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TECHNICAL PAPERS: Micro/Nanoscale Heat Transfer

Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation

[+] Author and Article Information
Ronggui Yang, Gang Chen, Marine Laroche

Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA 02139-4307

Yuan Taur

Department of Electrical & Computer Engineering, University of California, La Jolla, CA 92093-0407

J. Heat Transfer 127(3), 298-306 (Mar 24, 2005) (9 pages) doi:10.1115/1.1857941 History: Received October 30, 2003; Revised September 12, 2004; Online March 24, 2005
Copyright © 2005 by ASME
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Figures

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Schematic drawing of device geometry simulated in this paper: (a) confined surface heating at y=0,T1, and T0 represents emitted temperature in case I and equivalent equilibrium temperature in case II; and (b) a nanoscale heat source embedded in the substrate, which is similar to the heat generation and transport in the MOSFET device
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Numerical solution scheme of the ballistic-diffusive equations
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Local coordinate used in phonon Boltzmann transport simulation
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Directions of phonon transport in two-dimensional planes as given by different combinations of the directional cosines and corresponding differencing schemes used for the BTE solver
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Comparison of the transient temperature and heat flux in y direction at the centerline of the geometry for Kn=10 based on emitted temperature condition: (a) temperature and (b) heat flux qy*
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(a) Comparison of steady-state temperature distribution at the centerline using the Fourier theory, the Boltzmann equation, and the ballistic-diffusive equations for different Knudsen numbers. (b) Comparison of the heat flux qy* at the centerline for Kn=0.1 at t*=100.
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Comparison of transient temperature and heat flux distribution at the centerline using the Fourier theory, the Boltzmann equation, and the ballistic-diffusive equations based on thermalized temperature boundary conditions: (a) and (b) heat flux qy*, and (c) temperature
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The ballistic and diffusive component contributions to the total temperature and heat flux at the centerline: (a) temperature and (b) heat flux qy*
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Comparison of two-dimensional temperature rise distribution after the device is operated for 10 ps: (a) the Boltzmann equation, (b) the Ballistic-diffusive equations, and (c) the Fourier law
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(a) Comparison of the heat flux obtained by the Boltzmann equation, the ballistic-diffusive equations, and the Fourier law at the centerline. (b) Comparison of the peak temperature rise inside the device obtained by the Boltzmann equation, the Ballistic-diffusive equations and the Fourier law.

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