Computations of Sub-Micron Heat Transport in Silicon Accounting for Phonon Dispersion

2003 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Phonon Dispersion ◽  
Relaxation Times ◽  
Thermal Response ◽  
Boltzmann Transport ◽  
Proposed Model ◽  
Transverse Acoustic ◽  
Different Temperatures ◽  
Finite Volume Approach ◽  
Transient Thermal ◽  
Transient Thermal Response

In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the sub-micron 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 (TA) and longitudinal acoustic (LA) 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. Also, in the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model even at coarse phonon frequency band discretization.

Submicron Heat Transport Model in Silicon Accounting for Phonon Dispersion and Polarization

2004 ◽  
Vol 126 (6) ◽  
pp. 946-955 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Thermal Conductivity ◽  
Phonon Dispersion ◽  
Transport Model ◽  
Relaxation Times ◽  
Thermal Response ◽  
Boltzmann Transport ◽  
Wide Range ◽  
Submicron Scale ◽  
Different Temperatures ◽  
Finite Volume Approach

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.

Influence of Phonon Dispersion on Transient Thermal Response of Silicon-on-Insulator Transistors Under Self-Heating Conditions

2006 ◽  
Vol 129 (7) ◽  
pp. 790-797 ◽  
Author(s):  
Rodrigo A. Escobar ◽  
Cristina H. Amon
Keyword(s):  
Computational Models ◽  
Phonon Dispersion ◽  
Thermal Response ◽  
Domain Size ◽  
Phonon Transport ◽  
Silicon On Insulator ◽  
Nonlinear Relation ◽  
Temperature Levels ◽  
Transient Thermal ◽  
Transient Thermal Response

Lattice Boltzmann method (LBM) simulations of phonon transport are performed in one-dimensional (1D) and 2D computational models of a silicon-on-insulator transistor, in order to investigate its transient thermal response under Joule heating conditions, which cause a nonequilibrium region of high temperature known as a hotspot. Predictions from Fourier diffusion are compared to those from a gray LBM based on the Debye assumption, and from a dispersion LBM which incorporates nonlinear dispersion for all phonon branches, including explicit treatment of optical phonons without simplifying assumptions. The simulations cover the effects of hotspot size and heat pulse duration, considering a frequency-dependent heat source term. Results indicate that, for both models, a transition from a Fourier diffusion regime to a ballistic phonon transport regime occurs as the hotspot size is decreased to tens of nanometers. The transition is characterized by the appearance of boundary effects, as well as by the propagation of thermal energy in the form of multiple, superimposed phonon waves. Additionally, hotspot peak temperature levels predicted by the dispersion LBM are found to be higher than those from Fourier diffusion predictions, displaying a nonlinear relation to hotspot size, for a given, fixed, domain size.

Transient thermal response in ultrasonic additive manufacturing of aluminum 3003

2011 ◽  
Vol 17 (5) ◽  
pp. 369-379 ◽  
Author(s):  
David Schick ◽  
Sudarsanam Suresh Babu ◽  
Daniel R. Foster ◽  
Marcelo Dapino ◽  
Matt Short ◽  
...  
Keyword(s):  
Additive Manufacturing ◽  
Thermal Response ◽  
Ultrasonic Additive Manufacturing ◽  
Transient Thermal ◽  
Transient Thermal Response

Transient Thermal Response of the Media by Free Space Laser Heating in Heat Assisted Magnetic Recording

2016 ◽  
Author(s):  
Shaomin Xiong ◽  
Robert Smith ◽  
Na Wang ◽  
Dongbo Li ◽  
Erhard Schreck ◽  
...  
Keyword(s):  
Magnetic Recording ◽  
Heat Conduction Problem ◽  
Temperature Response ◽  
Thermal Response ◽  
Areal Density ◽  
Heat Assisted Magnetic Recording ◽  
Lumped Model ◽  
The Media ◽  
Transient Thermal ◽  
Transient Thermal Response

Heat assisted magnetic recording (HAMR) promises to deliver higher storage areal density than the current perpendicular magnetic recording (PMR) product. A laser is introduced to the HAMR system to heat the high coercively magnetic media above the Curie temperature (Tc) which is as high as 750 K in order to enable magnetic writing. The thermal response of the media becomes very critical for the success of the data writing process. In this paper, a new method is proposed to understand the transient thermal behavior of the HAMR media. The temperature response of the media is measured based on thermal erasure of the magnetically written signal. A lumped model is built to simplify the heat conduction problem to understand the transient thermal response. Finite element modeling (FEM) is implemented to simulate the transient thermal response of the media due to the laser pulse heating. The experimental and simulation results show fairly good agreement.

Measurement of Thermal Conductivity of a Flexible Substrate

2014 ◽  
Author(s):  
Vivek Vishwakarma ◽  
Ankur Jain
Keyword(s):  
Thermal Conductivity ◽  
Analytical Model ◽  
Flexible Substrate ◽  
Thermal Response ◽  
Experimental Methodology ◽  
Plastic Substrate ◽  
The Past ◽  
Thin Plastic ◽  
Transient Thermal ◽  
Transient Thermal Response

A number of past papers have described experimental techniques for measurement of thermal conductivity of substrates and thin films of technological interest. Nearly all substrates measured in the past are rigid. There is a lack of papers that report measurements on a flexible substrate such as thin plastic. The paper presents an experimental methodology to deposit a thin film microheater device on a plastic substrate. This device, comprising a microheater line and a temperature sensor line is used to measure the thermal conductivity of the plastic substrate using the transient thermal response of the plastic substrate to a heating current. An analytical model describing this thermal response is presented. Thermal conductivity of the plastic substrate is determined by comparison of experimental data with the analytical model. Results described in this paper may aid in development of an understanding of thermal transport in flexible substrates.

Transient Thermal Analysis of an Anisotropic Conductive Film Package Assembly Process

2000 ◽  
Author(s):  
Victor Adrian Chiriac ◽  
Tien-Yu Tom Lee
Keyword(s):  
Temperature Drop ◽  
Thermal Response ◽  
Heating Process ◽  
Assembly Process ◽  
Anisotropic Conductive Film ◽  
Conductive Film ◽  
Different Temperatures ◽  
Computational Fluid Dynamics Cfd ◽  
Nozzle Head ◽  
Transient Thermal

Abstract Transient thermal simulation was performed to analyze thermal response of the assembly process for a package using Anisotropic Conductive Film (ACF). Two assembly processes were modeled: a simplified process where the package was fixed at two different temperatures during assembly, and a detailed process where the package experienced a ramping heating process, followed by a constant temperature curing process. A 3D conjugate Computational Fluid Dynamics (CFD) study was first conducted, followed by a 3D conduction-only analysis due to the minimal effect of convection and radiation. Results from the detailed process modeling indicated that during the initial ramping, within 0.02 second, the die and nozzle head experienced a small temperature drop due to the cooling effect of the ACF material and substrate. The ACF material also displayed a steep increase in temperature after contacting the die, followed by a short decay, then ramped up again. At the end of the 10-second ramping process, the ACF reached a temperature of almost 203°C, while the die was at 206°C. During the 5 seconds of curing, all parts reached steady state in less than 2 seconds.

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