Advertisement

Kinetic Monte Carlo simulation of small vacancy clusters electromigration on clean and defective Cu(100) surface

  • Sergey V. KolesnikovEmail author
  • Alexander M. Saletsky
Regular Article
  • 29 Downloads

Abstract

Electromigration of small vacancy clusters on clean and defective Cu(100) surface is investigated on the atomic scale by performing self-learning kinetic Monte Carlo simulations. Drift velocity dependencies of vacancy clusters on their size, the substrate temperature, the direction and the absolute value of current density are obtained. The drift velocity dependence on the size of vacancy cluster has an oscillatory behavior. The nature of these oscillations is connected with the difference in diffusion mechanisms of “fast” and “slow” vacancy clusters. The presence of point defects leads to the monotonic decrease of the drift velocity of vacancy clusters. The drift velocity drops down if the diameter of the vacancy cluster is larger than the average distance between the point defects.

Graphical abstract

Keywords

Solid State and Materials 

References

  1. 1.
    J.R. Black, Proc. IEEE 57, 1587 (1969) CrossRefGoogle Scholar
  2. 2.
    H.B. Huntington, Diffusion in Solids (Academic, New York, 1975) Google Scholar
  3. 3.
    P.S. Ho, T. Kwok, Rep. Prog. Phys. 52, 301 (1989) ADSCrossRefGoogle Scholar
  4. 4.
    C. Tao, W.G. Cullen, E.D. Williams, Science 328, 736 (2010) ADSCrossRefGoogle Scholar
  5. 5.
    R. Hoffmann-Vogel, Appl. Phys. Rev. 4, 031302 (2017) ADSCrossRefGoogle Scholar
  6. 6.
    A. Latz, S. Sindermann, L. Brendel, G. Dumpich, F.-J. Meyer zu Heringdorf, D.E. Wolf, Phys. Rev. B 85, 035449 (2012) ADSCrossRefGoogle Scholar
  7. 7.
    K.H. Bevan, H.G. Guo, E.D. Williams, Z. Zhang, Phys. Rev. B 81, 235416 (2010) ADSCrossRefGoogle Scholar
  8. 8.
    K.H. Bevan, W. Zhu, G.M. Stocks, H. Guo, Z. Zhang, Phys. Rev. B 85, 235421 (2012) ADSCrossRefGoogle Scholar
  9. 9.
    A. Kumar, D. Dasgupta, D. Maroudas, Phys. Rev. Appl. 8, 014035 (2017) ADSCrossRefGoogle Scholar
  10. 10.
    D. Dasgupta, A. Kumar, D. Maroudas, Surf. Sci. 669, 25 (2018) ADSCrossRefGoogle Scholar
  11. 11.
    H. Mehl, O. Biham, O. Millo, Phys. Rev. B 61, 4975 (1999) ADSCrossRefGoogle Scholar
  12. 12.
    M. Rusanen, P. Kuhn, J. Krug, Phys. Rev. B 74, 245423 (2006) ADSCrossRefGoogle Scholar
  13. 13.
    A. Latz, S.P. Sindermann, L. Brendel, G. Dumpich, F.-J. Meyer zu Heringdorf, D.E. Wolf, J. Phys.: Condens. Matter 26, 055005 (2014) Google Scholar
  14. 14.
    M. Jongmanns, A. Latz, D.E. Wolf, Europhys. Lett. 110, 16001 (2015) ADSCrossRefGoogle Scholar
  15. 15.
    O. Kurnosikov, J.T. Kohlhepp, W.J.M. de Jonge, Europhys. Lett. 64, 77 (2003) ADSCrossRefGoogle Scholar
  16. 16.
    R. van Gastel, R. van Moere, H.J.W. Zandvliet, B. Poelsema, Surf. Sci. 605, 1956 (2011) ADSCrossRefGoogle Scholar
  17. 17.
    S.V. Kolesnikov, A.L. Klavsyuk, A.M. Saletsky, Eur. Phys. J. B 86, 399 (2013) ADSCrossRefGoogle Scholar
  18. 18.
    S.V. Kolesnikov, JETP Lett. 99, 286 (2014) ADSCrossRefGoogle Scholar
  19. 19.
    S.V. Kolesnikov, A.L. Klavsyuk, A.M. Saletsky, JETP 121, 616 (2015) ADSCrossRefGoogle Scholar
  20. 20.
    H. Jónsson, G. Mills, K.W. Jacobsen, in Nudged elastic band method for finding minimum energy paths of transitions (World Scientific, 1998), Chap. 16 Google Scholar
  21. 21.
    F. Cleri, V. Rosato, Phys. Rev. B 48, 22 (1993) ADSCrossRefGoogle Scholar
  22. 22.
    N.A. Levanov, V.S. Stepanyuk, W. Hergert, D.I. Bazhanov, P.H. Dederichs, A. Katsnelson, C. Massobrio, Phys. Rev. B 61, 2230 (2000) ADSCrossRefGoogle Scholar
  23. 23.
    N.N. Negulyaev, V.S. Stepanyuk, P. Bruno, L. Diekhöner, P. Wahl, K. Kern, Phys. Rev. B 77, 125437 (2008) ADSCrossRefGoogle Scholar
  24. 24.
    T. Siahaan, O. Kurnosikov, H.J.M. Swagten, B. Koopmans, S.V. Kolesnikov, A.M. Saletsky, A.L. Klavsyuk, Phys. Rev. B 94, 195435 (2016) ADSCrossRefGoogle Scholar
  25. 25.
    S.V. Kolesnikov, A.L. Klavsyuk, A.M. Saletsky, Phys. Rev. B 80, 245412 (2009) ADSCrossRefGoogle Scholar
  26. 26.
    V.S. Stepanyuk, A.L. Klavsyuk, L. Niebergall, A.M. Saletsky, W. Hergert, P. Bruno, Phase Trans. 78, 61 (2005) CrossRefGoogle Scholar
  27. 27.
    Š. Pick, V.S. Stepanyuk, A.L. Klavsyuk, L. Niebergall, W. Hergert, J. Kirschner, P. Bruno, Phys. Rev. B 70, 224419 (2004) ADSCrossRefGoogle Scholar
  28. 28.
    A.L. Klavsyuk, A.M. Saletsky, Physics–Uspekhi 58, 933 (2015) ADSGoogle Scholar
  29. 29.
    Š. Pick, P.A. Ignatiev, A.L. Klavsyuk, W. Hergert, V.S. Stepanyuk, P. Bruno, J. Phys.: Condens. Matter 19, 446001 (2007) ADSGoogle Scholar
  30. 30.
    R.S. Sorbello, Solid State Phys. 51, 159 (1997) CrossRefGoogle Scholar
  31. 31.
    J. Hoekstra, A.P. Sutton, T.N. Todorov, A.P. Horsfield, Phys. Rev. B 62, 8568 (2000) ADSCrossRefGoogle Scholar
  32. 32.
    S.V. Kolesnikov, A.L. Klavsyuk, A.M. Saletsky, Surf. Sci. 612, 48 (2013) ADSCrossRefGoogle Scholar
  33. 33.
    S.V. Kolesnikov, A.L. Klavsyuk, A.M. Saletsky, Phys. Rev. B 79, 115433 (2009) ADSCrossRefGoogle Scholar
  34. 34.
    V. Sadovnichy, A. Tikhonravov, V. Voevodin, V. Opanasenko, in Contemporary High Performance Computing: From Petascale toward Exascale (Chapman Hall/CRC Computational Science, Boca Raton, United States, 2013), p. 283307 Google Scholar

Copyright information

© EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Physics, Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations