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Diffusion in Potential Fields: Time-Dependent Capture on Radial and Rectangular Substrates

Published online by Cambridge University Press:  01 February 2011

J. A. Venables  and
P. Yang
J. A. Venables
Affiliation:
Department of Physics & Astronomy, Arizona State University, Tempe AZ 85287–1504, U.S.A School of Science and Technology, University of Sussex, Brighton, U.K
P. Yang
Affiliation:
Department of Physics & Astronomy, Arizona State University, Tempe AZ 85287–1504, U.S.A
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Abstract

In models of nucleation and growth on surfaces, it is usually assumed that the energy surface of the substrate is flat, that diffusion is isotropic, and that capture numbers can be calculated in the diffusion-controlled limit. We lift these restrictions analytically, and introduce a hybrid discrete FFT method of solving for the 2D time-dependent diffusion field of adparticles on general non-uniform substrates. The method, with periodic boundary conditions, is appropriate, for example, following nucleation on a regular (rectangular) array of defects. The programs, which have been realized in Matlab®6.5, are instructive for visualizing potential and diffusion fields, and for producing illustrative movies of crystal growth under various conditions. Here we demonstrate the time-dependence of capture numbers in the initial stages of annealing at high adparticle concentration in the presence of repulsive adparticle-cluster interactions; however it is clear that the method works in general for deposition, growth and annealing at all times.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 859: Symposium JJ – Modeling of Morphological Evolution at Surfaces and Interfaces , 2004 , JJ9.2
Copyright
Copyright © Materials Research Society 2005

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References

REFERENCES

1. Venables, J.A., Phil. Mag. 27, 697 (1973) and references quoted;Google Scholar
Venables, J.A., Phys. Rev. B 36, 4153 (1987); Surface Sci. 299, 798 (1994); Introduction to Surface and Thin Film Processes (Cambridge University Press: Cambridge, 2000), especially chapter 5.Google Scholar
2. Brune., H., Surface Sci. Rep. 31, 121 (1998).Google Scholar
3. Repp., J., Moresco., F., Meyer., G., Rieder., K-H., Hyldgaard, P. & Persson., M., Phys. Rev. Lett. 85, 2981 (2000);Google Scholar
Knorr., N., Brune., H., Epple., M., Hirstein., A., Schnieder, M.A. & Kern., K., Phys. Rev. B 65, 115420 (2002).Google Scholar
4. Bogicevic., A., Ovesson., S., Hyldgaard., P., Lundqvist, B.I., Brune, H. & Jennison, D.R., Phys. Rev. Lett. 85, 1910 (2000);Google Scholar
Ovesson., S., Bogicevic., A., Wahnström, G. & Lundqvist, B.I., Phys. Rev. B 64, 125423 (2001). See also refs 6 and 7 for more detailed comments.Google Scholar
5. Fichthorn, K.A. & Scheffler., M., Phys. Rev. Lett. 84, 5371 (2000);Google Scholar
Fichthorn, K.A., Merrick, M.L. & Scheffler., M., Appl. Phys. A 75, 17 (2002).Google Scholar
6. Ovesson., S., Phys. Rev. Lett. 88, 116102 (2002).Google Scholar
7. Venables, J.A. & Brune., H., Phys. Rev. B 66, 195404 (2002); for a shorter version, seeGoogle Scholar
Venables, J.A., Brune, H. & Drucker., J., Proc. Mater. Res. Soc. 749, 17 (2003).Google Scholar
8. Ratsch, C. & Venables, J.A., J. Vac. Sci. Tech. A 21, S96 (2003).Google Scholar
9. Yang, P. & Venables, J.A., Proc. Mater. Res. Soc., companion paper in this volume.Google Scholar
10. Grima, R. & Newman, T.J., Phys. Rev. E 70, 036703 (2004).Google Scholar
11. Bales, G. S. & Chrzan, D. C., Phys. Rev. B 50, 6057 (1994).Google Scholar
12. Brune., H., Bales., GS., Jacobsen., J., Boragno, C. & Kern., K., Phys. Rev. B 60, 5991 (1999).Google Scholar
13. Halpern., V., J. Appl. Phys. 40, 4627 (1969);Google Scholar
Stowell, M.J., Phil. Mag. 26, 349, 361 (1972). See alsoGoogle Scholar
Lewis, B. & Rees, G.J., Phil. Mag. 20, 1253 (1974), andGoogle Scholar
Lewis, B. & Anderson, J.C.: Nucleation and Growth of Thin Films (Academic Press, London, 1978) pages 238–246.Google Scholar
14. The Nernst-Einstein formulation is given in many places. For details, see comments and references in section IV of reference 7.Google Scholar
15. In ref [10], the same case is considered, but the velocity v(r) = +α∇Φ(r), where Φ(r) is a general scalar field. Here v(r) is directed down the potential gradient ∇V(r).Google Scholar
16. We thank Grima., R., Kay, D.A. and Newman, T.J. for useful conversations, preprints and joint work. More examples of MatLab®6.5 computations will be given in forthcoming publications.Google Scholar