Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-26T01:18:28.823Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Simulation of Diffusion Controlled Surface Evolution

Published online by Cambridge University Press:  15 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.
Get access

Abstract

As a model for Stranski-Krastanow island formation in strained heteroepitaxial layers, this paper investigates the surface-diffusion controlled morphological evolution of a two dimensional semi-infinite solid loaded in the lateral direction. Numerical Methods are developed to simulate the surface diffusion process, and examples are presented to demonstrate three distinct evolution patterns which are characterized by two critical wavelengths. The results show that, according to the wavelength, a slightly wavy surface can evolve into a cusped, a smoothly undulating, or a flat configuration. The diffusion wavelength and cusp-formation time compare favorably with recent experimental observations.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 317: Symposium B – Mechanisms of Thin Film Evolution , 1993 , 369
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

REFERENCES

1 Asaro, R. J. and Tiller, W. A., Metall. Trans. 3, 1789 (1972)CrossRefGoogle Scholar
2 Srolovitz, D. J., Acta Metall. 37, 621 (1989)CrossRefGoogle Scholar
3 Gao, H., Int. J. Solids Structures 28, 703 (1991)Google Scholar
4 Gao, H., J. Mech. Phys. solids 39, 443 (1991).Google Scholar
5 Gao, H., In Modern Theory of Anisotropie Elasticity and Applications, eds. Wu, J. J., Ting, T. C. T., and Barnett, D., SIAM, 139 (1991).Google Scholar
6 Grinfeld, M. A., J. Nonlin. Sci‥ 3, 35 (1993).Google Scholar
7 Spencer, B. J., Voorhees, P. W., and Davis, S. H., Phys. Rev. Lett. 67, 3696 (1991).Google Scholar
8 Freund, L. B., and Jonsdottir, F., J. Mech. Phys. Solids 41, 1245 (1993).Google Scholar
9 Stranski, I. N. and Krastanow, Von L., Akad. Wiss. Lit. Mainz Math.-Natur. KI. IIb 146, 797 (1939)Google Scholar
10 Asai, M., Ueba, H., and Tatsuyama, C., J. Appl. Phys. 58, 2577 (1985)Google Scholar
11 LeGoues, F. K., Copel, M., and Tromp, R. M., Phys. Rev. B 42, 11690 (1990).Google Scholar
12 Eaglesham, D. J., Gossmann, H.-J., and Cerullo, M., Phys. Rev. Lett. 65, 1227 (1990).CrossRefGoogle Scholar
13 Eaglesham, D. J. and Cerullo, M., Phys. Rev. Lett. 64, 1943 (1990).Google Scholar
14 Guha, S., Madhukar, A., and Rajkumar, K. C., Appl. Phys. Lett. 57, 2110 (199).CrossRefGoogle Scholar
15 Snyder, C. W., Orr, B. G., Kessler, D., and Sander, L. M., Phys. Rev. Lett. 66, 3032 (1991).Google Scholar
16 Chiu, C-h. and Gao, H., Int. J. Solids Structures. 30, 2983 (1993).Google Scholar
17 Gao, H., submitted to J. Mech. Phys. Solids.Google Scholar
18 Fleck, N. A., Proc. Roy. Soc. of London, A432, 55 (1991).Google Scholar
19 Hughes, T. J. R., The finite Element Method, Prentice-Hall, New Jersey.Google Scholar
20 Jesson, D. E., Pennycook, S. J., Baribeau, J.-M., and Houghton, D. C., Phys. Rev. Lett. 71, 1744 (1993).CrossRefGoogle Scholar