Advertisement

Simulation of Ostwald Ripening in Homoepitaxy

  • Frank Haußer
  • Axel Voigt
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 149)

Abstract

Ostwald ripening in homoepitaxy in the submonolayer regime is studied by means of numerical simulations. The simulations indicate, that the coarsening kinetics of the average island radius is described by a t1/a power law, where 2 ≤ a ≤ 3. Here a approaches 2, if the ripening is purely kinetics limited (low attachment rate at the island boundaries) and increases with increasing attachment rate — taking the value a = 3 if the ripening is purely diffusion limited (infinite attachment rate at the island boundaries). For the two limiting cases the classical LSW theory is reviewed and compared with the numerical simulations. Besides the scaling law we also investigate the asymptotic scaled island size distribution function and analyse the influence of anisotropic edge energies and the effect of edge diffusion.

Keywords

Ostwald ripening numerical simulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    N. Akaiwa, D.I. Meiron, Numerical simulation of two-dimensional late-stage coarsening for nucleation and growth. Phys. Rev. E 51 no.6 (1995), 5408–5421CrossRefGoogle Scholar
  2. [2]
    H.A. Atwater, C.M. Yang Island growth and coarsening in thin films — conservative and nonconservative systems. J. Appl. Phys. 67 (1990), 6202–6213CrossRefGoogle Scholar
  3. [3]
    N.C. Bartelt, W. Theis, R.M. Tromp, Ostwald ripening of two-dimensional islands on Si(001). Phys. Rev. B 54(16) (1996), 11741–11751CrossRefGoogle Scholar
  4. [4]
    E. Bänsch and F. Haußer and O. Lakkis and B. Li and A. Voigt, Finite Element Method for Epitaxial Growth with Attachment-Detachment Kinetics. J. Comput. Phys. 194 (2004), 409–434CrossRefGoogle Scholar
  5. [5]
    F. Haußer and A. Voigt, this volumeGoogle Scholar
  6. [6]
    E. Bänsch and F. Haußer and A. Voigt, Finite Element Method for epitaxial growth with thermodynamic boundary conditions. SIAM J. Sci. Comput. (2005), (to appear)Google Scholar
  7. [7]
    T.M. Rogers and R.C. Desai, Numerical study of late-stage coarsening for off-critical quenches in the Cahn-Hilliard equation of phase separation. Phys. Rev. B 39 no.16 (1989), 11956–11964CrossRefGoogle Scholar
  8. [8]
    M. Hillert, On the Theory of Normal and Abnormal Grain Growth. Acta Metall. 13 (1965), 227–238CrossRefGoogle Scholar
  9. [9]
    J. Krug, this volumeGoogle Scholar
  10. [10]
    I.M. Lifshitz, V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19 (1961), 35–50CrossRefGoogle Scholar
  11. [11]
    J.A. Marqusee, J. Ross, Kinetics of phase transitions: Theory of Ostwald ripening. J. Chem. Phys. 79(1) (1983), 373–378CrossRefGoogle Scholar
  12. [12]
    J.A. Marqusee, J. Ross, Theory of Ostwald ripening: Competitive growth and its dependence on volume fraction. J. Chem. Phys. 80(1) (1984), 536–543CrossRefGoogle Scholar
  13. [13]
    J.A. Marqusee, J. Ross, Dynamics of late stage phase separations in two dimensions. J. Chem. Phys. 81(2) (1984), 976–981CrossRefGoogle Scholar
  14. [14]
    B. Niethammer, F. Otto, Domain Coarsening in Thin Films. Comm. Pure and App. Math. LIV (2001), 361–384.CrossRefGoogle Scholar
  15. [15]
    B. Niethammer, R.L. Pego, Non-self-similar behavior in the LSW theory of Ostwald Ripening. J. Statist. Phys. 95 (1999), no. 5–6 867–902.CrossRefGoogle Scholar
  16. [16]
    M. Petersen, A. Zangwill, C. Ratsch, Homoepitaxial Ostwald Ripening. Surf. Sci. 536 (2003), 55–60CrossRefGoogle Scholar
  17. [17]
    L. Ratke, P.W. Voorhees, Growth and Coarsening: Ripening in Material Processing. Springer, 2002Google Scholar
  18. [18]
    P.W. Voorhees, The Theory of Ostald Ripening. J. Statist. Phys. 38 (1985), no. 1-1 231–252.CrossRefGoogle Scholar
  19. [19]
    C. Wagner, Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung). Z. Elektrochemie 65 (1961), 581–591Google Scholar
  20. [20]
    J.H. Yao, K.R. Elder, H. Guo, M. Grant, Theory and simulation of Ostwald ripening. Phys. Rev. B 47 no.21 (1993), 14110–14125CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Frank Haußer
    • Axel Voigt
      • 1
    1. 1.Crystal Growth groupBonnGermany

    Personalised recommendations