Using the Callaway Model to Deduce Relevant Phonon Scattering Processes: The Importance of Phonon Dispersion

Introduction: A new approach for expressing the lattice thermal conductivity of diatomic nanoscale materials is developed. Methods: The lattice thermal conductivity of two samples of GaAs nanobeam at 4-100K is calculated on the basis of monatomic dispersion relation. Phonons are scattered by nanobeam boundaries, point defects and other phonons via normal and Umklapp processes. Methods: A comparative study of the results of the present analysis and those obtained using Callaway formula is performed. We clearly demonstrate the importance of the utilised scattering mechanisms in lattice thermal conductivity by addressing the separate role of the phonon scattering relaxation rate. The formulas derived from the correction term are also presented, and their difference from Callaway model is evident. Furthermore their percentage contribution is sufficiently small to be neglected in calculating lattice thermal conductivity. Conclusion: Our model is successfully used to correlate the predicted lattice thermal conductivity with that of the experimental observation.

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A Modified Thermal Boundary Resistance Model for FCC Structures

ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer, Volume 2 ◽

10.1115/mnhmt2009-18175 ◽

2009 ◽

Author(s):

Ruijie Zhao ◽

Yunfei Chen ◽

Kedong Bi ◽

Meihui Lin ◽

Zan Wang

Keyword(s):

Phonon Scattering ◽

Phonon Dispersion ◽

Theoretical Calculations ◽

Theoretical Models ◽

Md Simulations ◽

Boundary Resistance ◽

Nonequilibrium Molecular Dynamics ◽

Thermal Boundary Resistance ◽

Inelastic Channel ◽

The Right

A modified lattice-dynamical model is proposed to calculate the thermal boundary resistance at the interface between two fcc lattices. The nonequilibrium molecular dynamics (MD) simulation is employed to verify the theoretical calculations. In our physical model, solid crystal argon is set at the left side and the right side structure properties are tunable by setting the atomic mass and the interactive energy strength among atoms with different values. In the case of mass mismatch, the predictions of the lattice-dynamical (LD) model agree well at low temperature while the calculations of the diffuse mismatch model (DMM) based on the detailed phonon dispersion agree well at high temperature with the MD simulations. The modified LD model, considering a partially specular and partially diffuse phonon scattering, can explain the simulations reasonably in the whole temperature rage. The good agreement between the theoretical calculations and the simulations may be attributed to that phonon scattering mechanisms are dominated by elastic scattering at the perfect interfaces. In the case of interactive energy strength mismatch, the simulations are under the predictions of both the theoretical models, which may be attributed to the fact that this mismatch can bring about an outstanding contribution to opening up an inelastic channel for heat transfer at the interfaces.

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Nuclear Scattering

Principles of Neutron Scattering from Condensed Matter ◽

10.1093/oso/9780198862314.003.0005 ◽

2020 ◽

pp. 127-184

Author(s):

Andrew T. Boothroyd

Keyword(s):

Cross Sections ◽

Phonon Scattering ◽

Phonon Dispersion ◽

Spin Echo ◽

Harmonic Approximation ◽

Approximate Expression ◽

Neutron Spin ◽

Response Functions ◽

Nuclear Scattering ◽

Scattering Cross

This chapter contains an overview of the different types of structural dynamics found in condensed matter, and the associated neutron scattering cross-sections. The scattering dynamics of the harmonic oscillator is discussed, and an expression for the Debye-Waller factor is obtained. In the case of crystalline solids, the vibrational spectrum in the harmonic approximation is described, including the phonon dispersion and the cross-sections for one-phonon coherent and incoherent scattering. Multi-phonon scattering is discussed briefly. For non-crystalline matter, the time-dependent van Hove correlation and response functions are introduced, and their relation to the scattering cross-section established. An approximate expression for the correlation function is obtained from the classical form. Partial correlation and response functions are defined for multicomponent systems. The technique of neutron Compton scattering as a probe of single-particle recoil dynamics is described. Quasielastic and neutron spin-echo spectroscopy are introduced, as well as examples of relaxational dynamics which these techniques can measure.

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Thermal transport in nanocrystalline Si and SiGe by ab initio based Monte Carlo simulation

Scientific Reports ◽

10.1038/srep44254 ◽

2017 ◽

Vol 7 (1) ◽

Cited By ~ 17

Author(s):

Lina Yang ◽

Austin J. Minnich

Keyword(s):

Thermal Conductivity ◽

Monte Carlo ◽

Ab Initio ◽

Grain Boundaries ◽

Thermal Transport ◽

Phonon Scattering ◽

Phonon Dispersion ◽

Computational Study ◽

Phonon Transport ◽

Nanocrystalline Si

Abstract Nanocrystalline thermoelectric materials based on Si have long been of interest because Si is earth-abundant, inexpensive, and non-toxic. However, a poor understanding of phonon grain boundary scattering and its effect on thermal conductivity has impeded efforts to improve the thermoelectric figure of merit. Here, we report an ab-initio based computational study of thermal transport in nanocrystalline Si-based materials using a variance-reduced Monte Carlo method with the full phonon dispersion and intrinsic lifetimes from first-principles as input. By fitting the transmission profile of grain boundaries, we obtain excellent agreement with experimental thermal conductivity of nanocrystalline Si [Wang et al. Nano Letters 11, 2206 (2011)]. Based on these calculations, we examine phonon transport in nanocrystalline SiGe alloys with ab-initio electron-phonon scattering rates. Our calculations show that low energy phonons still transport substantial amounts of heat in these materials, despite scattering by electron-phonon interactions, due to the high transmission of phonons at grain boundaries, and thus improvements in ZT are still possible by disrupting these modes. This work demonstrates the important insights into phonon transport that can be obtained using ab-initio based Monte Carlo simulations in complex nanostructured materials.

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Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

Journal of Nanoscience and Nanotechnology ◽

10.1166/jnn.2007.010 ◽

2007 ◽

Vol 7 (11) ◽

pp. 4094-4100 ◽

Cited By ~ 10

Author(s):

Jae Sik Jin ◽

Joon Sik Lee

Keyword(s):

Energy Density ◽

Group Velocity ◽

Phonon Scattering ◽

Phonon Dispersion ◽

Dispersion Model ◽

Hot Spot ◽

Interaction Model ◽

Phonon Interaction ◽

Electron Phonon Interaction ◽

Electron Phonon Scattering

An electron–phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscales. The high electron energy induced by the electric field in a transistor is transferred to the phonon system through electron–phonon interaction in the high field region of the transistor. Due to this fact, a hot spot occurs, which is much smaller than the phonon mean free path in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electron–phonon scattering is modeled through the intervalley and intravalley processes for silicon by introducing average electron energy. The simulation results are compared with those obtained by the full phonon dispersion model which treats the electron–phonon scattering as a volumetric heat source. The comparison shows that the peak temperature in the hot spot region is considerably higher and more localized than the previous results. The thermal characteristics of each phonon mode are useful to explain the above phenomena. The optical mode phonons of negligible group velocity obtain the highest energy density from electrons, and resides in the hot spot region without any contribution to heat transport, which results in a higher temperature in that region. Since the acoustic phonons with low group velocity show the higher energy density after electron–phonon scattering, they induce more localized heating near the hot spot region. The ballistic features are strongly observed when phonon–phonon scattering rates are lower than 4 × 1010 s−1.

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Manipulation of Band Degeneracy and Lattice Strain for Extraordinary PbTe Thermoelectrics

Research ◽

10.34133/2020/8151059 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Yixuan Wu ◽

Pengfei Nan ◽

Zhiwei Chen ◽

Zezhu Zeng ◽

Siqi Lin ◽

...

Keyword(s):

Lattice Strain ◽

Phonon Scattering ◽

Phonon Dispersion ◽

Large Strain ◽

X Ray Diffraction ◽

Fine Control ◽

Dispersion Measures ◽

Valence Bands ◽

Phonon Relaxation Time ◽

P Type

Maximizing band degeneracy and minimizing phonon relaxation time are proven to be successful for advancing thermoelectrics. Alloying with monotellurides has been known to be an effective approach for converging the valence bands of PbTe for electronic improvements, while the lattice thermal conductivity of the materials remains available room for being further reduced. It is recently revealed that the broadening of phonon dispersion measures the strength of phonon scattering, and lattice dislocations are particularly effective sources for such broadening through lattice strain fluctuations. In this work, a fine control of MnTe and EuTe alloying enables a significant increase in density of electron states near the valence band edge of PbTe due to involvement of multiple transporting bands, while the creation of dense in-grain dislocations leads to an effective broadening in phonon dispersion for reduced phonon lifetime due to the large strain fluctuations of dislocations as confirmed by synchrotron X-ray diffraction. The synergy of both electronic and thermal improvements successfully leads the average thermoelectric figure of merit to be higher than that ever reported for p-type PbTe at working temperatures.

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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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Electron–Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor

Journal of Nanoscience and Nanotechnology ◽

10.1166/jnn.2007.18084 ◽

2007 ◽

Vol 7 (11) ◽

pp. 4094-4100

Author(s):

Jae Sik Jin ◽

Joon Sik Lee

Keyword(s):

Energy Density ◽

Group Velocity ◽

Phonon Scattering ◽

Phonon Dispersion ◽

Dispersion Model ◽

Hot Spot ◽

Interaction Model ◽

Phonon Interaction ◽

Electron Phonon Interaction ◽

Electron Phonon Scattering

An electron–phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscales. The high electron energy induced by the electric field in a transistor is transferred to the phonon system through electron–phonon interaction in the high field region of the transistor. Due to this fact, a hot spot occurs, which is much smaller than the phonon mean free path in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electron–phonon scattering is modeled through the intervalley and intravalley processes for silicon by introducing average electron energy. The simulation results are compared with those obtained by the full phonon dispersion model which treats the electron–phonon scattering as a volumetric heat source. The comparison shows that the peak temperature in the hot spot region is considerably higher and more localized than the previous results. The thermal characteristics of each phonon mode are useful to explain the above phenomena. The optical mode phonons of negligible group velocity obtain the highest energy density from electrons, and resides in the hot spot region without any contribution to heat transport, which results in a higher temperature in that region. Since the acoustic phonons with low group velocity show the higher energy density after electron–phonon scattering, they induce more localized heating near the hot spot region. The ballistic features are strongly observed when phonon–phonon scattering rates are lower than 4 × 1010 s−1.

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Higher thermoelectric performance of Zintl phases (Eu0.5Yb0.5)1−xCaxMg2Bi2 by band engineering and strain fluctuation

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1608794113 ◽

2016 ◽

Vol 113 (29) ◽

pp. E4125-E4132 ◽

Cited By ~ 79

Author(s):

Jing Shuai ◽

Huiyuan Geng ◽

Yucheng Lan ◽

Zhuan Zhu ◽

Chao Wang ◽

...

Keyword(s):

Density Functional ◽

Phonon Scattering ◽

Theoretical Calculations ◽

Thermoelectric Performance ◽

Partial Substitution ◽

Zintl Phases ◽

Band Engineering ◽

Transmission Electron ◽

P Type ◽

Callaway Model

Complex Zintl phases, especially antimony (Sb)-based YbZn0.4Cd1.6Sb2 with figure-of-merit (ZT) of ∼1.2 at 700 K, are good candidates as thermoelectric materials because of their intrinsic “electron–crystal, phonon–glass” nature. Here, we report the rarely studied p-type bismuth (Bi)-based Zintl phases (Ca,Yb,Eu)Mg2Bi2 with a record thermoelectric performance. Phase-pure EuMg2Bi2 is successfully prepared with suppressed bipolar effect to reach ZT ∼ 1. Further partial substitution of Eu by Ca and Yb enhanced ZT to ∼1.3 for Eu0.2Yb0.2Ca0.6Mg2Bi2 at 873 K. Density-functional theory (DFT) simulation indicates the alloying has no effect on the valence band, but does affect the conduction band. Such band engineering results in good p-type thermoelectric properties with high carrier mobility. Using transmission electron microscopy, various types of strains are observed and are believed to be due to atomic mass and size fluctuations. Point defects, strain, dislocations, and nanostructures jointly contribute to phonon scattering, confirmed by the semiclassical theoretical calculations based on a modified Debye–Callaway model of lattice thermal conductivity. This work indicates Bi-based (Ca,Yb,Eu)Mg2Bi2 is better than the Sb-based Zintl phases.

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Synchrotron x-ray thermal diffuse scattering probes for phonons in Si/SiGe/Si trilayer nanomembranes

MRS Advances ◽

10.1557/adv.2016.352 ◽

2016 ◽

Vol 1 (48) ◽

pp. 3263-3268

Author(s):

Kyle M. McElhinny ◽

Gokul Gopalakrishnan ◽

Donald E. Savage ◽

David A. Czaplewski ◽

Max G. Lagally ◽

...

Keyword(s):

Diffuse Scattering ◽

Phonon Scattering ◽

Phonon Dispersion ◽

Elastic Anisotropy ◽

Sige Layer ◽

Reciprocal Space ◽

Thermal Diffuse Scattering ◽

X Ray ◽

Recent Developments ◽

Thermal Diffuse

ABSTRACTNanostructures offer the opportunity to control the vibrational properties of via the scattering of phonons due to boundaries and mass disorder as well as through changes in the phonon dispersion due to spatial confinement. Advances in understanding these effects have the potential to lead to thermoelectrics with an improved figure of merit by lowering the thermal conductivity and to provide insight into electron-phonon scattering rates in nanoelectronics. Characterizing the phonon population in nanomaterials has been challenging because of their small volume and because optical techniques probe only a small fraction of reciprocal space. Recent developments in x-ray scattering now allow the phonon population to be evaluated across all of reciprocal space in samples with volumes as small as several cubic micrometers. We apply this approach, synchrotron x-ray thermal diffuse scattering (TDS), to probe the population of phonons within a Si/SiGe/Si trilayer nanomembrane. The distributions of scattered intensity from Si/SiGe/Si trilayer nanomembranes and Si nanomembranes with uniform composition are qualitatively similar, with features arising from the elastic anisotropy of the diamond structure. The TDS signal for the Si/SiGe/Si nanomembrane, however, has higher intensity than the Si membrane of the same total thickness by approximately 3.75%. Possible origins of the enhancement in scattering from SiGe in comparison with Si include the larger atomic scattering factor of Ge atoms within the SiGe layer or reduced phonon frequencies due to alloying.

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