Free Path Of Phonons Research Articles

Phonon-drag in a graphite channel buried in diamond

While the phonon-drag effect can induce large Seebeck coefficients, it is associated with large mean free path phonons present in the vicinity of the maximum in temperature of the lattice thermal conductivity. In this paper, we initiate a new route by searching for the mutual drag between the electron and phonon-drag gases at the interface between two different media. In that respect, the temperature studies of the conductance and Seebeck coefficient of a model system consisting of an electrically conductive graphitic channel buried beneath the surface of a diamond crystal are shown. The observed behaviour is very similar to that of graphite, with a typical negative peak associated with the phonon-drag effect. Interestingly, this phonon-drag peak of the buried graphitic channel appears at a significantly higher temperature than that in pure graphite.

Thermal transport characteristics of diamond under stress

Diamond exhibits extremely high hardness and thermal conductivity, which makes it widely used in industrial fields such as diamond cutting tools and piezoelectric materials. At the same time, during the diamond applications, the internal characteristics and thermal transport properties of diamond will change under high stress, which has an important impact on its service life and device accuracy. However, the internal properties and thermal transport response of diamond under high stress have not been systematically studied. This paper employed first-principles software to investigate the reaction of the diamond lattice structure, electronic properties, lattice vibration properties, thermodynamic properties, lattice thermal conductivity, phonon group velocity, and phonon free path when subjected to uniaxial compressive stress, shear stress, and hydrostatic pressure. The results show that at a stress of 120 GPa, the response of diamond exhibited distinct anisotropic properties in three kinds of stress states. Changes occur in the position of the carbon atoms, CC bond length, and CC bond angle within the diamond structure when subject to the three kinds of stress fields. The main reason for the above phenomenon is that the stress caused the redistribution of charges around the C atoms in the diamond. Furthermore, the symmetry of the diamond crystal was broken, and the diamond lattice vibration properties undergone alteration, leading to a state of dynamic instability. The thermodynamic properties and phonon group characteristics of diamond changed, and the lattice thermal conductivity of diamond is 2380, 99, and 806 W·m-1K-1, respectively. This theoretical study offers valuable insights into the impact of stress fields on the heat transfer properties of diamonds, providing practical guidance for their use in high-stress environments.

Ultralong mean free path phonons in HKUST-1 and their scattering by water adsorbates

Metal-organic frameworks (MOFs) have shown big potential in energy storage and thermal management, which are closely related to their thermal properties. It has been believed for some time that the vibrational mean free path in MOFs is relatively small and the resulting thermal conductivity has weak size dependence. By studying one of the typical MOFs, i.e., ${\mathrm{Cu}}_{3}{(\mathrm{BTC})}_{2}$ where BTC is benzene-1,3,5-tricarboxylate, also referred to as HKUST-1, we computationally prove that the mean free path of these small wave vectors or equivalently low-frequency vibrations in HKUST-1 can be as large as \ensuremath{\sim}120 nm and the corresponding thermal conductivity is strongly size dependent, which is attributed to its good crystallinity. We further find that these long mean free path phonons are strongly scattered by the adsorbed water molecules and the thermal conductivity is decreased by \ensuremath{\sim}51.3% when the water molecules are adsorbed. Consequently, the thermal conductivity of HKUST-1 with water molecules is weakly size dependent. Two pathways for the thermal energy exchange, e.g., the phonons and the water molecules, exist in HKUST-1 with water molecules. The thermal conductivity of the adsorbed HKUST-1 is found to decrease and then increase with the quantity of the adsorbates owing to the competition between the two thermal pathways. Our study here provides a fundamental understanding on the thermal transport mechanisms in the metal-organic framework with consideration of adsorbates, which offers useful guidance for thermal management design in these thermal-related applications such as adsorption-driven heat pumps.

Hydrodynamic thermal transport in silicon at temperatures ranging from 100 to 300 K

Energy dissipation in current microelectronic devices is an inefficient process due to its non-Fourier behavior. By using thermoreflectance imaging, the authors measure the temperature distribution around nanoscale heaters of different sizes and shapes on a silicon substrate to test state-of-the-art modeling. The results indicate that hydrodynamiclike thermal transport equations successfully predict the local system response at temperatures ranging from 100 to 300 K. This is contrasted with kinetic interpretations based on the suppression of long mean free path phonons, which are shown not to become manifest in the experiments.

Suppressing thermal conductivity of nano-grained thermoelectric material using acoustically hard nanoparticles

We engineered the thermal conductivity of nano-grained Bi0.5Sb1.5Te3 (BST) by embedding SiO2 and diamond nanoparticles (NPs) with concentration ranging from 0.5 to 5 vol. %. The embedded NPs work as additional scattering centers for long mean free path phonons that are not effectively scattered by the grain boundaries. We found that both the SiO2 and diamond NPs materially reduced the lattice thermal conductivity (κlat) within the temperature range of 50–300 K, with stronger reduction occurring at a lower temperature. Furthermore, the diamond NPs were found to cause large reduction in κlat compared to the SiO2 NPs at the same concentrations. Further theoretical analysis showed that the diamond NPs possess about tenfold higher interfacial thermal resistance with the BST matrix compared to that of SiO2 NPs, due to the larger acoustic mismatch between diamond and BST as compared to SiO2 and BST. As a result of the large reduction of κlat, the thermoelectric figure of merit (ZT) was enhanced by 15% at room temperature with 0.5 vol. % diamond NP relative to the pristine nano-grained samples without the NPs.

Phonon-boundary scattering and thermal transport in AlxGa1−xN: Effect of layer thickness

Thermal conductivity of AlxGa1−xN layers with 0≤x≤0.96 and variable thicknesses is systematically studied by combined thermoreflectance measurements and a modified Callaway model. We find a reduction in the thermal conductivity of AlxGa1−xN by more than one order of magnitude compared to that of GaN, which indicates a strong effect of phonon-alloy scattering. It is shown that the short-mean free path phonons are strongly scattered, which leads to a major contribution of the long-mean free path phonons to the thermal conductivity. In thin layers, the long-mean free path phonons become efficiently scattered by the boundaries, resulting in a further decrease in the thermal conductivity. Also, an asymmetry of thermal conductivity as a function of Al content is experimentally observed and attributed to the mass difference between Ga and Al host atoms.

Extrapolation of thermal conductivity in non-equilibrium molecular dynamics simulations to bulk scale

Predictions of the bulk scale thermal conductivity of solids using non-equilibrium molecular dynamics (MD) simulations have relied on the linear extrapolation of the thermal resistivity versus the reciprocal of the system length in the simulations. Several studies have reported deviation of the extrapolation from linearity near the micro-scale, raising a concern of its applicability to large systems. To investigate this issue, present work conducted extensive MD simulations of silicon with two different potentials (EDIP and Tersoff-II) for unprecedented length scales up to 10.3 μm and simulation times up to 530 ns. For large systems ≥0.35 μm in size the non-linearity of the extrapolation of the reciprocal of the thermal conductivity is mostly due to ignoring the dependence of the thermal conductivity on temperature. To account for such dependence, the present analysis fixes the temperature range for determining the gradient for calculating the thermal conductivity values. However, short systems ≤0.23 μm in size show significant non-linearity in the calculated thermal conductivity values using a temperature window of 500 ± 10 K from the simulations results with the EDIP potential. Since these system sizes are shorter than the mean phonon free path in EDIP (~0.22 μm), the nonlinearity may be attributed to phonon transport. For the MD simulations with the Tersoff-II potential there is no significant non-linearity in the calculated thermal conductivity values for systems ranging in size from 0.05 to 5.4 μm.

Electronic, elastic, optical and thermal transport properties of penta-PdAs2 monolayer: First-principles study

PdAs2 monolayer, a new pentagonal two-dimensional (2D) material, greatly attracts widely research interest due to its extremely high carrier mobility with a direct band gap. We have systematically studied the electronic structure, elastic, optical and thermal transport properties of monolayer PdAs2 from first-principles calculations. Our electronic structure calculations show that the monolayer PdAs2 is a semiconductor with a direct band gap of 0.78 eV. Tensile strain has a good regulating effect on the band gap, which can be adjusted from 0.01 eV to 0.84 eV. The calculated elastic constants of monolayer PdAs2 confirm that the PdAs2 monolayer is mechanically stable. The calculated optical properties reveal that the energy range of the absorption spectrum is 1 eV–15 eV. The absorption range of PdAs2 monolayer is mainly visible and ultraviolet light. Under the tensile strain, the absorption spectrum shows obvious redshift. With the increase of strain, the reflectivity and refractivity increase. The calculated thermal conductivity of the monolayer PdAs2 at 300 K is 1.04 W/(mK), which is lower than that of known pentagonal monolayer. In addition, the effects of phonon free path, group velocity and phonon scattering rate on lattice thermal conductivity are analyzed.

Effect of electron-phonon interaction on lattice thermal conductivity of SiGe alloys

While it is well-known that electron-phonon scattering often determines the electron mobility, its impact on lattice thermal conductivity is less clear. Dominant phonon scattering mechanisms that determine the lattice thermal conductivity have been attributed to phonon-phonon and phonon-defect interactions. However, recent studies in silicon have shown that strong electron-phonon interaction can also lead to significant phonon scatterings at high carrier concentrations. Here, we use first-principles simulations to study thermal transport in SiGe alloys and show that the effect of electron-phonon interaction on thermal transport is even more significant than that in Si because mass disorder scattering leaves long mean free path phonons behind, which are more strongly scattered by electrons. At the carrier concentration of 1 × 1020 cm−3, the room temperature lattice thermal conductivity of the Si0.9Ge0.1 alloy including electron-phonon interaction is only 40% of the value without this interaction. The results show that thermal transport in alloys at a high doping level can be significantly impacted by the free carriers, providing important insights into heat conduction mechanisms in thermoelectric materials which are mostly based on heavily doped alloys.

Phonon relaxation time reconstruction from transient thermal grating experiments and comparison with density functional theory predictions

Phonon relaxation time and free path distributions are reconstructed from experimental measurements on a two-dimensional transient thermal grating and compared with density functional theory (DFT) results for silicon. The reconstruction is performed using the inverse problem formulation of Forghani et al. [Phys. Rev. B 94, 155439 (2016)]. The discrepancies observed between reconstructed and DFT results are analyzed in terms of the ability of each set of data to reproduce the experimental temperature relaxation profiles; the reconstructed data are found to predict temperature profiles in closer agreement with the experimental data than the DFT results, possibly due to discrepancies between the actual material and the idealized model studied in the DFT calculations. The reconstructed phonon properties accurately predict temperature relaxation profiles at grating length scales smaller than those spanned by the experimental data. This is a very important feature since in a variety of experimental setups, including the one providing the data in the present study, measurements are not available at all scales spanned by the material free paths.

Photoacoustic characterization of nanowire arrays formed by metal-assisted chemical etching of crystalline silicon substrates with different doping level

Silicon nanowire (SiNW) arrays were investigated by gas-microphone photoacoustic (PA) technique to evaluate the thermal conductivity and optical absorption. The arrays with SiNW's length from 3 to 25 μm were formed by metal-assisted chemical etching of (100)-oriented monocrystalline silicon (c-Si) substrates with the low and high concentration of doping impurities. PA responses of SiNWs were excited by sources with wavelengths of 460 and 630 nm in the frequency range from 15 to 1150 Hz. An analysis of the experimental data reveals that the thermal conductivities of SiNWs formed on the lightly and heavily doped substrates are about 4–7 and 0.17–0.22 W/(m K), respectively. The latter value is explained by the porous structure of the SiNWs, promoting a strong restriction of the phonon free path. The thermal conductivity and optical absorption of SiNW arrays depend on the doping level and length of SiNWs due to a combination of the phonon and light scattering processes.

Defect-engineered reduced graphene oxide sheets with high electric conductivity and controlled thermal conductivity for soft and flexible wearable thermoelectric generators

The direct use of graphene for potential thermoelectric material requires the opening of its bandgap without loss of its high electric conductivity. We herein demonstrate a synchronous reduction and assembly strategy to fabricate large-area reduced graphene oxide films with high electric conductivity and optimized low thermal conductivity assembly. The reduced graphene oxide films have a high electric conductivity and low thermal conductivity, which results from high longitudinal carrier mobility of the lattice domains as well as the enhanced scattering of phonons in the defects and their boundary that substantially reduces the mean phonon free path and the thermal conductivity. Flexible thermoelectric generators were prepared by assembling reduced graphene oxide film on 3D printed polydimethylsiloxane grids, demonstrating a remarkable output voltage of 57.33 mV/g at a temperature difference of 50 K. A wristband-type flexible thermoelectric generator with 7 repeating units generated a maximum power density of 4.19 µW/g at ambient temperature of 15 °C. The 3D printed generator is promising in providing power autonomy to wearable microwatt electronic devices. In addition, we believe that this work can be easily scaled up and can offer the pathway to produce large-scale manufacturing of graphene based materials for future microelectronics and large-scaled flexible and wearable energy harvesting systems.

Impact of pore anisotropy on the thermal conductivity of porous Si nanowires

Porous materials display enhanced scattering mechanisms that greatly influence their transport properties. Metal-assisted chemical etching (MACE) enables fabrication of porous silicon nanowires starting from a doped Si wafer by using a metal template that catalyzes the etching process. Here, we report on the low thermal conductivity (κ) of individual porous Si nanowires (NWs) prepared from MACE, with values as low as 0.87 W·m−1·K−1 for 90 nm diameter wires with 35–40% porosity. Despite the strong suppression of long mean free path phonons in porous materials, we find a linear correlation of κ with the NW diameter. We ascribe this dependence to the anisotropic porous structure that arises during chemical etching and modifies the phonon percolation pathway in the center and outer regions of the nanowire. The inner microstructure of the NWs is visualized by means of electron tomography. In addition, we have used molecular dynamics simulations to provide guidance for how a porosity gradient influences phonon transport along the axis of the NW. Our findings are important towards the rational design of porous materials with tailored thermal and electronic properties for improved thermoelectric devices.

EXPRESS METHODS FOR ANALYSING THERMO-ELECTRIC MATERIALS AND CONVERTER CHARACTERISTICS

Objectives. Recently, there has been a sharp increase in research interest in thermoelectricity (TE) and its applications. New designs for thermoelectric converters (TEC) are being proposed and a large number of new thermoelectric materials (TEM) with a thermoelectric figure of merit Z = a 2 s / k enhanced by the nanotechnological (NT) method are obtained. (Here a , s and k are the coefficient of thermal electromotive force (EMF), the specific electrical conductivity and the thermal conductivity, respectively). As a result, the need for a sharp increase in the labour productivity of researchers working in the thermoelectric (TE) industry has emerged, especially when determining the characteristics of thermoelectric materials and thermoelectric converters, as well as when processing an increased volume of literature data. The aim of the present work is to develop a set of methods for rapid analysis of the characteristics of thermoelectric materials and thermoelectric converters, allowing the labour productivity of researchers working in the TE industry to be increased. Methods. The problem was solved by selecting well-known methods for studying TEM and TEC, based on nonstationary measurement principles and computer calculations, as well as creating new methods. Results. The result of the work was an expansion of the capabilities of the established thermal probe and Harman methods used to measure the Z parameter and its components (a , s and k). The Harman method is expanded to multistage modules, allowing for the passive compensation of thermal losses when measuring in air (the switching of thermocouples (TP) in “head to head” mode). Methods for estimating the Eg – the band gap width of the TEM – according to the curves Z = f (T , as well as the calculation of the TEC using the Lenz rule, are developed. A method is proposed for diagnosing the “phonon glass electron crystal” (PGEC) phase ( 1 ~ l ph / a << λ e / a / a) by determining the mean free paths of phonons l ph and electrons λe. (Here, a = 3 nm is the shortest interatomic distance). The method of autoelectrochemical alloying of thermoelectric materials, as well as diagnostics of nanostructures (NS), is developed by determining the “physical property-NS identity period x ” dependencies. Examples of the developed technique using for analysing the characteristics of thermoelectric materials and thermoelectric converters are given. Conclusion The possibility of a sharp increase in the labour productivity of researchers working in the TE industry is indicated. Acknowledgment. The work was carried out according to the state task No. 007-00129-18-00.

Structural and thermoelectric properties of the type-I Sn clathrates Cs8Sn46−n(n=0,2) from Density Functional Theory (DFT)

Abstract:Sn clathrates are promising phonon glass, electron crystal materials (PGEC), in which the phonon free paths are short and the electron free paths are long. We analysed the relaxed structure of Sn clathrates using four different Density Funtional Exchange-Correlation functionals. The phonon structures were investigated as a first step in order to determine the phonon contribution to the thermal conductivity. We determined the Seebeck coefficient and electrical conductivity of the clathrate compound and the thermoelectric figure of merit. A glimpse into the dynamics of the system for the evaluation of the thermoelectric and electronic properties is presented.

Influence of phonon focusing on the Knudsen flow of phonon gas in single-crystal nanofilms of spintronic materials

Influence of the anisotropy of elastic energy on the phonon transport has been investigated in single- crystal nanofilms of Fe, Cu, MgO, InSb, and GaAs materials used for spintronic instruments and devices in the Knudsen flow regime of phonon gas. The dependences of the lattice thermal conductivity and lengths of free paths of phonons for all acoustic modes on the geometric parameters of the films have been considered for low temperatures with the dominance of the diffuse scattering of phonons at the boundaries. Physical aspects of the propagation of phonon modes in the films have been analyzed. It has been shown that the anisotropy of phonon transport in single-crystal films is due to the features of the propagation of phonon modes in elastically anisotropic films with a different relationship of the geometric parameters. The directions of heat flow and orientations of the film planes that yield the maximum and minimum thermal conductivity of phonons in film planes have been determined.

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.

Lattice Thermal Conductivity of Pristine Si Nanowires: Classical Nonequilibrium Molecular Dynamics Study

ABSTRACTWe investigate lattice thermal conductivities of Si nanowires (SiNWs) based on classical nonequilibrium molecular dynamics (NEMD) simulations. The SiNWs are supposed to have a crystalline diamond structure and extend along the [001] axial direction with the {100} sidewall facets on which the surface Si atoms are all dimerized and fully passivated by hydrogen. Various sizes in the square cross section are considered, and the lengths are varied to find the diffusive limits of the lattice thermal conductivities. The upper limits of the diffusive lattice thermal conductivities of SiNWs are 11.2, 16.0, 22.8, and 28.0 W/mK for SiNWs with widths of 2.7, 4.9, 8.1, and 11.3 nm, respectively. The mode-averaged mean free paths of phonons are 50, 52, 63, and 80 nm for the SiNWs, respectively, which are 7–19 times longer than the SiNW widths.

Electronic structure, lattice dynamics, and thermoelectric properties of bismuth nanowire from first-principles calculation

Abstract

Effect of phonon focusing on Knudsen flow of phonon gas in single-crystal nanowires made of spintronics materials

Effect of anisotropy of elastic energy on the phonon propagation in single-crystal nanowires made of Fe, Cu, MgO, InSb, and GaAs materials that are used to fabricate spintronics devices in the regime of the Knudsen flow of phonon gas has been studied. A new method of analyzing the focusing of quasi-transverse modes has been suggested, which made it possible to determine the average values of the densities of phonon states in the regions of focusing and defocusing slow and fast quasi-transverse modes. The effect of phonon focusing on the anisotropy of heat conductivity and lengths of the phonon free paths has been analyzed for all acoustic modes that exist in spintronics nanostructures. It has been shown that for all the nanowires investigated the angular dependences of the free paths of fast and slow transverse modes in the {100} and {110} planes correlate with the angular dependences of the densities of phonon states for these modes. Directions of the heat flux that ensure the maximum and minimum phonon heat conductivity in the nanowires have been determined.