Phonon Relaxation Time Research Articles

Uncertainty quantification of thermal conductivities from equilibrium molecular dynamics simulations

Equilibrium molecular dynamics (EMD) simulations along with the Green-Kubo formula have been widely used to calculate lattice thermal conductivities. Previous studies, however, focused primarily on the calculated thermal conductivities, with the uncertainty of the thermal conductivities remaining poorly understood. In this paper, we study the quantification of the uncertainty by using solid argon, silicon, and germanium as model material systems, and examine the origin of the observed uncertainty. We find that the uncertainty increases with the upper limit of the correlation time, tcorre,UL, and decreases with the total simulation time, ttotal, whereas the velocity initialization seed, simulation domain size, temperature, and type of material have minimal effects. The relative uncertainties of the thermal conductivities, σkx/kx,ave, for solid argon, silicon, and germanium under different simulation conditions all follow a similar trend, which can be fit with a “universal” square-root relation, as σkx/kx,ave=2(ttotal/tcorre,UL)-0.5. We have also conducted statistical analysis of the EMD-predicted thermal conductivities and derived a formula that correlates the relative error bound (Q), confidence level (P), tcorre,UL,ttotal, and number of independent simulations (N). We recommend choosing tcorre,UL to be 5–10 times the effective phonon relaxation time, τeff, and choosing ttotal and N based on the desired relative error bound and confidence level. This study provides new insights into understanding the uncertainty of EMD-predicted thermal conductivities. It also provides a guideline for running EMD simulations to achieve a desired relative error bound with a desired confidence level and for reporting EMD-predicted thermal conductivities.

Resonance phonon approach to phonon relaxation time and mean free path in one-dimensional nonlinear lattices.

We extend a previously proposed resonance phonon approach that is based on the linear response theory. By studying the complex response function in depth, we work out the phonon relaxation time besides the oscillating frequency of the phonons in a few one-dimensional nonlinear lattices. The results in the large wave-number-k regime agree with the expectations of the effective phonon theory. However, in the small-k limit they follow different scaling laws. The phonon mean free path can also be calculated indirectly. It coincides well with that derived from the anharmonic phonon approach. A power-law divergent heat conduction, i.e., the heat conductivity κ depends on lattice length N by κ∼N^{β} with β>0, then is supported for the momentum-conserving lattices. Furthermore, this approach can be applied to diatomic lattices. So obtained relaxation time quantitatively agrees with that from the effective phonon theory. As for the mean free path, the resonance phonon approach can detect both the acoustic and the optical branches, whereas the anharmonic phonon approach can only detect a combined branch, i.e., the acoustic branch for small k and the optical branch for large k.

Impact of grain boundary characteristics on lattice thermal conductivity: A kinetic theory study on ZnO

Grain boundaries are natural interfaces present in polycrystalline materials and have an important role in transport properties. In this work, the impact of grain boundary crystallographic mismatch, local impurity modulation, and spacing on lattice thermal conductivity is examined from the kinetic theory approach, with ZnO as a case study. We employ a dislocation-based model to describe the grain boundary scatterings of phonons, in which structural characteristics of grain boundaries are explicitly built-in and grain boundary scattering time depends on phonon frequency. This is in contrast to the gray model or the commonly used Casimir limit, which is blind to both grain boundary features and phonon frequency. We show that the lattice thermal conductivity generally decreases with grain boundary misorientation angle, and this dependence is significant for small grain boundary spacing while it tends to diminish for a large one. Intriguingly, our results show that local grain boundary chemistry can affect even more substantially than the crystallographic misfit on phonon relaxation time and interfacial thermal (Kapitza) resistance. Our results suggest new opportunities in tuning lattice thermal conductivity besides the nanostructure engineering approach, and demonstrates the synergetic effects of grain boundary characteristics on phonon conduction in polycrystals.

First principles kinetic-collective thermal conductivity of semiconductors

A fully predictive Kinetic Collective Model using first principles phonon spectra and relaxation times is presented. Thermal conductivity values obtained for Si, Ge, C (diamond) and GaAs in a wide range of sizes and temperatures have good agreement with experimental data without the use of any fitting parameter. This validation of the model open the door to discuss how the precise combination of kinetic and collective contributions to heat transport could provide a useful framework to interpret recent complex experiments displaying non-Fourier behavior.

A Practical Approach to Evaluate Lattice Thermal Conductivity in Two-Phase Thermoelectric Alloys for Energy Applications.

Modelling of the effects of materials’ microstructure on thermal transport is an essential tool for materials design, and is particularly relevant for thermoelectric (TE) materials converting heat into electrical energy. Precipitates dispersed in a TE matrix act as phonon-scattering centers, thereby reducing thermal conductivity. We introduce a practical approach to tailor a definite precipitate size distribution for a given TE matrix, and implement it for PbTe. We evaluate vibrational properties from first principles, and develop an expression for phonon relaxation time that considers both matrix vibrational properties and precipitate size distribution. This provides us with guidelines for optimizing thermal conductivity.

Thermal transport in graphene with defect and doping: Phonon modes analysis

The effects of defect and isotopic doping with different ratios on the thermal conductivity of graphene are investigated by using non-equilibrium molecular dynamics simulations and normal mode analysis method. In contrast to the persisted size dependent thermal conductivity in the pristine graphene, thermal conductivity of defected graphene quickly saturates when the size is greater than 100 nm. Similar to the pristine graphene, we find the thermal conductivity of defected and doped graphene follows ∼T−α behavior, and the power exponent α is sensitive to the defect and doping ratio. The spectral phonon relaxation time and normalized accumulation thermal conductivity with respect to the phonon mean free path (MFP) reveal that the long-MFP phonon modes are strongly suppressed in the defected and doped graphene, resulting in the suppressed size dependence and the weaker temperature dependence of the thermal conductivity compared to the pristine graphene. The phonon modal analysis in our work establishes a deep understanding of the defect and doping effects on the thermal transport in graphene, which would provide effective guidance to the graphene-based phonon engineering applications.

Variation of thermal expansion at low temperature and phonon relaxation time in graphene with temperature

Considering the anharmonic vibrations and the interactions between electron and phonon of atoms, in this article we study the temperature dependence of Grneisen parameter, thermal expansion coefficient at low temperature and phonon relaxation time by using the theory and method of solid state physics. The influences of the anharmonic vibration of the atom on the above parameters are further discussed. The obtained results are as follows. 1) The thermal expansion coefficient of graphene is a negative value when the temperature drops below room temperature. The absolute value of the thermal expansion coefficient of graphene increases monotonically with the increase of temperature. The thermal expansion coefficient of graphene is-3.64×10-6 K-1 at room temperature. 2) The value of Grneisen parameter is zero in the harmonic approximation. If the anharmonic vibration is considered, the Grneisen parameter will increase slowly with the increase of temperature. Its value is between 1.40 and1.42 and the change is almost linear. And we find that the influence of the second anharmonic term is less than that of the first anharmonic term on Grneisen parameter. 3) The phonon relaxation time decreases with the increase of temperature. The rate changes rapidly at low temperature (T<10 K), then it changes very slowly. The phonon relaxation time is almost inversely proportional to temperature when the temperature is higher than 300 K.

Thermal Transport and Rectification Properties of Bamboo-Like SiC Polytypes Nanowires

Bamboo-like SiC nanowires (NWs) have specific geometric shapes, which have the potential to suppress thermal conductivity by phonon boundary scattering. In this work, phonon transport behaviors in the 3C-SiC, 4H-SiC, and 6H-SiC crystal lattices are studied by the Monte Carlo (MC) method, including impurity scattering, boundary scattering, and Umklapp scattering. Phonon relaxation times for Umklapp (U) scattering for the above three SiC polytypes are calculated from the respective phonon spectra, which have not been reported in the literature. Diffuse boundary scattering and thermal rectification with different aspect ratios are also studied at different temperatures. It is found that the thermal conductivities of the bamboo-like SiC polytypes can be lowered by two orders of magnitude compared with the bulk values by contributions from boundary scattering. Compared with bamboo-like 4H-SiC and 6H-SiC NWs, 3C-SiC has the largest U scattering relaxation rate and boundary scattering rate, which leads to its lowest thermal conductivities. The thermal conductivity in the positive direction is larger than that in the negative direction because of its lower boundary scattering relaxation rate.

A systematic investigation of thermal conductivities of transition metal dichalcogenides

Although the thermal conductivities of MoS2 and WS2 have been reported by some experimental and theoretical studies, the results are inconsistent. Here, thermal transport properties of twelve types of single layer transition metal dichalcogenides (TMDs) MX2 (M=Cr, Mo, W; X=O, S, Se, Te) are investigated systematically, by solving Boltzmann transport equation based on first-principle calculations. After accurate considering the size effect and boundary scattering, we find that our calculations can fit the experimental results very well. Moreover, diverse transport properties in TMDs are revealed, and an abnormal dependence of thermal conductivity on atomic mass is observed. In most MX2 structures, the thermal conductivities decrease with the increase of mass of atom M or X. However, the thermal conductivities of sulfides MS2 and selenides MSe2 increase as the M changes from Cr to Mo to W, which is contradictory to our traditional understanding. A detailed calculation indicates that the abnormal trend is originated from the rapid increase of phonon relaxation time. Our studies provide important information for thermal transport abilities in TMDs.

Theoretical study of built-in-polarization effect on relaxation time and mean free path of phonons in Al x Ga1−x N alloy

In this article we have investigated theoretically the effect of built-in-polarization field on various phonon scattering mechanisms in Al x Ga 1−x N alloy. The built-in-polarization field of Al x Ga 1−x N modifies the elastic constant, group velocity of phonons and Debye temperature. As a result, various phonon scattering mechanisms are changed. Important phonon scattering mechanisms such as normal scattering, Umklapp scattering, point defect scattering, dislocation scattering and phonon–electron scattering processes have been considered in the computation. The combined relaxation time due to above-mentioned scattering mechanisms has also been computed as a function of phonon frequency for various Al compositions at room temperature. It is found that combined relaxation time is enhanced due to built-in-polarization effect and makes phonon mean free path longer, which is required for higher optical, electrical and thermal transport processes. The result can be used to determine the effect of built-in-polarization field on optical and thermal properties of Al x Ga 1−x N and will be useful, particularly, for improvement of thermoelectric performance of Al x Ga 1−x N alloy through polarization engineering.

Temperature Dependence of Anisotropic Thermal‐Conductivity Tensor of Bulk Black Phosphorus

The anisotropic thermal-conductivity tensor of bulk black phosphorus (BP) for 80 ≤T ≤ 300 K is reported. Despite the anisotropy, phonons are predominantly scattered by Umklapp processes in all the crystallographic orientations. It is also found that the phonon mean-free-paths of BP are rather long (up to 1 µm) in the through-plane direction.

Reconstruction of the phonon relaxation times using solutions of the Boltzmann transport equation

We present a method for reconstructing the phonon relaxation time distribution ${\ensuremath{\tau}}_{\ensuremath{\omega}}=\ensuremath{\tau}(\ensuremath{\omega})$ (including polarization) in a material from thermal spectroscopy data. The distinguishing feature of this approach is that it does not make use of the effective thermal conductivity concept and associated approximations. The reconstruction is posed as an optimization problem in which the relaxation times ${\ensuremath{\tau}}_{\ensuremath{\omega}}=\ensuremath{\tau}(\ensuremath{\omega})$ are determined by minimizing the discrepancy between the experimental relaxation traces and solutions of the Boltzmann transport equation for the same problem. The latter may be analytical, in which case the procedure is very efficient, or numerical. The proposed method is illustrated using Monte Carlo solutions of thermal grating relaxation as synthetic experimental data. The reconstruction is shown to agree very well with the relaxation times used to generate the synthetic Monte Carlo data and remains robust in the presence of uncertainty (noise).

Phonon thermal properties of graphene from molecular dynamics using different potentials.

Phonon thermal transport in graphene has attracted significant interest in recent years. Phonon thermal properties of graphene are investigated by molecular dynamics simulations using the Tersoff, Tersoff-2010, REBO, and AIREBO potentials. By calculating the phonon properties and thermal conductivity of graphene, the performance of the potentials is evaluated based on comparisons with experimental data. It shows that the Tersoff-2010 and REBO display better dispersion curves for graphene than the original Tersoff and AIREBO. The Tersoff-2010 correctly provides the Γ point phonon velocities of the LA and TA branches as well as the G peak frequency with a value of 46 THz. In addition, the acoustic phonon relaxation time derived from the Tersoff-2010 satisfies the ideal relation "τ-1 ∝ ν2." It is also found that the Tersoff-2010 provides the highest graphene thermal conductivity among the used potentials, and estimates about 30.0% contribution for flexural phonons to the total thermal conductivity. By comparison, the Tersoff-2010 potential is demonstrated to be the most suitable one to describe the phonon thermal properties of graphene.

Analysis of the temperature dependence of the thermal conductivity of insulating single crystal oxides

The temperature dependence of the thermal conductivity of 27 different single crystal oxides is reported from ≈20 K to 350 K. These crystals have been selected among the most common substrates for growing epitaxial thin-film oxides, spanning over a range of lattice parameters from ≈3.7 A to ≈12.5 A. Different contributions to the phonon relaxation time are discussed on the basis of the Debye model. This work provides a database for the selection of appropriate substrates for thin-film growth according to their desired thermal properties, for applications in which heat management is important.

Attenuation of 7 GHz surface acoustic waves on silicon

We measured the attenuation of GHz frequency surface acoustic waves (SAWs) on the Si (001) surface using an optical pump-probe technique at temperatures between 300 and 600 K. SAWs are generated and detected by a 700 nm Al grating fabricated by nanoimprint lithography. The grating for SAW generation is separated from the grating for SAW detection by $\ensuremath{\approx}150\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$. The amplitude of SAWs is attenuated by coupling to bulk waves created by the Al grating, diffraction due to the finite size of the source, and the intrinsic relaxational Akhiezer damping of elastic waves in Si. Thermal phonon relaxation time and Gr\"uneisen parameters are fitted using temperature-dependent measurement. The $fQ$ product of a hypothetical micromechanical oscillator limited by Akhiezer damping at this frequency is $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{13}$ Hz.

Boundary scattering effect on the thermal conductivity of nanowires

Tuning the surface boundary structures of crystal nanowires (NWs) is one of the most popular ways to control the thermal conductivity of NWs. In this paper, non-equilibrium molecular dynamic simulations (NEMD) and time domain normal mode analysis (TDNMA) are performed to investigate the thermal transport properties of Ar (length of 52.9 nm, width of 4.23 nm) and Ge (56.5 nm long and 4.52 nm wide) NWs with different surface boundary structures. Results show that both the total and modal thermal conductivity have a dramatic difference among the NWs with the same diameter (the maximal and minimal thermal conductivity of Ar (Ge) NWs are 1.25 (15.3) and 0.60 (5.64) W/mK, respectively), which suggests the efficiency of nanoscale thermoelectric devices and heat dissipation devices can be largely tuned by only changing the boundary orientation. The fundamental mechanism responsible for such a discrepancy is found to mainly originate from different phonon group velocity (combined with phonon relaxation time for Ar NWs). The results are quite helpful for understanding the boundary scattering effect on thermal transport and also facilitating the design of nanoscale devices by tailoring the boundary structures.

Exploration of the low thermal conductivities of γ-Y2Si2O7, β-Y2Si2O7, β-Yb2Si2O7, and β-Lu2Si2O7 as novel environmental barrier coating candidates

Thermal conductivities of γ-Y2Si2O7, β-Y2Si2O7, β-Yb2Si2O7, and β-Lu2Si2O7 were investigated by combined first-principles calculations and experimental evaluation. Theoretical calculation was used to predict the elastic properties, anisotropic minimum thermal conductivities, and temperature dependent lattice thermal conductivities. Experimentally, thermal conductivities of these disilicates were measured from room temperature to 1273K. In addition, their experimental intrinsic lattice thermal conductivities were determined from the corrected thermal diffusivity data after removing the extrinsic contributions from phonon scattering by defects and thermal radiation. The experimental lattice thermal conductivities match well with the theoretical predictions. Furthermore, Raman spectra of the disilicates was measured and used to estimate the optical phonon relaxation time. The present results clearly disclose the specific material parameters that determine the low thermal conductivity of RE2Si2O7 and may provide guidelines for the optimal thermal conductivity of rare earth disilicates.

Phonon transport in amorphous carbon using Green–Kubo modal analysis

Amorphous carbon (a-C) is an important material often used in microelectronics. Using a recently developed approach, termed Green–Kubo modal analysis, we were able to calculate the thermal conductivity of a-C, which yielded excellent agreement with experiments, by employing a simple correction to the specific heat. The results show that the heat capacity substantially limits the thermal conductivity of a-C at room temperature and it is dominated by contributions from diffusons between 10 and 40 THz. Furthermore, the phonon relaxation times in a-C do not vary significantly with increasing temperature, which is quite unusual by comparison with the behavior observed for other materials.

Built-in-polarization effect on relaxation time and mean free path of phonons in AlxGa1−xN/GaN heterostructure

In this paper, we have theoretically investigated the effect of built-in-polarization field on various phonon scattering mechanisms in Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure. The built-in-polarization field enhances the elastic constant, phonon velocity and Debye frequency of Al[Formula: see text]Ga[Formula: see text]N alloy. As a result, various phonon scattering mechanisms are modified. Important phonon scattering mechanisms such as normal scattering, Umklapp scattering, point defect scattering, dislocation scattering and phonon–electron scattering processes have been considered. The combined relaxation time due to above scattering mechanisms has also been computed as a function of phonon frequency for various Al contents at room temperature. Our result shows that built-in-polarization field suppresses scattering rates leading to enhanced combined relaxation time. Increased relaxation time implies longer phonon mean free path and enhanced optical and thermal transport properties. The result can be used to determine the effect of built-in-polarization field on optical and thermal properties of Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure and will be useful, particularly, for improvement of thermoelectric performance of Al[Formula: see text]Ga[Formula: see text]N/GaN heterostructure through polarization engineering.

Coherent phonon transport in short-period two-dimensional superlattices of graphene and boron nitride

Promoting coherent transport of phonons at material interfaces is a promising strategy for controlling thermal transport in nanostructures and an alternative to traditional methods based on structural defects. Coherent transport is particularly relevant in short-period heterostructures with smooth interfaces and long-wavelength heat-carrying phonons, such as two-dimensional superlattices of graphene and boron nitride. In this work, we predict phonon properties and thermal conductivities in these superlattices using a normal mode decomposition approach. We study the variation of the frequency dependence of these properties with the periodicity and interface configuration (zigzag and armchair) for superlattices with period lengths within the coherent regime. Our results showed that the thermal conductivity decreases significantly from the first period length (0.44 nm) to the second period length (0.87 nm), 13% across the interfaces and 16% along the interfaces. For greater periods, the conductivity across the interfaces continues decreasing at a smaller rate of 11 W/mK per period length increase (0.43 nm), driven by changes in the phonon group velocities (coherent effects). In contrast, the conductivity along the interfaces slightly recovers at a rate of 2 W/mK per period, driven by changes in the phonon relaxation times (diffusive effects). By changing the interface configuration from armchair to zigzag, the conductivities for all period lengths increase by approximately 7% across the interfaces and 19% along the interfaces.