Ballistic-Diffusive Approximation for Phonon Transport Accounting for Polarization and Dispersion

2003 ◽  
Author(s):  
J. Y. Murthy ◽  
S. R. Mathur
Keyword(s):  
Thermal Conductivity ◽  
Diffusion Approximation ◽  
Phonon Dispersion ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Conductivity Measurements ◽  
Bulk Silicon ◽  
Medium Component ◽  
Diffusive Approximation

A ballistic-diffusive approximation to the Boltzmann transport equation is developed for describing phonon transport in semi-conductors and dielectrics. The model incorporates the effects of phonon dispersion and polarization by considering longitudinal, transverse and optical branches. Each branch is divided into frequency bands, and scattering between branches and bands is incorporated subject to conservation rules. The phonon energy in each band is divided into a boundary and a medium component, with the latter being computed using a diffusion approximation. The approximation is shown to work well by comparing its predictions to exact solutions as well thermal conductivity measurements for bulk silicon.

Spectral Detail of Phonon Conduction and Scattering in Graphene

2011 ◽  
Author(s):  
Dhruv Singh ◽  
Jayathi Y. Murthy ◽  
Timothy S. Fisher
Keyword(s):  
Thermal Conductivity ◽  
Phonon Scattering ◽  
Interatomic Potential ◽  
Phonon Dispersion ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Phonon Transport ◽  
Temperature Perturbation ◽  
Boltzmann Transport ◽  
Wide Range

This paper examines the thermodynamic and thermal transport properties of the 2D graphene lattice. The interatomic interactions are modeled using the Tersoff interatomic potential and are used to evaluate phonon dispersion curves, density of states and thermodynamic properties of graphene as functions of temperature. Perturbation theory is applied to calculate the transition probabilities for three-phonon scattering. The matrix elements of the perturbing Hamiltonian are calculated using the anharmonic interatomic force constants obtained from the interatomic potential as well. An algorithm to accurately quantify the contours of energy balance for three-phonon scattering events is presented and applied to calculate the net transition probability from a given phonon mode. Under the linear approximation, the Boltzmann transport equation (BTE) is applied to compute the thermal conductivity of graphene, giving spectral and polarization-resolved information. Predictions of thermal conductivity for a wide range of parameters elucidate the behavior of diffusive phonon transport. The complete spectral detail of selection rules, important phonon scattering pathways, and phonon relaxation times in graphene are provided, contrasting graphene with other materials, along with implications for graphene electronics. We also highlight the specific scattering processes that are important in Raman spectroscopy based measurements of graphene thermal conductivity, and provide a plausible explanation for the observed dependence on laser spot size.

Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics Simulations and Theoretical Calculation

2011 ◽  
Vol 55-57 ◽  
pp. 1152-1155 ◽  
Author(s):  
Xing Li Zhang ◽  
Zhao Wei Sun
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Silicon Thin Films ◽  
Simulation Results ◽  
Dynamics Simulations ◽  
Good Agreement

Molecular, dynamics simulation and the Boltzmann transport equation are used respectively to analyze the phonon transport in Si thin film. The MD result is in good agreement with the theoretical analysis values. The results show that the calculated thermal conductivity decreases almost linearly as the film thickness reduced and is almost independent of the temperature at the nanoscale. It was observed from the simulation results that there exists the obvious size effect on the thermal conductivity.

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.

Solution of the Phonon Boltzmann Transport Equation Employing Rigorous Implementation of Phonon Conservation Rules

2006 ◽  
Author(s):  
Tianjiao Wang ◽  
Jayathi Y. Murthy
Keyword(s):  
Thin Film ◽  
Energy Conservation ◽  
Transport Equation ◽  
Phonon Dispersion ◽  
Boltzmann Transport Equation ◽  
Physical Space ◽  
Finite Volume Scheme ◽  
Boltzmann Transport ◽  
Bulk Silicon ◽  
Silicon Thin Film

A finite volume scheme is developed to solve the phonon Boltzmann transport equation in an energy form accounting for phonon dispersion and polarization. The physical space and the first Brillouin zone are discretized into finite volumes and the phonon BTE is integrated over them. Second-order accurate differencing schemes are used for the discretization. The scattering term employs a rigorous implementation of phonon momentum and energy conservation laws in determining the rate of normal and Umklapp processes. The method is applied to a variety of bulk silicon and silicon thin-film conduction problems and shown to perform satisfactorily.

scholarly journals Study of Phonon Transport Across Si/Ge Interfaces Using Full-Band Phonon Monte Carlo Simulation

2021 ◽  
Author(s):  
Ngoc Duc Le ◽  
Brice Davier ◽  
Philippe Dollfus ◽  
Jerome Saint Martin
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Monte Carlo ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Nanometer Scale ◽  
Boltzmann Transport ◽  
Ballistic Regime ◽  
Full Band ◽  
Micrometer Scale

Abstract A Full Band Monte Carlo simulatorhas been developed to considerphonon transmission across interfaces disposedperpendicularlyto the heat flux. This solver of the Boltzmann transport equation does not require any assumption on the shape the phonon distribution and can naturally consider all phonon transport regimes from the diffusive to the fully ballistic regime. This simulatoris used to study single and double Si/Ge heterostructures from the micrometer scale downto the nanometer scale,i.e. in all phonon transport regime from fully diffusive toballistic.A methodology to determine the thermal conductivity atthermal interfaces is presented.

Study of an Iterative Solution for Boltzmann Transport Equation and Calculation of Thermal Conductivity

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Calculation ◽  
Iterative Method ◽  
Transport Equation ◽  
Linear Systems ◽  
Heat Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Boltzmann Transport

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.

scholarly journals Highly Anisotropic Thermal Transport in LiCoO2

2019 ◽  
Author(s):  
Hui Yang ◽  
Jia-Yue Yang ◽  
Christopher Savory ◽  
Jonathan Skelton ◽  
Benjamin Morgan ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Lithium Ion Batteries ◽  
Phonon Dispersion ◽  
Lithium Ion ◽  
Boltzmann Transport ◽  
Heat Management ◽  
Positive Electrodes ◽  
Anharmonic Lattice ◽  
Anharmonic Interactions ◽  
The Impact

<div>LiCoO<sub>2</sub> is the prototype cathode in lithium ion batteries. It adopts a crystal structure with alternating Li<sup>+</sup> and CoO<sub>2</sub><sup>-</sup> layers along the hexagonal <0001> axis. It is well established that ionic and electronic conduction is highly anisotropic; however, little is known regarding heat transport. We analyse the phonon dispersion and lifetimes of LiCoO<sub>2</sub> using anharmonic lattice dynamics based on quantum chemical force constants. Around room temperature, the thermal conductivity in the hexagonal ab plane of the layered cathode is ≈ 6 times higher than that along the c axis based on the phonon Boltzmann transport. The low thermal conductivity (< 10Wm<sup>-1</sup>K<sup>-1</sup>) originates from a combination of short phonon lifetimes associated with anharmonic interactions between the octahedral face-sharing CoO<sub>2</sub><sup>-</sup> networks, as well as grain boundary scattering. The impact on heat management and thermal processes in lithium ion batteries based on layered positive electrodes is discussed.</div>

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 .

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