Abstract
The effect of normal phonon-phonon scattering processes on the thermal conductivity of silicon crystals with various degrees of isotope disorder is considered. The redistribution of phonon momentum in normal scattering processes is taken into account within each oscillation branch (the Callaway generalized model), as well as between different oscillation branches of the phonon spectrum (the Herring mechanism). The values of the parameters are obtained that determine the phonon momentum relaxation in anharmonic scattering processes. The contributions of the drift motion of longitudinal and transverse phonons to the thermal conductivity are analyzed. It is shown that the momentum redistribution between longitudinal and transverse phonons in the Herring relaxation model represents an efficient mechanism that limits the maximum thermal conductivity in isotopically pure silicon crystals. The dependence of the maximum thermal conductivity on the degree of isotope disorder is calculated. The maximum thermal conductivity of isotopically pure silicon crystals is estimated for two variants of phonon momentum relaxation in normal phonon-phonon scattering processes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. P. Zhernov and A. V. Inyushkin, Isotope Effects in Solids (Ross. Nauchn. Tsentr “ Kurchatovskii Institut,” Moscow, 2001).
M. Asen-Palmer, K. Bartkowski, E. Gmelin, et al., Phys. Rev. B 56, 9431 (1997).
V. I. Ozhogin, A. V. Inyushkin, A. N. Taldenkov, et al., Pis’ma Zh. Éksp. Teor. Fiz. 63, 463 (1996) [JETP Lett. 63, 490 (1969)].
A. N. Taldenkov, A. V. Inyushkin, V. I. Ozhogin, et al., in Proceedings of the IV Conference “ Physicochemical Processes under Atomic and Molecular Selection,” Zvenigorod 1999, Nauka, Moscow (1999).
T. H. Geballe and G. W. Hull, Phys. Rev. 110, 1773 (1958).
T. Ruf, R. W. Henn, M. Asen-Palmer, et al., Solid State Commun. 115, 243 (2000).
R. Berman, Phys. Rev. B 45, 5726 (1992).
W. S. Capinski, H. J. Maris, E. Bauser, et al., Appl. Phys. Lett. 71, 2109 (1997).
Lanhua Wei, P. K. Kuo, R. L. Thomas, et al., Phys. Rev. Lett. 70, 3764 (1993).
J. E. Graebner, M. E. Reiss, L. Seibles, et al., Phys. Rev. B 50, 3702 (1994).
J. R. Olson, R. O. Pohl, J. W. Vandersande, et al., Phys. Rev. B 47, 14 850 (1993).
A. P. Zhernov and D. A. Zhernov, Zh. Éksp. Teor. Fiz. 114, 1757 (1998) [JETP 87, 952 (1998)]; A. P. Zhernov, Fiz. Tverd. Tela (St. Petersburg) 41, 1185 (1999) [Phys. Solid State 41, 1079 (1999)].
I. G. Kuleev and I. I. Kuleev, Zh. Éksp. Teor. Fiz. 120, 649 (2001) [JETP 93, 568 (2001)].
J. Callaway, Phys. Rev. 113, 1046 (1959).
R. Berman, Thermal Conduction in Solids (Clarendon, Oxford, 1976; Mir, Moscow, 1979).
B. M. Mogilevskii and A. F. Chudnovskii, Thermal Conductivity of Semiconductors (Nauka, Moscow, 1972)
V. S. Oskotskii and I. A. Smirnov, Defects in Crystals and Thermal Conductivity (Nauka, Leningrad, 1972), p. 205.
B. H. Armstrong, Phys. Rev. B 32, 3381 (1985).
J. A. Krumhansl, Proc. Phys. Soc. London 85, 921 (1965).
M. G. Holland, Phys. Rev. 132, 2461 (1963).
K. Itoh, Low Temperature Carrier Transport Properties in Isotopically Controlled Germanium, PhD Thesis (University of California, Berkeley, 1994).
I. G. Kuleev, Fiz. Tverd. Tela (St. Petersburg) 44, 215 (2002) [Phys. Solid State 44, 223 (2002)].
C. Herring, Phys. Rev. 95, 954 (1954).
S. Simons, Proc. Phys. Soc. London 82, 401 (1963); 83, 749 (1964).
G. A. Slack and C. J. Glassbrenner, Phys. Rev. 120, 782 (1960).
B. Truel, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic, New York, 1969; Mir, Moscow, 1972).
G. Nilsson and G. Nelin, Phys. Rev. B 6, 3777 (1972).
J. P. Srivastava, J. Phys. Chem. Solids 41, 357 (1980).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 122, No. 3, 2002, pp. 558–569.
Original Russian Text Copyright © 2002 by I. G. Kuleev, I. I. Kuleev.
Rights and permissions
About this article
Cite this article
Kuleev, I.G., Kuleev, I.I. The effect of normal phonon-phonon scattering processes on the maximum thermal conductivity of isotopically pure silicon crystals. J. Exp. Theor. Phys. 95, 480–490 (2002). https://doi.org/10.1134/1.1513821
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1513821