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Showing papers on "Mean free path published in 2015"


Journal ArticleDOI
TL;DR: Surprisingly, the interaction of phonons originating from neighboring heat sources enables more efficient diffusive-like heat dissipation, even from nanoscale heat sources much smaller than the dominant phonon mean free paths, suggesting that thermal management in nanosystems including integrated circuits might not be as challenging as previously projected.
Abstract: Understanding thermal transport from nanoscale heat sources is important for a fundamental description of energy flow in materials, as well as for many technological applications including thermal management in nanoelectronics and optoelectronics, thermoelectric devices, nanoenhanced photovoltaics, and nanoparticle-mediated thermal therapies. Thermal transport at the nanoscale is fundamentally different from that at the macroscale and is determined by the distribution of carrier mean free paths and energy dispersion in a material, the length scales of the heat sources, and the distance over which heat is transported. Past work has shown that Fourier’s law for heat conduction dramatically overpredicts the rate of heat dissipation from heat sources with dimensions smaller than the mean free path of the dominant heat-carrying phonons. In this work, we uncover a new regime of nanoscale thermal transport that dominates when the separation between nanoscale heat sources is small compared with the dominant phonon mean free paths. Surprisingly, the interaction of phonons originating from neighboring heat sources enables more efficient diffusive-like heat dissipation, even from nanoscale heat sources much smaller than the dominant phonon mean free paths. This finding suggests that thermal management in nanoscale systems including integrated circuits might not be as challenging as previously projected. Finally, we demonstrate a unique capability to extract differential conductivity as a function of phonon mean free path in materials, allowing the first (to our knowledge) experimental validation of predictions from the recently developed first-principles calculations.

194 citations


Journal ArticleDOI
Woochul Kim1
TL;DR: In this article, a review of the representative strategies of phonon engineering by categorizing them into the methods affecting phonon thermal conductivity, i.e., specific heat, phonon group velocity, and mean free path, is presented.
Abstract: In this review, we discuss some of the representative strategies of phonon engineering by categorizing them into the methods affecting each component of phonon thermal conductivity, i.e., specific heat, phonon group velocity, and mean free path. In terms of specific heat, a large unit cell is beneficial in that it can minimize the fraction of thermal energy that can be transported since most of the energy is stored in the optical branches. In an artificial structure such as the superlattice, phonon bandgaps can be created through constructive interference by Bragg reflection, which reduces phonon group velocity. We further categorize the mean free path, i.e., scattering processes, into grain boundary scattering, impurity scattering, and phonon–phonon scattering. Rough-surfaced grains, nano-sized grains, and coated grains are discussed for enhancement of the grain boundary scattering. Alloy atoms, vacancies, nanoparticles, and nano-sized holes are treated as impurities, which limit the phonon mean free path. Lone pair electrons and acoustical-to-optical scattering are suggested for manipulating phonon–phonon scattering. We also briefly mention the limitation and temperature range in which the Wiedemann–Franz law is valid in order to achieve a better estimation of electronic thermal conductivity. This paper provides an organized view of phonon engineering so that this concept can be implemented synergistically with power factor enhancement approaches for design of thermoelectric materials.

191 citations


Journal ArticleDOI
TL;DR: In this article, the spectral phonon mean free paths (MFPs) of carbon nanotubes (CNTs) were determined from the phonon transmission function calculated using nonequilibrium molecular dynamics, fully accounting for the resistive phonon-phonon scattering processes through the anharmonic terms of the interatomic potential energy function.
Abstract: Owing to their long phonon mean free paths (MFPs) and high thermal conductivity, carbon nanotubes (CNTs) are ideal candidates for, e.g., removing heat from electronic devices. It is unknown, however, how the intrinsic phonon MFPs depend on vibrational frequency in nonequilibrium. We determine the spectrally resolved phonon MFPs in isotopically pure CNTs from the spectral phonon transmission function calculated using nonequilibrium molecular dynamics, fully accounting for the resistive phonon-phonon scattering processes through the anharmonic terms of the interatomic potential energy function. Our results show that the effective room temperature MFPs of low-frequency phonons ($fl0.5$ THz) exceed $10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$, while the MFP of high-frequency phonons ($f\ensuremath{\gtrsim}20$ THz) is in the range 10--100 nm. Because the determined MFPs directly reflect the resistance to energy flow, they can be used to accurately predict the thermal conductivity for arbitrary tube lengths by calculating a single frequency integral. The presented results and methods are expected to significantly improve the understanding of nonequilibrium thermal transport in low-dimensional nanostructures.

151 citations


Journal ArticleDOI
TL;DR: In this article, thermal conductivity measurements of thin Si membranes spanning a wide thickness range were used to characterize how bulk thermal conductivities are distributed over phonon mean free paths, and a noncontact transient thermal grating technique was used to measure the thermal conductive of suspended Si membranes ranging from 15-1500 nm in thickness.
Abstract: Knowledge of the mean-free-path distribution of heat-carrying phonons is key to understanding phonon-mediated thermal transport. We demonstrate that thermal conductivity measurements of thin membranes spanning a wide thickness range can be used to characterize how bulk thermal conductivity is distributed over phonon mean free paths. A noncontact transient thermal grating technique was used to measure the thermal conductivity of suspended Si membranes ranging from 15--1500 nm in thickness. A decrease in the thermal conductivity from 74--13% of the bulk value is observed over this thickness range, which is attributed to diffuse phonon boundary scattering. Due to the well-defined relation between the membrane thickness and phonon mean-free-path suppression, combined with the range and accuracy of the measurements, we can reconstruct the bulk thermal conductivity accumulation vs. phonon mean free path, and compare with theoretical models.

125 citations


Journal ArticleDOI
TL;DR: An implementation of a nanoscale thermal conductivity spectroscopy technique that allows for the study of mean free path distributions in optically absorbing materials with relatively simple fabrication and a straightforward analysis scheme.
Abstract: Heat conduction in semiconductors and dielectrics depends upon their phonon mean free paths that describe the average travelling distance between two consecutive phonon scattering events. Nondiffusive phonon transport is being exploited to extract phonon mean free path distributions. Here, we describe an implementation of a nanoscale thermal conductivity spectroscopy technique that allows for the study of mean free path distributions in optically absorbing materials with relatively simple fabrication and a straightforward analysis scheme. We pattern 1D metallic grating of various line widths but fixed gap size on sample surfaces. The metal lines serve as both heaters and thermometers in time-domain thermoreflectance measurements and simultaneously act as wire-grid polarizers that protect the underlying substrate from direct optical excitation and heating. We demonstrate the viability of this technique by studying length-dependent thermal conductivities of silicon at various temperatures. The thermal conductivities measured with different metal line widths are analyzed using suppression functions calculated from the Boltzmann transport equation to extract the phonon mean free path distributions with no calibration required. This table-top ultrafast thermal transport spectroscopy technique enables the study of mean free path spectra in a wide range of technologically important materials.

124 citations


Journal ArticleDOI
TL;DR: In this paper, a mixed concrete with 39.195% magnetite Fe 3 O 4 and 15.678% lead oxide PbO, named Concrete 6 in this study, has shown the best mass attenuation coefficient, exposure buildup factor and HVL values among other mixes thus minimizing the exposure rate to the acceptable levels.

111 citations


Journal ArticleDOI
TL;DR: It is demonstrated that the remarkably lower thermal conductivity of penta-graphene compared with graphene results from the lower phonon group velocities and fewer collective phonon excitations.
Abstract: Using classical equilibrium molecular dynamics simulations and applying the original Tersoff interatomic potential, we study the thermal transport property of the latest two dimensional carbon allotrope, penta-graphene. It is predicted that its room-temperature thermal conductivity is about 167 W/mK, which is much lower than that of graphene. With normal mode decomposition, the accumulated thermal conductivity with respect to phonon frequency and mean free path is analyzed. It is found that the acoustic phonons make a contribution of about 90% to the thermal conductivity, and phonons with mean free paths larger than 100 nm make a contribution over 50%. We demonstrate that the remarkably lower thermal conductivity of penta-graphene compared with graphene results from the lower phonon group velocities and fewer collective phonon excitations. Our study highlights the importance of structure-property relationship and provides better understanding of thermal transport property and valuable insight into thermal management of penta-graphene.

90 citations


Journal ArticleDOI
TL;DR: In this paper, the mean free path (MFP) of phonons associated with grain boundary scattering in polycrystalline nanostructures is calculated by developing a Monte Carlo ray tracing transmission model that can be applied to arbitrary geometries.
Abstract: We have calculated the mean free path (MFP) of phonons associated with grain boundary scattering in polycrystalline nanostructures, by developing a Monte Carlo ray tracing transmission model that can be applied to arbitrary geometries. The calculations for various log-normal grain-size distributions realized by Voronoi diagrams and genetic algorithms show that the boundary-scattering MFP in a polycrystalline nanostructure is 20%–30% longer than that in a simple cubic structure with the same average grain size (defined by matching grain volumes). The impact on thermal conductivity is quantified for nanocrystalline silicon by using Matthiessen's rule to combine boundary scattering with intrinsic phonon-phonon scattering. The result reveals that the thermal conductivity depends strongly on the average grain size but only weakly on the breadth of the grain-size distribution, and thus, the simple cubic structure is a reasonable approximation for the polydisperse grain structure of actual materials.

84 citations


Journal ArticleDOI
TL;DR: In this article, a semi-analytical series expansion method was proposed to solve the transient, frequency-dependent Boltzmann transport equation for thin films with thicknesses comparable to phonon mean free paths.
Abstract: Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films

78 citations


Journal ArticleDOI
TL;DR: In this paper, a reconstruction method was presented to obtain the mean free path (MFP) spectra of nanostructures from variable-length thermal conductivity measurements, showing that 70% of the heat in graphene is carried by phonons with MFPs longer than 1 micron.
Abstract: Thermal conductivity measurements over variable lengths on nanostructures such as nanowires provide important information about the mean free paths (MFPs) of the phonons responsible for heat conduction. However, nearly all of these measurements have been interpreted using an average MFP even though phonons in many crystals possess a broad MFP spectrum. Here, we present a reconstruction method to obtain MFP spectra of nanostructures from variable-length thermal conductivity measurements. Using this method, we investigate recently reported length-dependent thermal conductivity measurements on SiGe alloy nanowires and suspended graphene ribbons. We find that the recent measurements on graphene imply that 70% of the heat in graphene is carried by phonons with MFPs longer than 1 micron.

72 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a theoretical and experimental study on how thickness and microstructure affect the properties of Ag thin films, and they are able to successfully model the electrical resistivity and IR optical response using a thickness dependent electronic scattering time.
Abstract: The optical and electrical response of metal thin films approaching thicknesses in the range of the electron mean free path is highly affected by electronic scattering with the interfaces and defects. Here, we present a theoretical and experimental study on how thickness and microstructure affect the properties of Ag thin films. We are able to successfully model the electrical resistivity and IR optical response using a thickness dependent electronic scattering time. Remarkably, the product of electronic scattering time and resistivity remains constant regardless of the thickness (τx ρ = C), with a value of 59 ± 2 μΩ cm ⋅ fs for Ag films in the investigated range from 3 to 74 nm. Our findings enable us to develop a theoretically framework that allows calculating the optical response of metal thin films in the IR by using their measured thickness and resistivity. An excellent agreement is found between experimental measurements and predicted values. This study also shows the theoretical lower limit for emi...

Journal ArticleDOI
TL;DR: In this paper, the average phonon mean free path in the c-axis direction of graphite was shown to be around 200nm at room temperature, much larger than the commonly believed value of just a few nanometers.
Abstract: We report on experimental studies of the average phonon mean free path in the c-axis direction of graphite Through systematically measuring the cross-plane thermal conductivity of thin graphite flakes with thickness ranging from 24 nm to 714 nm via a differential three omega method, we demonstrate that the average phonon mean free path in the c-axis direction of graphite is around 200 nm at room temperature, much larger than the commonly believed value of just a few nanometers This study provides direct experimental evidence for the recently projected very long phonon mean free path along the c-axis of graphite

Journal ArticleDOI
TL;DR: In this paper, a review of the thermal conductivity accumulation function is presented, including transient thermal grating, time domain thermoreflectance, and broadband frequency domain thermodynamic properties.
Abstract: The thermal conductivity of a material or device is dependent on its characteristic dimension. When the characteristic dimension is commensurate to the mean free paths of thermal energy carriers, the thermal conductivity decreases. The precise relationship between characteristic size and thermal conductivity, which depends on the distribution of energy carrier mean free paths in the material, is not straightforward to determine experimentally. The utility of this relationship has led many researchers to study the mean free path dependent contributions of thermal energy carriers to the thermal conductivity of materials, known as the thermal conductivity accumulation function. This review highlights a number of recent experimental results and techniques used to study the thermal conductivity accumulation function, including transient thermal grating, time domain thermoreflectance, and broadband frequency domain thermoreflectance. In these techniques, nondiffusive thermal transport is induced (i.e., thermal ...

Journal ArticleDOI
TL;DR: In this paper, a systematic study of phonon thermal conductivity in multiple component solid solutions represented by Lennard-Jones (LJ) potentials was performed, and the conditions that minimize phonon mean free path via extreme alloy complexity, by varying the composition and the elements (differing in mass, atomic radii, and cohesive energy).

Journal ArticleDOI
TL;DR: The UGKS for frequency-dependent radiative system is developed and seems to be the first discrete ordinate method (DOM) for the accurate capturing of multiple frequency radiative transport physics from ballistic particle motion to the diffusive wave propagation.

Journal ArticleDOI
TL;DR: In this article, the authors developed a computational framework based on the Boltzmann transport equation (BTE) with the ability to compute thermal transport in nanostructured materials of any geometry using, as the only input, the bulk cumulative thermal conductivity.
Abstract: We develop a computational framework, based on the Boltzmann transport equation (BTE), with the ability to compute thermal transport in nanostructured materials of any geometry using, as the only input, the bulk cumulative thermal conductivity. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path (MFP) distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with the frequency-dependent (FD) approach. Second, when the MFP distribution is available from theoretical models, our approach allows one to include easily the material dispersion in the calculations without discretizing the phonon frequencies for all polarizations thereby reducing considerably computational effort. Furthermore, after deriving the ballistic and diffusive limits of our model, we develop a multiscale method that couples phonon transport across different scales, enabling efficient simulations of materials with wide phonon MFP distributions length. After validating our model against the FD approach, we apply the method to porous silicon membranes and find good agreement with experiments on mesoscale pores. By enabling the investigation of thermal transport in unexplored nanostructured materials, our method has the potential to advance high-efficiency thermoelectric devices.

Journal ArticleDOI
TL;DR: It is concluded that complete antibunching at room temperature requires an enhancement of the exciton-exciton annihilation rate that may become realizable in SWCNTs allowing for strong exciton localization.
Abstract: Pump-dependent photoluminescence imaging and second-order photon correlation studies have been performed on individual single-walled carbon nanotubes (SWCNTs) at room temperature. These studies enable the extraction of both the exciton diffusion constant and the Auger recombination coefficient. A linear correlation between these parameters is attributed to the effect of environmental disorder in setting the exciton mean free path and capture-limited Auger recombination at this length scale. A suppression of photon antibunching is attributed to the creation of multiple spatially nonoverlapping excitons in SWCNTs, whose diffusion length is shorter than the laser spot size. We conclude that complete antibunching at room temperature requires an enhancement of the exciton-exciton annihilation rate that may become realizable in SWCNTs allowing for strong exciton localization.

Journal ArticleDOI
TL;DR: In this article, the heating-frequency dependence of the apparent thermal conductivity in a semi-infinite body with periodic planar surface heating is explained by an analytical solution to the Boltzmann transport equation.
Abstract: The heating-frequency dependence of the apparent thermal conductivity in a semi-infinite body with periodic planar surface heating is explained by an analytical solution to the Boltzmann transport equation. This solution is obtained using a two-flux model and gray mean free time approximation and verified numerically with a lattice Boltzmann method and numerical results from the literature. Extending the gray solution to the nongray regime leads to an integral transform and accumulation-function representation of the phonon scattering spectrum, where the natural variable is mean free time rather than mean free path, as often used in previous work. The derivation leads to an approximate cutoff conduction similar in spirit to that of Koh and Cahill [Phys. Rev. B 76, 075207 (2007)] except that the most appropriate criterion involves the heater frequency rather than thermal diffusion length. The nongray calculations are consistent with Koh and Cahill's experimental observation that the apparent thermal conductivity shows a stronger heater-frequency dependence in a SiGe alloy than in natural Si. Finally these results are demonstrated using a virtual experiment, which fits the phase lag between surface temperature and heat flux to obtain the apparent thermal conductivity and accumulation function.

Journal ArticleDOI
TL;DR: An effective model is provided, which can successfully explain features of the absorption spectra at low frequencies, and is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.
Abstract: The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150≤T≤200 K, where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Journal ArticleDOI
TL;DR: In this article, the authors studied the thermal conduction in silicon nanowires that exhibit a diameter constriction and showed that thermal conductivity of the nanostructures can be adjusted by tailoring the constriction shape.

Journal ArticleDOI
TL;DR: In this article, angle-resolved photoelectron spectroscopy of aerosol particles is proposed as an alternative way to determine the electron mean free path of low energy electrons in solid and liquid materials.
Abstract: We propose angle-resolved photoelectron spectroscopy of aerosol particles as an alternative way to determine the electron mean free path of low energy electrons in solid and liquid materials. The mean free path is obtained from fits of simulated photoemission images to experimental ones over a broad range of different aerosol particle sizes. The principal advantage of the aerosol approach is twofold. First, aerosol photoemission studies can be performed for many different materials, including liquids. Second, the size-dependent anisotropy of the photoelectrons can be exploited in addition to size-dependent changes in their kinetic energy. These finite size effects depend in different ways on the mean free path and thus provide more information on the mean free path than corresponding liquid jet, thin film, or bulk data. The present contribution is a proof of principle employing a simple model for the photoemission of electrons and preliminary experimental data for potassium chloride aerosol particles.

Journal ArticleDOI
TL;DR: Electrical resistivity is shown to saturate in solid-density aluminum in the warm dense matter regime in the finite-temperature Ziman-Evans formula and the mean free path is estimated using the Drude law.
Abstract: Electrical resistivity is shown to saturate in solid-density aluminum in the warm dense matter regime. Calculations are done using the average-atom model SCAALP and the finite-temperature Ziman-Evans formula for electrical resistivity. The mean free path is estimated using the Drude law. This mean free path is shown to present a minimum of the order of the interatomic spacing.

Journal ArticleDOI
TL;DR: In this article, an analytic solution of the transient, frequency-dependent Boltzmann equation to highly anisotropic solids and examine its predictions for graphite is presented. But the authors do not consider the thermal properties of graphite.
Abstract: The thermal properties of anisotropic crystals are of both fundamental and practical interest, but transport phenomena in anisotropic materials such as graphite remain poorly understood because solutions of the Boltzmann equation often assume isotropy. Here, we extend an analytic solution of the transient, frequency-dependent Boltzmann equation to highly anisotropic solids and examine its predictions for graphite. We show that this simple model predicts key results, such as long c -axis phonon mean free paths and a negative correlation of cross-plane thermal conductivity with in-plane group velocity, that were previously observed with computationally expensive molecular-dynamics simulations. Further, using our analytic solution, we demonstrate a method to reconstruct the anisotropic mean free path spectrum of crystals with arbitrary dispersion relations without any prior knowledge of their harmonic or anharmonic properties using observations of quasiballistic heat conduction. These results provide a useful analytic framework to understand thermal transport in anisotropic crystals.

Journal ArticleDOI
TL;DR: In this paper, the authors derived an invariant of heat conduction and a simple formula for the crossplane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems.
Abstract: Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both the steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that these components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path (MFP), and they exhibit the diffusive behavior as predicted by the Fourier's law of heat conduction when this ratio is much larger than unity. In contrast, in the ballistic regime when this ratio is comparable to or smaller than unity, the steady-state temperature tends to be independent of position, while the amplitude and the phase of the modulated temperature appear to be lower than those determined by the Fourier's law. Furthermore, we derive an invariant of heat conduction and a simple formula for the cross-plane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems. This work represents the Boltzmann transport equation-based extension of the Rosencwaig and Gersho work [J. Appl. Phys. 47, 64 (1976)], which is based on the Fourier's law and has widely been used as the theoretical framework for the development of photoacoustic and photothermal techniques. This work might shed some light on developing a theoretical basis for the determination of the phonon MFP and relaxation time using ultrafast laser-based transient heating techniques.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed quasiballistic heat conduction in a two-dimensional transient grating experiment, which can occur both in and cross plane using an analytic Green's function of the Boltzmann equation.
Abstract: Transient grating spectroscopy has emerged as a useful technique to study thermal phonon transport because of its ability to perform thermal measurements over length scales comparable to phonon mean free path (MFPs). Although several prior works have performed theoretical studies of quasiballistic heat conduction in transient grating, the analysis methods are either restricted to one spatial dimension or require phenomenological fitting parameters. Here, we analyze quasiballistic transport in a two-dimensional transient grating experiment in which heat conduction can occur both in and cross plane using an analytic Green's function of the Boltzmann equation we recently reported that is free of fitting parameters. We demonstrate a method by which phonon MFPs can be extracted from these measurements, thereby extending the MFP spectroscopy technique using transient grating to opaque bulk materials.

Journal ArticleDOI
TL;DR: The results contradict the notion that phonon drag is negligible in degenerate semiconductors at temperatures relevant for thermoelectric energy conversion and recommend a revised theory of electron-phonon momentum exchange that accounts for a phonon mean free path spectrum.
Abstract: Existing theory and data cannot quantify the contribution of phonon drag to the Seebeck coefficient (S) in semiconductors at room temperature. We show that this is possible through comparative measurements between nanowires and the bulk. Phonon boundary scattering completely quenches phonon drag in silicon nanowires enabling quantification of its contribution to S in bulk silicon in the range 25–500 K. The contribution is surprisingly large (∼34%) at 300 K even at doping of ∼3 × 1019 cm–3. Our results contradict the notion that phonon drag is negligible in degenerate semiconductors at temperatures relevant for thermoelectric energy conversion. A revised theory of electron–phonon momentum exchange that accounts for a phonon mean free path spectrum agrees well with the data.

Journal ArticleDOI
TL;DR: In this article, effective attenuation lengths (EALs) for Si 2s1/2, Cu 2p3/2 and Ag 3d5/2 photoelectrons excited by Mg Kα and Al Kα X-rays were calculated from the TA formalism and from Monte Carlo simulations using photoionization cross sections from the dipole and non-dipole approximations.

Journal ArticleDOI
TL;DR: In this paper, the Boltzmann transport equation was applied to calculate the thermal conductivity of ZnS, ZnSe, and ZnTe at nanostructure sizes around 0.1-0.2 μm.
Abstract: Systematic first principles studies of zinc-chalcogenides have been performed to understand their thermal transport behaviour. We have applied the Boltzmann transport equation in the relaxation time approximation to calculate the thermal conductivity of ZnS, ZnSe, and ZnTe. We find a thermal conductivity cross-over between ZnS and ZnSe at nanostructure sizes around 0.1–0.2 μm and explain this in terms of the different contributions of phonon modes in these materials. We study the effect of nanostructuring using both the diffusive boundary scattering and confined mean free path limit and discuss the variations in the results. Furthermore, we show the strong influence of isotope scattering on the thermal conductivity. The calculated thermal conductivity is found to be strongly dependent on the volume and we explain the observed differences between local density and generalized gradient approximation calculations. We compare further calculated thermal properties, such as the thermal expansion coefficient, to experiment to validate our approach.

Journal ArticleDOI
TL;DR: In this article, the average distance traveled by gas molecules between intermolecular collisions, known as the mean free path (MFP), is a key parameter for characterizing gas flows in the entire Knudsen regime.
Abstract: Average distance traveled by gas molecules between intermolecular collisions, known as the mean free path (MFP), is a key parameter for characterizing gas flows in the entire Knudsen regime. Recent literature presents variations in MFP as a function of the surface confinement, which is in disagreement with the kinetic theory and leads to wrong physical interpretations of nanoscale gas flows. This controversy occurs due to erroneous definition and calculation practices, such as consideration of gas wall collisions, using local bins smaller than a MFP, and utilizing time frames shorter than a mean collision time in the MFP calculations. This study reports proper molecular MFP calculations in nanoscale confinements by using realistic molecular surfaces. We utilize molecular dynamics (MD) simulations to calculate gas MFP in three-dimensional periodic systems of various sizes and for force-driven gas flows confined in nano-channels. Studies performed in the transition flow regime in various size nano-channels and under a range of gas–surface interaction strengths have shown isotropic mean travelled distance and MFP values in agreement with the kinetic theory regardless of the surface forces and surface adsorption effects. Comparison of the velocity profiles obtained in MD simulations with the linearized Boltzmann solutions at predicted Knudsen values shows good agreement in the bulk of the channels, while deviations in the near wall region due to the influence of surface forces are reported.

Journal ArticleDOI
TL;DR: In this article, it was shown that at T∼ 1mK the density of quasiparticlesis so small that values of λ and Dare can be determined by the array of aerogel strands and do not depend on T.
Abstract: . Atlow enough temperatures (T<10mK) aerogel strandslimit the mean free path and the spin diffusion coeffi-cient, so that at T∼ 1mK the density of quasiparticlesis so small that values of λand Dare fully determinedby the array of aerogel strands and do not depend on T.Such behavior was observed in the first measurementsof spin diffusion in