Abstract
When very fast phenomena and small structure dimensions are involved, the classical law of Fourier becomes inaccurate. A more sophisticated model is then needed to describe the thermal conduction mechanisms in a physically acceptable way. In this paper the according diffusion equation is solved for a nano-scaled semiconductor substrate, in order to gain physical insight in the problem. Analytical solutions for the temperature and heat flux distributions are presented. The complex thermal impedance and thermal step response of the structure are discussed. The most remarkable fact is that the temperature inside the substrate can go below the ambient temperature for a short amount of time. The results also clearly demonstrate the wave character of the heat propagation and the analogy with RLC transmission lines.
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References
Cattaneo, C. (1958). Sur une forme de l’equation de la chaleur eliminant le paradoxe d’une propagation instantanee (in French). Comptes rendus de l’Académie des sciences, 247, 431–433.
Vernotte, P. (1958). Les paradoxes de la theorie continue de l’equation de la chaleur (in Frenh). Comptes rendus de l’Académie des sciences, 246, 3154–3155.
Codecasa, L. (2005). Thermal networks from heat wave equation. IEEE Transactions on Components and Packaging Technologies, 28, 14–22.
Haji-Sheikh, A., Minkowycz, W. J., & Sparrow, E. M. (2002). Certain anomalies in the analysis of hyperbolic heat equation. Transactions of the ASME—Journal of Heat Transfer, 124, 307–319.
Kawka, P. (2005). Thermal impedance measurements and dynamic modelling of electronic packages (PhD thesis). Ghent University (Gent, Belgium).
De Mey, G., Vermeersch, B., & Kawka, P. (2005) Thermal impedance simulations of electronic packages. In Proceedings of␣the 12th Internation Conference on Mixed Design of Integrated␣Circuits and Systems (MIXDES 2005), Krakow, Poland, pp. 267–269.
Vermeersch, B., & De Mey, G. (2006). Thermal impedance plots␣of micro-scaled devices. Microelectronics Reliability, 46, 174–177.
Kawka, P., De Mey, G., & Vermeersch, B. Thermal characterization of electronic packages using the Nyquist plot of the thermal impedance. Accepted with required revisions for publication in IEEE Transactions on Components and Packaging Technologies (under review).
Abramowitz, M., & Stegun, I. A. (Eds.) (1970). Handbook of mathematical functions. New York, USA: Dover Publications.
Debye, P. (1912). Ann. d Physik, 39, 789.
Acknowledgments
B. Vermeersch is preparing a PhD as a Research Assistant for the Research Foundation—Flanders (FWO—Vlaanderen) and wishes to thank FWO for supporting the presented work.
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This work concerns a slightly extended version of a paper that was presented at the latest MIXDES Conference (Gdynia, Poland). It is submitted for the Special Issue MIXDES 2006 of the Analog Integrated Circuits and Signal Processing journal upon invitation of the MIXDES Scientific Committee.
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Vermeersch, B., De Mey, G. Non-Fourier thermal conduction in nano-scaled electronic structures. Analog Integr Circ Sig Process 55, 197–204 (2008). https://doi.org/10.1007/s10470-007-9044-x
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DOI: https://doi.org/10.1007/s10470-007-9044-x