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A Numerical Study of Stress Controlled Surface Diffusion During Epitaxial Film Growth

Published online by Cambridge University Press:  21 February 2011

Cheng-Hsin Chiu  and
Huajian Gao
Cheng-Hsin Chiu
Affiliation:
Division of Applied Mechanics, Stanford University, CA 94305.
Huajian Gao
Affiliation:
Division of Applied Mechanics, Stanford University, CA 94305.
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Abstract

A two-dimensional numerical simulation is performed to model the morphological evolution of a strained film growing heteroepitaxially on a substrate under simultaneous action of vapor deposition and surface diffusion. To facilitate numerical implementation, a continuum boundary layer model is proposed to account for the influence of film/substrate interface on the film growth pattern. Discussions are focused on the Stranski-Krastanow growth mode, although our model is capable of explaining Frank-van der Merwe and Volmer-Weber growth modes as well. Both first-order perturbation and numerical results are developed to demonstrate that the film surface tends to remain flat during the initial stage of growth and that surface roughening occurs once the film thickness exceeds a critical value, in consistency with experimentally observed patterns of S-K growth. Numerical results further show that, depending on the deposition rate, the surface evolution could lead to a steady state morphology, unstable cusp formation, or growing islands with flattened valleys.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 356: Symposium B2 – Thin Films: Stresses and Mechanical Properties V , 1994 , 33
Copyright
Copyright © Materials Research Society 1995

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References

1 Tsao, J. Y., Materials Fundamentals of Molecular Beam Epitaxy, Academic Press Inc., Boston (1993).Google Scholar
2 Asaro, R. J. and Tiller, W. A., Metall. Trans. 3, 1789 (1972)Google Scholar
3 Srolovitz, D. J., Acta metall. 37, 621 (1989)Google Scholar
4 Gao, H., Int. J. Solids Structures 28, 703 (1991)Google Scholar
5 Gao, H., J. Mech. Phys. solids 39, 443 (1991).Google Scholar
6 Gao, H., In Modern Theory of Anisotropic Elasticity and Applications, eds. Wu, J. J., Ting, T. C. T., and Barnett, D., SIAM, 139 (1991).Google Scholar
7 Grinfeld, M. A., J. Nonlin. Sci.. 3, 35 (1993).Google Scholar
8 Spencer, B. J., Voorhees, P. W., and Davis, S. H., Phys. Rev. Lett. 67, 3696 (1991).Google Scholar
9 Freund, L. B., and Jonsdottir, F., J. Mech. Phys. Solids 41, 1245 (1993).Google Scholar
10 Freund, L. B., Acta Mechanica Sinica 10, 16 (1994)Google Scholar
11 Chiu, C.-h. and Gao, H., Int. J. Solids Structures 30, 2983 (1993).Google Scholar
12 Jesson, D. E., Pennycook, S. J., Baribeau, J.-M., and Houghton, C. D., Phys. Rev. Lett. 71, 1774 (1993).Google Scholar
13 Yang, W. H. and Srolovitz, D. J., Phys. Rev. Lett. 71, 1593 (1993).Google Scholar
14 Chiu, C.-h. and Gao, H., Mat. Res. Soc. Symp. Proc. 317, 369 (1994).Google Scholar
15 Spencer, B. J. and Meiron, D. I., submitted to Acta Metall. Meter.Google Scholar
16 Yang, W. H. and Srolovitz, D. J., J. Mech. Phys. Solid. 42, 1551 (1994).Google Scholar
17 Chiu, C.-h. and Gao, H., Manuscript in preparation.Google Scholar
18 Gao, H., J. Mech. Phys. Solid. 42, 741 (1994).Google Scholar
19 Eaglesham, D. J. and Cerullo, M., Phys. Rev. Lett. 64, 1943 (1990).Google Scholar
20 Mullins, W. W., J. Appl. Phys. 28, 333 (1957).Google Scholar
21 Nix, W. D., Metall. Trans. A 20A, 2217 (1989).Google Scholar
22 Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen-the Netherlands (1953).Google Scholar