Abstract
Thermal conductivity in semiconductors is investigated through the phonon transport description. From the former studies based on the gas kinetic theory to the recent ones using the Monte Carlo methods or the radiative multifux models, each technique involves the dispersion properties of the crystal lattice. Besides, most of these studies have been done in the frame of the relaxation time approximation of collision processes. In this study, the importance of the choice of the dispersion curves and time relaxation parameters are pointed out. A complete description of the transverse umklapp interaction is provided without any adjustment parameters. New insights of the energy conservation surface calculation, involved in phonon-phonon time relaxation expression, are provided. Using simple and more complex models, we have determined the heat transport properties, in the temperature range from 50 K to 1000 K in bulk silicon. We especially focused our attention on the thermal conductivity as a function of the phonon anharmonic resistive mechanisms for two models of dispersion: “linear” and “quadratic”. We demonstrate that very different thermal conductivity properties can be calculated according to the chosen description of lattice vibrations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Klemens, Proc. Roy. Soc. A 208, 108 (1951)
P. Klemens, Solid State Physics, Vol. 7 (Academic Press Inc., New York, 1958)
J. Callaway, Phys. Rev. 113, 1046 (1959)
M. Holland, Phys. Rev. 132, 2461 (1963)
P. Chantrenne, J. Barrat, X. Blase, J. Gale, J. Appl. Phys. 97, 104318 (2005)
M. Modest, Radiative Heat Transfer, 2nd edn. (Academic Press, San Diego, 2003)
A. Majumdar, ASME J. Heat Transfer 115, 7 (1993)
G. Chen, ASME J. Heat Transfer 119, 220 (1997)
K. Goodson, ASME J. Heat Transfer 118, 279 (1996)
D. Lemonnier, M. Lallemand, Int. J. Heat Technology 18, 63 (2000)
G. Chen, Phys. Rev. Lett. 86, 2297 (2001)
C. Jacobini, L. Reggiani, Rev. Mod. Phys. 55, 645 (1983)
M. Fischetti, S. Laux, Phys. Rev. B 38, 9721 (1988)
P. Lugli, P. Bordone, L. Reggiani, M. Rieger, P. Kocevar, S. Goodnick, Phys. Rev. B 39, 7852 (1989)
M. Fischetti, S. Laux, Phys. Rev. B 48, 2244 (1993)
E. Pop, R. Dutton, K. Goodson, J. Appl. Phys. 96, 4998 (2004)
E. Pop, R. Dutton, K. Goodson, Appl. Phys. Lett. 86, 082101 (2005)
R. Peterson, ASME J. Heat Transfer 116, 815 (1994)
S. Mazumder, A. Majumdar, ASME J. Heat Transfer 123, 749 (2001)
D. Lacroix, K. Joulain, D. Lemonnier, Phys. Rev. B 72, 064305 (2005)
R. Tubino, L. Piseri, G. Zerbi, J. Chem. Phys. 56, 1022 (1972)
G. Srivastava, The physics of phonons (Adam Hilger, Bristol, UK, 1990)
S. Usher, G. Srivastava, Phys. Rev. B 50, 14179 (1994)
J. Ziman, Electrons and Phonons (Oxford University Press, Oxford, 1960)
L. Landau, G. Rumer, Phys. Z. Sowjetunion 11, 18 (1937)
Y.J. Han, P. Klemens, Phys. Rev. B 48, 6033 (1993)
M. Roufosse, P. Klemens, Phys. Rev. B 7, 5379 (1973)
Y.J. Han, Phys. Rev. B 54, 8977 (1996)
P. Klemens, Thermochimica Acta 218, 247 (1993)
N. Ashcroft, N. Mermin, Solid state physics, international edn. (Saunders College, Philiadelphia, 1976)
C.J. Glassbrenner, G.A. Slack, Phys. Rev. 134, A1058 (1964)
C. Dames, A broad range of phonon mean free paths is important for heat conduction, in Proceedings of MNHT2008 (Micro/Nanoscale Heat Transfer International Conference, January 6–9, Tainan, Taiwan, 2008)
D. Terris, K. Joulain, D. Lacroix, D. Lemonnier, Arxiv (2008), submitted in january 2008, http://arxiv.org/abs/0803.3954
A. Balandin, K.L. Wang, Phys. Rev. B 58, 1544 (1998)
C. Dames, G. Chen, J. Appl. Phys. 89, 682 (2003)
Semiconductors on nsm, http://www.ioffe.rssi.ru/SVA/NSM/Semicond/
P. Klemens, Proc. Phys. Soc. A 68, 1113 (1955)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lacroix, D., Traore, I., Fumeron, S. et al. Phonon transport in silicon, influence of the dispersion properties choice on the description of the anharmonic resistive mechanisms. Eur. Phys. J. B 67, 15–25 (2009). https://doi.org/10.1140/epjb/e2008-00464-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2008-00464-6