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.

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

2017 ◽  
Vol 7 (1) ◽  
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.

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

2016 ◽  
Vol 139 (3) ◽  
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.

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

2009 ◽  
Author(s):  
Dhruv Singh ◽  
Jayathi Y. Murthy ◽  
Timothy S. Fisher
Keyword(s):  
Thermal Conductivity ◽  
Volume Fraction ◽  
Phonon Dispersion ◽  
Boltzmann Transport ◽  
Host Materials ◽  
Wide Range ◽  
Heterogeneous Interfaces ◽  
Silicon And Germanium ◽  
First Time ◽  
Superlattice Period

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.

Thermal Transport in Finite-Sized Nanocomposites

2008 ◽  
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.

Phonon Transport in SiGe-Based Nanocomposites and Nanowires for Thermoelectric Applications

2015 ◽  
Vol 1735 ◽  
Author(s):  
M. Upadhyaya ◽  
Z. Aksamija
Keyword(s):  
Thermal Conductivity ◽  
Silicon Germanium ◽  
Thermal Transport ◽  
Lattice Thermal Conductivity ◽  
Phonon Scattering ◽  
Voronoi Tessellation ◽  
Phonon Transport ◽  
Interface Properties ◽  
Boltzmann Transport ◽  
Rough Interfaces

ABSTRACTSilicon-germanium (SiGe) superlattices (SLs) have been proposed for application as efficient thermoelectrics because of their low thermal conductivity, below that of bulk SiGe alloys. However, the cost of growing SLs is prohibitive, so nanocomposites, made by a ball-milling and sintering, have been proposed as a cost-effective replacement with similar properties. Lattice thermal conductivity in SiGe SLs is reduced by scattering from the rough interfaces between layers. Therefore, it is expected that interface properties, such as roughness, orientation, and composition, will play a significant role in thermal transport in nanocomposites and offer many additional degrees of freedom to control the thermal conductivity in nanocomposites by tailoring grain size, shape, and crystal angle distributions. We previously demonstrated the sensitivity of the lattice thermal conductivity in SLs to the interface properties, based on solving the phonon Boltzmann transport equation under the relaxation time approximation. Here we adapt the model to a broad range of SiGe nanocomposites. We model nanocomposite structures using a Voronoi tessellation to mimic the grains and their distribution in the nanocomposite and show excellent agreement with experimentally observed structures, while for nanowires we use the Monte Carlo method to solve the phonon Boltzmann equation. In order to accurately treat phonon scattering from a series of atomically rough interfaces between the grains in the nanocomposite and at the boundaries of nanowires, we employ a momentum-dependent specularity parameter. Our results show thermal transport in SiGe nanocomposites and nanowires is reduced significantly below their bulk alloy counterparts.

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.

Simulation of Sub-Micron Thermal Transport in a MOSFET Using a Hybrid Fourier-BTE Model

2010 ◽  
Author(s):  
James M. Loy ◽  
Dhruv Singh ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Transport ◽  
Source Term ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Computational Cost ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Hybrid Solver ◽  
Solution Methodology ◽  
Electron Phonon Scattering

Self-heating has emerged as a critical bottleneck to scaling in modern transistors. In simulating heat conduction in these devices, it is important to account for the granularity of phonon transport since electron-phonon scattering occurs preferentially to select phonon groups. However, a complete accounting for phonon dispersion, polarization and scattering is very expensive if the Boltzmann transport equation (BTE) is used. Moreover, difficulties with convergence are encountered when the phonon Knudsen number becomes small. In this paper we simulate a two-dimensional bulk MOSFET hotspot problem using a partially-implicit hybrid BTE-Fourier solver which is significantly less expensive than a full BTE solution, and which shows excellent convergence characteristics. Volumetric heat generation from electron-phonon collisions is taken from a Monte Carlo simulation of electron transport and serves as a heat source term in the governing transport equations. The hybrid solver is shown to perform well in this highly non-equilibrium situation, matching the solutions obtained from a pure all-BTE solution, but at significantly lower computational cost. The paper establishes that this new model and solution methodology are viable for the simulation of thermal transport in other emerging transistor designs and in other nanotechnology applications as well.

scholarly journals Simulation of Heat Transport in Graphene Nanoribbons Using the Ab-Initio Scattering Operator

2014 ◽  
Author(s):  
Colin D. Landon ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Ab Initio ◽  
Heat Transport ◽  
Density Functional ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Graphene Nanoribbons ◽  
Phonon Transport ◽  
Stochastic Algorithm ◽  
Boltzmann Transport ◽  
Scattering Operator

We present a deviational Monte Carlo method for simulating phonon transport in graphene using the ab initio 3-phonon scattering operator. This operator replaces the commonly used relaxation-time approximation, which is known to neglect, among other things, coupling between out of equilibrium states that are particularly important in graphene. Phonon dispersion relations and transition rates are obtained from density functional theory calculations. The proposed method provides, for the first time, means for obtaining solutions of the Boltzmann transport equation with ab initio scattering for time- and spatially-dependent problems. The deviational formulation ensures that simulations are computationally feasible for arbitrarily small temperature differences; within this formulation, the ab initio scattering operator is treated using an efficient stochastic algorithm which, in the limit of large number of states, outperforms the more traditional deterministic methods used in solutions of the homogeneous Boltzmann equation. We use the proposed method to study heat transport in graphene ribbons.

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

2004 ◽  
Vol 126 (6) ◽  
pp. 946-955 ◽  
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.

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.

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