Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T09:06:42.493Z Has data issue: false hasContentIssue false
  • English
  • Français

the Critical Thickness of Dislocation-free Stranski-Krastanov Growth Atop a Deformabile Substrate

Published online by Cambridge University Press:  15 February 2011

Michael Grinfeld
Michael Grinfeld*
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903
Get access

Abstract

We investigate the influence of mass forces (in particular, of gravitation and van der Waals forces) on the critical film thickness of thin films attached to solid substrates and establish corresponding corrections of the earlier published formula Hcril = ΣΜ/τ2 (where Σ is the surface energy, Μ - the shear Modulus, and τ - the mismatch stress). It is assumed that the films’ particles are able to rearrange their relative positions in the lattices, and the equilibrium rearrangement is determined by minimizing the total static energy. Recently, it was demonstrated that morphological stability of interfaces in crystalline solids with the rearrangement is extremely sensitive to the presence of shear stresses. Equilibrium theory of elasticity of pre-stressed solids with the rearrangement of their material particles has already allowed the prediction of the appearance of corrugations in He4 films and to explain the dislocation-free Stranski-Krastanov pattern of epitaxial growth of thin solid films. The explicit asymptotic formulae announced here are especially useful in the case of small mass force, the effects of which can be detectable and even significant for some of the above mentioned phenomena.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 317: Symposium B – Mechanisms of Thin Film Evolution , 1993 , 161
Copyright
Copyright © Materials Research Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Solids Far From Equilibrium, edited by Godreche, C. (Cambridge Univ. Press, Cambridge, 1991).Google Scholar
2. Asaro, R. J. and Tiller, W.A., Metall. Trans. 3, 1789 (1972).Google Scholar
3. Grinfeld, M.A., Sov. Phys. Doklady, 31, 831 (1986).Google Scholar
4. Grinfeld, M.A., Thermodynamic Methods in the Theory of Heterogeneous Systems. (Longman, Sussex, 1991).Google Scholar
5. Grinfeld, M.A., J. Nonlinear Sci. 3, 35 (1993).CrossRefGoogle Scholar
6. Torii, R.H, and Balibar, S., Low, J. Temp. Phys., 89, 391 (1992);CrossRefGoogle Scholar
Thiel, M., Willibald, A., Evers, P., Levchenko, A., Leiderer, P., and Balibar, S., Europhys. Lett. 20, 707 (1992).CrossRefGoogle Scholar
7. Eaglesham, D.J. and Cernilo, M., Phys. Rev. Lett., 64, 1943 (1990);CrossRefGoogle Scholar
LeGoues, F.K., Copel, M. and Tromp, R.M., Phys. Rev., B, 42, 11690 (1990);Google Scholar
Guha, S., Madhukar, A. and Rajkumar, K.C., Appl. Phys. Lett., 57, 2110 (1990);CrossRefGoogle Scholar
Snyder, C.W., Orr, B.G., Kessler, D. and Sander, L.M., Phys. Rev. Lettr., 66 3032 (1991).Google Scholar
8. Grinfeld, M.A., Fluid Dynamics, 22, 169 (1987).Google Scholar
9. Noziéres, P., unpublished lectrures (1988); In: Solids Far From Equilibrium, edited by Godréche, C. (Cambridge University. Press, Cambridge, 1991).Google Scholar
10. Srolovitz, D.J., Acta Metall. 37, 621 (1989).Google Scholar
11. Freund, L.B. and Jonsdottir, F., J. Mech. Phys. Solids, 41, 1245 (1993).Google Scholar
12. Grinfeld, M. A., 1993 (submitted).Google Scholar
13. Grinfeld, M.A. and Srolovitz, D., 1993 (submitted).Google Scholar
14. Noziéres, P., J. Phys. 3, 681 (1993).Google Scholar
15. Spencer, B.J., Voorhees, P.W. and Davis, S.H., Phys. Rev. Lettr., 67, 3696 (1991).CrossRefGoogle Scholar
16. Gao, H.J., Mech. Phys. Solids, 39 (1991) 443; Int. J.|Solids Struct., 28, 701 (1991).CrossRefGoogle Scholar
17. Noziéres, P., (unpublished).Google Scholar