Skip to main content
SpringerLink
Log in

Phonon States in Bulk and Low-Dimensional Structures

  • Chapter
  • First Online:
Introduction to Isotopic Materials Science

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 248))

Abstract

The accumulated voluminous theoretical and experimental data suggest that the isotope composition of a crystal lattice exerts some influence on the thermal, elastic, and vibrational properties of solids. Since the vast majority of compounds derived from elements has more than one stable isotope, it is clear that phonon–phonon interactions lead to finite phonon lifetimes and additionally renormalization, including anharmonic interactions and elastic scattering. It is commonplace that two processes cannot be predicted easy. However, isotope enrichment allows to discriminate these processes. This chapter is devoted to the lattice dynamics of the bulk and low-dimensional isotope-mixed compounds. The results of this chapter are found in broad fields of applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. V.G. Plekhanov, Elementary excitations in isotope-mixed crystals. Phys. Rep. 410(N 1 – 3), 1–235 (2005)

    CAS  Google Scholar 

  2. M. Cardona, M.L.W. Thewalt, Isotope effect on the optical spectra of semiconductors. Rev. Mod. Phys. 77, 1173–1224 (2005). October

    CAS  Google Scholar 

  3. J.R. Hardy, A.M. Karo, The Lattice Dynamics and Statics of Alkali halide Crystals (Plenum, New York, 1979)

    Google Scholar 

  4. A.A. Abrikosov (ed.) The Achievement of the Electron Theory of Metals (Mir, Moscow, 1984). (in Russian)

    Google Scholar 

  5. J.F. Scott, Soft-mode spectroscopy: experimental studies of structural phase transition. Rev. Mod. Phys. 46(N 1), 83–128 (1974)

    CAS  Google Scholar 

  6. V.G. Plekhanov, Isotope Effect in Solid State Physics (Acdemic, San Diego, 2001)

    Google Scholar 

  7. G. Leibfried, W. Ludwig, Theory of anharmonic effects in crystals, in Solid State Physics, ed. by F. Seitz, D. Turnbull (Academic, New York, 1961), pp. 275–445

    Google Scholar 

  8. M.J. Kelly, Low-Dimensional Semiconductors: Materials, Physics, Technology, Devices (Clarendon, Oxford, 1995)

    Google Scholar 

  9. J.H. Davies, The Physics of Low-Dimensional Semiconductors (Cambridge University Press, Cmbridge, 1998)

    Google Scholar 

  10. J.M. Martinez-Duart, R.J. Martin-Palma, F. Aguello-Rueda, Nanotechnology for Microelectronics and Optoelectronics (Elsevier, Amsterdam, 2006)

    Google Scholar 

  11. K. Goser, P. Glösekőtter, J. Dienstuhl, Nanoelectronics and Nanosystems (Springer, Berlin, 2004)

    Google Scholar 

  12. W.A. Harrison, Electronic Structure and the Properties of Solids (CA, Freeman, San Francisco, 1980)

    Google Scholar 

  13. N.W. Aschcroft, N. David Mermin, Solid State Physics (Harcourt Brace College Publishers, New York, 1975)

    Google Scholar 

  14. M. Born, K. Huang, Dynamical Theory of Crystal Lattice (Oxford University Press, Oxford, 1988)

    Google Scholar 

  15. J. Pankove, Optical Processes in Semiconductors (Prentice-Hall, Englewood Cliffs, 1971)

    Google Scholar 

  16. G.P. Srivastawa, The Physics of Phonons (Hilger, Bristol, 1990)

    Google Scholar 

  17. J.M. Ziman, Principles of the Theory of Solids (Cambridge University Press, Cambridge, 1964)

    Google Scholar 

  18. H. Böttger, Principles of the Theory of Lattice Dynamics (Physik-Verlag, Weinheim, 1983)

    Google Scholar 

  19. P. Bruesch, Phonons: Theory and Experiments II (Springer, Berlin, 1986)

    Google Scholar 

  20. I.E. Tamm, Eine Bemerkung zur Diracschen Theorie der Lichterstroung und Dispersion. Zs. Phys. 62(N 9), 705–708 (1930)

    Google Scholar 

  21. M. Born, J. Oppenheimer, Zur Quantheorie der Molekulen. Ann. Phys. 389(N 20), 457–484 (1927)

    Google Scholar 

  22. V.G. Plekhanov, Lattice dynamics of isotope-mixed crystals (2010), arXiv:cond-mat/1007.5125

  23. S.I. Pekar, Untersuchungen uber die Elektronentheorie der Kristalle (Academic, Berlin, 1954). (in German)

    Google Scholar 

  24. V.G. Plekhanov, Isotope Low-Dimensional Structures (Springer, Heidelberg, 2012)

    Google Scholar 

  25. R.A. Cowley, Anharmonic crystals. Rep. Prog. Phys. 31(N 2), 123–166 (1968)

    CAS  Google Scholar 

  26. P.G. Klemens, Anharmonic decay of optical phonons. Phys. Rev. 148(N 2), 845–848 (1966)

    CAS  Google Scholar 

  27. T.R. Hart, R.L. Aggarval, B. Lax, Temperature dependence Raman scattering in silicon. ibid B1(N1), 638–642 (1970)

    Google Scholar 

  28. J. Menendez, M. Cardona, Temperature dependence of the first-order Raman scattering by phonons in Si, Ge and \(\alpha \)-Sn: anharmonic effect. ibid B29(N 4), 2051–2059 (1984)

    Google Scholar 

  29. M. Balkanski, R.F. Wallis, E. Harro, Theory of anharmonic damping and shift of the Raman mode in silicon. ibid B34(N 8), 5358–5367 (1986)

    Google Scholar 

  30. A.A. Maradudin, S. Califano, Theory of anharmonic processes in crystals with isotopic impurities. ibid B48(N 17), 12628–12636 (1993)

    Google Scholar 

  31. A. Debernardi, S. Baroni, E. Molinari, Anharmonic phonon lifetimes in semiconductors from density-functional perturbation theory. Phys. Rev. Lett. 75(N 9), 1819–1822 (1995)

    CAS  Google Scholar 

  32. A. Debernardi, Phonon linewidth in III-V semiconductors from density-functional perturbation theory. Phys. Rev. B57(N 20), 12847–12858 (1998)

    Google Scholar 

  33. A. Debernardi, Anharmonic effect in the phonons of III-V semiconductors: first principles calculations. Solid State Commun. 113(N1), 1–10 (2000)

    Google Scholar 

  34. G. Lang, K. Karch, M. Schmitt et al., Anharmonic line shift and linewidth of the Raman mode in covalent semiconductors. ibid B59(N 9), 6182–6188 (1999)

    Google Scholar 

  35. B. Steininger, P. Pavone, D. Strauch, Raman spectra of isotopic-disordered group IV semiconductors: a first principles approach. Phys. Stat. Sol. (b) 215(N 1), 127–130 (1999)

    CAS  Google Scholar 

  36. N. Vast, S. Baroni, Effect of disorder on the Raman spectra of crystals: theory and ab initio calculations for diamond and germanium. Phys. Rev. B61(N 14), 9387–9391 (2000)

    Google Scholar 

  37. P.W. Anderson, Absence of diffusion in certain random lattices. Phys. Rev. 109(N 5), 1492–1505 (1955); Solid State Phys. 2(N1), 193–243 (1970)

    Google Scholar 

  38. J.M. Ziman, Models of Disorder (Cambridge University Press, Cambridge, 1979)

    Google Scholar 

  39. V.G. Plekhanov, Experimental evidence of strong phonon scattering in isotopical disordered systems: the case LiH\(_{\rm x}\)D\(_{\rm 1-x}\). Phys. Rev. B 51(N14), 8874–8878 (1995)

    Google Scholar 

  40. V.G. Plekhanov, Isotope effect in lattice dynamics. Phys.-Uspekhi (Moscow) 46(N7), 689–715 (2003)

    CAS  Google Scholar 

  41. B.A. Weinstein, R. Zallen, in: M. Cardona, G. Guntherodt, (eds.), Light Scattering in Solids, Vol. 4, (Berlin, Springer, 1984)

    Google Scholar 

  42. W.J. Borer, S.S. Mitra, K.W. Namjoshi, Line shape and temperature dependence of the first-order Raman spectrum of diamond. Solid State Commun. 9(N16), 1377–1381 (1971)

    CAS  Google Scholar 

  43. W. Cochran, R.A. Cowley, Phonons in perfect crystals, Handbuch der Physik, vol. 25/2a (Springer, Berlin, 1967), pp. 59–156

    Google Scholar 

  44. V.G. Plekhanov, Isotope effect on the lattice dynamics of crystals. Mater. Sci. Eng. R35(N 4–6) , 139–237 (2001)

    Google Scholar 

  45. V.G. Plekhanov, Giant Isotope Effect in Solids (Stefan University Press, La Jolla, 2004)

    Google Scholar 

  46. R.J. Elliott, A.J. Krumhansl, P.L. Leath, The theory and properties of randomly disordered crystals and related physical systems. Rev. Mod. Phys. 46(N 3), 465–542 (1974)

    Google Scholar 

  47. W. Mason, R. Thurston (eds.), Physical Acoustics: Principles and Methods, vol. 1–3 (Academic, New York, 1968–1970)

    Google Scholar 

  48. R.J. Elliott, I.P. Ipatova (eds.), Optical Properties of Mixed Crystals (North-Holland, Amsterdam, 1988)

    Google Scholar 

  49. J. Emsley, The Elements (Clarendon, Oxford, 1998)

    Google Scholar 

  50. V.G. Plekhanov, Lattice dynamics of isotopically mixed crystals. Opt. Spectr. 82, 95–122 (1997)

    Google Scholar 

  51. I.M. Lifshitz, Selected Works (Science, Moscow, 1987). (in Russian)

    Google Scholar 

  52. E.N. Economou, Green’s Functions in Quantum Physics (Springer, Heidelberg, 1983)

    Google Scholar 

  53. K.C. Hass, M.A. Tamor, T.R. Anthony, W.F. Banholzer, Lattice dynamics and Raman spectra of isotopically mixed diamond. Phys. Rev. B45(N 13), 7171–7182 (1992)

    Google Scholar 

  54. P. Soven, Coherent-potential model for substitutional disordered alloys. Phys. Rev. 156, 809–817 (1967)

    CAS  Google Scholar 

  55. D.W. Taylor, Vibrational theory of imperfect crystals with large defect concentration. ibid, 156, 1017–1024 (1967)

    Google Scholar 

  56. S.E. Gűncer, D.K. Ferry, Momentum-dependent CPA approach to disorder-induced intervalley scattering in Al\(_{\rm x}\)Ga\(_{\rm 1-x}\)As. Phys. Rev. B 48, 17072–17079 (1993)

    Google Scholar 

  57. I.A. Abrikosov, B. Johansson, Applicability of the CPA in the theory of random alloys. ibid, B57, 14164–14169 (1998)

    Google Scholar 

  58. K. Koepernik, B. Velicky, R. Hayn, Analytic properties and accuracy of the generalized Blackman-Esterling-Berk coherent-potential-approximation. ibid, B58, 6944–6951 (1998)

    Google Scholar 

  59. K.C. Hass, M.A. Tamor, T.R. Anthony, W.F. Banholzer, Effect of isotopic disorder on the phonon spectrum of diamond. ibid, B44, 12046–12053 (1991)

    Google Scholar 

  60. J. Spitzer, P. Etchegoin, T.R. Anthony, Isotopic-disorder induced Raman scattering in diamond. Solid State Commun. 88, 509–513 (1983)

    Google Scholar 

  61. H.D. Fuchs, G.H. Grein, C. Thomsen, Comparison of the phonon spectra of \(^{70}\)Ge and \(^{\rm nat}\)Ge crystals: effects of isotopic disorder. Phys. Rev. B 43, 483–491 (1991)

    Google Scholar 

  62. D.T. Wang, A. Gobel, J. Zegenhagen et al., Raman scattering on \(\alpha \)-Sn: dependence on isotopic composition. ibid, B56, 13167–13171 (1997)

    Google Scholar 

  63. V.G. Plekhanov, Fundamentals and applications of isotope effect in modern technology, J. Nucl. Sci. Technol. (Japan) 43(4) 375–381 (2006)

    Google Scholar 

  64. H. Ehrenreich, W. Schwartz, The electronic structure of alloys, Solid State Physics, vol. 31 (Academic, New York, 1976), pp. 149–286

    Google Scholar 

  65. B. Dorner, Inelastic Neutron Scattering in Lattice Dynamics, vol. 93, Springer Tracts in Modern Physics (Springer, Berlin, 1982)

    Google Scholar 

  66. V.G. Plekhanov, Applications of the Isotopic Effect in Solids (Springer, Berlin, 2004)

    Google Scholar 

  67. M.A. Krivoglaz, Theory of scattering X-Rays and Thermal Neutrons by Real Crystals (Science, Moscow, 1967). (in Russian)

    Google Scholar 

  68. W. Cochran, The Dynamics of Atoms in Crystals (Arnold, London, 1973)

    Google Scholar 

  69. A.C. Anderson, J.P. Wolfe (eds.), Phonon Scattering in Condensed Matter (Springer, Berlin, 1986)

    Google Scholar 

  70. G. Dolling, Neutron spectroscopy and lattice dynamics, in Dynamical Properties of Solids, vol. 1, ed. by G.K. Horton, A.A. Maradudin (North-Holland, Amsterdam, 1974), pp. 543–629

    Google Scholar 

  71. G. Dolling, A.D.B. Woods, Thermal vibrations crystal lattice, in Thermal Neutron Scattering, ed. by P.A. Egelstaff (Academic, New York, 1965), pp. 178–262

    Google Scholar 

  72. E.B. Wilson, J.C. Decius, P.C. Gross, Molecular Vibrations (McGraw-Hill, New York, 1955)

    Google Scholar 

  73. H. Bilz, W. Kress, Phonon Dispersion Relations in Insulators (Springer, Berlin, 1979)

    Google Scholar 

  74. L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory (Pergamon, Oxford, 1977)

    Google Scholar 

  75. V.G. Plekhanov, Application of isotope effects in solids. J. Mater. Sci. 38, 3341–3429 (2003)

    CAS  Google Scholar 

  76. M.G. Zemlianov, E.G. Brovman, N.A. Chernoplekov, N.A. Shitikov, Study of dynamics of LiH and LiD by inelastic scattering of cold neutrons, Inelastic Scattering of Neutrons, vol. 2 (International Atomic Energy Agency, Vienna., 1965), pp. 431–439

    Google Scholar 

  77. J.L. Verble, J.L. Warren, J.L. Yarnell, Lattice dynamics of lithium hydride. Phys. Rev. 168(N 3), 989 (1968)

    Google Scholar 

  78. V.G. Plekhanov, The influence of the surface state on the testifation of exciton states in the wide-gap insulators. Opt. Spectr. 62(N 8), 1300–1307 (1987). (in Russian)

    Google Scholar 

  79. G.I. Pilipenko, O.I. Tyutyunnik, F.F. Gavrilov, D.V. Oparin, Luminescence of colour centres in LiHJ. Appl. Spectr (USSR)42(N 4), 657–662 (1985). (in Russian)

    Google Scholar 

  80. J.L. Warren, J.L. Yarnell, G. Dolling, R.A. Cowley, Lattice dynamics of diamond. Phys. Rev. 158(N 3), 805–808 (1967)

    Google Scholar 

  81. G. Dolling, R.A. Cowley, The thermodynamic and optical properties of germanium, silicon, diamond and gallium arsenide. Proc. Phys. Soc. 88(N2), 463–494 (1966)

    Google Scholar 

  82. V.I. Tyutyunnik, O.I. Tyutyunnik, Phonon structure of Raman scattering spectra of LiH crystals. Phys. Stat. Sol. (b) 162(N2), 597–604 (1990)

    Google Scholar 

  83. R. Tubino, L. Piseri, G. Zerbi, Lattice dynamics and spectroscopic properties by a valence force potential of diamolike crystals: C, Si, Ge and \(\alpha \)-Sn. J. Chem. Phys. 56(N3), 1022–1039 (1972)

    CAS  Google Scholar 

  84. S. Baroni, S. de Girancoli, A. Dal Corso, P. Gianozzi, Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001). August

    CAS  Google Scholar 

  85. J. Reissland, The Physics of Phonons (Benjamin/Cummings, London, 1973)

    Google Scholar 

  86. D. Laplaze, Lattice dynamics of LiH and LiD:effect of long-range three-body forces. J. Phys. C: Solid State Phys. 10(N18), 3519–3499 (1977)

    Google Scholar 

  87. A. Anderson, F. Lüty, Raman scattering, defect luminescence and phonon spectra of \(^{7}\)LiH, \(^{6}\)LiH and \(^{7}\)LiD crystals. Phys. Rev. B28(N 6), 3415–3421 (1983)

    Google Scholar 

  88. P. Pavone, K. Karch, O. Schutt, et al., Ab initio lattice dynamics of diamond. Phys. Rev. B48(N5), 3156–3163 (1993)

    Google Scholar 

  89. R. Tubino, J.L. Birman, Two - phonon spectrum of diamond. Phys. Rev. Lett. 35(14), 670–672 (1975)

    Google Scholar 

  90. C.A. Klein, T.M. Hartnet, C.J. Robinson, Critical point phonon frquencies of diamond. Phys. Rev. B 45, 12854 (1992)

    CAS  Google Scholar 

  91. S.A. Solin, A.K. Ramdas, Raman spectrum of diamond. Phys. Rev. B 1(N4), 1687–1699 (1970)

    Google Scholar 

  92. K. Uchinokuka, T. Sekina, E. Matsuuro, Critical point analysis of the two-phonon spectrum of silicon. J. Phys. Chem. Solids 35(N1), 171–180 (1974)

    Google Scholar 

  93. M.H. Cohen, J. Ruvalds, Phonon dispersion of diamond measured by inelastic X-ray scattering. Phys. Rev. Let. 23(24), 1378–1381 (1969)

    Google Scholar 

  94. D.C. Hurley, R.S. Gilmore, W.F. Banholzer, Ultrasounic phase velocity and elastic modulus in isotopically enriched manufactured diamond. J. Appl. Phys. 76(N12), 7726–7730 (1994)

    Google Scholar 

  95. D. Vanderbilt, S.G. Louie, M.L. Cohen, Calculation of phonon-phonon interactions and the absence of phonon bound states in diamond. Phys. Rev. Lett. 53(N15), 1477–1480 (1984)

    Google Scholar 

  96. C.Z. Wang, C.T. Chang, K.M. Ho, Two-phonon spectrum of diamond: a moleculen dynamics approach. Solid State Commun. 76(N4), 483–486 (1990)

    Google Scholar 

  97. W. Windl, P. Pavone, K. Karch, O. Schutt, Second-order Raman spectra of diamond from ab initio phonon calculations. Phys. Rev. B48(N5), 3164–3170 (1993)

    Google Scholar 

  98. J. Kulda, B. Doner, K. Karch, P. Pavone, A neutron scattering study of overbending of the [100] LO phonon mode in diamond. Solid State Commun. 99(N 11), 799–802 (1996)

    Google Scholar 

  99. M. Schwoerer-Bohning, A.T. Macrander, D.A. Arms, Phys. Rev. Lett. 80, 5572 (1998)

    Google Scholar 

  100. T. Ruf, M. Cardona, P. Pavone, Catodoluminescence investigation of isotope effect in diamond. Solid State Commun. 105(N5), 311–316 (1998)

    Google Scholar 

  101. P. Etchegoin, H.D. Fuchs, J. Weber, et al., Phonons in isotopically disordered Ge. Phys. Rev. B48(N17), 12661–12671 (1993)

    Google Scholar 

  102. V.F. Agekyan, V.M. Asnin, A.M. Kryukov, et al., Isotope effect in germany, Fiz. Tverd. Tela (Leningrad) 31(N12), 101–104 (1989). (in Russian)

    Google Scholar 

  103. S.S. Jaswal, G. Wolfram, T.R. Sharma, Two-phonon Raman spectra of LiH and LiD crystals. J. Phys. Chem. Solids 35(N4), 571–579 (1974)

    Google Scholar 

  104. M. Lax, E. Burstein, Infrared lattice absorption in ionic and homopolar crystals. Phys. Rev. 97(N1), 39–52 (1955)

    Google Scholar 

  105. R. Loudon, The Raman effect in crystals. Adv. Phys. 13(N2), 423–488 (1964)

    Google Scholar 

  106. P.A. Temple, C.E. Hathaway, Multiphonon Raman spectrum of silicon. Phys. Rev. B7(N8), 3685–3697 (1973)

    Google Scholar 

  107. J.I. Birman, Space group symmetry, Handbuch der Physik, vol. 25/26 (Springer, Berlin, 1974)

    Google Scholar 

  108. M. Klein, Vibrational Raman scattering from crystals, in [10], vol. 6, chapter 5 (1995), pp. 67–D127

    Google Scholar 

  109. D. Laplaze, Second-order Raman spectra of LiH. Phys. Stat. Sol. (b) 91(N1), 59–69 (1979)

    Google Scholar 

  110. V.S. Kogan, Isotope effect in structuring properties. Sov. Phys. Uspekhi 5(N4), 579–618 (1963)

    Google Scholar 

  111. W. Dyck, H. Jex, Lattice dynamics of alkali hydrides and deuterides with NaCl type structure. J. Phys. C: Solid State Phys. 14(N29) 4193–4215 (1981)

    Google Scholar 

  112. R.A. Cowley, Anharmonicity. J. Phys. (Paris) 26(N 3), 659–664 (1965)

    Google Scholar 

  113. S. Go, M. Cardona, Bond, charge, bond polarizibility, and phonon spectra in semiconductors. Phys. Rev. Lett. 34(N10), 580–583 (1975)

    Google Scholar 

  114. A.K. Ramdas, S. Rodriguez, Lattice vibrations and electronic excitations in isotopically controlled diamonds. Phys. Stat. Sol. (b) 215(N1), 71–80 (1999)

    Google Scholar 

  115. K. Karch, T. Dietrich, W. Windl et al., Contribution of quantum and thermal fluctuations to the elastice moduli in covalent semiconductors. Phys. Rev. B 53(N11), 7259–7266 (1996)

    CAS  Google Scholar 

  116. H.D. Fuchs, S.H. Grein, M. Cardona, et al., Comparison of the phonon spectra \(^{70}\)Ge and natural Ge crystals: effect of isotopic disorder. Phys. Rev. B43(N6), 4835–4841 (1991)

    Google Scholar 

  117. J. Menendez, J.B. Page, S. Guha, Vibrational spectroscopy of C\(_{60}\), in Light Scattering in Solids VIII, ed. by M. Cardona, G. Güntherodt (Springer, Berlin, 2001)

    Google Scholar 

  118. P. Yu, M. Cardona, Fundamentals of Semiconductors (Springer, Heidelberg, 1996)

    Google Scholar 

  119. J.M. Zhang, M. Giehler, A. Gobel et al., Optical phonons in isotopic Ge studied by Raman scattering. Phys. Rev. B57(N16), 1348–1351 (1998)

    Google Scholar 

  120. J.M. Zhang, M. Giehler, A. Gobel et al., Isotope effects on exciton energies in CdS. Phys. Rev. B57(N16), 9716–9722 (1998)

    Google Scholar 

  121. H.D. Fuchs, S.H. Grein, R.I. Devlen et al., Anharmonic decay time, isotopic scattering time, and inhomogeneous line broadening optical phonons in \(^{70}\)Ge, \(^{76}\)Ge and natural Ge crystals. ibid, B44(N16), 8633–8642 (1991)

    Google Scholar 

  122. J. Spitzer, T. Ruf, W. Dondl et al., Raman scarttering by optical phonons in isotopic \(^{70}\)(Ge)\(_{\rm n}\), \(^{74}\)(Ge)\(_{\rm n}\) superlattices. Phys. Rev. Lett. 72(N10), 1565–1568 (1994)

    Google Scholar 

  123. R.M. Chrenko, \(^{13}\)C-doped diamond: Raman spectra. J. Appl. Phys. 63(N12), 5873–5875 (1988)

    Google Scholar 

  124. H. Hanzawa, N. Umemura, Y. Nisida, H. Kanda, Disorder effect of nitrogen impurities, irradiation-induced defects and \(^{13}\)C isotope composition on the Raman spectrum in synthetic I\(^{\rm b}\) diamond. Phys. Rev. B54(N6), 3793–3799 (1996)

    Google Scholar 

  125. J.M. Zhang, T. Ruf, M. Stutzman, Raman spectra of isotopic GaN. Phys. Rev. B 56(N22), 14399–14406 (1997)

    CAS  Google Scholar 

  126. R. Fuchs, K.L. Kliewer, Optical modes of vibration in an ionic crystal slab. Phys. Rev. 140, A2076–A2088 (1965)

    Google Scholar 

  127. G. Fasol, M. Tanaka, H. Sakaki, Y. Horikoshi, Interface roughness and the dispersion of confined LO phonons in GaAs/AlAs quantum wells. Phys. Rev. B38(9), 6056–6065 (1988)

    Google Scholar 

  128. E. Molinari, C. Bungaro, M. Gulia, Electron-phonon interaction in two-dimensional systems: a microscopic approach. Semicond. Sci. Technol. 7, B67–72 (1992)

    CAS  Google Scholar 

  129. K. Kunc, R. Martin, Ab initio force constants of GaAs: a new approach to calculation of phonons and dielectric properties. Phys. Rev. Let. 48(2), 406–409 (1982)

    Google Scholar 

  130. C. Falter, A unifying approach to lattice dynamical and electronic properties of solids. Phys. Rep. 164(1–2) 1–117 (1988)

    Google Scholar 

  131. K.J. Nash, Electron-phonon interactions and lattice dynamics of optic phonons in semiconductor heterostructures. Phys. Rev. B 46, 7723–7744 (1992)

    CAS  Google Scholar 

  132. B.K. Ridley, Electrons and Phonons in Semiconductor Multilayers (Cambridge University Press, Cambridge, 1997)

    Google Scholar 

  133. P. Harrison, Quantum Wells, Wires and Dots (Wiley, New York, 2000)

    Google Scholar 

  134. S. Yip and Y.- C. Chang, Theory of phonon dispersion relations in semiconductor superlattices. Phys. Rev. B 30, 7037–7059 (1984)

    Google Scholar 

  135. M.A. Stroscio, M. Dutta, Phonons in Nanostructures (Cambridge University Press, Cambridge, 2005)

    Google Scholar 

  136. H. Goldstein, Classical Mechanics (Addison-Wesley, Cambridge, 1950)

    Google Scholar 

  137. L. Landau, E.M. Lifshitz, Theory of Elasticity (Pergamon, Oxford, 1986)

    Google Scholar 

  138. S.M. Rytov, Acoustic properties of a tinly laminated medium. Sov. Phys. Acoust. 2, 68–80 (1956)

    Google Scholar 

  139. Z. Wang, K. Reinhardt, M. Dutta et al., Phonons in bulk and low-dimensional systems, in Length-Scale Dependent Phonon Interactions, vol. 128, Topics in Applied Physics, ed. by S.L. Shinde, G.P. Srivastava (Springer, New York, 2014)

    Google Scholar 

  140. J.E. Zucker, A. Pinczuk, D.S. Chemla, Optical vibration modes and electron-phonon interaction in GaAs quantum wells. Phys. Rev. Lett. 53, 1280–1283 (1984)

    CAS  Google Scholar 

  141. B. Jusserand, M. Cardona, Raman spectroscopy of vibrations in superlattices, in Light Scattering in Solids, ed. by V.M. Cardona, G. Güntherodt (Springer, Heidelberg, 1991)

    Google Scholar 

  142. J. Menendez, Phonons in GaAs - Al\(_{\rm x}\)Ga\(_{\rm 1-x}\)As superlattices. J. lumin. 44, 285–314 (1989)

    CAS  Google Scholar 

  143. E. Richter, D. Strauch, Lattice dynamics of GaAs-AlAs superlattices. Solid State Commun. 64, 867–870 (1987)

    CAS  Google Scholar 

  144. G.W. Bryant, G.S. Solomon, Optics of Quantum Dots and Wires (Artech House, Boston, 2005)

    Google Scholar 

  145. P.G. Klemens, Anharmonic decay of optical phonons. Phys. Rev. 148, 845–848 (1966)

    CAS  Google Scholar 

  146. C.M. Sottomar-Torres, Spectroscopy of nanostructures, in Physics of Nanostructures, ed. by J.H. Davies, A.R. Long (IOP, Bristol, 1992)

    Google Scholar 

  147. M.V. Klein, Phonons in semiconductor supelattices. IEEE J. Q. Electron. QE–18, 1760–1770 (1986)

    Google Scholar 

  148. V.G. Plekhanov, V.I. Altukhov, Light scattering in LiH crystals with LO phonon emission. J. Raman Spectrosc. 16(6), 358–365 (1985)

    Google Scholar 

  149. A.A. Berezin, Isotope superlattices and isotopically ordered structures. Solid State Commun. 65, (8), 819 (1988)

    Google Scholar 

  150. E.E. Haller, Isotope heterostructures selectively doped by neutron transmutation. Semicond. Sci. Technol. 5, (4) 319 (1990)

    Google Scholar 

  151. L.M. Zhuravleva, V.G. Plekhanov, Nanotechnology of optical devices information transformation and processing on the base of isotope-mixed materials, in Proceedings of the 8 All-Russian Conference (Vladimir, 2009), pp. 4–7. (in Russian)

    Google Scholar 

  152. M. Nakajima, H. Harima, K. Morita et al., Coherent confined LO phonons in \(^{70}\)Ge/\(^{74}\)Ge isotope superlattices generated by ultrafast laser pulses. Phys. Rev. B63, 161304 (R) (2001)

    Google Scholar 

  153. V.G. Plekhanov, Isotope-based materials science. Univer. J. Math. Sci. 1, 87–147 (2013)

    Google Scholar 

  154. E. Silveira, W. Dondl, G. Abstreiter, Ge self-diffusion in isotopic \(^{70}\)(Ge)\(_{\rm n}^{74}\)(Ge)\(_{\rm m}\) superlattices: a Raman study. Phys. Rev. B 56, 2062–2069 (1997)

    CAS  Google Scholar 

  155. A.V. Kolobov, K. Morita, K.M. Itoh, A Raman scattering study of self-assembled pure isotope Ge/Si (100) quantum dots. Appl. Phys. Lett. 81, 3855–3857 (2002)

    CAS  Google Scholar 

  156. T. Kojima, R. Nebashi, Y. Shiraki et al., Growth and characterization of \(^{28}\)Si/\(^{30}\)Si isotope superlattices. Appl. Phys. Lett. 83(12), 2318–2320 (2003)

    Google Scholar 

  157. V.G. Plekhanov, Isotope Effect: Origin and Application (Palmarium Academic Publishing, Saarbrücken, 2014). (in Russian)

    Google Scholar 

  158. H. Watanabe, T. Koretsume, S. Nakashima, Isotope compotion dependence of the band-gap energy in diamond. Phys. Rev. B 88, 205420–5 (2013)

    Google Scholar 

  159. H. Watanabe, C.E. Nebel, S. Shikata, Isotopic homojunction band engineering from diamond. Science 324, 1425–1428 (2009)

    CAS  Google Scholar 

  160. K. Barnham, D. Vvedensky, Low-Dimensional Semiconductor Structures (Cambridge University Press, Cambridge, 2009)

    Google Scholar 

  161. N. Balkan (ed.), Hot Electrons in Semiconductors (Oxford University Press, Oxford, 1998)

    Google Scholar 

  162. P. Ballewt, J. B. Smathers, H. Yang et al., Control of size and density of InAs/(Al, Ga)as self-organized islands. J. Appl. Phys. 90(1), 481–487 (2001)

    Google Scholar 

  163. E.G. Britton, K.B. Alexander, W.M. Strobs, The atomic scale characterization of multilayer semiconductor structures using TEM. GEO. J. Res. 5, 31–39 (1987)

    Google Scholar 

  164. W.M. Strobs, Recently developed TEM approach for the characterization heterostructures and interfaces, in The Physics and Fabrication of Microstructures and Microdevices, ed. by M.S. Kelly, C. Weisbuch (Springer, Berlin, 1986), pp. 136–149

    Google Scholar 

  165. D.M. Bruls, P.M. Koenrad, H.W.M. Salemink et al., Stacked long-growth-rate InAs quantum dots studied at the atomic level by cross-sectional STM. Appl. Phys. Lett. 82(21), 3752–3755 (2003)

    Google Scholar 

  166. B. Grandidier, Y.M. Niquet, J.P. Nys et al., Imaging the wave–function amplitudes in cleaved semiconductor quantum boxes. Phys. Rev. Lett. 85(5), 1068–1071 (2000)

    Google Scholar 

  167. S. Kret, T. Benabbes, C. Delamarre et al., High resolution electron microscope analysis of lattice distortions and In segregation in highly strained In\(_{0.35}\)Ga\(_{0.65}\)As coherent islands grown on GaAs (001). J. Appl. Phys. 86(4), 1988–1993 (1999)

    Google Scholar 

  168. M. Babiker, Coupling of polar optical phonons to electrons in superlattice and isolated quantum wells. Semicond. Sci. Technol. 7, B52–B59 (1992)

    CAS  Google Scholar 

  169. S. Das Sarma, V.B. Campos, M.A. Stroscio, Confined phonon modes and hot-electron energy relaxation in semiconductor microstructures. Semicond. Sci. Technol. 7, B60–B66 (1992)

    CAS  Google Scholar 

  170. E. Molinari, C. Bungaro, M. Gulia et al., Electron-phonon interactions in two-dimensional systems: A microscopic approach. Semicond. Sci. Technol. 7, B67–B72 (1992)

    CAS  Google Scholar 

  171. T. Tchuchiya, T. Ando, Electron-phonon interaction in semiconductor superlattice. Semicond. Sci. Technol. 7, B73–B76 (1992)

    Google Scholar 

  172. S. Kiravittaya, A. Rastelli, O.G. Schmidt, Advanced quantum dot configurations. Rep. Prog. Phys. 72, 046502 (2009)

    Google Scholar 

  173. L. Challis (ed.), Electron-Phonon Interaction in Low-Dimensional Structures (Oxford University Press, Oxford, 2003)

    Google Scholar 

  174. N. Bannov, V. Mitin, M. Stroscio Confined acoustic phonons in semiconductor slabs and their interaction with electrons. Phys. Stat. Sol. (b) 183(1), 131–138 (1994)

    Google Scholar 

  175. G. Yu, K.W. Kim, M.A. Stroscio et al., Electron-phonon scattering rates in rectangular quantum wires. Phys. Rev. B 50, 1733–1738 (1994)

    CAS  Google Scholar 

  176. J.S. Blakemore, Semiconducting and other major properties of gallium arsenide. J. Appl. Phys. 53, R123–R181 (1982)

    CAS  Google Scholar 

  177. T. Inoshita, H. Sakaki, Electron relaxation in a quantum dot: significance of multiphonon processes. Phys. Rev. B 46, 7260–7263 (1992)

    CAS  Google Scholar 

  178. U. Bockelman, G. Bastard, Phonon scattering and energy relaxation in two -, one -, and zero-dimensional electron gases. Phys. Rev. B 42, 8947–8951 (1990)

    Google Scholar 

  179. U. Bockelman, Phonon scattering and relaxation properties of lower dimensional electron gases, Intersubband Transitions in Quantum Wells, vol. 288, NATO ASI Series B: Physics (Plenum, New York, 1993), pp. 105–118

    Google Scholar 

  180. J.I. Pankove, Optical Processes in Semiconductors (Prentice Hall, Englewood Cliffs, 1971)

    Google Scholar 

  181. M.P. Blencowe, Phonons in Low Dimensional Semiconductor Structures, in: Low-Dimensional Semiconductor Structures: Fundamentals and Device Applications, K. Barnham, D. Vvedensky (eds.) (Cambridge, Cambridge University Press, 2001), pp. 123 – 148

    Google Scholar 

  182. H. Bensity, C.M. Sotomayor-Torres, C. Weisbuch, Intrinsic mechanism for the poor luminescence properties of quantum-box systems. Phys. Rev. B 44, 10945–10948 (1991)

    Google Scholar 

  183. C. Weisbuch, B. Vinter, Quantum Semiconductor Structures (Academic, San Diego, 1991)

    Google Scholar 

  184. G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted, New York, 1988)

    Google Scholar 

  185. L.V. Keldysh, Excitons in semiconductor–dielectric nanostructures. Phys. Stat. Solidi (a) 164, 3–12 (1997)

    Google Scholar 

  186. V.I. Pipa, V.V. Mitin, M. Stroscio, Acoustic phonon bottleneck in quantum dots: role of deformation variation of electron effective mass. Solid State Commun. 117, 713–717 (2001)

    CAS  Google Scholar 

  187. F. Rossi, G. Goldoni, E. Molinari, Theory of excitonic confinement in semiconductor quantum wires. J. Phys. Condens. Matter 11, 5969–5988 (1999)

    CAS  Google Scholar 

  188. A.V. Akimov, Exciton–phonon interaction in quantum wires, in Electron-Phonon Interactions in Low-Dimensional Structures, ed. by L. Challis (Oxford University Press, Oxford, 2010), pp. 239–267

    Google Scholar 

  189. R.S. Knox, Theory of Excitons, Solid State Physics, Suppl 3 (Academic, New York, 1963)

    Google Scholar 

  190. V.G. Plekhanov, Wannier–Mott excitons in isotope—disordered crystals. Rep. Prog. Phys. 61(8), 1045–1095 (1998)

    Google Scholar 

  191. J. Lee, E.S. Koteles, M.O. Vassel, Luminescence linewidths of excitons in GaAs quantum wells below 150 K. Phys. Rev. B 33, 5512–5516 (1986)

    CAS  Google Scholar 

  192. R.J. Nelson, Excitons in semiconductor alloys, in Excitons, Ch. 8, ed. by E.I. Rashba, M.D. Sturge (North–Holland, Amsterdam, 1982), pp. 319–348

    Google Scholar 

  193. R. Cingolani, K. Ploog, Frequency and density dependent radiative recombination processes in III-V quantum wells and superlattice. Adv. Phys. 40, 535–623 (1991)

    CAS  Google Scholar 

  194. H. Hillmer, A. Forschel, S. Hausman, Optical investigations on the mobility of two-dimensional excitons in GaAs/Ga\(_{\rm 1-x}\)Al\(_{\rm x}\)As quantum wells. Phys. Rev. B 39, 10901–10912 (1989)

    CAS  Google Scholar 

  195. R. Tsu, Superlattice to Nanoelectronics (Elsevier Science, Amsterdam, 2005)

    Google Scholar 

  196. J.H. Collet, H. Kalt, Le.Si. Dang et al., Relaxation of excitons in coherently strained CdTe/ZnTe quantum wells. Phys. Rev. B 43, 6843–6846 (1991)

    Google Scholar 

  197. R.P. Stanley, J. Hegarty, R. Fischer, Hot-exciton relaxation in Cd\(_{\rm x}\)Zn\(_{\rm 1-x}\)Te/ZnTe multiple quantum wells. Phys. Rev. Lett. 67, 128–131 (1991)

    Google Scholar 

  198. D. Bimberg, M. Grundman, N.N. Ledentsov, Quantum Dot Heterostructure (Wiley, Chichester, 1999)

    Google Scholar 

  199. L. Jacak, P. Hawrylak, A. Wojs, Quantum Dots (Springer, Berlin, 1998)

    Google Scholar 

  200. G.W. Bryant, G.S. Solomon (eds.), Optics of Quantum Dots and Wires (Artech House, London, 2005)

    Google Scholar 

  201. H.C. Casey, M.B. Panish, Heterostructure Lasers (Academic, New York, 1978)

    Google Scholar 

  202. P.S. Zoty, Quantum Well Lasers (Academic, Boston, 1993)

    Google Scholar 

  203. Y. Arakawa, Semiconductor nano–structure lasers: fundamentals and applications, in Confined Electrons and Photons: New Physics and Applications, vol. 340, NATO Series B: Physics, ed. by E. Burstein, C. Weisbuch (Plenum, New York, 1995), pp. 647–673

    Google Scholar 

  204. L.A. Colderen, S.W. Corzine, Diode Lasers and Photonic Integrated Cicuits (Wiley, New York, 1995)

    Google Scholar 

  205. V.M. Ustinov, A.E. Zukov, AYu. Egorov, N.A. Maleen, Quantum Dot Lasers (Oxford University Press, Oxford, 2003)

    Google Scholar 

  206. K. Ikeda, H. Seguchi, F. Minami et al., Phonon bottleneck effects in InAs/GaInP quantum dots. J. Luminesc. 108, 273–276 (2004)

    CAS  Google Scholar 

  207. R. Heitz, M. Grundman, N.N. Ledentsov, Multiphonon-relaxation processes in self-organized InAs/GaAs quantum dots. Appl. Phys. Lett. 68, 361–363 (1996)

    CAS  Google Scholar 

  208. B. Damilano, N. Grandejan, J. Massies et al., Gan and GaInN quantum dots: an efficient way to get luminescence in the visible spectrum range. Appl. Surf. Sci. 164, 241–245 (2000)

    CAS  Google Scholar 

  209. Y. Kuwahara, Y. Fujiyama, M. Iwaya et al., Nitrides based light–emitting solar cell. Phys. Stat. Sol. (c) 7, 1807–1809 (2010)

    Google Scholar 

  210. V.G. Plekhanov, Isotopes in Condensed Matter (Springer, Heidelberg, 2013)

    Google Scholar 

  211. P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, 1958)

    Google Scholar 

  212. R.P. Feynman, R.P. Leighton, M. Sands, The Feynman Lecture in Physics, vol. 3 (Addison-Wesley, Reading, 1965)

    Google Scholar 

  213. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon Press, New York, 1977)

    Google Scholar 

  214. K. Kuroda, T. Kuroda, K. Watanabe et al., Distribution of exciton emission linewidth observed for GaAs quantum dots grown by droplet epitaxy. J. Luminesc. 130, 2390–2393 (2010)

    CAS  Google Scholar 

  215. D.W. Taylor, Phonon response theory and the infrared and Raman experiments, in [48], Chapter 2, pp. 35–132

    Google Scholar 

  216. G.L. Bir, G.E. Picus, Symmetry and Deformation in Semiconductors (Science, Moscow, 1972). (in Russian)

    Google Scholar 

  217. S.I. Pekar, Crystaloptics and Addition Waves (Naukova Dumka, Kiev, 1982). (in Russian)

    Google Scholar 

  218. N.N. Ledentsov, V.M. Ustinov, V.A. Shchukin et al., Quantum dot heterostructures: fabrication, properties, lasers. Fiz. Teh. Polup. (Physics and Technics of Semicond.) 32(4), 385–410 (1998). (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics and Physics Department, Computer Science College, Tallinn, Estonia

    Vladimir G. Plekhanov

Authors
  1. Vladimir G. Plekhanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir G. Plekhanov .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Plekhanov, V.G. (2018). Phonon States in Bulk and Low-Dimensional Structures. In: Introduction to Isotopic Materials Science. Springer Series in Materials Science, vol 248. Springer, Cham. https://doi.org/10.1007/978-3-319-42261-9_3

Download citation

Publish with us

Policies and ethics

Search

Navigation