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Phonon States in Bulk and Low-Dimensional Structures

  • Vladimir G. Plekhanov
Chapter
Part of the Springer Series in Materials Science book series (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.

References

  1. 1.
    V.G. Plekhanov, Elementary excitations in isotope-mixed crystals. Phys. Rep. 410(N 1 – 3), 1–235 (2005)CrossRefGoogle Scholar
  2. 2.
    M. Cardona, M.L.W. Thewalt, Isotope effect on the optical spectra of semiconductors. Rev. Mod. Phys. 77, 1173–1224 (2005). OctoberCrossRefGoogle Scholar
  3. 3.
    J.R. Hardy, A.M. Karo, The Lattice Dynamics and Statics of Alkali halide Crystals (Plenum, New York, 1979)CrossRefGoogle Scholar
  4. 4.
    A.A. Abrikosov (ed.) The Achievement of the Electron Theory of Metals (Mir, Moscow, 1984). (in Russian)Google Scholar
  5. 5.
    J.F. Scott, Soft-mode spectroscopy: experimental studies of structural phase transition. Rev. Mod. Phys. 46(N 1), 83–128 (1974)CrossRefGoogle Scholar
  6. 6.
    V.G. Plekhanov, Isotope Effect in Solid State Physics (Acdemic, San Diego, 2001)Google Scholar
  7. 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. 275–445Google Scholar
  8. 8.
    M.J. Kelly, Low-Dimensional Semiconductors: Materials, Physics, Technology, Devices (Clarendon, Oxford, 1995)Google Scholar
  9. 9.
    J.H. Davies, The Physics of Low-Dimensional Semiconductors (Cambridge University Press, Cmbridge, 1998)Google Scholar
  10. 10.
    J.M. Martinez-Duart, R.J. Martin-Palma, F. Aguello-Rueda, Nanotechnology for Microelectronics and Optoelectronics (Elsevier, Amsterdam, 2006)Google Scholar
  11. 11.
    K. Goser, P. Glösekőtter, J. Dienstuhl, Nanoelectronics and Nanosystems (Springer, Berlin, 2004)CrossRefGoogle Scholar
  12. 12.
    W.A. Harrison, Electronic Structure and the Properties of Solids (CA, Freeman, San Francisco, 1980)Google Scholar
  13. 13.
    N.W. Aschcroft, N. David Mermin, Solid State Physics (Harcourt Brace College Publishers, New York, 1975)Google Scholar
  14. 14.
    M. Born, K. Huang, Dynamical Theory of Crystal Lattice (Oxford University Press, Oxford, 1988)Google Scholar
  15. 15.
    J. Pankove, Optical Processes in Semiconductors (Prentice-Hall, Englewood Cliffs, 1971)Google Scholar
  16. 16.
    G.P. Srivastawa, The Physics of Phonons (Hilger, Bristol, 1990)Google Scholar
  17. 17.
    J.M. Ziman, Principles of the Theory of Solids (Cambridge University Press, Cambridge, 1964)Google Scholar
  18. 18.
    H. Böttger, Principles of the Theory of Lattice Dynamics (Physik-Verlag, Weinheim, 1983)Google Scholar
  19. 19.
    P. Bruesch, Phonons: Theory and Experiments II (Springer, Berlin, 1986)CrossRefGoogle Scholar
  20. 20.
    I.E. Tamm, Eine Bemerkung zur Diracschen Theorie der Lichterstroung und Dispersion. Zs. Phys. 62(N 9), 705–708 (1930)CrossRefGoogle Scholar
  21. 21.
    M. Born, J. Oppenheimer, Zur Quantheorie der Molekulen. Ann. Phys. 389(N 20), 457–484 (1927)CrossRefGoogle Scholar
  22. 22.
    V.G. Plekhanov, Lattice dynamics of isotope-mixed crystals (2010), arXiv:cond-mat/1007.5125
  23. 23.
    S.I. Pekar, Untersuchungen uber die Elektronentheorie der Kristalle (Academic, Berlin, 1954). (in German)Google Scholar
  24. 24.
    V.G. Plekhanov, Isotope Low-Dimensional Structures (Springer, Heidelberg, 2012)CrossRefGoogle Scholar
  25. 25.
    R.A. Cowley, Anharmonic crystals. Rep. Prog. Phys. 31(N 2), 123–166 (1968)CrossRefGoogle Scholar
  26. 26.
    P.G. Klemens, Anharmonic decay of optical phonons. Phys. Rev. 148(N 2), 845–848 (1966)CrossRefGoogle Scholar
  27. 27.
    T.R. Hart, R.L. Aggarval, B. Lax, Temperature dependence Raman scattering in silicon. ibid B1(N1), 638–642 (1970)Google Scholar
  28. 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. 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. 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. 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)CrossRefGoogle Scholar
  32. 32.
    A. Debernardi, Phonon linewidth in III-V semiconductors from density-functional perturbation theory. Phys. Rev. B57(N 20), 12847–12858 (1998)CrossRefGoogle Scholar
  33. 33.
    A. Debernardi, Anharmonic effect in the phonons of III-V semiconductors: first principles calculations. Solid State Commun. 113(N1), 1–10 (2000)CrossRefGoogle Scholar
  34. 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. 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)CrossRefGoogle Scholar
  36. 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)CrossRefGoogle Scholar
  37. 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)CrossRefGoogle Scholar
  38. 38.
    J.M. Ziman, Models of Disorder (Cambridge University Press, Cambridge, 1979)Google Scholar
  39. 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)CrossRefGoogle Scholar
  40. 40.
    V.G. Plekhanov, Isotope effect in lattice dynamics. Phys.-Uspekhi (Moscow) 46(N7), 689–715 (2003)CrossRefGoogle Scholar
  41. 41.
    B.A. Weinstein, R. Zallen, in: M. Cardona, G. Guntherodt, (eds.), Light Scattering in Solids, Vol. 4, (Berlin, Springer, 1984)Google Scholar
  42. 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)CrossRefGoogle Scholar
  43. 43.
    W. Cochran, R.A. Cowley, Phonons in perfect crystals, Handbuch der Physik, vol. 25/2a (Springer, Berlin, 1967), pp. 59–156Google Scholar
  44. 44.
    V.G. Plekhanov, Isotope effect on the lattice dynamics of crystals. Mater. Sci. Eng. R35(N 4–6) , 139–237 (2001)CrossRefGoogle Scholar
  45. 45.
    V.G. Plekhanov, Giant Isotope Effect in Solids (Stefan University Press, La Jolla, 2004)CrossRefGoogle Scholar
  46. 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)CrossRefGoogle Scholar
  47. 47.
    W. Mason, R. Thurston (eds.), Physical Acoustics: Principles and Methods, vol. 1–3 (Academic, New York, 1968–1970)Google Scholar
  48. 48.
    R.J. Elliott, I.P. Ipatova (eds.), Optical Properties of Mixed Crystals (North-Holland, Amsterdam, 1988)Google Scholar
  49. 49.
    J. Emsley, The Elements (Clarendon, Oxford, 1998)Google Scholar
  50. 50.
    V.G. Plekhanov, Lattice dynamics of isotopically mixed crystals. Opt. Spectr. 82, 95–122 (1997)Google Scholar
  51. 51.
    I.M. Lifshitz, Selected Works (Science, Moscow, 1987). (in Russian)Google Scholar
  52. 52.
    E.N. Economou, Green’s Functions in Quantum Physics (Springer, Heidelberg, 1983)CrossRefGoogle Scholar
  53. 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)CrossRefGoogle Scholar
  54. 54.
    P. Soven, Coherent-potential model for substitutional disordered alloys. Phys. Rev. 156, 809–817 (1967)CrossRefGoogle Scholar
  55. 55.
    D.W. Taylor, Vibrational theory of imperfect crystals with large defect concentration. ibid, 156, 1017–1024 (1967)Google Scholar
  56. 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)CrossRefGoogle Scholar
  57. 57.
    I.A. Abrikosov, B. Johansson, Applicability of the CPA in the theory of random alloys. ibid, B57, 14164–14169 (1998)Google Scholar
  58. 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. 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. 60.
    J. Spitzer, P. Etchegoin, T.R. Anthony, Isotopic-disorder induced Raman scattering in diamond. Solid State Commun. 88, 509–513 (1983)CrossRefGoogle Scholar
  61. 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)CrossRefGoogle Scholar
  62. 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. 63.
    V.G. Plekhanov, Fundamentals and applications of isotope effect in modern technology, J. Nucl. Sci. Technol. (Japan) 43(4) 375–381 (2006)CrossRefGoogle Scholar
  64. 64.
    H. Ehrenreich, W. Schwartz, The electronic structure of alloys, Solid State Physics, vol. 31 (Academic, New York, 1976), pp. 149–286Google Scholar
  65. 65.
    B. Dorner, Inelastic Neutron Scattering in Lattice Dynamics, vol. 93, Springer Tracts in Modern Physics (Springer, Berlin, 1982)CrossRefGoogle Scholar
  66. 66.
    V.G. Plekhanov, Applications of the Isotopic Effect in Solids (Springer, Berlin, 2004)CrossRefGoogle Scholar
  67. 67.
    M.A. Krivoglaz, Theory of scattering X-Rays and Thermal Neutrons by Real Crystals (Science, Moscow, 1967). (in Russian)Google Scholar
  68. 68.
    W. Cochran, The Dynamics of Atoms in Crystals (Arnold, London, 1973)Google Scholar
  69. 69.
    A.C. Anderson, J.P. Wolfe (eds.), Phonon Scattering in Condensed Matter (Springer, Berlin, 1986)Google Scholar
  70. 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. 543–629Google Scholar
  71. 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. 178–262Google Scholar
  72. 72.
    E.B. Wilson, J.C. Decius, P.C. Gross, Molecular Vibrations (McGraw-Hill, New York, 1955)Google Scholar
  73. 73.
    H. Bilz, W. Kress, Phonon Dispersion Relations in Insulators (Springer, Berlin, 1979)CrossRefGoogle Scholar
  74. 74.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory (Pergamon, Oxford, 1977)Google Scholar
  75. 75.
    V.G. Plekhanov, Application of isotope effects in solids. J. Mater. Sci. 38, 3341–3429 (2003)CrossRefGoogle Scholar
  76. 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. 431–439Google Scholar
  77. 77.
    J.L. Verble, J.L. Warren, J.L. Yarnell, Lattice dynamics of lithium hydride. Phys. Rev. 168(N 3), 989 (1968)CrossRefGoogle Scholar
  78. 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. 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. 80.
    J.L. Warren, J.L. Yarnell, G. Dolling, R.A. Cowley, Lattice dynamics of diamond. Phys. Rev. 158(N 3), 805–808 (1967)CrossRefGoogle Scholar
  81. 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)CrossRefGoogle Scholar
  82. 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)CrossRefGoogle Scholar
  83. 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)CrossRefGoogle Scholar
  84. 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). AugustCrossRefGoogle Scholar
  85. 85.
    J. Reissland, The Physics of Phonons (Benjamin/Cummings, London, 1973)Google Scholar
  86. 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)CrossRefGoogle Scholar
  87. 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. 88.
    P. Pavone, K. Karch, O. Schutt, et al., Ab initio lattice dynamics of diamond. Phys. Rev. B48(N5), 3156–3163 (1993)CrossRefGoogle Scholar
  89. 89.
    R. Tubino, J.L. Birman, Two - phonon spectrum of diamond. Phys. Rev. Lett. 35(14), 670–672 (1975)CrossRefGoogle Scholar
  90. 90.
    C.A. Klein, T.M. Hartnet, C.J. Robinson, Critical point phonon frquencies of diamond. Phys. Rev. B 45, 12854 (1992)CrossRefGoogle Scholar
  91. 91.
    S.A. Solin, A.K. Ramdas, Raman spectrum of diamond. Phys. Rev. B 1(N4), 1687–1699 (1970)CrossRefGoogle Scholar
  92. 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. 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. 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. 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)CrossRefGoogle Scholar
  96. 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. 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)CrossRefGoogle Scholar
  98. 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. 99.
    M. Schwoerer-Bohning, A.T. Macrander, D.A. Arms, Phys. Rev. Lett. 80, 5572 (1998)CrossRefGoogle Scholar
  100. 100.
    T. Ruf, M. Cardona, P. Pavone, Catodoluminescence investigation of isotope effect in diamond. Solid State Commun. 105(N5), 311–316 (1998)CrossRefGoogle Scholar
  101. 101.
    P. Etchegoin, H.D. Fuchs, J. Weber, et al., Phonons in isotopically disordered Ge. Phys. Rev. B48(N17), 12661–12671 (1993)CrossRefGoogle Scholar
  102. 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. 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)CrossRefGoogle Scholar
  104. 104.
    M. Lax, E. Burstein, Infrared lattice absorption in ionic and homopolar crystals. Phys. Rev. 97(N1), 39–52 (1955)CrossRefGoogle Scholar
  105. 105.
    R. Loudon, The Raman effect in crystals. Adv. Phys. 13(N2), 423–488 (1964)CrossRefGoogle Scholar
  106. 106.
    P.A. Temple, C.E. Hathaway, Multiphonon Raman spectrum of silicon. Phys. Rev. B7(N8), 3685–3697 (1973)CrossRefGoogle Scholar
  107. 107.
    J.I. Birman, Space group symmetry, Handbuch der Physik, vol. 25/26 (Springer, Berlin, 1974)Google Scholar
  108. 108.
    M. Klein, Vibrational Raman scattering from crystals, in [10], vol. 6, chapter 5 (1995), pp. 67–D127Google Scholar
  109. 109.
    D. Laplaze, Second-order Raman spectra of LiH. Phys. Stat. Sol. (b) 91(N1), 59–69 (1979)CrossRefGoogle Scholar
  110. 110.
    V.S. Kogan, Isotope effect in structuring properties. Sov. Phys. Uspekhi 5(N4), 579–618 (1963)Google Scholar
  111. 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)CrossRefGoogle Scholar
  112. 112.
    R.A. Cowley, Anharmonicity. J. Phys. (Paris) 26(N 3), 659–664 (1965)Google Scholar
  113. 113.
    S. Go, M. Cardona, Bond, charge, bond polarizibility, and phonon spectra in semiconductors. Phys. Rev. Lett. 34(N10), 580–583 (1975)CrossRefGoogle Scholar
  114. 114.
    A.K. Ramdas, S. Rodriguez, Lattice vibrations and electronic excitations in isotopically controlled diamonds. Phys. Stat. Sol. (b) 215(N1), 71–80 (1999)CrossRefGoogle Scholar
  115. 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)CrossRefGoogle Scholar
  116. 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. 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. 118.
    P. Yu, M. Cardona, Fundamentals of Semiconductors (Springer, Heidelberg, 1996)CrossRefGoogle Scholar
  119. 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)CrossRefGoogle Scholar
  120. 120.
    J.M. Zhang, M. Giehler, A. Gobel et al., Isotope effects on exciton energies in CdS. Phys. Rev. B57(N16), 9716–9722 (1998)CrossRefGoogle Scholar
  121. 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. 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)CrossRefGoogle Scholar
  123. 123.
    R.M. Chrenko, \(^{13}\)C-doped diamond: Raman spectra. J. Appl. Phys. 63(N12), 5873–5875 (1988)Google Scholar
  124. 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. 125.
    J.M. Zhang, T. Ruf, M. Stutzman, Raman spectra of isotopic GaN. Phys. Rev. B 56(N22), 14399–14406 (1997)CrossRefGoogle Scholar
  126. 126.
    R. Fuchs, K.L. Kliewer, Optical modes of vibration in an ionic crystal slab. Phys. Rev. 140, A2076–A2088 (1965)CrossRefGoogle Scholar
  127. 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)CrossRefGoogle Scholar
  128. 128.
    E. Molinari, C. Bungaro, M. Gulia, Electron-phonon interaction in two-dimensional systems: a microscopic approach. Semicond. Sci. Technol. 7, B67–72 (1992)CrossRefGoogle Scholar
  129. 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)CrossRefGoogle Scholar
  130. 130.
    C. Falter, A unifying approach to lattice dynamical and electronic properties of solids. Phys. Rep. 164(1–2) 1–117 (1988)CrossRefGoogle Scholar
  131. 131.
    K.J. Nash, Electron-phonon interactions and lattice dynamics of optic phonons in semiconductor heterostructures. Phys. Rev. B 46, 7723–7744 (1992)CrossRefGoogle Scholar
  132. 132.
    B.K. Ridley, Electrons and Phonons in Semiconductor Multilayers (Cambridge University Press, Cambridge, 1997)Google Scholar
  133. 133.
    P. Harrison, Quantum Wells, Wires and Dots (Wiley, New York, 2000)Google Scholar
  134. 134.
    S. Yip and Y.- C. Chang, Theory of phonon dispersion relations in semiconductor superlattices. Phys. Rev. B 30, 7037–7059 (1984)CrossRefGoogle Scholar
  135. 135.
    M.A. Stroscio, M. Dutta, Phonons in Nanostructures (Cambridge University Press, Cambridge, 2005)Google Scholar
  136. 136.
    H. Goldstein, Classical Mechanics (Addison-Wesley, Cambridge, 1950)Google Scholar
  137. 137.
    L. Landau, E.M. Lifshitz, Theory of Elasticity (Pergamon, Oxford, 1986)Google Scholar
  138. 138.
    S.M. Rytov, Acoustic properties of a tinly laminated medium. Sov. Phys. Acoust. 2, 68–80 (1956)Google Scholar
  139. 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. 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)CrossRefGoogle Scholar
  141. 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. 142.
    J. Menendez, Phonons in GaAs - Al\(_{\rm x}\)Ga\(_{\rm 1-x}\)As superlattices. J. lumin. 44, 285–314 (1989)CrossRefGoogle Scholar
  143. 143.
    E. Richter, D. Strauch, Lattice dynamics of GaAs-AlAs superlattices. Solid State Commun. 64, 867–870 (1987)CrossRefGoogle Scholar
  144. 144.
    G.W. Bryant, G.S. Solomon, Optics of Quantum Dots and Wires (Artech House, Boston, 2005)Google Scholar
  145. 145.
    P.G. Klemens, Anharmonic decay of optical phonons. Phys. Rev. 148, 845–848 (1966)CrossRefGoogle Scholar
  146. 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. 147.
    M.V. Klein, Phonons in semiconductor supelattices. IEEE J. Q. Electron. QE–18, 1760–1770 (1986)CrossRefGoogle Scholar
  148. 148.
    V.G. Plekhanov, V.I. Altukhov, Light scattering in LiH crystals with LO phonon emission. J. Raman Spectrosc. 16(6), 358–365 (1985)CrossRefGoogle Scholar
  149. 149.
    A.A. Berezin, Isotope superlattices and isotopically ordered structures. Solid State Commun. 65, (8), 819 (1988)CrossRefGoogle Scholar
  150. 150.
    E.E. Haller, Isotope heterostructures selectively doped by neutron transmutation. Semicond. Sci. Technol. 5, (4) 319 (1990)CrossRefGoogle Scholar
  151. 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. 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. 153.
    V.G. Plekhanov, Isotope-based materials science. Univer. J. Math. Sci. 1, 87–147 (2013)Google Scholar
  154. 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)CrossRefGoogle Scholar
  155. 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)CrossRefGoogle Scholar
  156. 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)CrossRefGoogle Scholar
  157. 157.
    V.G. Plekhanov, Isotope Effect: Origin and Application (Palmarium Academic Publishing, Saarbrücken, 2014). (in Russian)Google Scholar
  158. 158.
    H. Watanabe, T. Koretsume, S. Nakashima, Isotope compotion dependence of the band-gap energy in diamond. Phys. Rev. B 88, 205420–5 (2013)CrossRefGoogle Scholar
  159. 159.
    H. Watanabe, C.E. Nebel, S. Shikata, Isotopic homojunction band engineering from diamond. Science 324, 1425–1428 (2009)CrossRefGoogle Scholar
  160. 160.
    K. Barnham, D. Vvedensky, Low-Dimensional Semiconductor Structures (Cambridge University Press, Cambridge, 2009)Google Scholar
  161. 161.
    N. Balkan (ed.), Hot Electrons in Semiconductors (Oxford University Press, Oxford, 1998)Google Scholar
  162. 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. 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. 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. 136–149Google Scholar
  165. 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)CrossRefGoogle Scholar
  166. 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)CrossRefGoogle Scholar
  167. 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. 168.
    M. Babiker, Coupling of polar optical phonons to electrons in superlattice and isolated quantum wells. Semicond. Sci. Technol. 7, B52–B59 (1992)CrossRefGoogle Scholar
  169. 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)CrossRefGoogle Scholar
  170. 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)CrossRefGoogle Scholar
  171. 171.
    T. Tchuchiya, T. Ando, Electron-phonon interaction in semiconductor superlattice. Semicond. Sci. Technol. 7, B73–B76 (1992)CrossRefGoogle Scholar
  172. 172.
    S. Kiravittaya, A. Rastelli, O.G. Schmidt, Advanced quantum dot configurations. Rep. Prog. Phys. 72, 046502 (2009)CrossRefGoogle Scholar
  173. 173.
    L. Challis (ed.), Electron-Phonon Interaction in Low-Dimensional Structures (Oxford University Press, Oxford, 2003)Google Scholar
  174. 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)CrossRefGoogle Scholar
  175. 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)CrossRefGoogle Scholar
  176. 176.
    J.S. Blakemore, Semiconducting and other major properties of gallium arsenide. J. Appl. Phys. 53, R123–R181 (1982)CrossRefGoogle Scholar
  177. 177.
    T. Inoshita, H. Sakaki, Electron relaxation in a quantum dot: significance of multiphonon processes. Phys. Rev. B 46, 7260–7263 (1992)CrossRefGoogle Scholar
  178. 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)CrossRefGoogle Scholar
  179. 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. 105–118CrossRefGoogle Scholar
  180. 180.
    J.I. Pankove, Optical Processes in Semiconductors (Prentice Hall, Englewood Cliffs, 1971)Google Scholar
  181. 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 – 148Google Scholar
  182. 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)CrossRefGoogle Scholar
  183. 183.
    C. Weisbuch, B. Vinter, Quantum Semiconductor Structures (Academic, San Diego, 1991)CrossRefGoogle Scholar
  184. 184.
    G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted, New York, 1988)Google Scholar
  185. 185.
    L.V. Keldysh, Excitons in semiconductor–dielectric nanostructures. Phys. Stat. Solidi (a) 164, 3–12 (1997)CrossRefGoogle Scholar
  186. 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)CrossRefGoogle Scholar
  187. 187.
    F. Rossi, G. Goldoni, E. Molinari, Theory of excitonic confinement in semiconductor quantum wires. J. Phys. Condens. Matter 11, 5969–5988 (1999)CrossRefGoogle Scholar
  188. 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. 239–267Google Scholar
  189. 189.
    R.S. Knox, Theory of Excitons, Solid State Physics, Suppl 3 (Academic, New York, 1963)Google Scholar
  190. 190.
    V.G. Plekhanov, Wannier–Mott excitons in isotope—disordered crystals. Rep. Prog. Phys. 61(8), 1045–1095 (1998)CrossRefGoogle Scholar
  191. 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)CrossRefGoogle Scholar
  192. 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. 319–348Google Scholar
  193. 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)CrossRefGoogle Scholar
  194. 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)CrossRefGoogle Scholar
  195. 195.
    R. Tsu, Superlattice to Nanoelectronics (Elsevier Science, Amsterdam, 2005)Google Scholar
  196. 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)CrossRefGoogle Scholar
  197. 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)CrossRefGoogle Scholar
  198. 198.
    D. Bimberg, M. Grundman, N.N. Ledentsov, Quantum Dot Heterostructure (Wiley, Chichester, 1999)Google Scholar
  199. 199.
    L. Jacak, P. Hawrylak, A. Wojs, Quantum Dots (Springer, Berlin, 1998)CrossRefGoogle Scholar
  200. 200.
    G.W. Bryant, G.S. Solomon (eds.), Optics of Quantum Dots and Wires (Artech House, London, 2005)Google Scholar
  201. 201.
    H.C. Casey, M.B. Panish, Heterostructure Lasers (Academic, New York, 1978)Google Scholar
  202. 202.
    P.S. Zoty, Quantum Well Lasers (Academic, Boston, 1993)Google Scholar
  203. 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. 647–673CrossRefGoogle Scholar
  204. 204.
    L.A. Colderen, S.W. Corzine, Diode Lasers and Photonic Integrated Cicuits (Wiley, New York, 1995)Google Scholar
  205. 205.
    V.M. Ustinov, A.E. Zukov, AYu. Egorov, N.A. Maleen, Quantum Dot Lasers (Oxford University Press, Oxford, 2003)CrossRefGoogle Scholar
  206. 206.
    K. Ikeda, H. Seguchi, F. Minami et al., Phonon bottleneck effects in InAs/GaInP quantum dots. J. Luminesc. 108, 273–276 (2004)CrossRefGoogle Scholar
  207. 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)CrossRefGoogle Scholar
  208. 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)CrossRefGoogle Scholar
  209. 209.
    Y. Kuwahara, Y. Fujiyama, M. Iwaya et al., Nitrides based light–emitting solar cell. Phys. Stat. Sol. (c) 7, 1807–1809 (2010)CrossRefGoogle Scholar
  210. 210.
    V.G. Plekhanov, Isotopes in Condensed Matter (Springer, Heidelberg, 2013)CrossRefGoogle Scholar
  211. 211.
    P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, 1958)CrossRefGoogle Scholar
  212. 212.
    R.P. Feynman, R.P. Leighton, M. Sands, The Feynman Lecture in Physics, vol. 3 (Addison-Wesley, Reading, 1965)Google Scholar
  213. 213.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon Press, New York, 1977)Google Scholar
  214. 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)CrossRefGoogle Scholar
  215. 215.
    D.W. Taylor, Phonon response theory and the infrared and Raman experiments, in [48], Chapter 2, pp. 35–132CrossRefGoogle Scholar
  216. 216.
    G.L. Bir, G.E. Picus, Symmetry and Deformation in Semiconductors (Science, Moscow, 1972). (in Russian)Google Scholar
  217. 217.
    S.I. Pekar, Crystaloptics and Addition Waves (Naukova Dumka, Kiev, 1982). (in Russian)Google Scholar
  218. 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

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Authors and Affiliations

  1. 1.Mathematics and Physics DepartmentComputer Science CollegeTallinnEstonia

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