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.

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.

Theoretical Thermal Conductivity of Periodic Two-Dimensional Nanocomposites

2003 ◽  
Vol 793 ◽  
Author(s):  
Ronggui Yang ◽  
Gang Chen
Keyword(s):  
Thermal Conductivity ◽  
Lattice Thermal Conductivity ◽  
High Efficiency ◽  
Transport Model ◽  
Cell Interaction ◽  
Phonon Transport ◽  
Two Dimensional ◽  
Boltzmann Transport ◽  
Volumetric Fraction ◽  
Strong Function

ABSTRACTA phonon Boltzmann transport model is established to study the lattice thermal conductivity of nanocomposites with nanowires embedded in a host semiconductor material. Special attention has been paid to cell-cell interaction using periodic boundary conditions. The simulation shows that the temperature profiles in nanocomposites are very different from those in conventional composites, due to ballistic phonon transport at nanoscale. The thermal conductivity of periodic 2-D nanocomposites is a strong function of the size of the embedded wires and the volumetric fraction of the constituent materials. At constant volumetric fraction the smaller the wire diameter, the smaller is the thermal conductivity of periodic two-dimensional nanocomposites. For fixed silicon wire dimension, the lower the atomic percentage of germanium, the lower the thermal conductivity of the nanocomposites. The results of this study can be used to direct the development of high efficiency thermoelectric materials.

scholarly journals Deviational Phonons and Thermal Transport at the Nanoscale

2012 ◽  
Author(s):  
Jean-Philippe M. Péraud ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Simulation Method ◽  
Phonon Transport ◽  
Statistical Uncertainty ◽  
Small Temperature ◽  
Efficient Simulation ◽  
Transport Problems ◽  
Individual Particles

We present a new method for simulating phonon transport at the nanoscale. The proposed approach is based on the recently developed energy-based deviational Monte Carlo method by the authors [Phys. Rev. B 84, 205331, 2011] which achieves significantly reduced statistical uncertainty compared to standard Monte Carlo methods by simulating only the deviation from equilibrium. Here, we show that under linearized conditions (small temperature differences) the trajectories of individual particles simulating the deviation from equilibrium can be decoupled and can thus be simulated independently, without introducing any additional approximation. This leads to a particularly simple and efficient simulation method that can be used to treat steady and transient phonon transport problems in arbitrary three-dimensional geometries.

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.

Monte Carlo Simulation of Thermal Conductivities of Silicon Nanowires

2005 ◽  
Author(s):  
Yunfei Chen ◽  
Deyu Li ◽  
Jennifer R. Lukes ◽  
Zhonghua Ni
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Dispersion Relation ◽  
Thermal Transport ◽  
Phonon Transport ◽  
Si Nanowires ◽  
Nanowire Diameter ◽  
Energy Conversion Devices ◽  
Tens Nanometer

One-dimensional (1D) materials such as various kinds of nanowires and nanotubes have attracted considerable attention due to their potential applications in electronic and energy conversion devices. The thermal transport phenomena in these nanowires and nanotubes could be significantly different from that in bulk material due to boundary scattering, phonon dispersion relation change, and quantum confinement. It is very important to understand the thermal transport phenomena in these materials so that we can apply them in the thermal design of microelectronic, photonic, and energy conversion devices. While intensive experimental efforts are being carried out to investigate the thermal transport in nanowires and nanotube, an accurate numerical prediction can help the understanding of phonon scattering mechanisms, which is of fundamental theoretical significance. A Monte Carlo simulation was developed and applied to investigate phonon transport in single crystalline Si nanowires. The Phonon-phonon Normal (N) and Umklapp (U) scattering processes were modeled with a genetic algorithm to satisfy both the energy and the momentum conservation. The scattering rates of N and U scattering processes were given from the first perturbation theory. Ballistic phonon transport was modeled with the code and the numerical results fit the theoretical prediction very well. The thermal conductivity of bulk Si was then simulated and good agreement was achieved with the experimental data. Si nanowire thermal conductivity was then studied and compared with some recent experimental results. In order to study the confinement effects on phonon transport in nanowires, two different phonon dispersions, one based on bulk Si and the other solved from the elastic wave theory for nanowires, were adopted in the simulation. The discrepancy from the simulations based on different phonon dispersions increases as the nanowire diameter decreases, which suggests that the confinement effect is significant when the nanowire diameter goes down to tens nanometer range. It was found that the U scattering probability engaged in Si nanowires was increased from that in bulk Si due to the decrease of the frequency gap between different modes and the reduced phonon group velocity. Simulation results suggest that the dispersion relation for nanowire solved from the elasticity theory should be used to evaluate nanowire thermal conductivity as the nanowire diameter reduced to tens nanometer.

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.

Monte Carlo Simulation of Silicon Nanowire Thermal Conductivity

2005 ◽  
Vol 127 (10) ◽  
pp. 1129-1137 ◽  
Author(s):  
Yunfei Chen ◽  
Deyu Li ◽  
Jennifer R. Lukes ◽  
Arun Majumdar
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Silicon Nanowire ◽  
Wave Theory ◽  
Momentum Conservation ◽  
Phonon Transport ◽  
Recent Experimental Data ◽  
Si Nanowires ◽  
Nanowire Diameter

Monte Carlo simulation is applied to investigate phonon transport in single crystalline Si nanowires. Phonon-phonon normal (N) and Umklapp (U) scattering processes are modeled with a genetic algorithm to satisfy energy and momentum conservation. The scattering rates of N and U scattering processes are found from first-order perturbation theory. The thermal conductivity of Si nanowires is simulated and good agreement is achieved with recent experimental data. In order to study the confinement effects on phonon transport in nanowires, two different phonon dispersions, one from experimental measurements on bulk Si and the other solved from elastic wave theory, are adopted in the simulation. The discrepancy between simulations using different phonon dispersions increases as the nanowire diameter decreases, which suggests that the confinement effect is significant when the nanowire diameter approaches tens of nanometers. It is found that the U scattering probability in Si nanowires is higher than that in bulk Si due to the decrease of the frequency gap between different modes and the reduced phonon group velocity. Simulation results suggest that the dispersion relation for nanowires obtained from elasticity theory should be used to evaluate nanowire thermal conductivity as the nanowire diameter is reduced to the sub-100 nm scale.

scholarly journals Uncertainty Cost Functions in Climate-Dependent Controllable Loads in Commercial Environments

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2885
Author(s):  
Daniel Losada ◽  
Ameena Al-Sumaiti ◽  
Sergio Rivera
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Simulation Method ◽  
Electricity Sector ◽  
Cost Functions ◽  
Density Estimator ◽  
Monte Carlo Simulation Method ◽  
Commercial Building ◽  
Complementary Method ◽  
The Cost

This article presents the development, simulation and validation of the uncertainty cost functions for a commercial building with climate-dependent controllable loads, located in Florida, USA. For its development, statistical data on the energy consumption of the building in 2016 were used, along with the deployment of kernel density estimator to characterize its probabilistic behavior. For validation of the uncertainty cost functions, the Monte-Carlo simulation method was used to make comparisons between the analytical results and the results obtained by the method. The cost functions found differential errors of less than 1%, compared to the Monte-Carlo simulation method. With this, there is an analytical approach to the uncertainty costs of the building that can be used in the development of optimal energy dispatches, as well as a complementary method for the probabilistic characterization of the stochastic behavior of agents in the electricity sector.

scholarly journals Monte Carlo Modeling and Design of Photon Energy Attenuation Layers for >10× Quantum Yield Enhancement in Si-Based Hard X-ray Detectors

Instruments ◽  
2021 ◽  
Vol 5 (2) ◽  
pp. 17
Author(s):  
Eldred Lee ◽  
Kaitlin M. Anagnost ◽  
Zhehui Wang ◽  
Michael R. James ◽  
Eric R. Fossum ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Quantum Yield ◽  
Photon Energy ◽  
High Efficiency ◽  
High Energy ◽  
Yield Enhancement ◽  
X Ray ◽  
Simulation Results ◽  
Conversion Efficiencies

High-energy (>20 keV) X-ray photon detection at high quantum yield, high spatial resolution, and short response time has long been an important area of study in physics. Scintillation is a prevalent method but limited in various ways. Directly detecting high-energy X-ray photons has been a challenge to this day, mainly due to low photon-to-photoelectron conversion efficiencies. Commercially available state-of-the-art Si direct detection products such as the Si charge-coupled device (CCD) are inefficient for >10 keV photons. Here, we present Monte Carlo simulation results and analyses to introduce a highly effective yet simple high-energy X-ray detection concept with significantly enhanced photon-to-electron conversion efficiencies composed of two layers: a top high-Z photon energy attenuation layer (PAL) and a bottom Si detector. We use the principle of photon energy down conversion, where high-energy X-ray photon energies are attenuated down to ≤10 keV via inelastic scattering suitable for efficient photoelectric absorption by Si. Our Monte Carlo simulation results demonstrate that a 10–30× increase in quantum yield can be achieved using PbTe PAL on Si, potentially advancing high-resolution, high-efficiency X-ray detection using PAL-enhanced Si CMOS image sensors.

Sign in / Sign up

Export Citation Format

Share Document