Calculated Electronic Structures and Schottky Barrier Heights of (111) NiSi2/Si A- and B-Type Interfaces

  • G. P. Das
  • P. Blöchl
  • N. E. Christensen
  • O. K. Andersen
Part of the NATO ASI Series book series (NSSB, volume 195)


In recent years it has been proved possible to predict the valence-band offsets of lattice-matched semiconductor heterojunctions1,2 to an accuracy of about 0.1 eV using density functional theory in the local approximation (LDA). We have investigated whether, for well-characterised metal-semiconductor interfaces, the Schottky-barrier heights can be calculated with similar accuracy. In this paper we report on our findings.


Schottky Barrier Height Atomic Sphere Approximation Induce Charge Density Dipole Approach Supercell Calculation 
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.
    C.G. Van de Walle and R.M. Martin, Phys. Rev. B35, 8154 (1987).CrossRefGoogle Scholar
  2. 2.
    N.E. Christensen, Phys. Rev. B37, 4528 (1988).ADSCrossRefGoogle Scholar
  3. 3.
    L.J. Sham and W. Kohn, Phys. Rev. 145, 561 (1966); J.P. Perdew, R.P. Parr, M. Levy, and J.L. Balduz, Phys. Rev. Lett. 49, 1691 (1982).Google Scholar
  4. 4.
    R.T. Tung, Phys. Rev. Lett. 52, 462 (1984); J. Vac. Sci. Technol. B2, 465 (1984).Google Scholar
  5. 5.
    C. Tejedor, F. Flores, and E. Louis, J. Phys. C 10, 2163 (1977).ADSGoogle Scholar
  6. 6.
    J. Tersoff, Phys. Rev. Lett. 52, 465 (1984).ADSCrossRefGoogle Scholar
  7. 7.
    M. Cardona and N.E. Christensen, Phys. Rev. B35, 6182 (1987).ADSCrossRefGoogle Scholar
  8. 8.
    G.P. Das, P. Blochl, N.E. Christensen and O.K. Andersen, to be published. 9D. Cherns, G.R. Anstis, J.L. Hutchinson, and J.C.H. Spence, Phil. Mag. A46, 849 (1982).CrossRefGoogle Scholar
  9. 10.
    E. Vlieg, A.E.M.J. Fischer, J.F. van der Veen, B.N. Dev, and G. Materlik, Surf. Sci. 17, 36 (1986); J. Zegenhagen, K.-G. Huang, W.M. Gibson, B.D. Hunt, and L.J. Schowalter, Phys. Rev., to be published. Note that these two works show opposite trend in the magnitude of the interface contraction for A- and B-type NiSi2/Si interfaces, which is presumably due to different thicknesses of the samples used. However, the average value of the contraction can be taken to be ≈ 0.1 Å for both A— and B-type structures within the experimental error.Google Scholar
  10. 11.
    O.K. Andersen, Z. Pawlowska, and O. Jepsen, Phys. Rev. 34, 5253 (1986).ADSCrossRefGoogle Scholar
  11. 12.
    P. Blöchl, Ph. D. Thesis (University of Stuttgart, 1988) unpublished; and P. Blöchl and O.K. Andersen, to be published.Google Scholar
  12. 13.
    U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972); D.M. Ceperley and B.L. Alder, Phys. Rev. Lett. 45, 566 (1980).Google Scholar
  13. 14.
    P. Blöchl, G.P. Das, O.K. Andersen, and N.E. Christensen, unpublished.Google Scholar
  14. 15.
    We have also performed some calculations with a basis of , s-, p- and d-LMTOs on all atomic and empty sites. This reduces the bulk values of E-g, and E° by about 0.2 eV. But the zeroth order band offset = - E°, as well as the interface dipole remain unchanged.Google Scholar
  15. 16.
    O. Jepsen and O.K. Andersen, Phys. Rev. B 29, 5965 (1984); O.K Andersen, P. Blochl, and O. Jepsen, Bull. Am. Phys. Soc. 33, 804 (1988).Google Scholar
  16. 17.
    D. Glotzel, B. Segall and O.K. Andersen, Solid State Comm. 36, 403 (1980); W.R.L. Lambrecht, N.E. Christensen, and P. Blochl, Phys. Rev. 36, 2493 (1987). We repeated these bulk calculations for obtaining Ejj, and E° relative to the ASA zero.Google Scholar
  17. 18.
    D.R. Hamann, Phys. Rev. Lett. 60, 313 (1988).ADSCrossRefGoogle Scholar
  18. 19.
    P.J. van Hoek, W. Ravenek, and E.J. Baerends, Phys. Rev. Lett. 60, 1743 (1988).ADSCrossRefGoogle Scholar
  19. 20.
    O.K. Andersen and N.E. Christensen, unpublished.Google Scholar
  20. 21.
    A. Baldereschi, S Baroni and R. Resta, Phys. Rev. Lett. 61, 734 (1988).ADSCrossRefGoogle Scholar
  21. 22.
    W. Lambrecht, B. Segall and O.K. Andersen, to be published; and W. Lambrecht, B. Segall and, Phys. Rev. Lett. 61, 1764 (1988).ADSCrossRefGoogle Scholar
  22. 23.
    D.M. Bylander and L. Kleinman, Phys. Rev. Lett. 59, 2091 (1987).ADSCrossRefGoogle Scholar
  23. 24.
    W.A. Harrison, Phys. Rev. B31, 2121 (1985); ibid. B37, 864 (1988)Google Scholar
  24. 25.
    The fact that our estimate of Ep—Ey for the B—interface is now negative, and apparently unphysical, does not mean that the supercell charge density has holes in the valence band, but simply that the energy of the highest valence-band state of the (8+6)-supercell lies below Ey for the semi-infinite system, and below Ep. In terms of the thickness L = 5.9 a0 m of the’m’-layer Si-slab of the supercell (in our case m = 6 ), an estimate of this energy-lowering due to confinement is (7r/L)2 Ry « 0.1 eV. The order of magnitude is thus reasonable.Google Scholar
  25. 26.
    This correction amounts essentially to shifting the energies, C, of the Si and E s-orbitals upwards by respectively 0.22 and 1.88 eV.Google Scholar
  26. 27.
    W. Lambrecht, B. Segall and O.K. Andersen, to be published; and W. Lambrecht, B. Segall and, Phys. Rev. Lett. 61, 1764 (1988).ADSCrossRefGoogle Scholar
  27. 28.
    M.S. Hybertsen and S.G. Louie,Phys.Rev. B34, 5390 (1986) S.B. Zhang, D.T. Tomanek, S.G. Louie, M.L. Cohen and M.S. Hybertsen, Sol. St. Comm. 66, 585 (1988).Google Scholar
  28. 29.
    G.-X. Qian, R.M. Martin, and D.J. Chadi, Phys. Rev. B37, 1303 (1988).ADSCrossRefGoogle Scholar
  29. 30.
    Note that the GW calculations of the valence band maximum in GaAs differ, depending on the approximation in which it is treated; eg a recent calculation [ R. Godby, M. Schluter and L.J. Sham, Phys. Rev. 37, 10159, (1988) ] yields AEY = E V G W - E V L D A = +0.13 eV, while the calculation of Zhang et al in Ref. 28 gives AEV»-0.15eV. For Si, on the other hand, the GW calculations of Godby and of Hybertsen and Louie (Ref. 28) give identical results viz. AEY = + 0. 0 7 eV.Google Scholar
  30. 31.
    O. Jepsen, J. Madsen, and O.K. Andersen, Phys. Rev. B26, 2790 (1982); Y.K. Vekilov, V.D. Verner, and M.B. Samsonova, Sov. Phys. Usp. 30, 172 (1987).Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • G. P. Das
    • 1
  • P. Blöchl
    • 1
  • N. E. Christensen
    • 1
  • O. K. Andersen
    • 1
  1. 1.Max-Planck-Institut für FestkörperforschungFederal Republic of Germany

Personalised recommendations