Inelastic Scattering of Low Energy Electron Beams by Surface Vibrations: The Nature of Image Force

  • D. L. Mills
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 4)


Experimental studies have examined the inelastic scattering of low energy electron beams by surface vibrations of crystals with well characterized surfaces in ultra-high vacuum. We review the data with emphasis on the systematic features of the electron-surface vibration coupling revealed by the experiments. This coupling bears an intimate relation to the origin of the image potential. We also review recent theories of the image potential, with emphasis on the mechanisms that round off the l/z divergence obtained from elementary electrostatics.


Inelastic Scattering Image Potential Loss Peak Image Force Surface Vibration 
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.
    H. Ibach: Phys. Rev. Letters 24, 1416 (1970)CrossRefGoogle Scholar
  2. 2.
    H. Ibach: Phys. Rev. Letters 27, 253 (1971)CrossRefGoogle Scholar
  3. 3.
    We refer the reader to two review articles for a more complete review of the experiments performed to date, and related theory. See H. Froitzheim, Vol. 4 Topics in Current Physics, edited by H. Ibach, (Springer, New York, 1976). This paper reproduces many of the experimental spectra. The present author has prepared a review article that will appear shortly (D.L. Mills, Progress in Surface Science, to be published)Google Scholar
  4. 4.
    The frequency ωs is independent of Q11 only when retardation effects are ignored. Retardation effects are unimportant for cQ11 » ωs, where c is the velocity of light. More generally ωs(Q11 ) = cQ11 [ε(ω)/(l+ε(ω))]1/2, a result equivalent to (4) when cQ11 » ωs. The surface mode frequency ωs(Q11 ) lies between ωTO and the limiting frequency displayed in (4). The electron scattering experiments probe values of Q11 in the range 106 cm-1, and ωs/c ~ 103 cm-1, so for the present discussion neglect of retardation effects is well justifiedGoogle Scholar
  5. 5.
    A.A. Lucas, M. Sunjic: Prog. Surf. Sci. 2, 75 (1972)CrossRefGoogle Scholar
  6. 6.
    E. Evans, D.L. Mills: Phys. Rev. B5, 4126 (1972) and B7, 853 (1973)Google Scholar
  7. 7.
    H. Ibach (to be published)Google Scholar
  8. 8.
    J. Kirtley, D.J. Scalapino, P.K. Hansffia: Phys. Rev. B14, 3177 (1976)CrossRefGoogle Scholar
  9. 9.
    V. Roundy, D.L. Mills: Phys. Rev. B5, 1347 (1972)CrossRefGoogle Scholar
  10. 10.
    For example, see C.J. Powell: Phys. Rev. 175, 972 (1968)CrossRefGoogle Scholar
  11. 11.
    H. Froitzheim, H. Ibach, D.L. Mills: Phys. Rev. B11, 1980 (1975)Google Scholar
  12. 12.
    See R. Ludeke, L. Esaki: Phys. Rev. Letters 32, 653 (1974)CrossRefGoogle Scholar
  13. 13.
    A reasonably detailed discussion has been presented by D.L. Mills: Surface Science 48, 59 (1975)CrossRefGoogle Scholar
  14. 14.
    E. Evans, D.L. Mills: Phys. Rev. B8, 4004 (1973)CrossRefGoogle Scholar
  15. 15.
    T.D. Clark: Solid State Communications 16, 861 (1975)CrossRefGoogle Scholar
  16. 16.
    G.D. Mahan in Collective Properties of Physical Systems, edited by B. Lundqvist and S. Lundqvist (Nobel Foundation, Stockholm).Google Scholar
  17. 17.
    A crude description of these deviations follows upon calculating the second term on the right hand side of (8a) not by integrating over all Q11 as in the calculation that leads to (8b), but by cutting off the Q11 integration at the value Q11 = QC, where QC is the inverse of the Fermi-Thomas screening length.Google Scholar
  18. 18.
    D.M. Newns: J. Chem. Phys. 50, 4572 (1969), N.D. Lang, W. Kohn: Phys. Rev. B7, 3541 (1973)CrossRefGoogle Scholar
  19. 19.
    D.L. Mills: Phys. Rev. B15, 763 (1976)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • D. L. Mills
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaIrvineUSA

Personalised recommendations