Abstract
The effect of phonon focusing on the anisotropy and temperature dependences of the thermal conductivities of silicon nanofilms is analyzed using the three-mode Callaway model. The orientations of the film planes and the directions of the heat flux for maximal or minimal heat removal from silicon chip elements at low temperatures, as well as at room temperature, are determined. It is shown that in the case of diffuse reflection of phonons from the boundaries, the plane with the {100} orientation exhibits the lowest scattering ability (and the highest thermal conductivity), while the plane with the {111} orientation is characterized by the highest scattering ability (and the lowest thermal conductivity). The thermal conductivity of wide films is determined to a considerable extent by the orientation of the film plane, while for nanowires with a square cross section, the thermal conductivity is mainly determined by the direction of the heat flux. The effect of elastic energy anisotropy on the dependences of the thermal conductivity on the geometrical parameters of films is analyzed. The temperatures of transition from boundary scattering to bulk relaxation mechanisms are determined.
Similar content being viewed by others
References
D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
A. D. McConnell and K. E. Goodson, Annu. Rev. Heat Transfer 14, 128 (2005).
D. G. Cahill, P. V. Braun, G. Chen, D. R. Clarke, S. Fan, K. E. Goodson, P. Keblinski, W. P. King, G. D. Mahan, A. Majumdar, H. J. Maris, S. R. Phillpot, E. Pop, and L. Shi, J. Appl. Phys. Rev. 1, 011305 (2014).
D. Li, Y. Wu, P. Kim, L. Shi, P. Yang, and A. Majumdar. Appl. Phys. Lett. 83, 2934 (2003).
M. Asheghi, Y. K. Leung, S. S. Wong, and K. E. Goodson, Appl. Phys. Lett. 71, 1798 (1997); M. Asheghi, M.N. Touzelbaev, K. E. Goodson, Y. K. Leung, and S. S. Wong, J. Heat Transfer 120, 30 (1998).
W. Liu and M. Asheghi, Appl. Phys. Lett. 84, 3819 (2004).
I. G. Kuleyev, I. I. Kuleyev, and S. M. Bakharev, J. Exp. Theor. Phys. 118(2), 253 (2014).
I. I. Kuleyev, I. G. Kuleyev, S. M. Bakharev, and A. V. Inyushkin, Phys. Solid State 55(1), 31 (2013).
I. I. Kuleyev, I. G. Kuleyev, S. M. Bakharev, and A. V. Inyushkin, Physica B (Amsterdam) 416, 81 (2013).
H. B. G. Casimir, Physica (Amsterdam) 5, 495 (1938).
A. K. McCurdy, H. J. Maris, and C. Erlbaum, Phys. Rev. B: Solid State 2, 4077 (1970).
I. I. Kuleyev, I. G. Kuleyev, S. M. Bakharev, and A. V. Inyushkin, Phys. Status Solidi B 251, 991 (2014).
B. Taylor, H. J. Maris, and C. Elbaum, Phys. Rev. Lett. 23, 416 (1969).
H. J. Maris, J. Acoust. Soc. Am. 50, 812 (1971).
J. P. Wolfe, Imaging Phonons Acoustic Wave Propagation in Solids (Cambridge University Press, New York, 1998).
H. J. Maris and S. Tamura, Phys. Rev. B: Condens. Matter 85, 054304 (2012).
Y. F. Zhu, J. S. Lian, and Q. Jiang, Appl. Phys. Lett. 92, 113101 (2008).
J. Callaway, Phys. Rev. 113, 1046 (1959).
J. A. Krumhansl, Proc. Phys. Soc. 85, 921 (1965).
I. G. Kuleev and I. I. Kuleev, J. Exp. Theor. Phys. 93(3), 568 (2001); I. G. Kuleev and I. I. Kuleev, J. Exp. Theor. Phys. 95 (3), 480 (2002).
V. L. Gurevich, Kinetics of Phonon Systems (Nauka, Moscow, 1980) [in Russian].
R. Berman, Thermal Conduction (Oxford University Press, Oxford, 1976; Mir, Moscow, 1979).
B. M. Mogilevskii and A. F. Chudnovskii, Thermal Conductivity of Semiconductors (Nauka, Moscow, 1972) [in Russian].
G. Nilson and G. Nelin, Phys. Rev. B: Solid State 6, 3777 (1972).
I. I. Kuleyev, I. G. Kuleyev, S. M. Bakharev, and A. V. Inyushkin, Phys. Solid State 55(7), 1545 (2013).
S. Tamura, Phys. Rev. B: Condens. Matter 27, 858 (1983).
I. G. Kuleev and I. I. Kuleev, Phys. Solid State 49(9), 1643 (2007).
A. P. Zhernov and A. V. Inyushkin, Phys.-Usp. 44(8), 785 (2001); A. P. Zhernov and A. V. Inyushkin, Phys.-Usp. 45 (5), 527 (2002).
C. Herring, Phys. Rev. 95, 954 (1954).
L. Landau and J. Rumer, Phys. Z. Sowjetunion 11, 18 (1937).
R. Berman, F. E. Simon, and J. M. Ziman, Proc. R. Soc. London, Ser. A 220, 171 (1953); R. Berman, E. L. Foster, and J. M. Ziman, Proc. R. Soc. London, Ser. A 231, 130 (1955).
J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford University Press, Oxford, 1960).
Handbook of Semiconductor Silicon Technology, Ed. by W. C. O’Mara, R. B. Herring, and L. P. Hunt (Noyes, Park Ridge, 1990), p. 349.
Z. Aksamija and I. Knezevic, Phys. Rev. B: Condens. Matter 82, 045319 (2010).
J. E. Turney, A. J. H. McGaughey, and C. H. Amon, J. Appl. Phys. 107, 024317 (2010).
K. Fuchs, Proc. Cambr. Philos. Soc. 34, 100 (1938).
E. H. Sondheimer, Adv. Phys. 1, 1 (1952).
S. B. Soffer, J. Appl. Phys. 38, 1710 (1967).
M. P. Zaitlin, L. M. Scherr, and A. C. Anderson, Phys. Rev. B: Solid State 12, 4487 (1975).
I. I. Kuleyev, I. G. Kuleyev, and S. M. Bakharev, J. Exp. Theor. Phys. 119(3), 460 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.I. Kuleyev, S.M. Bakharev, I.G. Kuleyev, V.V. Ustinov, 2015, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2015, Vol. 147, No. 4, pp. 736–749.
Rights and permissions
About this article
Cite this article
Kuleyev, I.I., Bakharev, S.M., Kuleyev, I.G. et al. Phonon focusing and temperature dependences of thermal conductivity of silicon nanofilms. J. Exp. Theor. Phys. 120, 638–650 (2015). https://doi.org/10.1134/S1063776115020144
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776115020144