Unified Perturbation Theory for STM and SFM

  • C. J. Chen
Part of the Springer Series in Surface Sciences book series (SSSUR, volume 29)

Abstract

In this chapter, we describe perturbation theory for STM and SFM. To understand the influence of tip electronic states and the tip—sample interactions in the imaging process, and to interpret the observed images, perturbation theory provides a simple and straightforward picture. First, besides STM, there are a number of experimental methods which contribute to the understanding of the sample surface as well as the tip. From an experimental point of view, the perturbation theory can provide insights for the understanding of the images from the properties of the bare tip and the bare sample, thus to achieve a conceptual understanding of the relations among different experimental measurements. Second, first-principles numerical calculations of the electronic structures of the free sample and the free tip have reached a high level of sophistication that a detailed comparison with those experimental measurements has become everday practice. Perturbation theory can bring the results of those calculations together and make predictions to the STM and SFM images. A consistency among the results from different approaches is a sign of true understanding. In words, a natural way of bringing various theoretical and experimental fields into a unified picture is through a proper perturbation theory. Finally, the perturbation theory provides a natural linkage between the tunneling phenomenon and attractive atomic forces through the concept of resonance, which is the foundation of Pauling’s theory of the chemical bond. As we shall see, this brings about a unified perturbation theory of STM and AFM.

Keywords

Migration Graphite Helium Hexagonal Tungsten 

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References

  1. 7.1
    G. Binnig, H. Rohrer: Helv. Phys. Acta 55, 726 (1982).Google Scholar
  2. 7.2
    Scanning Tunneling Microscopy I and II, ed., H.-J. Güntherodt and R. Wiesendanger, Vols. 20 and 28, (Springer, Berlin, Heidelberg 1992)Google Scholar
  3. 7.3
    J.A. Stroscio, R.M. Feenstra, A.P. Fein: Phys. Rev. Lett. 57, 2579 (1986); R.M. Feenstra, J.A. Stroscio: Physica Scripta, T19, 55 (1987); R.M. Feenstra: Phys. Rev. B 44, 13791 (1991)ADSCrossRefGoogle Scholar
  4. 7.4
    V.M. Hallmark, S. Chiang, J.F. Rabolt, J.D. Swalen, R.J. Wilson: Phys. Rev. Lett. 59, 2879 (1987); A. Samsavar, E.S. Hirschorn,T. Miller, F.M. Leibsle, J.A. Eades, T.C. Chiang: T.C. Phys. Rev. Lett. 65, 1607 (1990)ADSCrossRefGoogle Scholar
  5. 7.5
    R.J. Behm: Scanning tunneling microscopy: Metal surfaces, adsorption and surface reactions: In R.J. Behm, N. Garcia, H. Rohrer, Scanning Tunneling Microscopy and Related Methods, ed. by (Kluwer, Dordrecht 1990), pp 173–209Google Scholar
  6. 7.6
    J. Wintterlin, J. Wiechers, H. Brune, T. Gritsch, H. Höfer, R.J. Behm: Phys. Rev. Lett. 62, 59 (1989)ADSCrossRefGoogle Scholar
  7. 7.7
    P. Zeppenfeld, C.P. Lutz, D.M. Eigler: Int’l Ultramicroscopy 42–44, 128 (1992)CrossRefGoogle Scholar
  8. 7.8
    G. Binnig, H. Fuchs, Ch. Gerber, H. Rohrer, E. Stoll, E. Tosetti: Europhys. Lett. 1, 31 (1986)ADSCrossRefGoogle Scholar
  9. 7.9
    U. Dürig, J.K. Gimzewski, D.W. Pohl, D.W. Phys. Rev. Lett. 57, 2403 (1986); U. Dürig, O. Züger, D.W. Pohl, J. Microscopy, 152, Part 1, 259 (1988)ADSCrossRefGoogle Scholar
  10. 7.10
    J.M. Soler, A.M. Baro, N. Garcia, H. Rohrer: Phys. Rev. Lett. 57, 444 (1986); H.J. Mamin, E. Ganz, D.W. Abraham, R.E. Thompson, J. Clarke; Phys. Rev. B 34, 9015 (1986)ADSCrossRefGoogle Scholar
  11. 7.11
    C.J. Chen, and R.J. Hamers, J. Vac. Sci. Technol. B 9, 230 (1991)Google Scholar
  12. 7.12
    E.C. Teague: Thesis, 1978. Reprinted on Journal of Research of the National Bureau of Standards, 91, 171 (1986)Google Scholar
  13. 7.13
    J. Bardeen: Phys. Rev. Lett. 6, 57 (1961)ADSCrossRefGoogle Scholar
  14. 7.14
    J. Bardeen, L.N. Cooper, J.R. Schrieffer: Phys. Rev. 108, 1175 (1957)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 7.15
    I. Giaever: Phys. Rev. Lett. 5, 147, 464 (1960)ADSCrossRefGoogle Scholar
  16. 7.16
    For example, L.D. Landau, L.M. Lifshitz: Quantum Mechanics (Pergamon, London 1977)Google Scholar
  17. 7.17
    C.B. Duke: Tunneling in Solids (Academic, New York 1969)Google Scholar
  18. 7.18
    J.R. Oppenheimer: Phys. Rev. 13, 66 (1928)ADSCrossRefGoogle Scholar
  19. 7.19
    C. Calori, R. Combescot, P. Nozieres, D. Saint-James: J. Phys. C 5, 21 (1972) and references thereinADSCrossRefGoogle Scholar
  20. 7.20
    T.E. Feuchtwang: Phys. Rev. B 20, 430 (1979), and references thereinADSCrossRefGoogle Scholar
  21. 7.21
    J. Tersoff, D.R. Hamann: Phys. Rev. Lett. 50, 1998 (1983); Phys. Rev. B 31, 805 (1985)ADSCrossRefGoogle Scholar
  22. 7.22
    A. Baratoff: Europhysics Conf. Abstracts 7b, 364 (1983); Physica Amsterdam) 127 B, 143 (1984)Google Scholar
  23. 7.23
    C.J. Chen: J. Vac. Sci. Technol. A 6, 319 (1988)ADSCrossRefGoogle Scholar
  24. 7.24
    C.J. Chen: Phys. Rev. Lett. 65, 448 (1990)ADSCrossRefGoogle Scholar
  25. 7.25
    C.J. Chen: Phys. Rev. B 42, 8841 (1990)ADSCrossRefGoogle Scholar
  26. 7.26
    C.J. Chen: J. Vac. Sci. Technol. A 9, 44 (1991)ADSCrossRefGoogle Scholar
  27. 7.27
    C.J. Chen: Mod. Phys. Lett. B 5, 107 (1991)ADSCrossRefGoogle Scholar
  28. 7.28
    C.J. Chen: J. Phys, Cond. Matter 3, 1227 (1991)ADSCrossRefGoogle Scholar
  29. 7.29
    C.J. Chen: Introduction to Scanning Tunneling Microscopy (Oxford Univ. Press, New York 1993)Google Scholar
  30. 7.30
    W. Heisenberg: Z. Phys. 38, 411 (1928)ADSGoogle Scholar
  31. 7.31
    L. Pauling: The Nature of the Chemical Bond (Cornell Univ. Press, Cornell 1977)Google Scholar
  32. 7.32
    T. Holstein: Westinghouse Research Report 60-94698-3-R9 (1955)Google Scholar
  33. 7.33
    D.R. Bates, K. Ledsman, A.L. Stewart: Phil. Trans. Roy. Soc. London, 246, 215 (1953)ADSMATHCrossRefGoogle Scholar
  34. 7.34
    J.C. Slater: Quantum Theory of Molecules and Solids, Vol. 1 (McGraw-Hill, New York 1963)MATHGoogle Scholar
  35. 7.35
    C. Herring: Rev. Mod. Phys. 34, 631 (1962)MathSciNetADSCrossRefGoogle Scholar
  36. 7.36
    J. Harris, A. Liebsch: Phys. Rev. Lett. 49, 341 (1982); A. Liebsch, J. Harris, M. Weinert: Surf. Sci. 145, 207 (1984)ADSCrossRefGoogle Scholar
  37. 7.37
    F.O. Goodman: J. Chem. Phys. 65, 1561 (1976); F.O. Goodman, H.Y. Wachman: Dynamics of Gas-Surface Scattering (Academic, New York 1976)ADSCrossRefGoogle Scholar
  38. 7.38
    D. Drakova, G. Doyen, F.V. Trentini: Phys. Rev. B 32, 6399 (1985)ADSCrossRefGoogle Scholar
  39. 7.39
    J.B. Pethica, W.C. Oliver: Physica Scripta T 19, 61 (1987); J.B. Pethica, A.P. Sutton, J. Vac. Sci. Technol. A 6, 2490 (1988)ADSCrossRefGoogle Scholar
  40. 7.40
    C.J. Chen: Ultramicroscopy, 42–44, 147 (1992)CrossRefGoogle Scholar
  41. 7.41
    H. Brunner, P.J. van der Houwen: The Numerical Solution of Volterra Equations, (North-Holland, Amsterdam 1986)MATHGoogle Scholar
  42. 7.42
    J.P. Pelz: Phys. Rev. B B 43, 6746 (1991)ADSCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1993

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  • C. J. Chen

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