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Equilibrium shapes of coherent islands in heteroepitaxial systems

Published online by Cambridge University Press:  22 November 2006

W. Zhou ,
C. Cai ,
S. Yin  and
C. Wang
W. Zhou*
Affiliation:
College of Mechanical and Electrical Engineering, Zhejiang University of Technology, Hangzhou 310032, China Department of Mechanical Engineering, West Branch of Zhejiang University of Technology, Quzhou 324000, China
C. Cai
Affiliation:
College of Mechanical and Electrical Engineering, Zhejiang University of Technology, Hangzhou 310032, China
S. Yin
Affiliation:
College of Science, Zhejiang University of Technology, Hangzhou 310032, China
C. Wang
Affiliation:
Department of Physics, Tsinghua University, Beijing 100084, China
*
[email protected]
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Abstract

An analytical expression of the free energy consisting of the strain energy, surface energy and interfacial energy for the coherent island/substrate system, as well as the evolving relations of aspect ratio against volume of the island and misfit of the system, which provides a broad perspective on island behavior, is obtained, and used to study the equilibrium shapes of the systems. Under certain growth conditions in systems with a film/substrate lattice misfit, deposed material is known to aggregate into islandlike shapes with geometries having triangular shaped cross-sections. A two-dimensional model assuming liner elastic behavior is used to analyze an isolated triangular shaped island with elastic properties similar to those of the substrate assumed to be semi-infinite. The results show that in order to minimize the total free energy, a coherent island will adopt a particular height-to-width aspect ratio that is a function of only the island volume. The effect of a misfit dislocation on the equilibrium shape of an island is in passing examined. These can serve as a basis for interpretation of experiments.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 37 , Issue 1 , January 2007 , pp. 33 - 37
Copyright
© EDP Sciences, 2006

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References

Shchukin, V.A., Ledentsov, N.N., Kop'ev, P.S., Bimberg, D., Phys. Rev. Lett. 75, 2968 (1995) CrossRef
Daruka, I., Barabasi, A.-L., Phys. Rev. Lett. 79, 3708 (1997) CrossRef
Daruka, I., Tersoff, J., Barabasi, A.-L., Phys. Rev. Lett. 82, 2753 (1999) CrossRef
Spencer, B.J., Tersoff, J., Phys. Rev. Lett. 79, 4858 (1997) CrossRef
Wang, L.G., Kratzer, P., Scheffler, M., Moll, N., Phys. Rev. Lett. 82, 4042 (1999) CrossRef
M.J. Kelly, Low-dimensional Semiconductors: Materials, Physics, Technology, Devices (Oxford University Press, Oxford, 1995)
Shchukin, V.A., Bimberg, D., Rev. Mod. Phys. 71, 1125 (1999) CrossRef
Spencer, B.J., Voorhees, P.W., Davis, S.H., J. Appl. Phys. 73, 4955 (1993) CrossRef
Freund, L.B., Johnson, H.T., Kukta, R.V., Evolution of Epitaxial Structure and Morphology, edited by A. Zangwill et al., Mater. Res. Soc. Proc., Pittsburgh 399, 359 (1996)
Tersoff, J., Tromp, R.M., Phys. Rev. Lett. 70, 2782 (1993) CrossRef
Mo, Y.-W., Savage, D.E., Swartzentruber, B.S., Lagally, M.G., Phys. Rev. Lett. 65, 1020 (1990) CrossRef
K.L. Johnson, Contact Mechanics (Cambridge University Press, 1985)
Johnson, H.T., Freund, L.B., J. Appl. Phys. 81, 6081 (1997) CrossRef
Budimen, R.A., Ruda, H.E., J. Appl. Phys. 88, 4586 (2000) CrossRef
Krishnamurthy, M., Drucker, J.S., Venables, J.A., J. Appl. Phys. 69, 6461 (1991) CrossRef
Eaglesham, D.J., Cerullo, M., Phys. Rev. Lett. 64, 1943 (1990) CrossRef
Kukta, R.V., Freund, L.B., J. Mech. Phys. Solids 45, 1835 (1997) CrossRef
LeGoues, F.K., Reuter, M.C., Tersoff, J., Hammar, M., Tromp, R.M., Phys. Rev. Lett. 73, 300 (1994) CrossRef
Ovid'ko, I.A., Sheinerman, A.G., Phys. Rev. B 66, 245309 (2002) CrossRef
Ovid'ko, I.A., Phys. Rev. Lett. 88, 46103 (2002) CrossRef