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.

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Phonon Scattering ◽  
Computational Domain ◽  
Optical Phonons ◽  
Phonon Modes ◽  
Silicon Thin Film ◽  
Silicon Thin Films

Abstract The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium 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 three-phonon 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>200 K), 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, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50–200 K) and to increase it at high temperature (>200 K), especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures.

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.

Silicon Thin Film Thermal Conductivity in Ballistic and Diffusive Regimes Predicted by Molecular Dynamics

2005 ◽  
Author(s):  
Carlos J. Gomes ◽  
Marcela Madrid ◽  
Javier V. Goicochea ◽  
Cristina H. Amon
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Film Thickness ◽  
Interatomic Potential ◽  
Mean Free Path ◽  
Technical Conference ◽  
Silicon Thin Film ◽  
Silicon Thin Films ◽  
Out Of Plane

The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relationship and the Stillinger-Weber interatomic potential. Film thicknesses range from 2 to 220 nm and temperatures from 300 to 1000 K. In this range of temperatures, the relation between the phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (≫ ds) to the diffusive, bulk-like regime (≪ ds). We show that equilibrium molecular dynamics and the Green-Kubo relationship can be applied to the study of the thermal conductivity of thin films in the ballistic, transitional and diffusive regimes. When the film is thin enough, the thermal conductivity becomes orthotropic and decreases with decreasing film thickness as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300 K. In the ballistic limit, in accordance with the kinetic theory, the predicted out-of-plane thermal conductivity varies linearly with the film thickness and is temperature-independent for temperatures near or above Debye’s temperature.   This paper was also originally published as part of the Proceedings of the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems.

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.

Silicon Thin-Film Lattice Dynamics and Thermal Transport Properties

2012 ◽  
Author(s):  
Bruce L. Davis ◽  
Mehmet Su ◽  
Ihab El-Kady ◽  
Mahmoud I. Hussein
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Thermal Conductivity ◽  
Transport Properties ◽  
Lattice Dynamics ◽  
Dielectric Materials ◽  
Phonon Transport ◽  
Solid State Physics ◽  
Silicon Thin Film ◽  
Silicon Thin Films

Thin films composed of dielectric materials are attracting growing interest in the solid state physics and nanoscale heat transfer communities. This is primarily due to their unique thermal and electronic properties and their extensive use as components in optoelectronic, and potentially in thermoelectric, devices. In this paper, an elaborate study is presented on silicon thin films ranging from a few nanometers in thickness to very thick bulk-like thicknesses. Full lattice dynamics calculations are performed incorporating the entire film cross section and the relaxation of the free surfaces. The phonon properties emerging from these calculations are then incorporated into Holland-Callaway models to predict the thermal conductivity and other phonon transport properties. A rigorous curve fitting process to a limited set of available experimental data is carried out to obtain the scattering lifetimes. Our results demonstrate the importance of proper consideration of the full thin-film dispersion description and provide insights into the relationship between thermal conductivity, film thickness and temperature.

Thermal Conductivity and Phonon Engineering in Low-Dimensional Structures

1998 ◽  
Vol 545 ◽  
Author(s):  
G. Chen ◽  
S. G. Volz ◽  
T. Borca-Tasciuc ◽  
T. Zeng ◽  
D. Song ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Model Based ◽  
Conduction Mechanisms ◽  
Interface Scattering ◽  
Low Dimensional

AbstractUnderstanding phonon heat conduction mechanisms in low-dimensional structures is of critical importance for low-dimensional thermoelectricity. In this paper, we discuss heat conduction mechanisms in two-dimensional (2D) and one-dimensional (1D) structures. Models based on both the phonon wave picture and particle picture are developed for heat conduction in 2D superlattices. The phonon wave model, based on the acoustic wave equations, includes the effects of phonon interference and tunneling, while the particle model, based on the Boltzmann transport equation, treats the internal as well interface scattering of phonons. For 1D systems, both the Boltzmann transport equation and molecular dynamics simulation approaches are employed. Comparing the modeling results with experimental data suggest that the interface scattering of phonons plays a crucial role in the thermal conductivity of low-dimensional structures. We also discuss the minimum thermal conductivity of low-dimensional structures based on a generalized thermal conductivity integral, and suggest that the minimum thermal conductivities of low-dimensional systems may differ from those of their corresponding bulk materials. The discussion leads to alternative ways to reduce thermal conductivity based on the propagating phonon modes.

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