A Fast Coupled Solver for Phonon Transport in Composites

2013 ◽  
Author(s):  
James M. Loy ◽  
Ajay Vadakkepatt ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Times ◽  
Computational Procedure ◽  
Phonon Transport ◽  
Superior Performance ◽  
Wave Number ◽  
Computational Techniques ◽  
Boltzmann Transport ◽  
Spatial Coupling ◽  
Sequential Solution ◽  
Solution Techniques

In recent years, computational techniques for solving phonon transport have been developed under the framework of the semiclassical Boltzmann Transport Equation (BTE). Early work addressed gray transport, but more recent work has begun to resolve wave vector and polarization dependence, including that in relaxation times. Because the relaxation time in typical materials of interest spans several orders of magnitude, typical solution techniques must address an enormous range of Knudsen numbers in the same problem. Calculation procedures which solve the BTE in phase space sequentially work well in the ballistic limit, but are slow to converge in the thick limit. Unfortunately, both extremes may be encountered simultaneously in typical wave-number (K) -resolved phonon transport problems. In previous work, we developed the coupled ordinate method (COMET) to address this problem. COMET employs a point-coupled solution to resolve coupling in K-space, and embeds this point solver as a relaxation sweep in a geometric multigrid method to maintain spatial coupling. We have demonstrated speedups of up to 200 over conventional sequential solution procedures using this method. COMET also exhibits excellent scaling on multiprocessor platforms, far beyond those obtained by sequential solvers. In this paper, we extend COMET to address interface transport in composites. Just as scattering couples phonons of different wave vectors in the bulk, reflection and transmission couple different wave vectors together at interfaces. Again, sequential solution procedures perform poorly because of the poor algorithmic coupling in K space. A computational procedure based on COMET is developed for composites, addressing multigrid agglomeration strategies to promote stronger K-space coupling at interfaces. The technique is applied to canonical superlattice geometries and superior performance over typical sequential solvers is demonstrated. Furthermore, the method is applied to realistic particle composites employing computational meshes developed from x-ray computed tomography (CT) scans of particulate beds. It is demonstrated to yield solutions where sequential solution techniques fail to converge at all.

Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Thermal Transport ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Oxide Semiconductor ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time model employs a single-mode relaxation time, but the relaxation time is derived from detailed consideration of three-phonon interactions satisfying conservation rules, and is a function of wave vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior. A critical issue in the model development is the role of three-phonon normal (N) scattering processes. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulations by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted thermal conductivities of bulk silicon and silicon thin films with experimental measurements. The model is then used for simulating thermal transport in a silicon metal-oxide-semiconductor field effect transistor (MOSFET) and leads to results close to the full-scattering model, but uses much less computation time.

Modeling the Hotspot Temperature in AlGaN/GaN High Electron Mobility Transistors Using a Non-Gray Phonon BTE Solver

2012 ◽  
Author(s):  
Fatma Nazli Donmezer ◽  
Munmun Islam ◽  
Samuel Graham ◽  
Douglas Yoder
Keyword(s):  
Relaxation Times ◽  
High Electron Mobility Transistors ◽  
Phonon Transport ◽  
Discrete Ordinates ◽  
High Electron ◽  
Boltzmann Transport ◽  
Electron Mobility Transistors ◽  
Drain Side ◽  
Numerical Solver ◽  
Gate Edge

In this work, we utilize electron-phonon Monte Carlo simulations of AlGaN/GaN HEMTs to determine the energy loss rate of electrons in the channel of the transistor as a function of bias conditions. Intense energy transfer from electrons to phonons is observed near the gate edge on the drain side of such devices where the peak electric field exists. This intense energy exchange results in nanometer sized hotspots in the vicinity of the gate edge. In order to account for effects of ballistic phonon transport on temperature near the hotspots, a non-gray Discrete Ordinates Method (DOM) is used as a numerical solver for the phonon Boltzmann Transport Equation (BTE). The non-gray model accounts for dispersion effects of GaN by splitting the dispersion curve of GaN into a finite number of frequency bands. The phonons in each frequency band are assumed to have the same properties with the other phonons in the same band and the relaxation times between these bands are calculated. The results show how energy is redistributed among the available phonon bands and demonstrates which modes are most effective at transporting the thermal energy. Finally, the hotspot temperature predictions obtained by the model are compared to temperatures obtained by gray and continuum modeling approaches to show the discrepancies between different techniques.

scholarly journals Non-Gray Phonon Transport Using a Hybrid BTE-Fourier Solver

2009 ◽  
Author(s):  
James M. Loy ◽  
Dhruv Singh ◽  
Jayathi Y. Murthy
Keyword(s):  
Lattice Energy ◽  
Phonon Transport ◽  
Lattice Temperature ◽  
Boltzmann Transport ◽  
Knudsen Numbers ◽  
Large Spread ◽  
Sequential Solution ◽  
Fourier Model ◽  
Typical Solution ◽  
Fourier Equation

Non-gray phonon transport solvers based on the Boltzmann transport equation (BTE) are frequently employed to simulate sub-micron thermal transport. Typical solution procedures using sequential solution schemes encounter numerical difficulties because of the large spread in scattering rates. For frequency bands with very low Knudsen numbers, strong coupling between the directional BTEs results in slow convergence for sequential solution procedures. In this paper, we present a hybrid BTE-Fourier model which addresses this issue. By establishing a phonon group cutoff (say Kn = 0.1), phonon bands with low Knudsen numbers are solved using a modified Fourier equation which includes a scattering term as well as corrections to account for boundary temperature slip. Phonon bands with high Knudsen numbers are solved using a BTE solver. Once the governing equations are solved for each phonon group, their energies are then summed to find the total lattice energy and correspondingly, the lattice temperature. An iterative procedure combining the lattice temperature determination and the solutions to the modified Fourier and BTE equations is developed. The procedure is shown to work well across a range of Knudsen numbers.

Thermal Conductivity and Phonon Transport Properties of Silicon Using Perturbation Theory and the Environment-Dependent Interatomic Potential

2009 ◽  
Author(s):  
Jose´ A. Pascual-Gutie´rrez ◽  
Jayathi Y. Murthy ◽  
Raymond Viskanta
Keyword(s):  
Thermal Conductivity ◽  
Perturbation Theory ◽  
Carrier Transport ◽  
Interatomic Potential ◽  
Relaxation Times ◽  
Momentum Conservation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Bulk Silicon ◽  
Energy And Momentum

Perturbation theory is used to compute the strength of three-phonon and isotope scattering mechanisms in silicon using the Environment-Dependent Interatomic Potential (EDIP) without resorting to any parameter-fitting. A detailed methodology to accurately find three-phonon processes satisfying energy- and momentum-conservation rules is described. Bulk silicon thermal conductivity values are computed across a range of temperatures and shown to match experimental data well. It is found that about two-thirds of the heat transport in bulk silicon may be attributed to transverse acoustic modes. Effective relaxation times and mean free paths are computed in order to provide a more complete picture of the detailed transport mechanisms and for use with carrier transport models based on the Boltzmann transport equation.

Improved Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2009 ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation ◽  
Thermal Conductivities

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time phonon BTE model employs a single-mode relaxation time idea, but the relaxation time is a function of wave-vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior as well as relaxation times satisfying conservation rules. A critical issue in the model development is the accounting for the role of three-phonon N scattering processes. Direct inclusion of N processes into the anisotropic relaxation time model is not possible because such an inclusion would engender thermal resistance. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulation by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted bulk thermal conductivities of silicon and silicon thin-film thermal conductivities with experimental measurements.

A Fast Hybrid Fourier–Boltzmann Transport Equation Solver for Nongray Phonon Transport

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
James M. Loy ◽  
Jayathi Y. Murthy ◽  
Dhruv Singh
Keyword(s):  
Transport Equation ◽  
Thermal Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Phonon Transport ◽  
Computational Effort ◽  
Boltzmann Transport ◽  
Knudsen Numbers ◽  
Sequential Solution ◽  
Hybrid Solver

Nongray phonon transport solvers based on the Boltzmann transport equation (BTE) are being increasingly employed to simulate submicron thermal transport in semiconductors and dielectrics. Typical sequential solution schemes encounter numerical difficulties because of the large spread in scattering rates. For frequency bands with very low Knudsen numbers, strong coupling between other BTE bands result in slow convergence of sequential solution procedures. This is due to the explicit treatment of the scattering kernel. In this paper, we present a hybrid BTE-Fourier model which addresses this issue. By establishing a phonon group cutoff Knc, phonon bands with low Knudsen numbers are solved using a modified Fourier equation which includes a scattering term as well as corrections to account for boundary temperature slip. Phonon bands with high Knudsen numbers are solved using the BTE. A low-memory iterative solution procedure employing a block-coupled solution of the modified Fourier equations and a sequential solution of BTEs is developed. The hybrid solver is shown to produce solutions well within 1% of an all-BTE solver (using Knc = 0.1), but with far less computational effort. Speedup factors between 2 and 200 are obtained for a range of steady-state heat transfer problems. The hybrid solver enables efficient and accurate simulation of thermal transport in semiconductors and dielectrics across the range of length scales from submicron to the macroscale.

scholarly journals Band degeneracy enhanced thermoelectric performance in layered oxyselenides by first-principles calculations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ning Wang ◽  
Menglu Li ◽  
Haiyan Xiao ◽  
Zhibin Gao ◽  
Zijiang Liu ◽  
...  
Keyword(s):  
Density Functional ◽  
Transport Theory ◽  
Relaxation Times ◽  
Wide Band ◽  
Type Systems ◽  
Model Systems ◽  
Boltzmann Transport ◽  
Seebeck Coefficients ◽  
Boltzmann Transport Theory ◽  
P Type

AbstractBand degeneracy is effective in optimizing the power factors of thermoelectric (TE) materials by enhancing the Seebeck coefficients. In this study, we demonstrate this effect in model systems of layered oxyselenide family by the density functional theory (DFT) combined with semi-classical Boltzmann transport theory. TE transport performance of layered LaCuOSe and BiCuOSe are fully compared. The results show that due to the larger electrical conductivities caused by longer electron relaxation times, the n-type systems show better TE performance than p-type systems for both LaCuOSe and BiCuOSe. Besides, the conduction band degeneracy of LaCuOSe leads to a larger Seebeck coefficient and a higher optimal carrier concentration than n-type BiCuOSe, and thus a higher power factor. The optimal figure of merit (ZT) value of 1.46 for n-type LaCuOSe is 22% larger than that of 1.2 for n-type BiCuOSe. This study highlights the potential of wide band gap material LaCuOSe for highly efficient TE applications, and demonstrates that inducing band degeneracy by cations substitution is an effective way to enhance the TE performance of layered oxyselenides.

Topological phase and thermoelectric properties of bialkali bismuthide compounds (Na,K)2RbBi from first-principles

2021 ◽  
Author(s):  
Shahram Yalameha ◽  
Zahra Nourbakhsh ◽  
Daryoosh Vashaee
Keyword(s):  
Density Functional ◽  
Transport Coefficients ◽  
Relaxation Times ◽  
Surface States ◽  
Topological Phase ◽  
Boltzmann Transport ◽  
Thermoelectric Power Factor ◽  
Practical Applications ◽  
Wide Range ◽  
P Type

Abstract We report the topological phase, thermal, and electrical properties of bialkali bismuthide compounds (Na,K)2RbBi, as yet hypothetical. The topological phase transitions of these compounds under hydrostatic pressure are investigated. The calculated topological surface states and Z2 topological index confirm the nontrivial topological phase. The electronic properties and transport coefficients are obtained using the density functional theory combined with the Boltzmann transport equation. The relaxation times are determined using the deformation potential theory to calculate the electronic thermal and electrical conductivity. The calculated mode Grüneisen parameters are substantial, indicating strong anharmonic acoustic phonons scattering, which results in an exceptionally low lattice thermal conductivity. These compounds also have a favorable thermoelectric power factor leading to a relatively flat p-type figure-of-merit over a broad temperature range. Furthermore, the mechanical properties and phonon band dispersions show that these structures are mechanically and dynamically stable. Therefore, they offer excellent candidates for practical applications over a wide range of temperatures.

A High Thermoelectric Performance ZT in p-Type LaSe2 Crystal

2021 ◽  
Vol 871 ◽  
pp. 203-207
Author(s):  
Jian Liu
Keyword(s):  
Thermal Conductivity ◽  
Power Factor ◽  
High Power ◽  
Density Functional ◽  
Lattice Thermal Conductivity ◽  
Phonon Transport ◽  
Thermoelectric Performance ◽  
Boltzmann Transport ◽  
High Power Factor ◽  
P Type

In this work, we use first principles DFT calculations, anharmonic phonon scatter theory and Boltzmann transport method, to predict a comprehensive study on the thermoelectric properties as electronic and phonon transport of layered LaSe2 crystal. The flat-and-dispersive type band structure of LaSe2 crystal offers a high power factor. In the other hand, low lattice thermal conductivity is revealed in LaSe2 semiconductor, combined with its high power factor, the LaSe2 crystal is considered a promising thermoelectric material. It is demonstrated that p-type LaSe2 could be optimized to exhibit outstanding thermoelectric performance with a maximum ZT value of 1.41 at 1100K. Explored by density functional theory calculations, the high ZT value is due to its high Seebeck coefficient S, high electrical conductivity, and low lattice thermal conductivity .

Long-term aging characteristics of co-filled nano-silica and micro-ATH in HTV silicone rubber composite insulators

2020 ◽  
Vol 29 (1) ◽  
pp. 40-56 ◽  
Author(s):  
Arooj Rashid ◽  
Jawad Saleem ◽  
Muhammad Amin ◽  
Sahibzada Muhammad Ali
Keyword(s):  
Mechanical Properties ◽  
Aging Time ◽  
Structural Changes ◽  
Erosion Resistance ◽  
Breakdown Strength ◽  
Accelerated Aging ◽  
Dielectric Strength ◽  
Superior Performance ◽  
Wave Number

Multiple environmental stresses produce complex phenomena of aging in polymeric insulators. The main aim of this research is to investigate the improved aging characteristics of silica (SiO2)/alumina trihydrate (ATH) hybrid samples (HSs) in high-temperature vulcanized rubber. For this purpose, three HSs comprising 20% micro-ATH with 2% nano-SiO2 (S2), 4% nano-SiO2 (S4), 6% nano-SiO2 (S6) along with sample-virgin (SV) are subjected to long-term accelerated aging of 9000 h. A special aging chamber is fabricated for the aging process of samples. The aging characteristics of these samples are investigated by measuring leakage current (LC) and hydrophobicity classification (HC) after every weathering cycle. Similarly, Fourier transform infrared (FTIR) spectroscopy is performed to observe the important structural changes over the entire aging time. The dielectric strength of AC is also performed after every 1000 h of aging. Tracking and erosion resistance and mechanical properties are also investigated before and after aging. From the critical investigation, it is observed that HSs possess improved results in all the conducted tests. S2 has the lowest LC and HC values throughout the aging time. Similarly, S6 described the highest breakdown strength at the end of the accelerated aging. In the case of FTIR, it is analyzed that the important wave numbers remain intact for all the HSs in the accelerated aging environment. The loss percentage in the wave number for SV is higher, compared to the HSs. After performing the tracking and erosion resistance test, HSs have superior performance. For some of the mechanical properties, HSs showed improved values. Thus, from the experimental analysis, it is deducted that the sample S2 offers the highest resistance to the aging conditions, compared to the SV and other HSs.

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