Advertisement

Multiscale modeling of submonolayer growth for Fe/Mo (110)

  • Martin Mašín
  • Miroslav Kotrla
  • Bo Yang
  • Mark Asta
  • Mika O. Jahma
  • Tapio Ala-Nissila
Regular Article

Abstract

We use a multiscale approach to study a lattice-gas model of submonolayer growth of Fe/Mo (110) by Molecular Beam Epitaxy. To begin with, we construct a two-dimensional lattice-gas model of the Fe/Mo (110) system based on our first-principles calculations of the monomer diffusion barrier and adatom-adatom interactions. The model is investigated by equilibrium Monte Carlo (MC) simulations to compute the diffusion coefficients of Fe islands of different sizes. These diffusion coefficients are used as input to the coarse-grained kinetic rate equation (KRE) approach. We also evaluate effects of the range of Fe-Fe interaction, restriction of interaction to third nearest neighbors allowed to develop feasible atomistic kinetic Monte Carlo (KMC) model. We calculate time evolution of the island size distributions by both KMC and KRE methods and find good agreement between the two methods.

Keywords

Solid State and Materials 

References

  1. 1.
    J.A. Venables, G.D.T. Spiller, M. Hanbucken, Rep. Prog. Phys. 47, 399 (1984)ADSCrossRefGoogle Scholar
  2. 2.
    K. Reichelt, Vacuum 38, 1083 (1988)CrossRefGoogle Scholar
  3. 3.
    T. Michely, J. Krug, Islands, mounds, and atoms: patterns and processes in crystal growth far from equilibrium (Springer Verlag, 2004), Vol. 42Google Scholar
  4. 4.
    M. Kotrla, Comput. Phys. Commun. 97, 82 (1996)ADSCrossRefGoogle Scholar
  5. 5.
    H. Jonsson, Proc. Natl. Acad. Sci. 108, 944 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    G. Nandipati, Y. Shim, J.G. Amar, Phys. Rev. B 81, 235415 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    C.R. Stoldt et al., J. Chem. Phys. 111, 5157 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    I. Koponen, M. Rusanen, J. Heinonen, Phys. Rev. E 58, 4037 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    I.T. Koponen et al., Phys. Rev. Lett. 92, 086103 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    J.W. Evans, P. Thiel, M. Bartelt, Surf. Sci. Rep. 61, 1 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    B.C. Hubartt, Y.A. Kryukov, J.G. Amar, Phys. Rev. E 84, 021604 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    U. Köhler et al., Philos. Mag. Part B 80, 283 (2000)ADSGoogle Scholar
  13. 13.
    U. Köhler et al., Surf. Sci. 454, 676 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    O. Fruchart et al., J. Phys.: Condens. Matter 19, 053001 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    K. Reshöft, C. Jensen, U. Köhler, Surf. Sci. 421, 320 (1999)ADSCrossRefGoogle Scholar
  16. 16.
    I. Marchenko, Vacuum 81, 700 (2007)CrossRefGoogle Scholar
  17. 17.
    Y.M. Yu, R. Backofen, A. Voigt, Phys. Rev. E 77, 051605 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    J.M. Rogowska, Surf. Sci. 507, 340 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    D. Goykolov, M. Kotrla, Central Eur. J. Phys. 7, 220 (2009)ADSCrossRefGoogle Scholar
  20. 20.
    G. Boisvert, L.J. Lewis, M. Scheffler, Phys. Rev. B 57, 1881 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    H. Gollisch, Surf. Sci. 175, 249 (1986)ADSCrossRefGoogle Scholar
  22. 22.
    J. Malzbender et al., Surf. Sci. 414, 187 (1998)ADSCrossRefGoogle Scholar
  23. 23.
    P.O. Jubert, O. Fruchart, C. Meyer, Phys. Rev. B 64, 115419 (2001)ADSCrossRefGoogle Scholar
  24. 24.
    H. Brune et al., Phys. Rev. B 52, 14380 (1995)ADSCrossRefGoogle Scholar
  25. 25.
    M. Schroeder, D.E. Wolf, Surf. Sci. 375, 129 (1997)ADSCrossRefGoogle Scholar
  26. 26.
    R. Sabiryanov et al., J. Magn. Magn. Mater. 258, 365 (2003)ADSCrossRefGoogle Scholar
  27. 27.
    S. Clarke, D. Vvedensky, J. Appl. Phys. 63, 2272 (1988)ADSCrossRefGoogle Scholar
  28. 28.
    C. Ratsch et al., Phys. Rev. Lett. 72 , 3194 (1994)ADSCrossRefGoogle Scholar
  29. 29.
    S. Murphy et al., Phys. Rev. B 66, 195417 (2002)ADSCrossRefGoogle Scholar
  30. 30.
    D. Vanderbilt, Phys. Rev. B 41, 7892 (1990)ADSCrossRefGoogle Scholar
  31. 31.
    G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996)ADSCrossRefGoogle Scholar
  32. 32.
    G. Kresse, J. Furthmüller, Comput. Mater. Sci. 54, 15 (1996)CrossRefGoogle Scholar
  33. 33.
    J.P. Perdew et al., Phys. Rev. B 46, 6671 (1992)ADSCrossRefGoogle Scholar
  34. 34.
    T. Ala-Nissila, J. Kjoll, S.C. Ying, Phys. Rev. B 46, 846 (1992)ADSCrossRefGoogle Scholar
  35. 35.
    I. Vattulainen et al., Phys. Rev. B 57, 1896 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    T. Ala-Nissila, R. Ferrando, S.C. Ying, Adv. Phys. 51, 949 (2002)ADSCrossRefGoogle Scholar
  37. 37.
    S.C. Ying et al., Phys. Rev. B 58, 2170 (1998)ADSCrossRefGoogle Scholar
  38. 38.
    S.C. Wang, G. Ehrlich, Surf. Sci. 239, 301 (1990)ADSCrossRefGoogle Scholar
  39. 39.
    S.C. Wang, U. Kürpick, G. Ehrlich, Phys. Rev. Lett. 81, 4923 (1998)ADSCrossRefGoogle Scholar
  40. 40.
    K. Kyuno, G. Ehrlich, Phys. Rev. Lett. 84, 2658 (2000)ADSCrossRefGoogle Scholar
  41. 41.
    J. Heinonen et al., Phys. Rev. Lett. 82, 2733 (1999)ADSCrossRefGoogle Scholar
  42. 42.
    O.S. Trushin, P. Salo, T. Ala-Nissila, Phys. Rev. B 62, 1611 (2000)ADSCrossRefGoogle Scholar
  43. 43.
    P. Salo et al., Phys. Rev. B 64, 161405 (2001)ADSCrossRefGoogle Scholar
  44. 44.
    O.S. Trushin et al., Surf. Sci 482-485, 365 (2001)ADSCrossRefGoogle Scholar
  45. 45.
    J. Heinonen et al., in Collective Diffusion on Surfaces: Correlation Effects and Adatom Interactions, edited by M.C. Tringides, Z. Chvoj (Kluwer, 2001), pp. 317–325Google Scholar
  46. 46.
    S.V. Khare, N.C. Bartelt, T.L. Einstein, Phys. Rev. Lett. 75, 2148 (1995)ADSCrossRefGoogle Scholar
  47. 47.
    S.V. Khare, T.L. Einstein, Phys. Rev. B 54, 11752 (1996)ADSCrossRefGoogle Scholar
  48. 48.
    M.C. Bartelt, J.W. Evans, Phys. Rev. B 46, 12675 (1992)ADSCrossRefGoogle Scholar
  49. 49.
    G.S. Bales, D.C. Chrzan, Phys. Rev. B 50, 6057 (1994)ADSCrossRefGoogle Scholar
  50. 50.
    G.S. Bales, D.C. Chrzan, Phys. Rev. Lett. 74, 4879 (1995)ADSCrossRefGoogle Scholar
  51. 51.
    M.O. Jahma et al., Surf. Sci. 598, 246 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    I.T. Koponen et al., Phys. Rev. Lett. 92, 086103 (2004)ADSCrossRefGoogle Scholar
  53. 53.
    P.A. Maksym, Semicond. Sci. Technol. 3, 594 (1988)ADSCrossRefGoogle Scholar
  54. 54.
    Y. Shim, J.G. Amar, Phys. Rev. Lett. 108, 076102 (2012)ADSCrossRefGoogle Scholar
  55. 55.
    K. Kang, S. Redner, Phys. Rev. Lett. 52, 955 (1984)MathSciNetADSCrossRefGoogle Scholar
  56. 56.
    P.L. Krapivsky, J.F.F. Mendes, S. Redner, Eur. Phys. J. B 4, 401 (1998)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Martin Mašín
    • 1
  • Miroslav Kotrla
    • 1
  • Bo Yang
    • 2
  • Mark Asta
    • 3
  • Mika O. Jahma
    • 4
  • Tapio Ala-Nissila
    • 4
    • 5
  1. 1.Institute of PhysicsAcademy of Science of the Czech RepublicPragueCzech Republic
  2. 2.Department of Chemical Engineering and Materials ScienceUniversity of CaliforniaDavisUSA
  3. 3.Department of Materials Science and EngineeringUniversity of California BerkeleyBerkeleyUSA
  4. 4.Department of Applied Physics and COMP CoEAalto University School of ScienceAalto, EspooFinland
  5. 5.Department of PhysicsBrown UniversityProvidenceUSA

Personalised recommendations