Dynamics of Nanostructure Formation During Thin Film Deposition

  • Daniel Walgraef
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 114)


Coverage evolution, during atomic deposition on a substrate may be described, on mesoscopic scales, by dynamical models of the reaction-diffusion type, which combine reaction terms representing chemical processes such as adsorption-desorption and nonlinear diffusion terms. Below a critical temperature, uniform deposited layers are unstable, which leads to the formation of nanostructures corresponding to regular spatial variations of substrate coverage. For increasing mean coverage close to one-half, the dynamics is of the Cahn-Hilliard type, and one should observe a succession of structures going from hexagonal arrays of high coverage dots, to stripes and finally to hexagonal arrays of low coverage dots. For mean coverage close to one, the nanostructures are highly nonlinear, and have to be obtained numerically. Structures obtained in the case of Al layers deposited on TiN substrates are presented. Comparisons between weakly and highly nonlinear structures are performed.

Key words

thin film deposition nanostructure reaction-diffusion dynamics instability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. Abraham and G. White, J. Appl. Phys. 41, 1841 (1970).CrossRefGoogle Scholar
  2. [2]
    G.H. Gilmer and P. Bennema, J. Appl. Phys. 43, 1347 (1972).CrossRefGoogle Scholar
  3. [3]
    H. Huang, G.H. Gilmer and T. Diaz de la Rubia, “An Atomistic Simulator for Thin Film Deposition in Three Dimensions”, J. Appl. Phys. 84, 3636 (1998).CrossRefGoogle Scholar
  4. [4]
    Gao, H. and Nix, W.D., “Surface Roughening of Heteroepitaxial Thin Films”, Annual Review of Materials Science 29, 173 (1999).CrossRefGoogle Scholar
  5. [5]
    Léonard, F., Laradji, M. and Desai, R.C., “Molecular beam epitaxy in the presence of phase separation”, Phys.Rev. B 55, 1887 (1997).CrossRefGoogle Scholar
  6. [6]
    Léonard, F. and Desai, R.C., “Alloy decomposition and surface instabilities in thin films” Thys.Rev. B 57, 4805 (1998).CrossRefGoogle Scholar
  7. [7]
    Suo, Z. and Lu, W., “Self-organizing nanophases on a solid surface”, in Multiscale Deformation and Fracture in Materials and Structures, The James R. Rice 60th Anniversary volume, edited by T.J. Chuang and J.W. Rudnicki, Kluwer Academic Publishers, Dordrecht, 107–122 (2000)Google Scholar
  8. [8]
    Suo, Z. and Lu, W., “Forces that drive nanoscale self-assembly on solid surfaces”, Journal of Nanoparticle Research 2, 333–344 (2000).CrossRefGoogle Scholar
  9. [9]
    Ghoniem, N. M., Heinisch, H., Huang, H., Yip, S. and Yu, J., eds., Journal of Computer Aided Materials Design, Special Issue for Multiscale Materials Modeling Symposium of the 5th IUMRS, Kluwer, Dordrecht (1999).Google Scholar
  10. [10]
    Walgraef, D., “Nanostructure Initiation during the Early Stages of Thin Film Growth”, Physica E 15, 33 (2002).CrossRefGoogle Scholar
  11. [11]
    Walgraef, D., “Reaction-Diffusion approach to nanostructure formation during thin film deposition“, to appear, Phil. Mag. A.Google Scholar
  12. [12]
    Walgraef, D., “Spatio-Temporal Pattern Formation (with examples in physics, chemistry and materials science”, Springer Verlag, New York, 1996.Google Scholar
  13. [13]
    Verdasca, J., Borckmans, P. and Dewel, G., “Chemically frozen phase separation in an adsorbed layer”, Phys. Rev. E. 52, R4616 (1995).CrossRefGoogle Scholar
  14. [14]
    Walgraef, D. and Clerc, M.G., to appear.Google Scholar
  15. [15]
    Mishin, Y., Farkas, D., Mehl, M.J. and Papaconstantopoulos, D.A., “Interatomic potentials for monoatomic metals from experimental data and ab initio calculations“, Phys.Rev. B 59, 3393–3407 (1999).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Daniel Walgraef
    • 1
  1. 1.Center for Nonlinear Phenomena and Complex SystemsFree University of BrusselsBrusselsBelgium

Personalised recommendations