Advertisement

Continuum Mechanics and Thermodynamics

, Volume 17, Issue 5, pp 373–386 | Cite as

Microstructure morphology transitions at mesoscopic epitaxial surfaces

  • Heike Emmerich
  • Christof Eck
Original Article

Abstract

Spiral surface growth is well understood in the limit where motion of the spiral ridge is controlled by the local supersaturation of adatoms in its surrounding. In liquid epitaxial growth, however, spirals can form governed by both, transport of heat as well as solute. We propose for the first time a two-scale model of epitaxial growth which takes into account all of these transport processes. This new model assumes a separation of length scales for the transport of heat compared to that of the solutal field. It allows for the first time numerical simulations of extended surface regions by at the same time taking into account microstructure evolution and microstructure interaction. We apply this model successfully to extend the scaling relation for the step spacing given by the BCF theory [Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] to microstructure evolution governed by heat and solute diffusion. Further applications to understand the mechanisms and consequences of spiral interaction at epitaxial surfaces, in particular the resulting morphology transitions, are discussed.

Keywords

Epitaxy Homogenization Phase field models Spiral growth morphology 

PACS

81.10.Aj 81.15.-z 68.35.-p 68.55.-a 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ihle, T., Mueller-Krumbhaar, H.: Phys. Rev. E 49, 2972 (1994)CrossRefGoogle Scholar
  2. 2.
    Brener, E., Mueller-Krumbhaar, H., Saito, Y., Temkin, D.: Phys. Rev. E 47, 1151 (1993)CrossRefGoogle Scholar
  3. 3.
    Emmerich, H., Schleussner, D., Kassner, K., Ihle, T.: Phys, J.: Condens. Matter 11, 8981 (1999)CrossRefGoogle Scholar
  4. 4.
    Brener, E., Melnikov, V.I.: JETP 80, 341 (1995)Google Scholar
  5. 5.
    Brener, E., Melnikov, V.I., Adv. Phys. 40, 53 (1991)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Zuo, J.-K., and Wendelken, J.F.: Phys. Rev. Lett. 78, 2791 (1997); Ernst, H.-J. et al., ibid. 72, 112 (1994); Jorritsma, L.C.: et al., ibid. 78, 911 (1997); Stroscio, J.A.: et al., ibid. 75, 4246 (1997); Van Nostrand, J.E.: et al., ibid. 74, 1127 (1995)Google Scholar
  7. 7.
    Bales, G.S., and Zangwill, A.: Phys. Rev. B 41, 5500 (1990); Pierre-Louis, O., D'Orsogna, M.R., Einstein, T.L.: Phys. Rev. Lett. 82, 3661 (1999); Emmerich, H.: Phys. Rev. B 65, 233406 (2002)Google Scholar
  8. 8.
    Krug, J.: Origins of scale invariance in growth processes, FZ Jülich, technical report Jül-3031, ISSN 0944-2952 (1995) and references thereinGoogle Scholar
  9. 9.
    Pierre-Louis, O., Misbah, C., Sait, Y., Krug, J. and Politi, P.: Phys. Rev. Lett. 80, 4221 (1998); Politi, P.: Phys, J. I (France) 7, 797 (1997); Zhang, Z., Detch, J., and Metiu, H.: Phys. Rev. B 48, 4972 (1993); Politi, P., and Villain, J.: Phys. Rev. B 54, 5114 (1996)Google Scholar
  10. 10.
    Burton, W.K., Cabrera, N., and Frank, F.C.: Philos. Trans. Soc, R. London, Ser. A 243, 299 (1951)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Cabrera, N. and Levine, M.M.: Phil. Mag. 1, 450 (1956)zbMATHGoogle Scholar
  12. 12.
    Cabrera, N. and Coleman, R.V.: in: J, J. Gilman (Ed.), The Art and Science of Growing Crystals, John Wiley, New York (1963)Google Scholar
  13. 13.
    Surek, T., Hirth, J.P. and Pound, G.M.: Cryst, J. Growth 18, 20 (1973)CrossRefGoogle Scholar
  14. 14.
    van der Eerden, J.P., Cryst, J.: Growth 53, 305, 315 (1981); see also van der Eerden, P.J.: in: Hurle, T.D.J. (ed) Handbook of Crystal Growth, Vol. 1a, Elsevier (1993)Google Scholar
  15. 15.
    Karma, A., and Plapp, M.: Phys. Rev. Lett. 81, 4444 (1998)CrossRefGoogle Scholar
  16. 16.
    Liu, F., Metiu, H.: Phys. Rev. E 49, 2601 (1994)CrossRefGoogle Scholar
  17. 17.
    Godunov, G.H., Ryabenkii, V.S.: Difference Schemes, North Holland (1987)Google Scholar
  18. 18.
    Karma, A., and Rappel, W.-J.: Phys. Rev. Lett 77, 4050 (1996); Phys. Rev. E 57, 4323 (1998)Google Scholar
  19. 19.
    Villain, J.: J. Phys. I (France) 1, 19 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Heike Emmerich
    • 1
  • Christof Eck
    • 1
  1. 1.Institute of Minerals Engineering, Computational Materials EngineeringRWTHAachenGermany

Personalised recommendations