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Collective Modes Of Misfit Dislocations in Lattice - Mismatched Thin Films

Published online by Cambridge University Press:  10 February 2011

L. B. Hovakimian  and
Shun-Ichiro Tanaka
L. B. Hovakimian
Affiliation:
Tanaka Solid Junction Project, ERATO, Japan Science and Technology Corporation, 1–1–1 Fukuura, Kanazawa-ku, Yokohama 236, Japan
Shun-Ichiro Tanaka
Affiliation:
Tanaka Solid Junction Project, ERATO, Japan Science and Technology Corporation, 1–1–1 Fukuura, Kanazawa-ku, Yokohama 236, Japan
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Abstract

We study the nature and spectrum of fundamental vibrational excitations in the assembly of misfit accomodating dislocations. The physical system considered is a Lomer array of equispaced dislocations in a lattice-mismatched interface between a substrate and a thin film with similar elastic properties. Within the framework of the isotropie elasticity theory we calculate the effective force constants of harmonic springs that establish the dynamical correlations between the oscillating dislocations. Our interest is concentrated on the case where the thickness of the overlay er is much less than the separation between the nearest-neighbor dislocations. We show how in this situation the free surface of the film exerts a profound screening influence on the dislocation-dislocation correlations; it is demonstrated that the force constants exhibit sensitive dependence not only on the lattice mismatch, but also on the film thickness. We then deduce the dispersion of collective dislocation excitations and find that the latter propagate along the interface much more slowly than the ordinary sound waves. Our results reveal the manner in which the thickness of the film controls the magnitude of the vibrational quantum that characterizes the natural oscillations of arrayed dislocations. It is shown that this anomalous energy quantum manifests itself in the low-temperature heat capacity of the misfit array.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 472: Symposium I – Polycrystalline Thin Films - Structure, Texture, Properties..III , 1997 , 143
Copyright
Copyright © Materials Research Society 1997

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References

REFERENCES

1. Matthews, J. W., J. Vac. Sci. Technol. 12, 126 (1975); inGoogle Scholar
Dislocations in Solids, edited by Nabarro, F. R. N. (North-Holland, Amsterdam, 1979), Vol. 2, p. 461.Google Scholar
2. Sutton, A. P. and Balluffi, R. W., Interfaces in Crystalline Materials (Clarendon, Oxford, 1995), Chap 2.Google Scholar
3. Willis, J. R., Jain, S. C, and Bullough, R., Philos. Mag. 62, 115 (1990).Google Scholar
4. Rockett, A. and Kiely, C. J., Phys. Rev. B 44, 1154 (1991).Google Scholar
5. van der Merwe, J. H., J. Appl. Phys. 34, 117 (1963).Google Scholar
6. Mader, W. and Knauss, D., Acta Metall. Mater. 40, S 207 (1992).Google Scholar
7. Grinfeld, M., Phys. Rev. B 49, 8310(1994).Google Scholar
8. Speck, J. S. and Pompe, W., J. Appl. Phys. 76, 466 (1994).Google Scholar
9. Hovakimian, L. B. and Tanaka, S., Phys. Rev. B 54, 15125 (1996).Google Scholar
10. Mura, T., in Advances in Materials Research, edited by Herman, H. (Interscience, New York, 1968), Vol. 3, p. 1;Google Scholar
Dundurs, J., in Mathematical Theory of Dislocations, edited by Mura, T. (ASME, New York, 1969), p. 70.Google Scholar
11. Fischer, A., Kuhne, H., and Richter, H., Phys. Rev. Lett. 73, 2712 (1994).Google Scholar
12. (a) Barsch, G. R., Horovitz, B., and Krumhansl, J. A., Phys. Rev. Lett. 59, 1251 (1987);Google Scholar
(b) Horovitz, B., Barsch, G. R., and Krumhansl, J. A., Phys. Rev. B 43, 1021 (1991).Google Scholar
13. Granato, A., Phys. Rev. 113, 740 (1958).Google Scholar
14. Ahlers, G., Rev. sei. Instrum. 37, 477 (1966).Google Scholar
15. Bevk, J., Philos. Mag. 28, 1379 (1973).Google Scholar