Abstract
The subject of this chapter is the propagation of thermal energy through crystalline solids at low temperatures. A remarkable observation is that thermal energy emanating from a point source of heat is strongly channelled into various directions in the crystal. This effect is simply caused by the elastic anisotropy of the crystal and is known as phonon focusing. Over the past several years phonon imaging techniques have been developed which graphically demonstrate phonon focusing and use it to study the scattering of high frequency phonons in crystals. We will review here the experimental methods and the physics learned from such experiments. We begin with a general discussion of ballistic heat propagation in real crystals.
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References
Anderson, A.C., and Malinowski, M.E., 1971, Interaction between thermal phonons and dislocations in LiF, Phys. Rev. B5, 3199.
Anderson, A.C., 1976, The thermal boundary resistance, in: “Phonon scattering in solids”, L.J. Challis V.W. Rampton, and A.F.G. Wyatt, eds., ( Plenum, New York).
Anderson, A.C., 1981, The Kapitza thermal boundary resistance between two solids, in: “Nonequilibrium superconductivity, phonons, and Kapitza boundaries”, K.E. Gray, ed., ( Plenum, New York).
Armbruster, D., Dangelmayr, G., and Guttinger, W., 1984, Nonlinear phonon focusing, in: “Phonon Scattering in Condensed Matter”, W. Eisenmenger, K. Lassmann, and S. Dottinger, eds., ( Springer-Verlag, Berlin).
Bagaev, V.S, Galkina, T.I., and Sibeldin, N.N., 1983, Interaction of EHD with deformation field, ultrasound and non-equilibrium phonons, in: “Electron-hole droplets in semiconductors”, C.D. Jeffries and L.V. Keldysh, ed., ( Elsevier, New York).
Berman, R., 1976, “Thermal Conduction in Solids”, ( Clarendon, Oxford).
Bron, W.E., 1980, Spectroscopy of High Frequency Phonons, Rep. Prog. Phys. 43, 20.
Brown, R.A., 1981, The effect of dislocations on thermal conductivity, in: “International conference on phonon physics”, W.E. Bron, ed., (J. Phys. (Paris) 42, C6).
Cady, W.G., 1946, “Piezoelectricity”, ( McGraw-Hill, New York ).
Carruthers, P., 1961, Theory of thermal conductivity of solids at low temperatures, Rev. Mod. Phys. 33, 92.
Christoffel, E.B.,1877, Ann. Mat. Pura. Appl. 8,193.
Cotts, E.J., Miliotis, D.M., and Anderson, A. C., 1981, Thermal transport in deformed LiF, Phys. Rev. B24, 7336.
Dietsche, W., Northrop, G.A., and Wolfe, J.P., 1981, Phonon focusing of large-k acoustic phonons in Germanium, Phys. Rev. Lett. 47, 660.
Dietsche, W., Kirch, S.J., and Wolfe, J.P., 1982, Phonon spectroscopy of the electron-hole liquid in Ge, Phys. Rev. B26, 780.
Eichele, R., Huebener, R.P., and Seifert, H., 1982a, Phonon focusing in quartz and sapphire imaged by electron beam scanning, Z. Phys. B48, 89.
Eichele, R., Huebener, R.P., Seifert, H., and Selig, K.P., 1982b, Imaging of ballistic phonon propagation in quartz by electron beam scanning, Phys. Lett. 87A, 469.
Eisenmenger, W., and Dayem, A.H., 1967, Quantum generation and detection of incoherent phonons in superconductors, Phys. Rev. Lett. 18,125.
Eisenmenger, W., 1976, Superconducting Tunnel Junctions as Phonon Generators and Detectors, Physical Acoustics, Vol. 12, ed. W. P. Mason and R. N. Thurston ( New York: Academic ), p. 79.
Eisenmenger, W., 1979, Phonon Detection by the Fountain Preassure in Superfluid Helium Films, in: “Phonon Scattering in Condensed Matter”, H.J. Maris, ed., ( Plenum, New York ).
Every, A.G., 1980, General closed-form expressions for acoustic waves in elastically anisotropic solids, Phys. Rev. B22, 1746.
Every, A.G., 1981, Ballistic phonons and the shape of the ray surface in cubic crystals, Phys. Rev. B24, 3456.
Every, A.G., Koos, G.L., and Wolfe, J.P., 1984, Ballistic phonon imaging in sapphire: bulk focusing and critical-cone channeling effects, Phys. Rev. B29, 2190.
Granato, A.V., 1958, Thermal properties of mobile defects, Phys. Rev. 111, 740.
Greenstein, M., and Wolfe, J.P., 1978, Anisotropy in the shape of the electron-hole-drop cloud in germanium, Phys. Rev. Lett. 41, 715.
Greenstein, M., and Wolfe, J.P., 1981, Phonon-wind-induced anisotropy of the electron-hole droplet cloud in Ge, Phys. Rev. B24, 3318.
Greenstein, M., Tamor, M.A., and Wolfe, J.P., 1982, Propagation of laser-generated heat pulses in crystals at low temperature: Spatial filtering of ballistic phonons, Phys. Rev. B26, 5604.
Guseinov, N.M., and Levinson, Y.B., 1983, Diffusion of nondecaying TA phonons, Solid State Commun. 45, 371.
Hensel, J. C., Phillips, T.G., and Thomas, G.A., and Rice, T.M., 1977, The electron-hole liquid in semiconductors in: “Solid State Physics”, Vol. 32, H. Ehrenreich, F. Seitz, and D. Turnbull, eds., ( Academic Press, New York).
Hensel, J.C., and Dynes, R.C.,1977, Interactions of electron-hole drops with ballistic phonons in heat pulses: the phonon wind, Phys. Rev. Lett. 39, 969.
Hensel, J.C., and Dynes, R.C., 1979, Observation of singular behavior in the focusing of ballistic phonons in Ge, Phys. Rev. Lett. 43, 1033.
Hurley, D.C., and Wolfe, J.P., 1984, Phonon focusing in cubic crystals (to be published).
Hurley, D.C., Every, A.G., and Wolfe, J.P., 1984, Ballistic Phonon Imaging of Diamond, J. Phys. C.: Solid State Phys. 17, 3157.
Keldysh, L.V., 1976, Phonon wind and dimensions of electron-hole drops in semiconductors, JETP Lett. 23, 86.
Kinder, H., Lassmann, K., and Eisenmenger, W., 1970, Phonon emission by quasiparticle decay in superconducting tunnel junctions, Phys. Lett. 31A, 475.
Kinder, H., 1975, Phonon spectroscopy at ultrahigh frequencies, in: “Proceedings of the 14th international conference on low temperature physics”, Vol. 5, M. Krusius and M. Vuorio, eds., (North-Holland, New York ).
Kittel, C., 1976, “Introduction to Solid State Physics”, Fifth edition ( Wiley, New York).
Kirch, S.J., and Wolfe, J.P., 1984, Phonon-absorption imaging of the electron-hole liquid in Ge, Phys. Rev. B29, 3382.
Klemens, P.G., 1958, Thermal conductivity and lattice vibrational modes in: “Solid State Physics”, Vol. 7, F. Seitz and D. Turnbull, eds., ( Academic Press, New York).
Kneezel, G.A., and Granato, A.V., 1982, Effect of independent and coupled vibrations of dislocations on low-temperature thermal conductivity in alkali halides, Phys. Rev. B25, 2851.
Koos, G.L. and Wolfe, J.P., 1984, Piezoelectricity and ballistic heat flow, Phys. Rev. B29, 6015.
Koos, G.L., Every, A.G., Northrop, G.A. and Wolfe, J.P., 1984, Ballistic Phonon Imaging in Sapphire: Bulk Focusing and Critical-cone Channeling Effects, Phys. Rev. B29, 2190.
Koos, G.L., Every, A.G., Northrop, G.A., and Wolfe, J.P., 1983, Critical-cone channeling of thermal phonons at a sapphiremetal interface, Phys. Rev. Lett. 51, 276.
Koos, G.L., and Wolfe, J.P., 1984a, Phonon focusing in piezo-electric crystals: Quartz and lithium niobate, Phys. Rev. B (September 15 ).
Kunc, K., Nielsen, O. Holm, 1979a, Lattice dynamics of zincblende structure compounds using deformation-dipole model and rigid ion model, Comp. Phys. Comm. 16, 181.
Kunc, K., Nielsen, O. Holm, 1979b, Lattice dynamics of zincblende structure compounds: II. Shell model, Comp. Phys. Comm. 17, 413.
Lax, M., and Narayanamurti, V., 1980, Phonon magnification and the gaussian curvature of the slowness surface in anisotropic media: detector shape effects with application to GaAs, Phys. Rev. B22, 4876.
Maris, H.J., 1971, Enhancement of heat pulses in crystals due to elastic anisotropy, J. Acoust. Soc. Am. 50, 812.
Marx, D., Buck, J., Lassmann, K., and Eisenmenger, W., 1978, Reflection of high frequency phonons at free silicon surfaces, Journal de Physique 39, C6, 1015.
Marx, D., and Eisenmenger, W., 1981, Reflection of high-frequency phonons at silicon-solid interfaces, Phys. Lett. 82A, 291.
Marx, D., and Eisenmenger, W., 1982, Phonon scattering at siliconcrystal surfaces, Z. Phys. B48, 277.
McCurdy, A.K., Maris, H.J., and Elbaum, C., 1970, Anisotropic heat conduction in cubic crystals in the boundary scattering regime, Phys. Rev. B2, 4077.
Metzger, W., Eichele, R., Seifert, H., and Huebener, R.P., 1984, Phonon focusing in germanium imaged by electron-beam scanning, in: “Phonon Scattering in Condensed Matter”, W. Eisenmenger, K. Lassmann, and S. Dottinger, eds., ( Springer-Verlag, Berlin).
Musgrave, M.J.P., “Crystal Acoustics”, 1970, ( Holden-Day, San Francisco).
Northrop, G.A., 1982a, Acoustic phonon anisotropy: phonon focusing, Comp. Phys. Comm. 28, 103.
Northrop, G.A., 1982b, Phonon focusing of dispersive phonons in Ge, Phys. Rev. B26, 903.
Northrop, G.A., and Wolfe, J.P., 1979, Ballistic phonon imaging in solids - a new look at phonon focusing, Phys. Rev. Lett. 43, 1424; 1980, Ballistic phonon imaging in germanium, Phys. Rev. B22, 6196.
Northrop, G.A.,Cotts, E.J., Anderson, A. C., and Wolfe, J. P., 1982, Phonon imaging of highly dislocated LiF, Phys. Rev. Lett. 49, 54; 1983, Anisotropic phonon-dislocation scattering in deformed Li F, Phys. Rev. B27, 6395.
Northrop, G.A., and Wolfe, J.P., 1984, Phonon reflection imaging: A determination of specular versus diffuse boundary scattering, Phys. Rev. Lett. 52, 2156.
Northrop,G.A., Hebboul, S., and Wolfe, J.P., 1985, to be published.
Parrott, J.E., and Stukes, Audrey, 1975, “Thermal Conductivity of Solids”, ( Pion, London ).
Rösch, F., and Weis, O., 1976, Geometric propagation of acoustic phonons in monocrystals within anisotropic continuum acoustics, Part I, Z. Physik B25, 101; 1976, Geometric propagation of acoustic phonons in monocrystals within anisotropic continuum acoustics, Part II, Z. Physik B25, 115.
Rösch, F., and Weis, O., 1977, Phonon transmission from incoherent radiators into Quartz, Sapphire, Diamond, Silicon, and Germainium within anisotropic continuum acoustics, Z. Physik B27, 33.
Stock,B., Ulbrich, R.G., and Fieseler,M., 1984, Direct observation of ballistic large-wavevector phonon propagation in gallium arsenide, in: “Phonon Scattering in Condensed Matter”, W. Eisenmenger, K. Lassmann, and S. Dottinger, eds., ( Springer-Verlag, Berlin).
Taborek, P., and Goodstein, D., 1980a, Phonon focusing catastrophes, Sol. St. Comm. 33, 1191.
Taborek, P., and Goodstein, D., 1980b, Diffuse reflection of phonons and the anomalous Kapitza resistance, Phys. Rev. B22, 1550.
Tamor, M.A., Greenstein, M., and Wolfe, J.P., 1983, Time-resolved studies of electron-hole-droplet transport in Ge,Phys.Rev.B27, 7353.
Tamura, S., 1982, Focusing of high-frequency dispersive phonons, Phys. Rev. B25, 1415.
Tamura, S., 1983a, Isotope scattering of dispersive phonons in Ge, Phys. Rev. B27, 858.
Tamura, S., 1983b, Large-wavevector phonons in highly dispersive crystals: Phonon-focusing effects, Phys. Rev. B28, 897.
Taylor, B., Maris, H.J., and Elbaum, C., 1969, Phonon focusing in solids, Phys. Rev. Lett. 23, 416.
Taylor, B., Maris, H.J., and Elbaum, C., 1971, Focusing of phonons in crystalline solids due to elastic anisotropy, Phys. Rev. B3, 1462.
Ulbrich, R.G., Narayanamurti, V., and Chin, M.A., 1980, Propagation of large wave vector acoustic phonons in semiconductors, Phys. Rev. Lett. 45, 1432; 1981, Ballistic transport and decay of near zone-edge non-thermal phonons in semiconductors, in: “International conference on phonon physics”, W.E. Bron, ed., (J. Phys. (Paris) 42, C6).
von Gutfeld, R.J., and Nethercot, A.H., 1964, Heat pulses in Quartz and Sapphire at low temperatures, Phys. Rev. Lett. 12, 641.
von Gutfeld, R.J., 1968, Heat Pulse Transmission,in: “Physical Acoustics”, Vol. 5, ed. W.P. Mason (Academic, New York).
Weber, J., Sandemann, W., Dietsche, W., and Kinder, H., 1978, Absence of anomalous Kapitza conductance on freshly cleaved surfaces, Phys. Rev. Lett. 40, 1469.
Weis, O., 1969, Thermal phonon radiation, Z. Angew. Phys.26, 325.
Weis, O., 1972, The solid-solid interface in thermal phonon radiation, J. Phys. (France) 33, C-4, 48.
Wolfe, J.P., 1980, Ballistic heat pulses in crystals, Phys. Today, 33, 44. (December)
Wolfe, J.P., 1982, Thermodynamics of excitons in semiconductors, Phys. Today, 35, 46. (March)
Wolfe, J.P., Greenstein, M., Northrop, G.A., and Tamor, M.A., 1980, Images of electron-hole droplets and ballistic phonons inGe, in: “Phonon Scattering in Condensed Matter”, H.J. Maris, ed., ( Plenum, New York ).
Wolfe, J.P., and Jeffries, C.D., 1983, Strain-confined excitons and electron-hole liquid, in: “Electron-hole droplets in semiconductors”, C.D. Jeffries and L.V. Keldysh, ed., ( Elsevier, New York ).
Wolfe, J.P., and Northrop, G.A., 1984, Search for large k-vector phonons in GaAs, in: “Phonon Scattering in Condensed Matter”, W. Eisenmenger, K. Lassmann, and S. Dottinger, eds., ( Springer-Verlag, Berlin ).
Wyatt, A.F.G., 1981, Kapit za conductance of solid-liquid He interfaces, in: “Nonequilibrium superconductivity, phonons, and Kapitza boundaries”, K.E. Gray, ed., ( Plenum, New York).
Zdetsis, A.D., and Wang, C.S., 1979, Lattice dynamics of Ge and Si using the Born-von Karman model, Phys. Rev. B19, 2999.
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Northrop, G.A., Wolfe, J.P. (1985). Phonon Imaging: Theory and Applications. In: Bron, W.E. (eds) Nonequilibrium Phonon Dynamics. NATO ASI Series, vol 124. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2501-7_5
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DOI: https://doi.org/10.1007/978-1-4613-2501-7_5
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