Advertisement

Density-Functional Approach to the Electronic Structure of Metal Surfaces and Metal-Adatom Systems

  • N. D. Lang
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 16)

Abstract

The density-functional formalism of Hohenberg, Kohn and Sham(1,2) provides a convenient framework for the study of the electronic structure of metal surfaces and of metal-adatom systems.

Keywords

Work Function Background Model Electron Number Density Simple Metal High Work Function 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964)CrossRefGoogle Scholar
  2. (2).
    W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965)CrossRefGoogle Scholar
  3. a)Atomic units are used.Google Scholar
  4. (3).
    Cf. J.C. Stoddart and N.H. March, Proc. Roy. Soc. A299, 279 (1967)Google Scholar
  5. (3a).
    L.J. Sham and W. Kohn, Phys. Rev. 145, 561 (1966)CrossRefGoogle Scholar
  6. (3b).
    L. Hedin and B.I. Lundgvist, J. Phys. C 4, 2064 (1971)CrossRefGoogle Scholar
  7. (4).
    Other partitionings into “surface” and “bulk” terms can be found in the literature. Confusion sometimes arises when surface components defined in different ways are compared (see discussion by N.D. Lang and W. Kohn, Phys. Rev. B8, 6010 (1973)).Google Scholar
  8. A partioning of the work function into bulk and surface terms was recognized by E. Wigner and J. Bardeen, Phys. Rev. 48, 84 (1935).CrossRefGoogle Scholar
  9. (5).
    F.K. Schulte, J. Phys. C8, L001 (1974)Google Scholar
  10. (6).
    For discussion and references, see N.D. Lang, “The Density-Functional Formalism and the Electronic Structure of Metal Surfaces”, Solid State Physics, ed. F. Seitz, D. Turnbull and H. Ehrenreich (Academic Press, New York, 1973) Vol. 28, p. 225Google Scholar
  11. (7).
    J.R. Smith, Ph.D. Thesis, Ohio State University, Columbus (1968)Google Scholar
  12. (8).
    J.R. Smith, Phys. Rev. 181, 522 (1969)CrossRefGoogle Scholar
  13. (9).
    J. Bardeen, Phys. Rev. 49, 653 (1936)CrossRefGoogle Scholar
  14. (10).
    A. J. Bennett and C.B. Duke, in Structure and Properties of Solid Surfaces, ed.G.A. Somorjai (Wiley, New York, 1969) Ch.25Google Scholar
  15. (11).
    N.D. Lang, Solid State Commun. 7, 1047 (1969)CrossRefGoogle Scholar
  16. (12).
    N.D. Larg and W. Kohn, Phys. Rev. B1, 4555 (1970)CrossRefGoogle Scholar
  17. (13).
    N.D. Lang and W. Kohn, Phys. Rev. B3, 1215 (1971)CrossRefGoogle Scholar
  18. (13a).
    Cf. also F.K. Schulte, Ph.D. Thesis, Ludwig-Maximilians-Universität Munchen (1973) (thin films)Google Scholar
  19. (14).
    J. Schmit and A.A. Lucas, Solid State Commun. 11, 415 (1972)CrossRefGoogle Scholar
  20. (15).
    V. Peuckert, Z. Phys. 241, 191 (1971)CrossRefGoogle Scholar
  21. (16).
    R.A. Craig, Phys. Rev. B 6, 1134 (1972)CrossRefGoogle Scholar
  22. (17).
    N.D. Lang and L.J. Sham, Solid State Commun. 17 (to be published); J. Harris and R.O. Jones, J. Phys. F4, 1170 (1974);CrossRefGoogle Scholar
  23. E. Wikborg and J.E. Inglesfield, Solid State Commun. 16, 335 (1975);CrossRefGoogle Scholar
  24. M. Jonson and G. Srinivasan, Physica Scripta 10, 262 (1974);CrossRefGoogle Scholar
  25. J. Vannimenus and H.F. Budd, Solid State Commun. 15, 1739 (1974);CrossRefGoogle Scholar
  26. A. Griffin, H. Kranz and J. Harris, J. Phys. F 4, 1744 (1974);CrossRefGoogle Scholar
  27. G. Paasch, Phys. Stat. Sol. (b) 65, 221 (1974);CrossRefGoogle Scholar
  28. J. Heinrichs, Phys. Rev. B 11, 3637 (1975);CrossRefGoogle Scholar
  29. P.J. Feibelman, Solid State Commun. 13, 319 (1973);CrossRefGoogle Scholar
  30. W. Kohn, Solid State Commun. 13, 323 (1973).CrossRefGoogle Scholar
  31. (18).
    C. Werner, F.K. Schulte and H. Bross, to be publishedGoogle Scholar
  32. (19).
    H.F. Budd and J. Vannimenus, Phys. Rev. Lett. 31, 1218 (1973) and erratum; and Ref.17 above. Cf. also G.D. Mahan and W.L. Schaich, Phys. Rev. B 10, 2647 (1974)Google Scholar
  33. (20).
    Some other sum rules for static and dynamic properties that we do not discuss here include A. Sugiyama, J. Phys. Soc. Japan 15, 965 (1960);CrossRefGoogle Scholar
  34. D.C. Langreth, Phys. Rev. B 5, 2842 (1972) and 11, 2155 (1975);Google Scholar
  35. P. Feibelman, Phys. Rev. B3, 220 (1971);CrossRefGoogle Scholar
  36. J.A. Appelbaum and E.I. Blount, Phys. Rev. B 8, 483 (1973);CrossRefGoogle Scholar
  37. J.E. Inglesfield and E. Wikborg, Solid State Commun. 15, 1727 (1974);CrossRefGoogle Scholar
  38. D. Wagner, to be published; J. Heinrichs and N. Kumar Phys. Rev. B (to be published). Cf. also V. Peuckert, J. Phys.C7, 2221 (1974) (high-density limit of the work function)Google Scholar
  39. (21).
    N.D. Lang and W. Kohn, Phys. Rev. B 7, 3541 (1973). See also V.E. Kenner, R.E. Allen, and W.M. Saslow, Phys. Rev. B 8, 576 (1973);Google Scholar
  40. A.K. Theophilou and A. Modinos, Phys. Rev. B 6, 801 (1972);CrossRefGoogle Scholar
  41. A.K. Theophilou, J.’Phys. F 2, 1124 (1972).CrossRefGoogle Scholar
  42. (22).
    Cf. N.D. Lang and A.R. Williams, Phys. Rev. Lett. 34, 531 (1975)CrossRefGoogle Scholar
  43. (23).
    H.F. Budd and J. Vannimenus, Phys. Rev. (to be published), have been able to obtain curves such as that of Fig.9 by using only ood(x) for d - ∞Google Scholar
  44. (24).
    Eg., A.W. Dweydari and C.H.B. Mee, Phys. Stat.Sol.(a) 27, 223 (1975); P.O. Gartland, S. Berge and B.J. Slagsvold, Phys. Rev. Lett. 28, 738 (1972)CrossRefGoogle Scholar
  45. (25).
    E.g., H.O.K. Kirchner and G.A. Chadwick, Phil.Mag.[8] 20, 405Google Scholar
  46. ); M. McLean and B. Gale, ibid., p. 1033. But note, for example, the results of U. Jeschkowski and E. Menzel, Surface Sci. 15, 333 (1968)Google Scholar
  47. (26).
    E.g.,J.K.Grepstad, P.O.Gartland,B.J. Slagsvold, to be published.Google Scholar
  48. (27).
    An excellent review of this work has been given G. Allan, in Surface Properties and Surface States of Materials, ed. L. Dobrzynski (Dekker, New York, to be published)Google Scholar
  49. (28).
    Cf., e.g., K.H. Johnson and R.P. Messmer, J. Vac. Sci. Technol. 11, 236 (1974)Google Scholar
  50. (29).
    E.g., F. Forstmann, Z. Phys. 235, 69 (1970);CrossRefGoogle Scholar
  51. D.S. Boudreaux, Surf. Sci. 28, 344 (1971);CrossRefGoogle Scholar
  52. V. Hoffstein, Solid State Commun. 10, 605 (1972);CrossRefGoogle Scholar
  53. J.B. Pendry and S.J. Gurman, Surf. Sci. 49, 87 (1975);CrossRefGoogle Scholar
  54. D. Spanjaard, D.W. Jepsen and P.M. Marcus, to be published.Google Scholar
  55. (30).
    J.A. Appelbaum and D.R. Hamann, Phys. Rev. B 6, 2166 (1972)CrossRefGoogle Scholar
  56. (31).
    G.P. Alldredge and L.Kleinman, Phys. Rev. B 10, 559 (1974)CrossRefGoogle Scholar
  57. (32).
    E. Caruthers, L. Kleinman and G.P. Alldredge, Phys. Rev. B 8, 4570 (1973); 9, 3325 (1974); 9, 3330 (1974)Google Scholar
  58. (33).
    Eg., I.P. Batra and 0. Robaux, J. Vac. Sci. Technol. 12, 242 (1975)CrossRefGoogle Scholar
  59. (34).
    Gunnarsson and P. Johansson, Int. J. Quant. Chem. (to be published)Google Scholar
  60. (34a).
    A.R. Williams and J. van W. Morgan, J. Phys. C 7, 37 (1974)CrossRefGoogle Scholar
  61. (35).
    But cf. J.A. Appelbaum and D.R. Hamann, Phys. Rev. Lett. 34, 806 (1975) (H/Si)CrossRefGoogle Scholar
  62. (36).
    N.D. Lang, Solid State Commun. 9, 1015 (1971);CrossRefGoogle Scholar
  63. N.D. Lang.Phys. Rev. B4, 4234 (1971). See also C. Warner, “Thermionic Conversion Specialists Conference, San Diego, 1971” (Institute of Electrical and Electronics Engineers, New York, 1972 ) (extended Thomas-Fermi analysis)Google Scholar
  64. (37).
    J.R. Smith, S.C. Ying and W. Kohn, Phys. Rev. Lett. 30, 610 (1973);CrossRefGoogle Scholar
  65. S.C. Ying, J.R. Smith and W. Kohn, Phys. Rev. B 11, 1483 (1975)CrossRefGoogle Scholar
  66. (38).
    N.D. Lang and A.R. Williams, Ref. 22Google Scholar
  67. (39).
    H.B. Huntington, L.A. Turk and W.W. White, III, Surf. Sci. 48, 187 (1975)CrossRefGoogle Scholar
  68. (40).
    L.M. Kahn and S.C. Ying, Solid State Commun. 16, 799 (1975)CrossRefGoogle Scholar
  69. (41).
    The formal relationship between the eigenstate density associated with Eq.(1.12a) and the quasiparticle energy spectrum is discussed above in connection with Eq.(1.16), and in references 3a and 3b.Google Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • N. D. Lang
    • 1
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations