DSMC Scheme for Phonon Transport in Solid Thin Films

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Mitsuhiro Matsumoto ◽  
Masaya Okano ◽  
Yusuke Masao
Keyword(s):  
Thin Films ◽  
Input Parameter ◽  
Direct Simulation Monte Carlo ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Phonon Dynamics ◽  
Solid Thin Films ◽  
Simulation Monte Carlo ◽  
Phonon Model

Analysis of phonon dynamics based on a linearized Boltzmann transport equation is widely used for thermal analysis of solid thin films, but couplings among various phonon modes appear in some situations. We propose a direct simulation Monte Carlo (DSMC) scheme to simulate the phonon gas starting without the conventional linearization approximation. This requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes. A prototype code based on a simple phonon model was developed, and energy flux was evaluated for thin films of various thickness as a test calculation.

DSMC for Phonon Transport in Solid Thin Films

2009 ◽  
Author(s):  
Mitsuhiro Matsumoto ◽  
Masaya Okano
Keyword(s):  
Heat Transfer ◽  
Thin Films ◽  
Relaxation Time ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Thermal Design ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Phonon Dynamics ◽  
Solid Thin Films

As the scale of electronic devices decreases, heat transfer analysis and thermal design becomes more important. In particular, heat transfer through various solid thin films is strongly affected by thickness dependence of thermal conductivity and interfacial thermal resistance. Analysis of phonon dynamics based on a linearized Boltzmann transport equation, or the so-called relaxation time approximation, has been widely used, but detailed analysis using molecular dynamics simulation reveals that couplings among various phonon modes can affect the energy transfer. In this study, we propose a DSMC scheme to simulate phonon dynamics starting from the original Boltzmann transport equation. In contrast to the linearized model, this scheme requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes, although we have to assume some appropriate model of phonon-phonon collisions. As a test calculation, energy flux was evaluated for model thin films of various thicknesses, and a phenomenon similar to the Casimir limit was retrieved. This scheme will enable us to include other factors, such as phonon-electron couplings.

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 beta-gallium oxide thin-film using non-gray Boltzmann transport equation

2021 ◽  
Author(s):  
Nitish Kumar ◽  
Matthew Barry ◽  
Satish Kumar
Keyword(s):  
Thin Films ◽  
Temperature Distribution ◽  
Energy Dissipation ◽  
Thermal Transport ◽  
Energy Exchange ◽  
Domain Size ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Abstract Phonon transport  in β-Ga2O3 thin films and metal–oxide field effect transistors (MESFETs) are investigated using non-gray Boltzmann transport equations (BTE) to decipher the effect of  ballistic-diffusive phonon transport. The effects of domain size, and  energy dissipation to various phonon modes and subsequent phonon-phonon energy exchange on the thermal transport and temperature distribution is investigated using non-gray BTE. Our analysis deciphered that domain size plays a major role in thermal transport in β-Ga2O3 but energy dissipation to various phonon modes and subsequent phonon-phonon energy exchange does not affect the temperature field significantly.   Phonon transport in β-Ga2O3 MESFETs on diamond substrate is investigated using coupled non-gray BTE and Fourier model. It is established that the ballistic effects need to be considered for devices with β-Ga2O3 layer thickness less than 1 µm. A non-gray phonon BTE model should be used near hotspot in the thin β-Ga2O3 layer as the Fourier model may not give accurate temperature distribution. The results from this work will help in understanding the mechanism of phonon transport in the β-Ga2O3 thin films and energy efficient design of its FETs.

FREQUENCY DEPENDENT PHONON TRANSPORT IN TWO-DIMENSIONAL SILICON AND DIAMOND THIN FILMS

2012 ◽  
Vol 26 (17) ◽  
pp. 1250104 ◽  
Author(s):  
B. S. YILBAS ◽  
S. BIN MANSOOR
Keyword(s):  
Thin Films ◽  
Boltzmann Transport Equation ◽  
Diamond Films ◽  
Equilibrium Temperature ◽  
Phonon Transport ◽  
Two Dimensional ◽  
Boltzmann Transport ◽  
Frequency Dependent ◽  
Aluminum Films ◽  
The Difference

Phonon transport in two-dimensional silicon and aluminum films is investigated. The frequency dependent solution of Boltzmann transport equation is obtained numerically to account for the acoustic and optical phonon branches. The influence of film size on equivalent equilibrium temperature distribution in silicon and aluminum films is presented. It is found that increasing film width influences phonon transport in the film; in which case, the difference between the equivalent equilibrium temperature due to silicon and diamond films becomes smaller for wider films than that of the thinner films.

scholarly journals Computational Study of In-Plane Phonon Transport in Si Thin Films

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Xinjiang Wang ◽  
Baoling Huang
Keyword(s):  
Thin Films ◽  
Thermal Transport ◽  
Computational Study ◽  
Isotope Effects ◽  
Phonon Transport ◽  
Phonon Confinement ◽  
Phonon Modes ◽  
Scattering Rate ◽  
Si Films ◽  
Thermal Conductivities

Abstract We have systematically investigated the in-plane thermal transport in Si thin films using an approach based on the first-principles calculations and lattice dynamics. The effects of phonon mode depletion induced by the phonon confinement and the corresponding variation in interphonon scattering, which may be important for the thermal conductivities of ultra-thin films but are often neglected in precedent studies, are considered in this study. The in-plane thermal conductivities of Si thin films with different thicknesses have been predicted over a temperature range from 80 K to 800 K and excellent agreements with experimental results are found. The validities of adopting the bulk phonon properties and gray approximation of surface specularity in thin film studies have been clarified. It is found that in ultra-thin films, while the phonon depletion will reduce the thermal conductivity of Si thin films, its effect is largely offset by the reduction in the interphonon scattering rate. The contributions of different phonon modes to the thermal transport and isotope effects in Si films with different thicknesses under various temperatures are also analyzed.

Direct Simulation of the Nonlinear Boltzmann Transport Equation for Phonons

2011 ◽  
Author(s):  
Yusuke Masao ◽  
Mitsuhiro Matsumoto
Keyword(s):  
Transport Equation ◽  
Rarefied Gas ◽  
Boltzmann Transport Equation ◽  
Direct Simulation Monte Carlo ◽  
Face Centered Cubic ◽  
Direct Simulation ◽  
Boltzmann Transport ◽  
Phonon Dynamics ◽  
Cubic Model ◽  
Face Centered

In order to solve a Boltzmann transport equation (BTE) of phonons for investigating heat conduction in non-metallic solids, we propose to employ a DSMC (direct simulation Monte Carlo) scheme to simulate dynamics of phonons in analogy with rarefied gas. In this paper, we describe the DSMC scheme for phonon dynamics and present some results with our prototype codes for a face-centered cubic model. The dynamics of phonons with two branches of acoustic modes is discussed, in the case where the distribution of phonons in strong nonequilibrium situation is driven into equilibrium.

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films: Role of Optical Phonons

2009 ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Optical Phonons ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Silicon Thin Film ◽  
Silicon Thin Films

The Monte Carlo (MC) method has found prolific use in the solution of the Boltzmann Transport Equation (BTE) for phonons for the prediction of non-equilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions—in particular, optical phonons. A procedure to calculate scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that Transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T > 200K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes. At room temperature, optical modes are found to carry about 25% of the energy at steady state in Silicon thin films. Most importantly, inclusion of optical phonons results in better match with experimental observations for Silicon thin-film thermal conductivity.

A Split-Flux Model for Phonon Transport Near Hotspots

2004 ◽  
Author(s):  
S. Sinha ◽  
E. Pop ◽  
K. E. Goodson
Keyword(s):  
Electric Fields ◽  
Phonon Scattering ◽  
Semiconductor Device ◽  
Longitudinal Optical ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Relaxation Time Approximation ◽  
Occupation Numbers ◽  
The Impact

Intense electron-phonon scattering near the peak electric field in a semiconductor device results in nanometer-scale phonon hotspots with power densities on the order of 1 W/μm3. To study the impact of the hotspot on phonon transport, we solve the phonon Boltzmann transport equation under the relaxation time approximation to yield the departure from equilibrium amongst phonon modes. The departure function is split into two contributions: one arising from the far-from-equilibrium emitted phonons and the other from the near-equilibrium thermal phonons. The model predictions are compared with existing data on ballistic phonon transport in silicon. Computations of transient and steady state phonon occupation numbers for a device geometry show the predominance of longitudinal optical phonons for electric fields on the order of 1 MV/m. Due to the low group velocity of these modes, there is an energy stagnation at the hotspot which results in an excess temperature rise of about 13% for a 90 nm bulk silicon device. During device switching, emitted phonons have sufficient time to relax completely when the duty cycle is 30% on a period of 100 ps.

Phonon Transport in Thin Films: A Lattice Dynamics/Boltzmann Transport Equation Study

2010 ◽  
Author(s):  
Daniel P. Sellan ◽  
Joseph E. Turney ◽  
Eric S. Landry ◽  
Alan J. H. McGaughey ◽  
Cristina H. Amon
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Lattice Dynamics ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Bulk Phonon ◽  
Plane Direction ◽  
The Cross ◽  
Phonon Properties

The cross-plane and in-plane phonon thermal conductivities of Stillinger-Weber (SW) silicon thin films are predicted using the Boltzmann transport equation under the relaxation time approximation. We model the thin films using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. The cross-plane and in-plane thermal conductivities are reduced from the corresponding bulk value. This reduction is more severe for the cross-plane direction than for the in-plane direction. For the in-plane direction, we find that the predicted reduction in thermal conductivity gives a good lower bound to available experimental results. Including the effects of boundary scattering using the Matthiessen rule, which assumes that scattering mechanisms are independent, yields thermal conductivity predictions that are at most 12% lower than our more accurate results. Neglecting optical phonon modes, while valid for bulk systems, introduces 22.5% error when modeling thin films. Using phonon properties along the [001] direction (i.e., the isotropic approximation) yields bulk predictions that are 15% lower than that when all of the phonon modes are considered. For thin films, this deviation increases to 25%. Our results show that a single bulk phonon mean free path is an inadequate metric for predicting the thermal conductivity reduction in thin films.

Heat generation in silicon nanometric semiconductor devices

2014 ◽  
Vol 33 (4) ◽  
pp. 1198-1207 ◽  
Author(s):  
Orazio Muscato ◽  
Wolfgang Wagner ◽  
Vincenza Di Stefano
Keyword(s):  
Heat Generation ◽  
Semiconductor Devices ◽  
Direct Simulation Monte Carlo ◽  
Generation Rate ◽  
Boltzmann Transport ◽  
Approximation Properties ◽  
Heat Generation Rate ◽  
Content Type ◽  
Statistical Fluctuations ◽  
Simulation Monte Carlo

Purpose – The purpose of this paper is to deal with the self-heating of semiconductor nano-devices. Design/methodology/approach – Transport in silicon semiconductor devices can be described using the Drift-Diffusion model, and Direct Simulation Monte Carlo (MC) of the Boltzmann Transport Equation. Findings – A new estimator of the heat generation rate to be used in MC simulations has been found. Originality/value – The new estimator for the heat generation rate has better approximation properties due to reduced statistical fluctuations.

Sign in / Sign up

Export Citation Format

Share Document