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RESEARCH PAPERS: Micro/Nanoscale Heat Transfer

Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-Insulator Transistors

[+] Author and Article Information
Sreekant V. Narumanchi1

Institute for Complex Engineered Systems and Department of Mechanical Engineering,  Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213

Jayathi Y. Murthy

School of Mechanical Engineering, Purdue University, 585 Purdue Mall, W. Lafayette, IN 47907jmurthy@ecn.purdue.edu.

Cristina H. Amon

Institute for Complex Engineered Systems and Department of Mechanical Engineering,  Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213

1

Current address: National Renewable Energy Laboratory Golden, CO 80601

J. Heat Transfer 127(7), 713-723 (Mar 01, 2005) (11 pages) doi:10.1115/1.1924571 History: Received August 11, 2003; Revised March 01, 2005

The problem of self-heating in microelectronic devices has begun to emerge as a bottleneck to device performance. Published models for phonon transport in microelectronics have used a gray Boltzmann transport equation (BTE) and do not account adequately for phonon dispersion or polarization. In this study, the problem of a hot spot in a submicron silicon-on-insulator transistor is addressed. A model based on the BTE incorporating full phonon dispersion effects is used. A structured finite volume approach is used to solve the BTE. The results from the full phonon dispersion model are compared to those obtained using a Fourier diffusion model. Comparisons are also made to previously published BTE models employing gray and semi-gray approximations. Significant differences are found in the maximum hot spot temperature predicted by the different models. Fourier diffusion underpredicts the hot spot temperature by as much as 350% with respect to predictions from the full phonon dispersion model. For the full phonon dispersion model, the longitudinal acoustic modes are found to carry a majority of the energy flux. The importance of accounting for phonon dispersion and polarization effects is clearly demonstrated.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Experimental dispersion curve in the [001] direction in silicon at 300K(27); (b) spline curve fit to the LA and TA branches

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Figure 2

Coordinates axes and representative phonon direction ŝ

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Figure 3

Bulk thermal conductivity of silicon. Experimental data from Holland (27)

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Figure 4

Undoped silicon thin film in-plane thermal conductivity. Experimental data are from Asheghi (29) (for the 0.42 and 1.6μm films), and from Asheghi (30) (for the 3.0μm film)

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Figure 5

Doped 3.0μm silicon thin film in-plane thermal conductivity. Experimental data are from Asheghi (30)

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Figure 6

Two-dimensional computational domain of the silicon-on-insulator transistor

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Figure 7

Energy balance at the silicon/silicon dioxide interface

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Figure 8

Transmission coefficient in silicon as a function of frequency, 6×6×1 frequency bands

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Figure 9

Total lattice temperature contours in the domain using: (a) Fourier diffusion, (b) gray model, (c) semi-gray model, (d) full dispersion model

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Figure 10

Temperature contours in the silicon layer for the different frequency bands in the phonon branches: (a) LA band 1, (b) LA band 3, (c) LA band 6, (d) TA band 1, (e) TA band 3, (f) TA band 6, (g) optical band

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