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.

In-Plane and Out-Of-Plane Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics

2006 ◽  
Vol 128 (11) ◽  
pp. 1114-1121 ◽  
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 ◽  
Free Boundaries ◽  
Silicon Thin Films ◽  
Out Of Plane ◽  
Bulk Phonon

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 relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2to217nm and temperatures from 300to1000K. The relation between the bulk phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (Λ⪢ds) at 300K to the diffusive, bulk-like regime (Λ⪡ds) at 1000K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease 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 300K. In the ballistic limit, in accordance with the kinetic and phonon radiative transfer theories, the predicted out-of-plane thermal conductivity varies linearly with the film thickness, and is temperature-independent for temperatures near or above the Debye’s temperature.

scholarly journals Effect of Grain Size and Film Thickness on the Thermoelectric Properties of Flexible Sb2Te3 Thin Films

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Pornsiri Wanarattikan ◽  
Piya Jitthammapirom ◽  
Rachsak Sakdanuphab ◽  
Aparporn Sakulkalavek
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Grain Size ◽  
Film Thickness ◽  
Seebeck Coefficient ◽  
Thermoelectric Properties ◽  
Flexible Substrate ◽  
Rf Magnetron Sputtering ◽  
Mean Free Path

In this work, stoichiometric Sb2Te3 thin films with various thicknesses were deposited on a flexible substrate using RF magnetron sputtering. The grain size and thickness effects on the thermoelectric properties, such as the Seebeck coefficient (S), electrical conductivity (σ), power factor (PF), and thermal conductivity (k), were investigated. The results show that the grain size was directly related to film thickness. As the film thickness increased, the grain size also increased. The Seebeck coefficient and electrical conductivity corresponded to the grain size of the films. The mean free path of carriers increases as the grain size increases, resulting in a decrease in the Seebeck coefficient and increase in electrical conductivity. Electrical conductivity strongly affects the temperature dependence of PF which results in the highest value of 7.5 × 10−4 W/m·K2 at 250°C for film thickness thicker than 1 µm. In the thermal conductivity mechanism, film thickness affects the dominance of phonons or carriers. For film thicknesses less than 1 µm, the behaviour of the phonons is dominant, while both are dominant for film thicknesses greater than 1 µm. Control of the grain size and film thickness is thus critical for controlling the performance of Sb2Te3 thin films.

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.

Molecular Dynamics Simulation on the Out-of Plane Thermal Conductivity of Single-Crystal Carbon Thin Films

2009 ◽  
Vol 60-61 ◽  
pp. 430-434 ◽  
Author(s):  
Xing Li Zhang ◽  
Zhao Wei Sun ◽  
Guo Qiang Wu
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Potential Energy ◽  
Film Thickness ◽  
Single Crystal ◽  
Diamond Crystal ◽  
Dynamics Simulation ◽  
Crystal Direction

In this article, we select corresponding Tersoff potential energy to build potential energy model and investigate the thermal conductivities of single-crystal carbon thin-film. The equilibrium molecular dynamics (EMD) method is used to calculate the nanometer thin film thermal conductivity of diamond crystal at crystal direction (001), and the non-equilibrium molecular dynamics (NEMD) is used to calculate the nanometer thin film thermal conductivity of diamond crystal at crystal direction (111). The results of calculations demonstrate that the nanometer thin film thermal conductivity of diamond crystal is remarkably lower than the corresponding bulk experimental data and increase with increasing the film thickness, and the nanometer thin film thermal conductivity of diamond crystal relates to film thickness linearly in the simulative range. The nanometer thin film thermal conductivity also demonstrates certain regularity with the change of temperature. This work shows that molecular dynamics, applied under the correct conditions, is a viable tool for calculating the thermal conductivity of nanometer thin films.

Thin Film In-Plane Silicon Thermal Conductivity Dependence on Molecular Dynamics Surface Boundary Conditions

2004 ◽  
Author(s):  
Carlos J. Gomes ◽  
Marcela Madrid ◽  
Cristina H. Amon
Keyword(s):  
Thin Film ◽  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Mean Free Path ◽  
Surface Boundary ◽  
Repulsive Potential ◽  
Surface Boundary Conditions ◽  
Weber Potential

The in-plane thermal conductivity of thin silicon films is predicted using equilibrium molecular dynamics, the Stillinger-Weber potential and the Green-Kubo relationship. Film thicknesses range from 2 to 200 nm. Periodic boundary conditions are used in the directions parallel to the thin film surfaces. Two different strategies are evaluated to treat the atoms on the surfaces perpendicular to the thin film direction: adding four layers of atoms kept frozen at their crystallographic positions, or restraining the atoms near the surfaces with a repulsive potential. We show that when the thin-film thickness is smaller than the phonon mean free path, the predictions of the in-plane thermal conductivity at 1000K differ significantly depending on the potential applied to the atoms near the surfaces. In this limit, the experimentally observed trend of decreasing thermal conductivity with decreasing film thickness is predicted when the surface atoms are subject to a repulsive potential in addition to the Stillinger-Weber potential, but not when they are limited by frozen atoms.

Interface and Strain Effects on the Thermal Conductivity of Heterostructures: A Molecular Dynamics Study

2002 ◽  
Vol 124 (5) ◽  
pp. 963-970 ◽  
Author(s):  
Alexis R. Abramson ◽  
Chang-Lin Tien ◽  
Arun Majumdar
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Film Thickness ◽  
Molecular Dynamics Simulations ◽  
Effective Thermal Conductivity ◽  
Lattice Strain ◽  
Unit Length ◽  
Single Interface ◽  
Dynamics Simulations

Molecular dynamics simulations are used to examine how thermal transport is affected by the presence of one or more interfaces. Parameters such as film thickness, the ratio of respective material composition, the number of interfaces per unit length, and lattice strain are considered. Results indicate that for simple nanoscale strained heterostructures containing a single interface, the effective thermal conductivity may be less than half the value of an average of the thermal conductivities of the respective unstrained thin films. Increasing the number of interfaces per unit length, however, does not necessarily result in a corresponding decrease in the effective thermal conductivity of the superlattice.

Thermal Conductivity of Ordered Mesoporous Silicon Thin Films Made From Magnesium Reduction of Polymer Templated Silica

2011 ◽  
Author(s):  
Jin Fang ◽  
Laurent Pilon ◽  
Chris B. Kang ◽  
Sarah H. Tolbert
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Film Thickness ◽  
Crystalline Silicon ◽  
Average Crystallite Size ◽  
Face Centered Cubic ◽  
Mesoporous Silicon ◽  
X Ray ◽  
Silicon Thin Films ◽  
The Cross

This paper reports the cross-plane thermal conductivity of ordered polycrystalline mesoporous silicon thin films between 30 and 320 K. The films were produced by a combination of evaporation induced self-assembly (EISA) of mesoporous silica followed by magnesium reduction. The periodic ordering of pores in mesoporous silicon was characterized by a combination of 1D X-ray diffraction, 2D small angle X-ray scattering, and direct SEM imaging. The average crystallite size, porosity, and film thickness were about 13–18 nm, 25–35%, and 140–260 nm, respectively. The pores were arranged in a face-centered cubic lattice. Finally, the cross-plane thermal conductivity of the meso-porous silicon thin films was measured using the 3ω method. The measured thermal conductivity was about 3 to 5 orders of magnitude smaller than that of the bulk dense crystalline silicon for the temperature range considered. The effects of temperature and film thickness on the thermal conductivity were investigated.

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.

Molecular Dynamics Simulation of Thermal Conductivity of Silicon Films Using Environment-Dependent Interatomic Potential

Volume 4 ◽  
2004 ◽  
Author(s):  
Xinwei Wang ◽  
Cecil Lawrence
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Film Thickness ◽  
Lattice Boltzmann ◽  
Interatomic Potential ◽  
Silicon Films ◽  
Dynamics Simulation ◽  
Nonequilibrium Molecular Dynamics ◽  
Boltzmann Method ◽  
Weber Potential

In this work, nonequilibrium molecular dynamics is used to predict the thermal conductivity of nanoscale thin silicon films in the thickness direction. Recently developed environment-dependent interatomic potential for silicon, which offers considerable improvement over the more common Stillinger-Weber potential, is used. Silicon films of various thicknesses are modeled to establish the variation of thermal conductivity with the film thickness. The obtained relationship between the thermal conductivity and the film thickness is compared with the results of the Lattice Boltzmann method, and sound agreement is observed.

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