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Three Dimensional Simulation of the Morphological Evolution of a Strained Film on a Thick Substrate

Published online by Cambridge University Press:  10 February 2011

Cheng-hsin Chiu*
Affiliation:
Institute of Materials Research and Engineering, Blk S7 Level 3, National University of Singapore, Singapore119260
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Abstract

This paper presents a three-dimensional simulation for the surface evolution of a strained film on a thick substrate. The simulation shows that an initially random morphology will first transform into a profile dominated by two-dimensional ridges, and then into a three-dimensional island surface. The simulation also demonstrates that the ridge-island transition is a kinetic process which can be delayed by changing the initial morphology.

Type
Research Article
Copyright
Copyright © Materials Research Society 1998

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References

[1] Eaglesham, D. J. and Cerullo, M., Phys. Rev. Lett. 64, 1943 (1990).Google Scholar
[2] Cullis, A. G., MRS Bulletin 21, 21 (1996).Google Scholar
[3] Ozkan, C. S., Ph.D. dissertation, Stanford University (1996).Google Scholar
[4] Tersoff, J. and LeGoues, R K., Phys. Rev. Lett. 72, 3570 (1994).Google Scholar
[5] Bimberg, D., Grundmann, M., and Ledentsov, N. N., MRS Bulletin 23 No. 2, 31 (1998).Google Scholar
[6] Asaro, R. J. and Tiller, W. A., Metall. Trans. 3, 1789 (1972).Google Scholar
[7] Srolovitz, D. I., Acta metall. 37, 621 (1989).Google Scholar
[8] Gao, H., Int. J. Solids Structures 28, 703 (1991).Google Scholar
[9] Spencer, B. J., Voorhees, P. W., and Davis, S. H., Phys. Rev. Lett. 67, 3696 (1991).Google Scholar
[10] Grinfeld, M. A., J. Nonlinear Sci. 3, 35 (1993).Google Scholar
[11] Freund, L. B. and Jonsdottir, F., J. Mech. Phys. Solids 41, 1245 (1993).Google Scholar
[12] Guyer, J. E. and Voorhees, P. W., Phys. Rev. Lett. 74, 4031 (1995).Google Scholar
[13] Chiu, C.-h., and Freund, L. B., Morphological instability of a strained film on a compliant substrate. Manuscript in preparation.Google Scholar
[14] Chiu, C-h. and Freund, L. B., In Thin Films: Stresses and Mechanical Properties VI, eds. Gerberich, W. W., Gao, H., Sundgren, J.-E., and Baker, S. P., MRS Sym. Proc. 436, 517 (1996).Google Scholar
[15] Kukta, R. V. and Freund, L. B., ibid, 493 (1996).Google Scholar
[16] Spencer, B. J. and Tersoff, J., Phys. Rev. Lett, in press.Google Scholar
[17] Chiu, C-h. and Gao, H., Int. J. Solids Structures 30, 2983 (1993).Google Scholar
[18] Yang, W. H. and Srolovitz, D. J., Phys. Rev. Lett. 71, 1593 (1993).Google Scholar
[19] Chiu, C.-h. and Gao, H., In Mechanisms of Thin Film Evolution, eds. Yalisove, S. M., Thompson, C. V., and Eaglesham, D. J., MRS Symp. Proc. 317, 369 (1994).Google Scholar
[20] Jonsdottir, F and Freund, L. B., ibid, 309 (1994).Google Scholar
[21] Freund, L. B., Acta Mech. Sinica 10, 16 (1994).Google Scholar
[22] Spencer, B. J. and Meiron, D. I., Acta metall. 42, 3629 (1994).Google Scholar
[23] Freund, L. B., Int. J. Solids Structures 32, 911 (1995).Google Scholar
[24] Chiu, C.-h. and Gao, H., In Thin Films: Stresses and Mechanical Properties V eds. Baker, S. P., Ross, C. A., Townsend, P. H., Volkert, C. A., and Borgesen, P., MRS Symp. Proc. 356, 33 (1995).Google Scholar
[25] Chiu, C-h., Ph.D. dissertation, Stanford University (1995).Google Scholar
[26] Gao, H., J. Mech. Phys. Solids 42, 741 (1994).Google Scholar
[27] Mullins, W. W., J. AppL. Phys. 28, 333 (1957).Google Scholar
[28] Weatherburn, M. A., Differential Geometry of Three Dimensions, Cambridge University Press, London (1927).Google Scholar
[29] Chiu, C-h., High-order boundary perturbation analysis for three-dimensional elasticity problems and its application in simulating the surface evolution of a strained film. Manuscript in preparation.Google Scholar
[30] This can be understood from the first-order perturbation result [6–9]; this is also indicated in our simulation that both the ridges and the islands can grow during the evolution.Google Scholar