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.

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.

Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-Insulator Transistors

2005 ◽  
Vol 127 (7) ◽  
pp. 713-723 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Phonon Dispersion ◽  
Dispersion Model ◽  
Hot Spot ◽  
Phonon Transport ◽  
Silicon On Insulator ◽  
Boltzmann Transport ◽  
Transport Models ◽  
Microelectronic Devices ◽  
Finite Volume Approach ◽  
Spot Temperature

The problem of self-heating in microelectronic devices has begun to emerge as a bottleneck to device performance. Published models for phonon transport in microelectronics have used a gray Boltzmann transport equation (BTE) and do not account adequately for phonon dispersion or polarization. In this study, the problem of a hot spot in a submicron silicon-on-insulator transistor is addressed. A model based on the BTE incorporating full phonon dispersion effects is used. A structured finite volume approach is used to solve the BTE. The results from the full phonon dispersion model are compared to those obtained using a Fourier diffusion model. Comparisons are also made to previously published BTE models employing gray and semi-gray approximations. Significant differences are found in the maximum hot spot temperature predicted by the different models. Fourier diffusion underpredicts the hot spot temperature by as much as 350% with respect to predictions from the full phonon dispersion model. For the full phonon dispersion model, the longitudinal acoustic modes are found to carry a majority of the energy flux. The importance of accounting for phonon dispersion and polarization effects is clearly demonstrated.

scholarly journals A FOURTH ORDER DIFFUSION MONTE CARLO ALGORITHM FOR SOLVING QUANTUM MANY-BODY PROBLEMS

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1752-1755 ◽  
Author(s):  
H. A. FORBERT ◽  
S. A. CHIN
Keyword(s):  
Monte Carlo ◽  
Fourth Order ◽  
Planck Equation ◽  
Monte Carlo Algorithm ◽  
Bulk Liquid ◽  
Many Body ◽  
Diffusion Monte Carlo ◽  
Step Size ◽  
Wide Range ◽  
Gaussian Random Walk

We derive a fourth-order diffusion Monte Carlo algorithm for solving quantum many-body problems. The method uses a factorization of the imaginary time propagator in terms of the usual local energy E and Langevin operators L as well as an additional pseudo-potential consisting of the double commutator [EL, [L, EL]]. A new factorization of the propagator of the Fokker-Planck equation enables us to implement the Langevin algorithm to the necessary fourth order. We achieve this by the addition of correction terms to the drift steps and the use of a position-dependent Gaussian random walk. We show that in the case of bulk liquid helium the systematic step size errors are indeed fourth order over a wide range of step sizes.

Monte Carlo Modeling of Phonon Transport Using Scattering Phase Functions

2008 ◽  
Author(s):  
Neil Zuckerman ◽  
Jennifer R. Lukes
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo ◽  
Numerical Methods ◽  
Ballistic Transport ◽  
Simulation Method ◽  
Phonon Transport ◽  
Nanometer Scale ◽  
Boltzmann Transport ◽  
Length Scales ◽  
Scale Structures

The calculation of heat transport in nonmetallic materials at small length scales is important in the design of thermoelectric and electronic materials. New designs with quantum dot superlattices (QDS) and other nanometer-scale structures can change the thermal conductivity in ways that are difficult to model and predict. The Boltzmann Transport Equation can describe the propagation of energy via mechanical vibrations in an analytical fashion but remains difficult to solve for the problems of interest. Numerical methods for simulation of propagation and scattering of high frequency vibrational quanta (phonons) in nanometer-scale structures have been developed but are either impractical at micron length scales, or cannot truly capture the details of interactions with nanometer-scale inclusions. Monte Carlo (MC) models of phonon transport have been developed and demonstrated based on similar numerical methods used for description of electron transport [1-4]. This simulation method allows computation of thermal conductivity in materials with length scales LX in the range of 10 nm to 10 μm. At low temperatures the model approaches a ballistic transport simulation and may function for even larger length scales.

Analytical Model for Lattice Thermal Conductivity Predictions of Periodic Nanoporous Structures

2016 ◽  
Author(s):  
Qing Hao ◽  
Yue Xiao ◽  
Hongbo Zhao
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Lattice Thermal Conductivity ◽  
Phonon Transport ◽  
Kinetic Relationship ◽  
Wide Range ◽  
Edge Scattering ◽  
Bulk Phonon ◽  
Nanoporous Structures

Phonon transport within nanoporous bulk materials or thin films is of importance to applications in thermoelectrics, gas sensors, and thermal insulation materials. Considering classical phonon size effects, the lattice thermal conductivity KL can be predicted assuming diffusive pore-edge scattering of phonons and bulk phonon mean free paths. In the kinetic relationship, kL can be computed by modifying the phonon mean free paths with the characteristic length ΛPore of the porous structure. Despite some efforts using the Monte Carlo ray tracing method to extract ΛPore, the resulting KL often diverges from that predicted by phonon Monte Carlo simulations. In this work, the effective ΛPore is extracted by directly comparing the predictions by the kinetic relationship and phonon Monte Carlo simulations. The investigation covers a wide range of period sizes and volumetric porosities. In practice, these ΛPore values can be used for thermal analysis of general nanoporous materials.

Monte Carlo Simulation of the Thermal Conductivity and Phonon Transport in Nanocomposites

2005 ◽  
Author(s):  
Ming-Shan Jeng ◽  
Ronggui Yang ◽  
David Song ◽  
Gang Chen
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Silicon Germanium ◽  
High Efficiency ◽  
Three Dimensional ◽  
Simulation Method ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Nanoparticle Composites

This paper presents a Monte Carlo simulation scheme to study the phonon transport and thermal conductivity of nanocomposites. Special attention has been paid to the implementation of periodic boundary condition in Monte Carlo simulation. The scheme is applied to study the thermal conductivity of silicon germanium (Si-Ge) nanocomposites, which are of great interest for high efficiency thermoelectric material development. The Monte Carlo simulation was first validated by successfully reproducing the results of (two dimensional) nanowire composites using the deterministic solution of the phonon Boltzmann transport equation and the experimental thermal conductivity of bulk germanium, and then the validated simulation method was used to study (three dimensional) nanoparticle composites, where Si nanoparticles are embedded in Ge host. The size effects of phonon transport in nanoparticle composites were studied and the results show that the thermal conductivity of nanoparticle composites can be lower than alloy value. It was found that randomly distributed nanopaticles in nanocomposites rendered the thermal conductivity values close to that of periodic aligned patterns.

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.

Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization

2001 ◽  
Vol 123 (4) ◽  
pp. 749-759 ◽  
Author(s):  
Sandip Mazumder ◽  
Arunava Majumdar
Keyword(s):  
Thin Films ◽  
Monte Carlo ◽  
Monte Carlo Study ◽  
Past Research ◽  
Phonon Transport ◽  
Solution Technique ◽  
Boltzmann Transport ◽  
Linear Dispersion ◽  
Silicon Thin Films ◽  
Solid Thin Films

The Boltzmann Transport Equation (BTE) for phonons best describes the heat flow in solid nonmetallic thin films. The BTE, in its most general form, however, is difficult to solve analytically or even numerically using deterministic approaches. Past research has enabled its solution by neglecting important effects such as dispersion and interactions between the longitudinal and transverse polarizations of phonon propagation. In this article, a comprehensive Monte Carlo solution technique of the BTE is presented. The method accounts for dual polarizations of phonon propagation, and non-linear dispersion relationships. Scattering by various mechanisms is treated individually. Transition between the two polarization branches, and creation and destruction of phonons due to scattering is taken into account. The code has been verified and evaluated by close examination of its ability or failure to capture various regimes of phonon transport ranging from diffusive to the ballistic limit. Validation results show close agreement with experimental data for silicon thin films with and without doping. Simulation results show that above 100 K, transverse acoustic phonons are the primary carriers of energy in silicon.

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.

Sign in / Sign up

Export Citation Format

Share Document