Raman Scattering from Phonons in Quasiperiodic Superlattices Based on Generalizations of the Fibonacci Sequence

  • T. A. Gant
  • D. J. Lockwood
  • J.-M. Baribeau
  • A. H. MacDonald
Part of the NATO ASI Series book series (NSSB, volume 206)


Recently there has been a great deal of interest in the structural, vibrational, and electronic properties of nonperiodic superlattices.1 This work has been stimulated by the discovery of quasicrystals2 and the realization that 1-D analogs of quasicrystals could be created artificially in multilayer systems.3 By far the majority of the work in these systems has concentrated on quasiperiodic Fibonacci superlattices.4 The Fibonacci structure is a particular case of a class of quasiperiodic structures defined by the recursion relation5
$$ {{S}_{j}} = {{({{S}_{{j - 1}}})}^{n}}{{S}_{{j - 2}}} $$
By defining the basic building blocks S1 and S2 in terms of layers of different materials and thicknesses we have attached a basis to the quasiperiodic lattice. Table 1 illustrates how the recursion relation (1) is used to build up the first 5 generations in terms of S1 and S2.


Raman Spectrum Wavelength Dependence Fibonacci Sequence Plane Wave Approximation Quasiperiodic Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    See, for example, the review by R. Merlin, IEEE J. Quantum Electr. 24, 1791 (1988).CrossRefGoogle Scholar
  2. 2.
    D. Schechtman, I. Bloch, D. Gratias and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).ADSCrossRefGoogle Scholar
  3. 3.
    R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang and P. K. Bhattacharya, Phys. Rev. Lett. 55, 1768 (1985).ADSCrossRefGoogle Scholar
  4. 4.
    See the review by A. H. MacDonald, in “Interfaces, Quantum Wells, and Superlattices”, C. R. Leavens and R. Taylor, eds., Plenum, New York, 1987, p. 347.Google Scholar
  5. 5.
    G. Gumbs and M. K. Ali, Phys. Rev. Lett. 60, 1081 (1988).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    C. Colvard, T. A. Gant, M. V. Klein, R. Merlin, R. Fischer, H. Morkoç, and A. C. Gossard, Phys. Rev. B 31, 2080 (1985).ADSCrossRefGoogle Scholar
  7. 7.
    V. Elser, Phys. Rev. B 32, 4892 (1985).ADSCrossRefGoogle Scholar
  8. 8.
    R. K. Zia and W. J. Dallas, J. Phys. A 18, L341 (1985).ADSCrossRefGoogle Scholar
  9. 9.
    M. Holzer, Phys. Rev. B 38, 1709 (1988).MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    M. W. C. Dharma-wardana, A. H. MacDonald, D. J. Lockwood, J.-M. Baribeau and D. C. Houghton, Phys. Rev. Lett. 58, 1761 (1987).ADSCrossRefGoogle Scholar
  11. 11.
    These identities, given in Ref. 4 for the Fibonacci case, easily generalize to n≠1.Google Scholar
  12. 12.
    J.-M. Baribeau, T. E. Jackman, P. Maigné, D. C. Houghton, and M. W. Denhoff, J. Vac. Sci. Tech. A 5, 1898 (1987).ADSCrossRefGoogle Scholar
  13. 13.
    D. J. Lockwood, A. H. MacDonald, G. C. Aers, M. W. C. Dharmawardana, R. L. S. Devine, and W. T. Moore, Phys. Rev. B 36, 9286 (1987).ADSCrossRefGoogle Scholar
  14. 14.
    J. M. Baribeau, Appl. Phys. Lett. 52, 105 (1987).Google Scholar
  15. 15.
    D. J. Lockwood, J.-M. Baribeau and P. Y. Timbrell, J. Appl. Phys. 65, 3049 (1989).ADSCrossRefGoogle Scholar
  16. 16.
    J. He, J. Sapriel and H. Brugger, Phys. Rev. B 39, 5919 (1989).ADSCrossRefGoogle Scholar
  17. 17.
    J. Humlicek, M. Garriga, M. I. Alonso and M. Cardona, J. Appl. Phys. 65, 2827 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • T. A. Gant
    • 1
  • D. J. Lockwood
    • 1
  • J.-M. Baribeau
    • 1
  • A. H. MacDonald
    • 2
  1. 1.National Research CouncilOttawaCanada
  2. 2.Physics DepartmentIndiana UniversityBloomingtonUSA

Personalised recommendations