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Onset of size effects in lattice thermal conductivity and lifetime of low-frequency thermal phonons

Published online by Cambridge University Press:  14 February 2012

A.A. Maznev
A.A. Maznev*
Affiliation:
Dept. of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
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Abstract

The onset of size effects in phonon-mediated thermal transport along a thin film at temperatures comparable or greater than the Debye temperature is analyzed theoretically. Assuming a quadratic frequency dependence of phonon relaxation rates in the low-frequency limit, a simple closed-form formula for the reduction of the in-plane thermal conductivity of thin films is derived. The effect scales as the square root of the film thickness, which leads to the prediction of measurable size-effects even at “macroscopic” distances ~100 μm. However, this prediction needs to be corrected to account for the deviation from the ω−2 dependence of phonon lifetimes at sub-THz frequencies due to the transition from Landau-Rumer to Akhiezer mechanism of phonon dissipation.

Keywords

thermal conductivitythin filmSi
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1404: Symposium W – Phonons in Nanomaterials–Theory, Experiments and Applications , 2012 , mrsf11-1404-w03-09
Copyright
Copyright © Materials Research Society 2012

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References

REFERENCES

1. Majumdar, A., ASME J. Heat Transfer 115, 7 (1993).Google Scholar
2. Cahill, D. G., Ford, W. K., Goodson, K. E., Mahan, G. D., Maris, H. J., Majumdar, A., Merlin, R. and Phillpot, S. R., J. Appl. Phys. 93, 793 (2003).Google Scholar
3. Chen, G., Nanoscale Energy Transport and Conversion (Oxford University Press, New York, 2005).Google Scholar
4. Blakemore, J. S., Solid State Physics (Cambridge Univercity Press, Cambridge, 1985).Google Scholar
5. Henry, A. and Chen, G., J. Comp. Theor. Nanosci. 5, 1 (2008).Google Scholar
6. Ward, A. and Broido, D. A., Phys. Rev. B 81, 085205 (2010).Google Scholar
7. Esfarjani, K., Chen, G. and Stokes, H.T., Phys. Rev. B 84, 085204 (2011).Google Scholar
8. Johnson, J. A., Maznev, A. A., Eliason, J. K., Minnich, A., Collins, K., Chen, G., Cuffe, J., Kehoe, T., Sotomayor Torres, C. M., and Nelson, K. A., in Proc. 2011 MRS Spring Meeting, to be published.Google Scholar
9. Turney, J. E., McGaughey, A. J. H., and Amon, C. H., J. Appl. Phys. 107, 024317 (2010).Google Scholar
10. Sellan, D. P., Turney, J. E., McGaughey, A. J. H., and Amon, C. H., J. Appl. Phys. 108, 113524 (2010).Google Scholar
11. Maris, H. J., in Physical Acoustics, edited by Mason, W. P. and Thurston, R. N. (Academic, New York, 1971), Vol. 8, p. 279.Google Scholar
12. Daly, B.C. et al. ., Phys. Rev. B 80, 174112 (2009).Begin typing text here.Google Scholar
13. Thomson, J. J., Proc. Cambridge Phil. Soc. 11, 120 (1901).Google Scholar
14. Fuchs, K., Proc. Cambridge Philos. Soc. 34, 100 (1938).Google Scholar
15. Sondheimer, E. H., Adv. Phys. 1, 1 (1952).Google Scholar
16. Asheghi, M., Touzelbaev, M. N., Goodson, K. E., Leung, Y. K., and Wong, D S. S., J. Heat Transfer, 120, 30 (1998).Google Scholar
17. Asheghi, M., Leung, Y. K., Wong, S. S., and Goodson, K. E., Appl. Phys. Lett., 71, 1798 (1997).Google Scholar
18. Maznev, A.A., Johnson, J.A. and Nelson, K.A., Phys. Rev. B. 84, 195206 (2011).Google Scholar
19. Maznev, A.A., Manke, K.J., Lin, K.-H., Nelson, K.A., Sun, C.-K., and Chyi, J.-I., Ultrasonics 52, 1 (2012).Google Scholar