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Journal ArticleDOI

Simulation of Unsteady Small Heat Source Effects in Sub-Micron Heat Conduction

01 Oct 2003-Journal of Heat Transfer-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 125, Iss: 5, pp 896-903
TL;DR: In this article, the authors present a study of hot spot behavior in the phonon Boltzmann transport equation (BTE) in the retardation fiber approximation using a finite volume method.
Abstract: In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller them the phonon mean free path in the medium. In this paper we present a study of unsteady hot spot behavior. The unsteady gray phonon Boltzmann transport equation (BTE) is solved in the retardation fibre approximation using a finite volume method. Electron-phonon interaction is represented as a heat source term in the phonon BTE. The evolution of the temperature profile is governed by the interaction of four competing time scales: the phonon residence time in the hot spot and in the domain, the duration of the energy source, and the phonon relaxation time. The influence of these time scales on the temperature is investigated. Both boundary scattering and heat source localisation effects are observed to have considerable impact on the thermal predictions. Comparison of BTE solutions with conventional Fourier diffusion analysis reveals significant discrepancies.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a model based on the Boltzmann transport equation (BTE) was proposed for predicting thermal transport in dielectrics and semiconductors at the submicron scale.
Abstract: In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the submicron scale. However, most published studies make a gray assumption and do not account for either dispersion or polarization. In this study, we propose a model based on the BTE, accounting for transverse acoustic and longitudinal acoustic phonons as well as optical phonons. This model incorporates realistic phonon dispersion curves for silicon. The interactions among the different phonon branches and different phonon frequencies are considered, and the proposed model satisfies energy conservation. Frequency-dependent relaxation times, obtained from perturbation theory, and accounting for phonon interaction rules, are used. In the present study, the BTE is numerically solved using a structured finite volume approach. For a problem involving a film with two boundaries at different temperatures, the numerical results match the analogous exact solutions from radiative transport literature for various acoustic thicknesses. For the same problem, the transient thermal response in the acoustically thick limit matches results from the solution to the parabolic Fourier diffusion equation. In the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model. Experimental in-plane thermal conductivity data for silicon thin films over a wide range of temperatures are also matched satisfactorily.

190 citations

Journal ArticleDOI
TL;DR: In this article, the transient ballistic-diffusive heat conduction equations (BDE) were developed as an approximation to the phonon Boltzmann equation (BTE) for nanoscale heat convection problems.
Abstract: Heat conduction. in micro- and nanoscale and in ultrafast processes may deviate from the predictions of the Fourier law, due to boundary and interface scattering, the ballistic nature of the transport, and the finite relaxation time of heat carriers. The transient ballistic-diffusive heat conduction equations (BDE) were developed as an approximation to the phonon Boltzmann equation (BTE) for nanoscale heat conduction problems. In this paper, we further develop BDE for multidimensional heat conduction, including nanoscale heat source term and different boundary conditions, and compare the simulation results with those obtained from the phonon BTE and the Fourier law. The numerical solution strategies for multidimensional nanoscale heat conduction using BDE are presented. Several two-dimensional cases are simulated and compared to the results of the transient phonon BTE and the Fourier heat conduction theory. The transient BTE is solved using the discrete ordinates method with a two Gauss-Legendre quadratures. Special attention has been paid to the boundary conditions. Compared to the cases without internal heat generation, the difference between the BTE and BDE is larger for the case studied with internal heat generation due to the nature of the ballistic-diffusive approximation, but the results from BDE are still significantly better than those from the Fourier law. Thus we conclude that BDE captures the characteristics of the phonon BTE with much shorter computational time.

169 citations

Journal ArticleDOI
TL;DR: In this paper, the lattice Boltzmann method is used to investigate one-dimensional, multi-length and -time scale transient heat conduction in crystalline semiconductor solids, in which sub-continuum effects are important.

127 citations


Cites background or methods or result from "Simulation of Unsteady Small Heat S..."

  • ...The LBM again shows a similar hot boundary temperature slip to that for the BDE but exhibit a higher temperature inside the domain exhibiting a more prominent ballistic behavior than BDE....

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  • ...Both the Fourier and Cattaneo equations exhibited the diffusive temperature profiles which are in general agreement to those by the LBM and the BDE....

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  • ...Results for the LBM are similar to those for the BDE, which itself is an approximation of the phonon BTE, with both approaches exhibiting clear diffusive behavior, owing to the large length and time scales....

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  • ...In addition, the silicon dioxide layer has poor thermal conductivity and, as a result, most of the heat generated within the SOI device remains confined to the thin silicon film, making it susceptible to thermal failure under electrostatic discharge (ESD) events or even under normal switching activity during continuous operation [5,6]....

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  • ...The BDE also captures the ballistic behavior as LBM with similar temperature jump at the hot boundary but exhibit a higher diffusive component resulting in more temperature drop across the film as compared to the LBM....

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Journal ArticleDOI
TL;DR: Recent advances in both computation and experiment are enabling an unprecedented microscopic view of thermal transport by phonons in both bulk and nanostructured crystals, from the level of atomic bonding to mesoscopic transport in complex devices.
Abstract: Heat conduction by phonons is a ubiquitous process that incorporates a wide range of physics and plays an essential role in applications ranging from space power generation to LED lighting. Heat conduction has been studied for over two hundred years, yet many of the microscopic details have remained unknown in most crystalline solids, including which phonon–phonon interactions are primarily responsible for thermal resistance and how heat is distributed among the broad thermal spectrum. This lack of knowledge was the result of limitations on the available tools to study heat conduction. However, recent advances in both computation and experiment are enabling an unprecedented microscopic view of thermal transport by phonons in both bulk and nanostructured crystals, from the level of atomic bonding to mesoscopic transport in complex devices. In this topical review, we examine these techniques and the microscopic insights gained into the science and engineering of heat conduction.

114 citations

Journal ArticleDOI
TL;DR: This survey, although extensive cannot include every paper; some selection is necessary, is intended to encompass the English language heat transfer papers published in 2003, including some translations of foreign language papers.

106 citations


Additional excerpts

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References
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Book
01 Jan 1980
TL;DR: In this article, the authors focus on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms.
Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.

21,858 citations

Book
01 Jan 1993
TL;DR: In this article, the Monte Carlo method for thermal radiation was used to estimate the radiative properties of one-dimensional Gray Media, and the method of Spherical Harmonics (PN-Approximation) was used for the same purpose.
Abstract: 1. Fundamentals of Thermal Radiation 2. Radiative Property Predictions from Electromagnetic Wave Theory 3. Radiative Properties of Real Surfaces 4. View Factors 5. Radiative Exchange Between Gray, Diffuse Surfaces 6. Radiative Exchange Between Partially-Specular Gray Surfaces 7. Radiative Exchange Between Nonideal Surfaces 8. Surface Radiative Exchange in the Presence of Conduction and Convection 9. The Equation of Radiative Transfer in Participating Media 10. Radiative Properties of Molecular Gases 11. Radiative Properties of Particulate Media 12. Radiative Properties of Semitransparent Media 13. Exact Solutions for One-Dimensional Gray Media 14. Approximate Solution Methods for One-Dimensional Media 15. The Method of Spherical Harmonics (PN-Approximation) 16. The Method of Discrete Ordinates (SN-Approximation) 17. The Zonal Method 18. The Treatment of Collimated Irradiation 19. The Treatment of Nongray Extinction Coefficients 20. The Monte Carlo Method for Thermal Radiation 21. Radiation Combined with Conduction and Convection 22. Inverse Radiative Heat Transfer A. Constants and Conversion Factors B. Tables for Radiative Properties of Opaque Surfaces C. Blackbody Emissive Power Table D. View Factor Catalogue E. Exponential Integral Functions F. Computer Codes Author Index Subject Index

4,907 citations

Journal ArticleDOI
TL;DR: Based on Boltzmann transport theory, an equation of phonon radiative transfer (EPRT) was developed in this paper, where the phonon-scattering mean free path was used to analyze heat transport by lattice vibrations or phonons.
Abstract: Heat conduction in dielectric thin films is a critical issue in the design of electronic devices and packages. Depending on the material properties, there exists a range of film thickness where the Fourier law, used for macroscale heat conduction, cannot be applied. In this microscale regime, heat transport by lattice vibrations or phonons can be analyzed as a radiative transfer problem. Based on Boltzmann transport theory, an equation of phonon radiative transfer (EPRT) is developed. In the acoustically thick limit, ξ L >>1, or the macroscale regime, where the film thickness is much larger than the phonon-scattering mean free path, the EPRT reduces to the Fourier law

831 citations

Journal ArticleDOI
TL;DR: In this paper, the authors derived transport equations for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs.
Abstract: Transport equations are derived for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs. Care is taken to state and discuss the assumptions which are made in the derivation. The collision processes are expressed in terms of relaxation times. The accuracy is improved by considering these to depend on the average kinetic energy rather than the electron temperature. Other transport equations used in the literature are discussed, and shown to be incomplete and inaccurate in many cases. In particular, the usual assumption that the mobility and diffusion constant depend locally on the electric field strength is shown to be incorrect. Rather, these quantities should be taken as functions of the local average velocity of electrons in the lower valley.

765 citations

Journal ArticleDOI
TL;DR: In this paper, the Boltzmann transport equation is used to model the transport of electrons and electron lattice interactions during ultrafast laser heating of metals from a microscopic point of view.
Abstract: This work studies heat transfer mechanisms during ultrafast laser heating of metals from a microscopic point of view. The heating process is composed of three processes: the deposition of radiation energy on electrons, the transport of energy by electrons, and the heating of the material lattice through electron-lattice interactions. The Boltzmann transport equation is used to model the transport of electrons and electron lattice interactions. The scattering term of the Boltzmann equation is evaluated from quantum mechanical considerations, which shows the different contributions of the elastic and inelastic electron-lattice scattering processes on energy transport. By solving the Boltzmann equation, a hyperbolic two-step radiation heating model is rigorously established. It reveals the hyperbolic nature of energy flux carried by electrons and the nonequilibrium between electrons and the lattice during fast heating processes. Predictions from the current model agree with available experimental data during subpicosecond laser heating. 20 refs., 7 figs., 2 tabs.

709 citations