆过程来降低热导率.本文采用含有限温度效应的第一性原理分子动力学方法模拟了YbFe_4Sb_(12)的动力学过程,并通过温度相关有效势场方法得到了充分包含非线性作用的等效非谐力常数,研究了微扰近似下的声子输运性质.结果显示,在填充原子振动全部参与三声子倒逆散射过程的近似下,相比于纯方钴矿体系,声子寿命大幅地降低,填充原子的振动是热阻的重要来源.但即便如此,理论计算结果与实验的晶格热导率之间仍存在明显偏离.不同填充原子振动之间的较弱关联性质也揭示其明显偏离经典的声子图像,表现为一种强烈的局域特征振动模式,并以此散射其他晶格声子,因而对热阻的贡献也超出了传统三声子的理论框架.通过将填充原子Yb振动模式的寿命进行共振散射形式的修正,可以使晶格热导率与实验结果符合较好.以上结果表明,YbFe_4Sb_(12)的低晶格热导率是由声子间相互作用以及具有局域振动特征的共振散射两方面因素导致.     

Transient response of hot electrons in narrow-gap semiconductors at low temperatures in the presence of a longitudinal quantizing magnetic field

Transient response of hot electrons in narrow-gap semiconductors to a step electric field in the presence of a longitudinal quantizing magnetic field has been studied at low temperatures using displaced Maxwellian distribution. The energy and momentum balance equations are used assuming acoustic phonon scattering via deformation potential responsible for the energy relaxation and elastic acoustic phonon scattering together with ionized impurity scattering for momentum relaxation. The calculations for the variation of drift velocity and electron temperature as functions of time are made for n-Hg_0.8Cd_0.2 Te in the extreme quantum limit at 1.5 K and 4.2 K. The momentum and energy relaxation times are found to be of the same order of magnitudes as with the experimental values. The magnetic field and lattice temperature dependences of the relaxation rates have been investigated.One of the authors, Suchandra Bhaumik, acknowledges the Council of Scientific and Industrial Research (New Delhi) for financial support.     

Predicting mode-dependent phonon thermal conductivity of silicon nanoparticle using Boltzmann transport equation

With the advent of nanotechnology, silicon nanoparticles have shown promising applications in the manufacturing sector. In this letter, we examine the lattice thermal conductivity predictions for a silicon nanoparticle using three popular formulations of the Boltzmann transport equation. The models as proposed by Klemens, Callaway and Holland, essentially differ in the phonon scattering mechanisms and the vibrational modes considered in the respective formulations. At low temperatures, results from all three models show strong agreement with experimental measurements, but deviate significantly with increasing temperatures. Estimates from the Holland model, which explicitly accounts for the normal and Umklapp scattering processes of the transverse and longitudinal modes, concur with the measured values. Similar predictions are obtained from both Holland and Callaway models at high temperatures since phonon transport is dominated by longitudinal modes, as revealed from our analyses of the relaxation times. In conclusion, the letter infers the importance of mode dependent thermal conduction in silicon nanoparticle at elevated temperatures.     

Effect of phonon scattering mechanisms on the lattice thermal conductivity of skutterudite-related compound

We have prepared the skutterudite-related compounds FeCo_3Sb_{12} and La_{0.75}Fe_3CoSb_{12} with different average grain sizes (about 0.8 and 3.9μm) by hot pressing. Samples were characterized by XRD, EPMA and SEM. The lattice thermal conductivity was investigated in the temperature range from room temperature to 200℃. Based on the Debye model, we analyse the change in lattice thermal conductivity due to various phonon scattering mechanisms by examining the relationship between the weighted phonon relaxation time τ(ω/ω_D)^2 and the reduced phonon frequency ω/ω_D. The effect of grain boundary scattering to phonon is negligible within the range of grain sizes considered in this study. The large reduction in lattice thermal conductivity of FeCo_3Sb_{12} compound contributes to the electron－phonon scattering. As for La_{0.75}Fe_3CoSb_{12} compound, the atoms of La filled into the large voids in the structure of the skutterudite produce more significant electron－phonon scattering as well as more substitute of Fe at Co site at the same time. Moreover, the point-defect scattering appears due to the difference between the atoms of La and the void. In addition, the scattering by the rattling of the rare-earth atoms in the void is another major contribution to the reduced lattice thermal conductivity. Introducing the coupling of the electron－phonon scattering with the point-defect scattering and the scattering by the rattling of the rare-earth atom is an effective method to reduce the lattice thermal conductivity of the skutterudite-related compounds by substitution of Fe for Co and the atoms of La filled in the large voids in the skutterudite structure.     

Effect of phonon focussing on thermal conductivity of silicon

Thermal conductivity of a cubic crystal in the boundary scattering regime is calculated, taking into account the difference between the phonon phase and group velocities. Numerical estimates in the case of silicon indicate appreciable anisotropy in conductivity as a result of phonon focussing, its maximum value being about 90% larger than the minimum. The contributions of the individual polarization branches are found to be more strongly dependent on direction than the total conductivity. It is further observed that the angle between the phonon phase and group velocities can be sometimes as large as 10°, 24° and 18° in the case of the longitudinal and the two transverse acoustic branches, respectively.     

Effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in germanium crystals

A method has been proposed for approximating a phonon spectrum of cubic crystals, which has been obtained from data on inelastic neutron scattering for symmetric directions, over the entire Brillouin zone in the form appropriate for studying relaxation characteristics of phonon systems. The effect of dispersion and damping of thermal phonon states on the longitudinal ultrasonic absorption in anharmonic processes of scattering with the participation of three longitudinal phonons has been investigated for germanium crystals. It has been shown that the inclusion of the dispersion leads to a decrease in the anisotropy of ultrasonic absorption in the LLL relaxation mechanism and makes it possible to fit the results obtained from calculations of the ultrasonic absorption coefficients to the experimental data in the low-temperature range. The temperature dependence and anisotropy of the relaxation rate of longitudinal thermal phonons in germanium crystals have been determined from experimental data on ultrasonic absorption. The performed analysis has refined values of the relaxation parameters obtained from the interpretation of the data on thermal conductivity of germanium crystals with different isotopic compositions in the isotropic-medium model.     

β型锑烯热电输运性质的第一性原理研究

利用第一性原理与半经典玻尔兹曼方程，计算并分析β型锑烯的声子色散、声子群速度、声子弛豫时间、晶格热导率及不同温度下的塞贝克系数、电导率和电子热导率随化学势的变化；结果表明：β型锑烯由于非平面六角结构，三支声学声子在Γ点附近均呈线性变化；声学声子对整个晶格热导率的贡献高达96.68%，而光学声子仅仅占到3.32%；由于较大的声光带隙（a-o gap）导致LA支在声子群速度和弛豫时间中占据主导地位，从而增大了LA支声子对整个热导的贡献；热电优值随温度的升高而增大，在费米面附近其绝对值最大可达0.275.     

Thermal conductivity of polycrystalline CVD diamond: Experiment and theory

The temperature dependences of thermal conductivity κ of polycrystalline CVD diamond are measured in the temperature range from 5 to 410 K. The diamond sample is annealed at temperatures sequentially increasing from 1550 to 1690°C to modify the properties of the intercrystallite contacts in it. As a result of annealing, the thermal conductivity decreases strongly at temperatures below 45 K, and its temperature dependence changes from approximately quadratic to cubic. At T > 45 K, the thermal conductivity remains almost unchanged upon annealing at temperatures up to 1650°C and decreases substantially at higher annealing temperatures. The experimental data are analyzed in terms of the Callaway theory of thermal conductivity [9], which takes into account the specific role of normal phonon-phonon scattering processes. The thermal conductivity is calculated with allowance for three-phonon scattering processes, the diffuse scattering by sample boundaries, the scattering by point and extended defects, the specular scattering by crystallite boundaries, and the scattering by intercrystallite contacts. A model that reproduces the main specific features of the thermal conductivity of CVD diamond is proposed. The phonon scattering by intercrystallite contacts plays a key role in this model.     

Phonon heat transport in gallium arsenide

The lifetimes of quantum excitations are directly related to the electron and phonon energy linewidths of a particular scattering event. Using the versatile double time thermodynamic Green’s function approach based on many-body theory, an ab-initio formulation of relaxation times of various contributing processes has been investigated with newer understanding in terms of the linewidths of electrons and phonons. The energy linewidth is found to be an extremely sensitive quantity in the transport phenomena of crystalline solids as a collection of large number of scattering processes, namely, boundary scattering, impurity scattering, multiphonon scattering, interference scattering, electron–phonon processes and resonance scattering. The lattice thermal conductivities of three samples of GaAs have been analysed on the basis of modified Callaway model and a fairly good agreement between theory and experimental observations has been reported.     

Electron transport in wurtzite InN

Using ensemble Monte Carlo simulation technique, we have calculated the transport properties of InN such as the drift velocity, the drift mobility, the average electron, energy relaxation times and momentum relaxation times at high electric field. The scattering mechanisms included scattering mechanisms are polar optical phonon, ionized impurity, acoustic phonon and intervalley phonon. It is found that the maximum peak velocity only occurs when the electric field is increased to a value above a certain critical field. This critical field is strongly dependent on InN parameters. The steady-state transport parameters are in fair agreement with other recent calculations.     

Theoretical analysis of the thermal conductivity of high-temperature superconductors

Summary The thermal conductivity of YBa₂Cu₃O_7−δ high-T _c superconductor is analysed self-consistently on both normal and superconducting states on the base of the Bardeen-Rickayzen-Tewordt extended theory to take into account the effects of magnetic field and superconducting fluctuations. It is shown that experimental data are in a quantitative agreement with theory even if the number and variation intervals of adjustable parameters are substantially reduced in comparison with previous works. Phonon relaxation rates due to different mechanisms of phonon scattering as well as the parameters of electron-phonon interaction are estimated. It is shown that thermal conductivity in YBa₂Cu₃O_7−δ is consistent with the BCS model with intermediate electron-phonon coupling λ=1–3 the phonon-electron and electron-phonon relaxation times near critical temperature are evaluated to be 10⁻¹⁰s and 10⁻¹²s, respectively.     

A study of electronic structure and lattice dynamics of CoSb3 skutterudite

The novel filled skutterudite materials have attracted much interest in recent years and experimental studies have revealed that electrical properties (electrical conductivity and Seebeck coefficient) in these materials are dominated by their electronic structure while the effective suppression of thermal conductivity is mainly determined by their lattice dynamics. To clarify the relationship between microstructure and properties in further, we report a systematic study of electronic structures and lattice dynamics of CoSb₃ in this paper using linearized augmented plane waves based on the density functional theory of first principles. By calculating band structure and partial density of states (PDOS), effects of electronic structures of CoSb₃ on electrical properties were investigated. Based on the calculated results of phonon dispersions and phonon density of states of CoSb₃, lattice dynamics of CoSb₃ (heat capacity, Debye temperature, mean free path and lattice thermal conductivity) are discussed in detail. The calculated results are excellently consistent with other work and experimental data.     

Electronic thermal conductivity in suspended and supported bilayer graphene

Electronic thermal conductivity κ_e is investigated, using Boltzmann transport equation approach, in a suspended and supported bilayer graphene (BLG) as a function of temperature and electron concentration. The electron scattering due to screened charged impurity, short-range disorder and acoustic phonon via deformation potential are considered for both suspended and supported BLG. Additionally, scattering due to surface polar phonons, is considered in supported BLG. In suspended BLG, calculated κ_e is compared with the experimental data leaving the phonon thermal conductivity. It is emphasized that κ_e is important in samples with very high electron concentration and reduced phonon thermal conductivity. κ_e is found to be about two times smaller in supported BLG compared to that in suspended BLG. With the reduced extrinsic disorders, in principle, the intrinsic scattering by acoustic phonons can set a fundamental limit on possible intrinsic κ_e.