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Electromigration and Electronic Structure

  • A. Lodder
  • J. P. Dekker

Abstract

Regarding the two different contributions to the driving force, the direct force and the wind force, the rôle of the electronic structure has been quite different for the two. For the wind force increasingly sophisticated descriptions have been used, namely pseudopotential models, finite cluster models and, at the end, an ab initio Korringa-Kohn-Rostoker (KKR) Green’s function description. We will illustrate this by showing for which systems by now the wind force has been calculated, which include almost all FCC and BCC metals, while both self-electromigration and impurity migration have been treated. Some new results will be presented as well, which simulate electromigration along a grain boundary and over a surface.

The direct force, on the other hand, has mainly been discussed in terms of the simple free electron, or jellium model. However, it will be shown that we have arrived at a point, at which more sophisticated descriptions of the electronic structure involved are becoming important. A recent analysis of new experimental results leads to the conclusion that a migrating hydrogen atom effectively can have a direct valence smaller than unity, depending on the metal studied. By this it becomes challenging to perform calculations of the electronic structure of an interstitial, not only at its equilibrium position, but also at positions lying along the jump path.

Keywords

Direct Force Wind Force Migrate Atom Jellium Model Multiple Scattering Effect 
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.

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References

  1. [1]
    I. A. Blech and C. Herring, “Stress generation by electromigration ”.Appl. Phys. Lett. 29 (1976) 131. [2] P. S. Ho and T. Kwok, “Electromigration in metals”. Rep. Progr. Phys. 52 (1989) 301.ADSCrossRefGoogle Scholar
  2. [2]
    P. S. Ho and T. Kwok, “Electromigration in metals”. Rep. Progr. Phys. 52 (1989) 301.ADSCrossRefGoogle Scholar
  3. [3]
    J. van Ek and A. Lodder, “Electromigration in transition metals: II. Light interstitials in Cu, Ag, Ni, Pd, Al, V, Nb and Ta”. J. Phys.: Cond. Mat. 3 (1991) 7331.ADSCrossRefGoogle Scholar
  4. [4]
    J. P. Dekker, A. Lodder, and J. van Ek, “Theory for the electromi- gration wind force in dilute alloys“. Phys. Rev. B56 (1997) 12167.ADSGoogle Scholar
  5. [5]
    J. P. Dekker and A. Lodder, “Electromigration in dilute body- centred cubic alloys”. J. Phys.: Cond. Mat. 10 (1998) 6687.ADSCrossRefGoogle Scholar
  6. [6]
    C. Bosvieux and J. Friedel, “Sur 1’electrolyse des alliages met- alliques”. J. Phys. Chem. Solids 23 (1962) 123.ADSCrossRefGoogle Scholar
  7. [7]
    R. S. Sorbello, “Theory of Electromigration”, in Solid State Physics, Vol. 51, Eds. H. Ehrenreich and F. Spaepen (Academic Press, San Diego, 1998), page 159.Google Scholar
  8. [8]
    For a review see J. van Ek and A. Lodder, “Electromigration of Hydrogen in Metals: Theory and Experiment”. Defect and Diff. Forum 115–116 (1994) 1.Google Scholar
  9. [9]
    A. H. Verbruggen, and R. Griessen, “Experimental evidence for nonintegral direct-force valence in electromigration”. Phys. Rev. B 32 (1985) 1426.ADSGoogle Scholar
  10. [10]
    A. Lodder, “Electromigration of hydrogen in V, Nb and Ta: a new description of the measured sample-resistivity-dependent effective valence”. J. Phys.: Cond. Matter 3 (1991) 399.ADSCrossRefGoogle Scholar
  11. [11]
    R. S. Sorbello, A. Lodder, and S. J. Hoving, “Finite-cluster description of electromigration”. Phys. Rev. B 25(1982) 6178.ADSGoogle Scholar
  12. [12]
    R. S. Sorbello, “Basic Concepts in Electromigration”. Mat. Res. Soc. Symp. Proc. 225 (1991) 3.CrossRefGoogle Scholar
  13. [13]
    R. S. Sorbello, “A pseudopotential based theory of the driving forces for electromigration in metals”. J. Phys. Chem. Solids 34 (1973) 937.ADSCrossRefGoogle Scholar
  14. [14]
    R. S. Sorbello, “Atomic configuration effects in electromigration”, J. Phys. Chem. Solids 42 (1981) 309.ADSCrossRefGoogle Scholar
  15. [15]
    A. Lodder, and M. G. E. Brand, ”Electromigration in transition-metal hydridres: a finite-cluster-model study” J. Phys. F: Metal Phys. 14 (1984) 2955.ADSCrossRefGoogle Scholar
  16. [16]
    Hellmann, H., Einführung in die Quantenchemie, Deuticke, Leipzig and Vienna, 1937.Google Scholar
  17. [17]
    Feynman, R. P., “Forces in Molecules”. Phys. Rev. 56 (1939) 340.ADSzbMATHCrossRefGoogle Scholar
  18. [18]
    Sorbello, R. S., and Dasgupta, B. B., “Force on an atom in an electrostatic field: Feynman-Hellmann theorem and oscillator strengths”. Phys. Rev. B 21(1980) 2196.ADSGoogle Scholar
  19. [19]
    A. Lodder and J. P. Dekker, “The Electromigration Force in Metallic Bulk”, in Stress Induced Phenomena in Metallization, Fourth Int. Workshop (Tokyo, Japan, 1997), Eds. H. Okabayashi, S. Shin-gubara, and P. S. Ho, (Am. Inst. Phys, Woodbury, N.Y., 1998), 315.CrossRefGoogle Scholar
  20. [20]
    Kumar, P., and Sorbello, R. S., “Linear Response Theory of the Driving Forces for Electromigration”. Thin Solid Films 25(1975) 25.ADSCrossRefGoogle Scholar
  21. [21]
    Erckmann and H. Wipf, “Electrotransport of Interstitial H and D in V, Nb, and Ta as Experimental Evidence for the Direct Field Force”. Phys. Rev. Lett. 37 (1976) 341.ADSCrossRefGoogle Scholar
  22. [22]
    J. P. Dekker and A. Lodder, “Calculated electromigration wind force in face-centered-cubic and body-centered-cubic metals”. J. Appl. Phys. 84 (1998) 1958.ADSCrossRefGoogle Scholar
  23. [23]
    J. P. Dekker, P. Gumbsch, E. Arzt, and A. Lodder, “Calculation of the elctromigration wind force in Al alloys”. Phys. Rev. B59 (1999) 7451.ADSGoogle Scholar
  24. [24]
    D. N. Bly and P. J. Rous “Theoretical study of the electromigration wind force for adatom migration at metal surfaces”. Phys. Rev. B53 (1996) 13909.ADSGoogle Scholar
  25. [25]
    R. Pietrzak, R. Szatanik, and M. Szuszkiewicz, “Investigation of diffusion and electromigration of hydrogen in palladium and PdAg alloy”. J, Alloys Comp. 282 (1999) 130.CrossRefGoogle Scholar
  26. [26]
    A. Lodder and K. Hashizume, “The direct force on electromigrating hydrogen isotopes”. J. Alloys Comp. 288 (1999).Google Scholar
  27. [27]
    K. Hashizume, K. Fujii, and M. Sugisaki, “Effective valence of tritium in the alpha phase of niobium”. Fusion Techn. 28 (1995) 1179.Google Scholar
  28. [28]
    S. Ellialtioglu, H. Akai, R. Zeller, and P. H. Dederichs, ”Ab-initio calculations of interstitial impurities in Cu” Ann. Int. Symp. Electr. Str. Met. All. 15 (1985) 99.Google Scholar
  29. [29]
    J. P. Dekker, A. Lodder, R. Zeller and A. F. Tatarchenko, ”Accurate evaluation of the interstitial KKR Green function” Phys. Rev. B 54 (1996) 4531.ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • A. Lodder
    • 1
  • J. P. Dekker
    • 2
  1. 1.Faculty of Sciences, Division Physics and AstronomyFree UniversityAmsterdamThe Netherlands
  2. 2.Max-Planck-Institut für MetallforschungStuttgartGermany

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