Abstract
The propagation of high-frequency phonons through crystals at low temperatures is characterized by both ballistic and diffusive processes. Ballistic propagation of heat pulses is highly anisotropic due to phonon focusing, while diffusive propagation is expected to be nearly isotropic in cubic crystals. By using phonon imaging techniques, we have attempted to identify the heat flux from ballistic and scattered phonons in GaAs. Comparison of this data to Monte Carlo calculations which incorporate elastic scattering shows that the flux from phonons scattered a few times in the bulk retains a significant degree of anisotropy. In particular, a sharp feature discovered by Stock, Ulbrich, and Fieseler and attributed to ballistic propagation of phonons with frequencies up to 1.5 THz is now identified with the scattering of sub-THz phonons. Our analysis provides insights into the evolution of heat propagation from the ballistic to diffusive regimes.
Similar content being viewed by others
References
Von Gutfeld, R.J., Nethercot, Jr., A.H.: Phys. Rev. Lett.12, 641 (1964)
For some recent reviews see: Nonequilibrium phonon dynamics. Bron, W.E. (ed.) New York: Plenum Press 1985 and [3]
Maris, H.J.: Nonequilibrium phonons in nonmetallic crystals. Eisenmenger, W., Kaplyanskii, A.A. (eds.), p. 51. Amsterdam: North-Holland 1986
Hensel, J.C., Dynes, R.C.: Phys. Rev. Lett.39, 969 (1977)
Greenstein, M., Tamor, M.A., Wolfe, J.P.: Phys. Rev. B26, 5604 (1982)
Levinson, Y.B.: Nonequilibrium phonons in nonmetallic crystals. Eisenmenger, W., Kaplyanskii, A.A. (eds.), p. 91 Amsterdam: North-Holland 1986
Ulbrich, R.G., Narayanamurti, V., Chin, M.A.: Phys. Rev. Lett.45, 1432 (1980); J. Phys. (Paris)42, 226 (1981)
Stock, B., Ulbrich, R.G., Fieseler, M.: Phonon scattering in condensed matter. Eisenmenger, W. et al. (eds.), p. 97 Berlin, Heidelberg, New York: Springer 1984
Lax, M., Hu, P., Narayanamurti, V.: Phys. Rev. B23, 3095 (1981)
Lax, M., Narayanamurti, V., Hu, P., Weber, W.: J. Phys. (Paris)42, 161 (1981)
Narayanamurti, V.: J. Phys. (Paris)42, 221 (1981)
Tamura, S.: Phys. Rev B30, 849 (1984)
Bron, W.E., Levinson, Y.B., O'Connor, J.M.: Phys. Rev. Lett.49, 209 (1982). See also [6]
Lax, M., Narayanamurti, V., Ulbrich, R.G.: Phonon scattering in condensed matter. Eisenmenger, W. et al. (eds.), p. 103 Berlin, Heidelberg, New York: Springer 1984
Lax, M., Narayanamurti, V., Fultin, R.C., Holzwarth, N.: Phonon scattering in condensed matter V. Anderson, A.C., Wolfe, J.P. (eds.), p. 335 Berlin, Heidelberg, New York: Springer 1986
Lax, M.: In: Laser optics of condensed matter. Proceeding of the 3rd Binational USA-USSR Symposium. New York: Plenum Press: (to be published)
Strom, U., Culbertson, J.C., Klein, P.B., Wolf, S.A.: Proceedings of the 17th International Conference on the Physics of Semiconductors. Chadi, J.D., Harrison, W.A. (eds.), p. 1173 Berlin, Heidelberg, New York: Springer 1985
Culbertson, J.C., Strom, U., Klein, P.B., Wolf, S.A.: Phys. Rev. B29, 7054 (1984)
Culbertson, J.C., Strom, U., Wolf, S.A.: Phys. Rev. B36, 2962 (1987)
Dietsche, W., Northrop, G.A., Wolfe, J.P.: Phys. Rev. Lett.47, 660 (1981); Hebboul, S.E., Wolfe, J. P.: Phys. Rev. B34, 3948 (1986)
Wolfe, J.P., Northrop, G.A.: Phonon scattering in condensed matter. Eisenmenger, W. et al. (eds.), p. 100 Berlin, Heidelberg New York: Springer 1984
Northrop, G.A., Hebboul, S.E., Wolfe, J.P.: Phys. Rev. Lett.55, 95 (1985)
Stock, B., Fieseler, M., Ulbrich, R.G.: Proceedings of the 17th International Conference on the Physics of Semiconductors. Chadi, J.D., Harrison, W.A. (eds.), p. 1177. Berlin, Heidelberg New York: Springer 1985
Ulbrich, R.G.: Nonequilibrium phonon dynamics. Bron, W.E., (ed.), p. 101 New York: Plenum Press 1985
Schreiber, M., Fieseler, M., Mazur, A., Pollman, J., Stock, B., Ulbrich, R.G.: Proceedings of the 18th International Conference on the Physics of Semiconductors. Engström, O. (ed.), p. 1373. Singapore: World Scientific 1987
Hebboul, S.E., Wolfe, J.P.: (to be publised)
Klemens, P.G.: Proc. Phys. Soc. London, Sect. A68, 1113 (1955)
Undoped, semi-insulating GaAs (ρ=108 Ω-cm) provided by E. Swiggard of the Naval Research Laboratory. The sample was polished on both sides with 0.2% Br in Methanol, removing 75–100 μm
The sample was polished with alumina and finally mechanically and chemically polished with Syton colloidal silica
This sample was originally from Wacker Chemitronics and was given to us by W.E. Bron of University of California at Irvine It was melt grown in a BN crucible and chromium free witl ρ=106Ω-cm. It was mechanically polished with clumina and finally mechanically and chemically polished with Syton
For a recent review of the phonon imaging technique, see Northrop, G.A., Wolfe, J.P.: Nonequilibrium phonon dynamics. bron, W.E. (ed.), p. 165 New York: Plenum Press 1985
Hebboul, S.E., Wolfe, J.P.: Proceedings of the 18th International Conference on the Physics of Semiconductors. Engström, O. (ed.), p. 1377. Singapore: World Scientific 1987
Tamura, S.: Phys. Rev. B28, 897 (1983)
Tamura, S.: Phys. Rev B31, 2574 (1985); Phonon scattering in condensed matter V. Anderson, A.C., Wolfe, J.P. (eds.), p. 288 Berlin, Heidelberg, New York: Springer 1986
Okubo, K., Tamura, S.: Phys. Rev B28, 4847 (1983)
Happek, U., Renk, K.F., Ayant, Y., Buisson, R.: Phonon scattering in condensed matter V Anderson, A.C., Wolfe, J.P. (eds.), p. 347. Berlin, Heidelberg, New York: Springer 1986
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ramsbey, M.T., Wolfe, J.P. & Tamura, S. Phonon focusing of elastically scattered phonons in GaAs. Z. Physik B - Condensed Matter 73, 167–178 (1988). https://doi.org/10.1007/BF01305734
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01305734