The temperature rise in sub-micrometer silicon devices is predicted at present by solving the heat diffusion equation based on the Fourier law. The accuracy of this approach needs to be carefully examined for semiconductor devices in which the channel length is comparable with or smaller than the phonon mean free path. The phonon mean free path in silicon at room temperature is near 300 nm and exceeds the channel length of contemporary transistors. This work numerically integrates the two-dimensional phonon Boltzmann transport equation (BTE) within the silicon region of a silicon-on-insulator (SOI) transistor. The BTE is solved together with the classical heat diffusion equation in the silicon dioxide layer beneath the transistor. The predicted peak temperature rise is nearly 160 percent larger than a prediction using the heat diffusion equation for the entire domain. The disparity results both from phonon-boundary scattering and from the small dimensions of the region of strongest electron-phonon energy transfer. This work clearly shows the importance of sub-continuum heat conduction in modern transistors and will facilitate the development of simpler calculation strategies, which are appropriate for commercial device simulators.
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Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors
Per G. Sverdrup,
Per G. Sverdrup
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305
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Y. Sungtaek Ju, Associate Mem. ASME,
Y. Sungtaek Ju, Associate Mem. ASME
IBM Corporation, Almaden Research Center
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Kenneth E. Goodson, Associate Professor, Associate Mem. ASME
Kenneth E. Goodson, Associate Professor, Associate Mem. ASME
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305
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Per G. Sverdrup
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305
Y. Sungtaek Ju, Associate Mem. ASME
IBM Corporation, Almaden Research Center
Kenneth E. Goodson, Associate Professor, Associate Mem. ASME
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division September 23, 1999; revision received June 25, 2000. Associate Editor: A. Majumdar.
J. Heat Transfer. Feb 2001, 123(1): 130-137 (8 pages)
Published Online: June 25, 2000
Article history
Received:
September 23, 1999
Revised:
June 25, 2000
Citation
Sverdrup, P. G., Sungtaek Ju, Y., and Goodson, K. E. (June 25, 2000). "Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors ." ASME. J. Heat Transfer. February 2001; 123(1): 130–137. https://doi.org/10.1115/1.1337651
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