Hostname: page-component-7bb8b95d7b-pwrkn Total loading time: 0 Render date: 2024-09-12T02:51:04.413Z Has data issue: false hasContentIssue false
  • English
  • Français

The Critical Thickness of the Dislocation-Free Stranski Krastanow Pattern of Growth.

Published online by Cambridge University Press:  15 February 2011

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

Abstract

It was demonstrated earlier [1,2] in the framework of equilibrium thermodynamics that the morphological stability of the free boundaries and interfaces in crystals is extremely sensitive to the presence of shear stresses. Relying on that idea we have established the formula H = μσ/τ2 of a critical thickness of solidifying He4 films and of the dislocation-free Stranski-Krastanow growth of epitaxial films (where σ – the coefficient of surface tension, μ - the shear module of the crystal, τ - the external or misfit stress). In this report we present certain facts pertaining to possible patterns of the growing corrugations and introduce the second critical thickness at which a symmetry change in the patterns has to occur.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 290: Symposium N – Dynamics in Small Confining Systems , 1992 , 233
Copyright
Copyright © Materials Research Society 1993

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. Nozieres, P., in Solids Far From Equilibrium, edited by Godreche, C. (Cambridge University Press, Cambridge, 1991): S. Balibar, D.O. Edwards and W.F. Saam, J. Low Temp. Phys. 82, 119, (1991).Google Scholar
2. Grinfeld, M.A., Dokl. AN SSSR 283, 1139 (1985) [Doklady, Earth Sci., 283, 27 (1985)]; Dokl. AN SSSR 290, 1358 (1986) [Soy. Phys. Dokl. 31, 831]; Mekh. Zhidk. Gaza 1987 (2), 3 [Fluid Dyn. 22, 169]; PMM, 51, 628 (1987) [PMM USSR, 51, 489 (1987)].Google Scholar
3. Grinfeld, M.A., The Stress Driven Instabilities in Crystals: Mathematical Models and Physical Manifestations. IMA Preprint Series #819, June (1991). (to appear in: J. Nonlinear Science).Google Scholar
4. Torii, R. and Balibar, C., Helium Crystals Under Stress: the Grinfeld Instability. Intl. Symp. “Quantum Fluids and Solids”, Penn. State, (1992) (to appear: J. Low Temp. Phys.).Google Scholar
5..Eaglesham, D.J. and Cerullo, M., Phys. Rev. Lett., 64, 1943 (1990).Google Scholar
6. LeGoues, F.K., Copel, M., Tromp, R.M., Phys. Rev. B, 42,11690 (1990).Google Scholar
7. Srolovitz, D.J., Acta Metall., 37, 621 (1989), J. Tersoff, Phys. Rev. B,43, 9377 (1991); D. Vanderbilt and L.K. Wickham (Mat. Res. Soc. Symp. Proc. 202, Pittsburgh, PA 1991) pp. 555–560; B.J. Spencer, P.W. Voorhees and S.H. Davis, Phys. Rev. Lettr., 67, 3696 (1991); M.A. Grinfeld, (Mat. Res. Soc. Symp. Proc. 237, 239, Pittsburgh, PA 1992), L.B. Freund, F.Jonsdottir (Mat. Res. Soc. Symp. Proc., Pittsburgh, PA 1993; to appear)Google Scholar
8. Grinfeld, M.A., Equilibrium Shape and Instabilities of Deformable Elastic Crystals. Lecture given in Heirot-Watt University, Edinburgh (1989).Google Scholar
9. Grinfeld, M.A., Thermodynamic Methods in the Theory of Heterogeneous Systems, pp. 325, 364. Longman, Sussex (1991).Google Scholar
10. Grinfeld, M.A., J. Intell. Mater. Syst. Struct. (1993; to appear), J. Phys. C: Condenced Matter (1992; to appear), Mech. Res. Comm. (1992; to appear).Google Scholar
11. Andreev, A.F., and Parshin, A.Ya., Zh. Exp. Teor. Fiz, 75, 1511 (1978) (In Russian; English translation in: Soy. Phys. JETP, 48, 763).Google Scholar