Phonon Conductivity Research Articles

The lattice thermal conductivity of a semiconductor nanowire

It has been found experimentally as well as theoretically that the lattice thermal conductivity can be largely reduced by the size confinement effect. The significant boundary scattering effect is one of the dominant factors. In most existing lattice thermal conductivity models, an empirical relation is used for this scattering rate. An unconfined or confined phonon distribution obtained based on the phonon Boltzmann equation and the relaxation time approximation is then employed to calculate the lattice thermal conductivity. In this work, we first attempt to derive an analytical form of the boundary scattering rate for phonon conduction in a semiconductor nanowire and then claim two reasonable ways to take it into account correctly. Consistent mathematical models in the sense that the effects of the size confinement on (i) the phonon dispersion relation, (ii) the phonon distribution, (iii) the phonon group and phase velocities, and (iv) the Debye temperature are finally proposed.

Thermal diffusivity and thermal conductivity of thoria–lanthana solid solutions up to 10 mol.% LaO 1.5

A series of thorium oxide–lanthanum oxide solid solutions has been prepared by solid-state reaction. The phase behavior of thoria doped lanthanum oxide has been ascertained by X-ray diffraction technique. A complete solid solubility of LaO 1.5 up to 30 mol.% has been observed. Thermal diffusivity of a range of thoria–lanthana solid solutions has been measured in the compositional range from pure thoria to 10 mol.% LaO 1.5 by the laser flash method covering a temperature range from 373 to 1773 K. Thermal conductivity values have been calculated from measured diffusivity, density and specific heats of these solid solutions. An attempt has also been made to delineate a suitable mechanism for heat conduction in these solid solutions with the help of the standard phonon conduction equation for dielectric materials.

The linear thermal expansion and the thermal diffusivity measurements for near-stoichiometric (U, Ce)O 2 solid solutions

The thermal diffusivities of near-stoichiometric (U, Ce)O 2 solid solutions containing CeO 2 up to 22 mol% were investigated in the temperature range of 298–1273 K using the laser flash method. Also, linear thermal expansion measurements were performed in the temperature range of 298–1673 K using a thermomechanical analysis. The thermal conductivities were determined by a calculation of the thermal diffusivity, the density and the specific heat. The thermal conductivities of the tested samples could be expressed as a function of the temperature by the phonon conduction equation k = ( A + BT) −1. The thermal conductivity decreased gradually with an increasing Ce content. This was attributable to the increasing lattice defect thermal resistance caused by the U 4+, Ce 4+ and O 2− ions as phonon scattering centers.

Thermal Transport Due to Phonons in Random Nano-particulate Media in the Multiple and Dependent (Correlated) Elastic Scattering Regime

Effects of multiple and dependent or correlated elastic scattering of phonons due to nanoparticles on thermal transport in random nano-particulate media (random phononic crystals) are investigated in this paper under various approximations. Multiple scattering means that the scattered wave from one particle is incident on another particle to be scattered again. Dependent scattering means far-field interference of the scattered waves due to phase difference, which is ignored in the independent scattering regime. Multiple and dependent scattering effects become important when the interparticle distance is comparable to the wavelength of phonons. Results show that multiple scattering primarily affects the velocity and density of states of phonons and dependent scattering primarily affects the mean free path of phonons. Effects of both multiple and dependent scattering increases with increasing volume fraction of nanoparticles. Modification of these parameters affects the equilibrium phonon intensity and the thermal conductivity of phonons.

An experimental investigation of thermal contact conductance of stainless steel at low temperatures

An investigation is carried out to study the effects of surface topography and interfacial temperature on the thermal contact conductance of the pressed stainless steel 304 contacts in the range 125–210 K and 1–7 MPa. The surface roughness of test specimens is between 1.5 μm and 17.6 μm. A theoretical model is used to predict the results and gives a reasonable agreement. The combined effect of phonon conductivity and electronic conductivity to thermal conductivity at low temperatures is described using a proposed correlation. The small contact conductance at low temperatures can ascribe to the decreased thermal conductivity and the increased hardness. It is demonstrated that rms roughness and mean absolute slope are both needed for evaluating contact heat transfer.

Evaluation of thermal conductivity of hypostoichiometric (U, Pu)O 2− x solid solution by molecular dynamics simulation at temperatures up to 2000 K

The thermal conductivities of hypostoichiometric U 1− y Pu y O 2− x solid solutions have been investigated by the molecular dynamics (MD) simulation between 300 and 2000 K using the Born–Mayer–Huggins interatomic potential with the partially ionic model. In the present equilibrium MD system, the thermal conductivity was calculated by the time-integral of auto-correlation function of energy current based on the Green–Kubo relationship. For stoichiometric U 1− y Pu y O 2.0 crystals ( y = 0.0–0.3), the thermal conductivity was almost constant as a function of Pu content y. On the other hand, for hypostoichiometric U 0.8Pu 0.2O 2− x solid solutions ( x = 0.0–0.06), the effect of oxygen deficiency x on the thermal conductivity became larger with increasing x, and their thermal conductivities were lower than that of the stoichiometric oxide, while the temperature dependence was weakened. These results were caused by that oxygen vacancies as lattice defects disordered phonon conduction, which was elucidated by the vibration analyses, i.e. the correlation function of energy current and the phonon-level density.

Thermal conductivity of near-stoichiometric (U, Er)O 2 solid solutions

Thermal diffusivities of UO 2 and UO 2 doped with 1, 3, 5, 7 and 10 mol % ErO 1.5 were measured in the range of 298–1673 K by a laser flash method and their thermal conductivities were calculated from the thermal diffusivity, the measured sample density and published specific heat capacity data. The temperature dependence of the thermal conductivity up to 1673 K in UO 2 and UO 2-doped with ErO 1.5 was found to be modeled well using the phonon conduction equation, K = ( A + BT) −1. The thermal conductivities of the UO 2 and (U, Er)O 2 solid solutions gradually decreased with the temperature. The thermal conductivity of the doped UO 2 decreased relative to UO 2 with an increase of ErO 1.5 content at low temperatures, while it was independent of the ErO 1.5 content at higher temperatures. The variation of parameters A and B as a function of ErO 1.5 content is found experimentally and it is found that the dependence of the thermal conductivity of (U, Er)O 2 on temperature up to 1673 K and on the ErO 1.5 content can be expressed as K = K UO 2 1 + K UO 2 ( k A y + k B yT ) .

The combined influences of variable thermal conductivity, temperature- and pressure-dependent viscosity and core–mantle coupling on thermal evolution

Most convection studies of thermal history have not considered explicitly the thermal interaction between the mantle flow and the core. We have investigated the influences of variable thermal conductivity and variable viscosity (temperature- and pressure-dependent) on the boundary layer and thermal characteristics of the D ″ layer, and the evolution of the thermo-mechanical profiles of horizontally averaged viscosity and thermal conductivity. Viscosity contrast due to temperature dependence of up to 30,000 has been considered. Our results show clearly that variable thermal conductivity, though small in magnitude as compared to variations in the viscosity, does exert a significant delaying influence on mantle cooling, thereby keeping the Urey ratio low, reducing the growth of the bottom thermal boundary layer, and changing the viscosity profiles over time. A higher temperature at the core–mantle boundary increases the overall time-dependent behavior of the thermal boundary layers. Enhanced radiative conductivity results in faster cooling, opposite to the effect of the phonon conductivity component and a superadiabatic temperature gradient in the deep lower mantle. Finally, the initial value of the core–mantle boundary temperature can be inferred to wield a strong influence on the subsequent mantle thermal evolution in this model with both variable thermal conductivity and viscosity. We may conjecture that other rheological and conductivity complexities, such as grain-size dependence of mantle properties, would also have an impact on the current state of the mantle resulting from the primordial thermal condition.

High-temperature carrier transport and thermoelectric properties of heavily La- or Nb-doped SrTiO3 single crystals

Electron and thermal transport properties, i.e., electrical conductivity, carrier concentration, Hall mobility, Seebeck coefficient, thermal conductivity, of heavily La- or Nb-doped SrTiO3 (STO) bulk single crystals were measured at high temperatures, (300–1050K) to clarify the influence of doping upon the thermoelectric performance of STO. The temperature dependence of Hall mobility and Seebeck coefficient changed at ∼750K in all samples because the dominant mechanism for carrier scattering changed with increasing temperature from coupled scattering by polar optical phonons and acoustic phonons to mere acoustic phonon scattering. The density-of-states effective mass of Nb-doped STO, which was estimated from the carrier concentration and Seebeck coefficient, was larger than that of La-doped STO. Thermal conductivity of the samples, which was similar to that of undoped STO single crystal, decreased proportionally to T−1, indicating that the phonon conduction takes place predominantly and the electronic contribution to thermal conductivity is negligible.

Review: Multiscale Thermal Modeling in Nanoelectronics

Subcontinuum phonon conduction phenomena impede the cooling of field-effect transistors with gate lengths less than 100 nm, which degrades their performance and reliability. Thermal modeling of these nanodevices requires attention to a broad range of length scales and physical phenomena, ranging from continuum heat diffusion to atomic-scale interactions and phonon confinement. This review describes the state of the art in subcontinuum thermal modeling. Although the focus is on the silicon field-effect transistor, the models are general enough to apply to other semiconductor devices as well. Special attention is given to the recent advances in applying statistical and atomistic simulation methods to thermal transport.

TRANSMISSION OF PHONON MODES IN QUASI-ONE-DIMENSIONAL WAVEGUIDES VIA DOUBLE L-SHAPED JOINT NANOSTRUCTURES

The influence of a special class of atomic nanostructures embedded on a waveguide is analyzed for the scattering and transmission of elastic waves in quasi-one-dimensional multicanal waveguides. The quasi-one-dimensional waveguide is constructed of double chains of atoms, and the nanostructures consist of geometrical configurations, where the double chains are arranged to form several types of double L-shaped joints. Numerical results are presented for the three types of nanostructures, using the matching method. The theoretical approach allows us to calculate the reflection and the transmission probabilities as well as the average phonon conductance of the system along the waveguide. The results show that the transmission probabilities and the average conductance depend strongly on the type of geometrical joint nanostructure. The pronounced fluctuations in the transmission and conductance spectra as a function of the frequency can be understood as Fano resonances that result from the coherent coupling between the propagating modes and the localized vibrational modes induced by the nanostructures.

Heat Capacities and Thermal Conductivities of Perovskite Type BaZrO3 and BaCeO3.

Abstract Polycrystalline perovskite type oxides, BaZrO3 and BaCeO3, have been prepared by mixing the appropriate amounts of ZrO2, CeO2, and BaCO3 followed by reacting at 1273 K and sintering at 1773 K. The thermal conductivities of BaZrO3 and BaCeO3 have been evaluated from the heat capacity, thermal diffusivity, and density. The heat capacity has been measured by using a differential scanning calorimeter (DSC) in a high purity argon atmosphere. In the temperature range from room temperature to about 1400 K, the thermal diffusivity has been measured by a laser flash method in vacuum. The thermal conductivities of both BaZrO3 and BaCeO3 decrease with increasing temperature, showing phonon conduction characteristics. The thermal conductivity at room temperature of BaZrO3 is 5.2 Wm−1K−1, which is about 3 times larger than that of BaCeO3.

Dispersive effects and correction term in two-mode phonon conduction model for Ge

A complete analysis of the phonon conductivity κ, still lacking in the literature, is presented in the two-mode conduction model for Germanium. First a method is derived from which the correction term κ c of the Callaway model is separated into its longitudinal and transverse parts and then the effects of strong phonon dispersion and the role of longitudinal and transverse phonons on κ c are studied. For this purpose we have also proposed some new empirical expressions for the three phonon relaxation rates τ 3ph −1's which are valid in the entire temperature range. This improvised model, when applied simultaneously to the phonon conductivity data of both normal and enriched Ge, yields some new results. These are (i) κ c neglected by the earlier workers in the two-mode phonon conduction model, gives a substantial contribution beyond the conductivity maximum and (ii) the longitudinal phonons are the major carriers of heat at high temperature.

Thermoelectric Properties of Ni‐ and Zn‐Doped Nd2CuO4.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Heat capacities and thermal conductivities of perovskite type BaZrO 3 and BaCeO 3

Polycrystalline perovskite type oxides, BaZrO 3 and BaCeO 3, have been prepared by mixing the appropriate amounts of ZrO 2, CeO 2, and BaCO 3 followed by reacting at 1273 K and sintering at 1773 K. The thermal conductivities of BaZrO 3 and BaCeO 3 have been evaluated from the heat capacity, thermal diffusivity, and density. The heat capacity has been measured by using a differential scanning calorimeter (DSC) in a high purity argon atmosphere. In the temperature range from room temperature to about 1400 K, the thermal diffusivity has been measured by a laser flash method in vacuum. The thermal conductivities of both BaZrO 3 and BaCeO 3 decrease with increasing temperature, showing phonon conduction characteristics. The thermal conductivity at room temperature of BaZrO 3 is 5.2 Wm −1K −1, which is about 3 times larger than that of BaCeO 3.

Thermoelectric properties of Ni- and Zn-doped Nd 2CuO 4

The electrical resistivity, Seebeck coefficient, and thermal conductivity of Nd 2(Cu 0.98M 0.02)O 4 (M: Ni and Zn) have been measured in the temperature range from room temperature to about 1000 K. Ni- and Zn-doping decreases the electrical resistivity and the absolute values of the Seebeck coefficient. The thermal conductivity decreases with increasing temperature, showing phonon conduction, and also decreases by doping. The power factor of Nd 2(Cu 0.98Ni 0.02)O 4 reaches 1.02×10 −4 W m −1 K −2 and the figure of merit is 1.35×10 −5 K −1 at 320 K. The relatively low figure of merit compared with that of the state-of-the-art thermoelectric materials is due to the high thermal conductivity.

Electron-phonon interaction and phonon conductivity in Li-doped silicon with intermediate donor concentration

Phonon conductivity in intermediately doped n-type silicon still remains unexplained. In this paper we have calculated the phonon conductivity in Li-doped silicon for Nex < Nc using Mikoshiba's inhomogeneity model. We have introduced spherical polar coordinates for the phonon polarization vectors in Sota and Suzuki's theory in order to take into account the realistic picture of the scattered phonons. Deformation potential for different polarizations λ has been evaluated for the metallic region. Present calculations show that Mikoshiba's inhomogeneity model is able to explain the phonon conductivity of Li-doped silicon having intermediate donor concentration very well.

Transient radiation-conductive heat transfer problems: “The quadrupole method”

This paper presents a statement of the works performed in L.E.M.T.A by the members of the thermal and mechanical heterogeneous media research group during the last six years concerning the solving of coupled conductive and radiative heat transfers within a multilayer and semi-transparent “wall”. Out of the authors, this paper allows to take inspiration from the works of D. Maillet, M. Lazard and V. Manias[19, 20, 21]. The aim of these works is to represent in a macroscopic way, with the minimum number of thermophysical parameters, the heat transfers in a plane system composed of semi-transparent media. The approach we propose is semi-analytic (Kernel substitution technique, Laplace transformation) and allow to obtain in the Laplace domain an analytical solution that can be easily used. This method can be applied in two main scopes of applications: the estimation of thermophysical properties (phononic conductivity, optical thickness, Planck number for instance) of semi-transparent materials (glasses, crystals, glass wool, semi-conductors, synthetic diamonds, vitroceramics and so on) and the modelling of processes with semitransparent walls (for instance bottles forming, flat glass production, drying of paper). The method will be first presented and validated and two examples of applications will be then given. This method can be applied to semitransparent walls that emit, absorb and scatter the radiant energy (participating medium). It appears from the principle of a Kernel substitution technique applied to the radiative flux expression and initially introduced by Lick[1] that allows to change the character of the governing heat equation from the integro-differential form to a purely differential one. In the case of limiting cases of purely scattering and purely absorbing media, the solution of the radiative transfer equation is exact. In the general case, we make a two-flux approximation. In all cases, we assume a linear transfer and use the Laplace transform. The method can be applied to grey or grey by bands media, with isotropic or anisotropic scattering. The advantage of the method is fast computational times for good precision.

Magnetization and specific heat of the Ho 3Co compound

The magnetization processes of the Ho 3Co single crystal along three basic symmetry axes were investigated and possible magnetic structure is suggested. Specific heat measurements of the compound have been performed at temperature range of 2–300 K. The phonon conduction electron and magnetic contributions to the total specific heat are determined and discussed. Two peaks observed on the magnetic part of the specific heat correspond to magnetic ordering transition ( T N=20 K) and Schottky anomaly ( T Sch∼30 K).

On the concept of an optimal hot-electron bolometer with NIS tunnel junctions

Optimization of the hot-electron bolometer with a normal metal–insulator–superconductor (NIS) tunnel junction as a temperature sensor has been done theoretically. The responsivity and the noise equivalent power (NEP) of the bolometer are obtained numerically for typical experimental parameters. We demonstrate that electron cooling by the NIS junction, which serves as a thermometer, can improve the sensitivity of the device. This effect is especially useful in the presence of a finite power load. Optimization of the hot-electron bolometer in the presence of a finite power load is discussed. It has been shown that the optimal regime can be realized when thermal conductance through the tunnel junctions is larger than the electron–phonon conductance. The electron–phonon noise is negligible and the NEP is determined mainly by the noise of the NIS junctions because of practically full transference of power of the incoming signal to a readout amplifier through the junctions.