Effect of Phonon Dispersion on Thermal Conduction Across Si/Ge Interfaces

We report finite volume simulations of the phonon Boltzmann transport equation (BTE) for heat conduction across the heterogeneous interfaces in SiGe superlattices. We employ the diffuse mismatch model with full details of phonon dispersion and polarization. Simulations are performed over a wide range of Knudsen numbers. Similar to previous studies we establish that thermal conductivity of a superlattice is much lower than the host materials for superlattice period in the submicron regime. Details of the non-equilibrium between optical and acoustic phonons that emerge due to the mismatch of phonon spectrum in silicon and germanium are delineated for the first time. Conditions are identified for which this can lead to a significant additional thermal resistance than that attributed primarily to boundary scattering of phonons. We report results for thermal conductivity for various volume fraction and superlattice periods.

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Spectral Detail of Phonon Conduction and Scattering in Graphene

ASME 2011 Pacific Rim Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Systems, MEMS and NEMS: Volume 1 ◽

10.1115/ipack2011-52243 ◽

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.

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Thermal Transport in Finite-Sized Nanocomposites

Heat Transfer: Volume 1 ◽

10.1115/ht2008-56385 ◽

2008 ◽

Cited By ~ 1

Author(s):

Dhruv Singh ◽

Jayathi Y. Murthy ◽

Timothy S. Fisher

Keyword(s):

Thermal Conductivity ◽

Phonon Transport ◽

Boltzmann Transport ◽

Host Materials ◽

Individual Host ◽

Wide Range ◽

Heterogeneous Interfaces ◽

The Individual ◽

Nanoscale Composites ◽

Bulk Behavior

We report finite volume simulations of the phonon Boltzmann Transport Equation (BTE) for heat conduction in periodic nanowire composites. Models for phonon transport across heterogeneous interfaces are developed, and simulations are performed over a wide range of Knudsen numbers. Conditions are identified under which the thermal conductivity of the composite material is less than the bulk thermal conductivity of the individual host materials and under which the alloy limit of thermal conductivity is recovered. We also compute the length scale needed to achieve bulk behavior in nanoscale composites. The results of this study are expected to inform and improve applications such as thermoelectric devices and flexible macroelectronics.

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Submicron Heat Transport Model in Silicon Accounting for Phonon Dispersion and Polarization

Journal of Heat Transfer ◽

10.1115/1.1833367 ◽

2004 ◽

Vol 126 (6) ◽

pp. 946-955 ◽

Cited By ~ 125

Author(s):

Sreekant V. J. Narumanchi ◽

Jayathi Y. Murthy ◽

Cristina H. Amon

Keyword(s):

Thermal Conductivity ◽

Phonon Dispersion ◽

Transport Model ◽

Relaxation Times ◽

Thermal Response ◽

Boltzmann Transport ◽

Wide Range ◽

Submicron Scale ◽

Different Temperatures ◽

Finite Volume Approach

In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the submicron scale. However, most published studies make a gray assumption and do not account for either dispersion or polarization. In this study, we propose a model based on the BTE, accounting for transverse acoustic and longitudinal acoustic phonons as well as optical phonons. This model incorporates realistic phonon dispersion curves for silicon. The interactions among the different phonon branches and different phonon frequencies are considered, and the proposed model satisfies energy conservation. Frequency-dependent relaxation times, obtained from perturbation theory, and accounting for phonon interaction rules, are used. In the present study, the BTE is numerically solved using a structured finite volume approach. For a problem involving a film with two boundaries at different temperatures, the numerical results match the analogous exact solutions from radiative transport literature for various acoustic thicknesses. For the same problem, the transient thermal response in the acoustically thick limit matches results from the solution to the parabolic Fourier diffusion equation. In the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model. Experimental in-plane thermal conductivity data for silicon thin films over a wide range of temperatures are also matched satisfactorily.

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Highly Anisotropic Thermal Transport in LiCoO2

10.26434/chemrxiv.8874404.v2 ◽

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>LiCoO2 is the prototype cathode in lithium ion batteries. It adopts a crystal structure with alternating Li+ and CoO2- 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 LiCoO2 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-1K-1) originates from a combination of short phonon lifetimes associated with anharmonic interactions between the octahedral face-sharing CoO2- 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>

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Highly Anisotropic Thermal Transport in LiCoO2

10.26434/chemrxiv.8874404 ◽

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>LiCoO2 is the prototype cathode in lithium ion batteries. It adopts a crystal structure with alternating Li+ and CoO2- 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 LiCoO2 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-1K-1) originates from a combination of short phonon lifetimes associated with anharmonic interactions between the octahedral face-sharing CoO2- 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>

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Simulation of Phonon Transport in Semiconductors Using a Population-Dependent Many-Body Cellular Monte Carlo Approach

Journal of Heat Transfer ◽

10.1115/1.4035042 ◽

2016 ◽

Vol 139 (3) ◽

Cited By ~ 1

Author(s):

Flavio F. M. Sabatti ◽

Stephen M. Goodnick ◽

Marco Saraniti

Keyword(s):

Monte Carlo ◽

Phonon Dispersion ◽

Phonon Transport ◽

Space Distribution ◽

Boltzmann Transport ◽

Many Body ◽

Simulation Code ◽

Conservation Of Energy ◽

Wide Range ◽

Cellular Monte Carlo

A Monte Carlo rejection technique for numerically solving the complete, nonlinear phonon Boltzmann transport equation (BTE) is presented in this work, including three particles interactions. The technique has been developed to explicitly model population-dependent scattering within a full-band cellular Monte Carlo (CMC) framework, to simulate phonon transport in semiconductors, while ensuring conservation of energy and momentum for each scattering event within gridding error. The scattering algorithm directly solves the many-body problem accounting for the instantaneous distribution of the phonons. Our general approach is capable of simulating any nonequilibrium phase space distribution of phonons using the full phonon dispersion without the need of approximations used in previous Monte Carlo simulations. In particular, no assumptions are made on the dominant modes responsible for anharmonic decay, while normal and umklapp scattering are treated on the same footing. In this work, we discuss details of the algorithmic implementation of both the three-particle scattering for the treatment of the anharmonic interactions between phonons, as well as treating isotope and impurity scattering within the same framework. The simulation code was validated by comparison with both analytical and experimental results; in particular, the simulation results show close agreement with a wide range of experimental data such as thermal conductivity as function of the isotopic composition, the temperature, and the thin-film thickness.

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Heat Conduction of a Porous Material

Journal of Heat Transfer ◽

10.1115/1.4005709 ◽

2012 ◽

Vol 134 (5) ◽

Cited By ~ 7

Author(s):

Koji Miyazaki ◽

Saburo Tanaka ◽

Daisuke Nagai

Keyword(s):

Thermal Conductivity ◽

Heat Conduction ◽

Porous Material ◽

Boundary Conditions ◽

Periodic Boundary ◽

Phonon Dispersion ◽

Bulk Material ◽

Periodic Boundary Conditions ◽

Boltzmann Transport ◽

Time Space

In this study, we introduce our numerical and experimental works for the thermal conductivity reduction by using a porous material. Recently thermal conductivity reduction has been one of the key technologies to enhance the figure of merit (ZT) of a thermoelectric material. We carry out numerical calculations of heat conduction in porous materials, such as phonon Boltzmann transport (BTE) and molecular dynamics (MD) simulations, in order to investigate the mechanism of the thermal conductivity reduction of a porous material. In the BTE, we applied the periodic boundary conditions with constant heat flux to calculate the effective thermal conductivity of porous materials.In the MD simulation, we calculated the phonon properties of Si by using the Stillinger–Weber potential at constant temperature with periodic boundary conditions in the x, y, and z directions. Phonon dispersion curves of single crystal of Si calculated from MD results by time-space 2D FFT are agreed well with reference data. Moreover, the effects of nanoporous structures on both the phonon group velocity and the phonon density of states (DOS) are discussed. At last, we made a porous p-type Bi2Te3 by nanoparticles prepared by a beads milling method. The thermal conductivity is one-fifth of that of a bulk material as well as keeping the same Seebeck coefficient as the bulk value. However, electrical conductivity was much reduced, and the ZT was only 0.048.

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Effect of Phonon Dispersion on Transport Properties of Single-Crystalline Dielectrics

Electronic and Photonic Packaging, Electrical Systems Design and Photonics, and Nanotechnology ◽

10.1115/imece2004-62244 ◽

2004 ◽

Cited By ~ 3

Author(s):

Mehdi Asheghi ◽

Wenjun Liu ◽

K. E. Goodson

Keyword(s):

Thermal Conductivity ◽

Phonon Dispersion ◽

Additional Insight ◽

Transverse Modes ◽

Scattering Rate ◽

Magnitude Variation ◽

Silicon And Germanium ◽

Conductivity Modeling ◽

Insight Into ◽

Mass Fluctuation

Thermal conductivity modeling using the Debye approximation can significantly reduce the complexity involved in the evaluation of thermal conductivity integral. Nevertheless, there are several compelling reasons (e.g., inconsistency between the estimations of the density of states used for heat capacity and thermal conductivity) that motivate more detailed modeling of the phonon dispersion in silicon or other diamond-like dielectrics. This manuscript presents closed-form expressions for the dispersion of the longitudinal and transverse modes in diamond-like dielectrics, which are then used to estimate the isotopic scattering rate, phonon spectrum and specific heat. The combinations of the above parameters are then used to predict the thermal conductivity of the bulk silicon and germanium with orders of magnitude variation in the mass fluctuation of isotopes and for the temperature range 2 to 1000 K. While this approach offers an elegant and consistent account of the phonon dispersion in diamond-like materials, however, provides no additional insight into the relative contributions of the longitudinal and transverse phonons to the heat transport.

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First Principles Investigation of Anomalous Pressure-Dependent Thermal Conductivity of Chalcopyrites

Materials ◽

10.3390/ma12213491 ◽

2019 ◽

Vol 12 (21) ◽

pp. 3491

Author(s):

Loay Elalfy ◽

Denis Music ◽

Ming Hu

Keyword(s):

Thermal Conductivity ◽

Phonon Dispersion ◽

Negative Thermal Expansion ◽

Building Blocks ◽

Boltzmann Transport ◽

Energy Devices ◽

Acoustic Modes ◽

Group I ◽

Dispersion Data ◽

Phonon Relaxation Time

The effect of compression on the thermal conductivity of CuGaS2, CuInS2, CuInTe2, and AgInTe2 chalcopyrites (space group I-42d) was studied at 300 K using phonon Boltzmann transport equation (BTE) calculations. The thermal conductivity was evaluated by solving the BTE with harmonic and third-order interatomic force constants. The thermal conductivity of CuGaS2 increases with pressure, which is a common behavior. Striking differences occur for the other three compounds. CuInTe2 and AgInTe2 exhibit a drop in the thermal conductivity upon increasing pressure, which is anomalous. AgInTe2 reaches a very low thermal conductivity of 0.2 W·m−1·K−1 at 2.6 GPa, being beneficial for many energy devices, such as thermoelectrics. CuInS2 is an intermediate case. Based on the phonon dispersion data, the phonon frequencies of the acoustic modes for CuInTe2 and AgInTe2 decrease with increasing pressure, thereby driving the anomaly, while there is no significant pressure effect for CuGaS2. This leads to the negative Grüneisen parameter for CuInTe2 and AgInTe2, a decreased phonon relaxation time, and a decreased thermal conductivity. This softening of the acoustic modes upon compression is suggested to be due to a rotational motion of the chalcopyrite building blocks rather than a compressive oscillation. The negative Grüneisen parameters and the anomalous phonon behavior yield a negative thermal expansion coefficient at lower temperatures, based on the Grüneisen vibrational theory.

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