Excitation of Dielectric Spheres by Electron Beams

  • P. M. Echenique
Part of the NATO ASI Series book series (NSSB, volume 188)


Recent new developments and applications of the scanning transmission microscope(STEM) have stimulated renewed interest in the interaction of high-energy electron beams with small particles and surfaces[1–7]. Usually the classical theory of energy loss has been employed to analyze the experimental energy-loss spectra for planar, spherical or cylindrical geometries [8–14]. A new general approach, based on the self-energy formalism of the many body problem has been presented recently[15]. In this approach, the mean potential energy Σo of the incoming electron, in a state defined by a wave function ψo(r) and energy Eo is written as the average of an effective local potential Veff(r), representing the complex interaction of the incoming electron with the many body target
$${\Sigma_o}=\int{\psi_o^*} (\bar r){V_{eff}}(r){\psi_o}(\bar r)dr$$
We use atomic units (e2 = h = m) throughout this paper. The real part of Σo gives us the lowering of the energy of the particle due to virtual excitations of the medium, and the imaginary part is directly related to the probability of energy loss due to creation of real excitations. The effective potential is written as a spatial integral of the non local self-energy[16], Σ (r, r’, Eo), which in turn can be expressed in terms of the Green’s function G(r, r’, ω+E0) and the causal screened interaction W(r, r’, ω)[16].


Impact Parameter Dipole Contribution Incoming Electron Energy Loss Rate Dielectric Sphere 
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  1. 1.
    P. E. Batson, Solid State Commun. 34:447 (1980).ADSCrossRefGoogle Scholar
  2. 2.
    P. E. Batson, Ultramicroscopy 9:277 (1982).CrossRefGoogle Scholar
  3. 3.
    P. E. Batson, Phys.Rev.Lett. 49:936 (1982).ADSCrossRefGoogle Scholar
  4. 4.
    J. M. Cowley, Surf.Sci. 114:587 (1982).ADSCrossRefGoogle Scholar
  5. 5.
    J. M. Cowley, Phys.Rev. B25:1407 (1982).ADSGoogle Scholar
  6. 6.
    C. Colliex, Ultramicroscopy 18:131 (1985).CrossRefGoogle Scholar
  7. 7.
    A. Howie and R. H. Milne, J.Microscopy 136:279 (1984).CrossRefGoogle Scholar
  8. 8.
    A. Howie, Ultramicroscopy 11:141 (1983).CrossRefGoogle Scholar
  9. 9.
    A. Howie and R. H. Milne, Ultramicroscopy 18:427 (1985).CrossRefGoogle Scholar
  10. 10.
    T. L. Ferrell and P. M. Echenique, Phys.Rev.Lett. 55:1526 (1985).ADSCrossRefGoogle Scholar
  11. 11.
    P. M. Echenique, A. Howie and D. J. Wheatley, Phil.Mag. B56, 335 (1987).Google Scholar
  12. 12.
    T. L. Ferrell, R. L. Warmack, V. E. Anderson and P. M. Echenique, Phys.Rev. B35:7365 (1987).ADSGoogle Scholar
  13. 13.
    Z. L. Wang and J. M. Cowley, Ultramicroscopy 21:77 (1987).CrossRefGoogle Scholar
  14. 14.
    N. Zabala, A. Rivacoba and P. M. Echenique, to be published.Google Scholar
  15. 15.
    P. M. Echenique, J. Bausells and A. Rivacoba, Phys.Rev. B35:1521 (1987).ADSGoogle Scholar
  16. 16.
    L. Medin and S. Lundqvist, Solid State Physics 23:1 (1969).Google Scholar
  17. 17.
    J. D. Jackson, Classical Electrodynamics, 2nd Ed. Wiley, New York (1975).MATHGoogle Scholar
  18. 18.
    F. Fujimoto and Komaki, J.Phys.Soc.Japan 25:1679 (1968).ADSCrossRefGoogle Scholar
  19. 19.
    N. Barberán and J. Bausells, Phys.Rev. B31:6354 (1985).ADSGoogle Scholar
  20. 20.
    J. Bausells, A. Rivacoba and P.M. Echenique, to be published.Google Scholar
  21. 21.
    P. E. Batson and M. J. Treacy, in; “Proceedings of the Electron Microscopy Society of America,” San Francisco, California (Claitor’s, Baton Rouge) (1980).Google Scholar
  22. 22.
    H. J. Hagemann, W. Gudat and C. Kunz, Deutsches Elektronen Synchrotron Report No. DESY-SR-74/7 (unpublished).Google Scholar
  23. 23.
    M. Schmeits, J. Phys C 14:1203 (1981).ADSCrossRefGoogle Scholar
  24. 24.
    H. Kohl, Ultramicroscopy 11:53 (1983).CrossRefGoogle Scholar
  25. 25.
    J. Bausells, A. Rivacoba and P. M. Echenique, Surf.Sci., 189/190, 1015 (1987).ADSCrossRefGoogle Scholar
  26. 26.
    S. Munnix and M. Schmeits, Phys.Rev. B32:4192 (1985).ADSGoogle Scholar
  27. 27.
    R. H. Ritchie and A. Howie, to be published.Google Scholar
  28. 28.
    R. H. Ritchie and A. L. Marusak, Surf.Science 4:234 (1966).ADSCrossRefGoogle Scholar
  29. 29.
    P. M. Echenique, Phil.Mag. B52:L9 (1985).Google Scholar
  30. 30.
    R. García-Molina, A. Gras-Martí, A. Howie and R. H. Ritchie, J.Phys. C18:5335 (1985).ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • P. M. Echenique
    • 1
  1. 1.Departamento de Físcia, Facultad de QuimicasEuskal Herriko UnibertsitateaEuskadiSpain

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