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Surface-phonons at a free-111-surface of Si

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Abstract

In a crystal with a free surface the translational symmetry in one direction is raised. In this case it is possible to reduce the equation of motion of the crystal to a form which is analogous to the equation of motion of a semi-infinite generalized linear chain. In this picture the surface-phonons correspond to boundary vibrations of the chain. Methods to calculate the frequencies and the “damping” constant of the surface-phonons are shown. If the surface exhibits a symmetric structure it is possible to classify the frequencies according to the irreducible representations of a subgroup of the surface-space-group.

Model-calculations are performed for a free Si-111-surface using a six-parameter potential (fitted to dispersion curves). The change of the force constants near the surface is considered and fitted to the experiment of Ibach (ν=13.3×1012 sec−1). With the obtained weakening of the potential near the surface, dispersion-curves for surface-phonons are calculated.

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References

  1. W. Ludwig:Recent Developments in Lattice Theory; Springer Tracts Mod. Phys.43, 206–230 (1967)

  2. R. Fuchs, K.L. Kliewer: Phys. Rev.140 A, 2076 (1965);144, 495 (1966);150, 573 (1966)

    Article  ADS  Google Scholar 

  3. R.F. Wallis, D.L. Mills, A.A. Maradudin:Localized Exitations in Solids, ed. by R.F. Wallis (Plenum, New York 1968) p. 403

    Google Scholar 

  4. R. Engelman, R. Ruppin:Localized Exitations in Solids, ed. by R.F. Wallis (Plenum, New York 1968) p. 411

    Google Scholar 

  5. A.A. Lucas: J. Chem. Phys.48, 3156 (1968)

    Article  Google Scholar 

  6. R.E. Allen, G.P. Aldredge, F.W. de Wette: Phys. Rev. Letters23, 1285 (1969); Phys. Rev. B4, 1648 (1971)

    Article  ADS  Google Scholar 

  7. T.S. Chen, R.E. Allen, G.P. Aldredge, F.W. de Wette: Phys. Rev. Letters26, 1543 (1971)

    Article  ADS  Google Scholar 

  8. K. Thoma, R. Zimmermann: Z. Physik252, 168 (1972)

    Article  Google Scholar 

  9. H. Ibach: Phys. Rev. Letters27, 253 (1971)

    Article  ADS  Google Scholar 

  10. R. Zimmermann: Dissertation (D 26), Gießen (1973)

  11. A.A. Lucas, E. Kartheuser, R.G. Badro: Phys. Rev. B2, 2488 (1970)

    Article  ADS  Google Scholar 

  12. A.A. Lucas, M. Sunjic: Phys. Rev. Letters26, 229 (1971)

    Article  ADS  Google Scholar 

  13. V. Roundy, D.L. Mills: Phys. Rev. B5, 1347 (1972)

    Article  ADS  Google Scholar 

  14. E. Evans, D.L. Mills: Phys. Rev. B5, 4126 (1972)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Institut für Theoretische Physik II, Universität, D-4400, Münster, Fed. Rep. Germany

    R. Zimmermann

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  1. R. Zimmermann
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Extract from dissertation (D 26), Gießen 1973.

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Zimmermann, R. Surface-phonons at a free-111-surface of Si. Appl. Phys. 3, 235–239 (1974). https://doi.org/10.1007/BF00884503

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  • DOI: https://doi.org/10.1007/BF00884503

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