Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T02:22:27.175Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic Models of Epitaxial Growth

Published online by Cambridge University Press:  07 March 2011

Dionisios Margetis ,
Paul N. Patrone  and
T. L. Einstein
Dionisios Margetis
Affiliation:
Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742, U.S.A.
Paul N. Patrone
Affiliation:
Department of Physics, University of Maryland, College Park, MD 20742, U.S.A.
T. L. Einstein
Affiliation:
Department of Physics, University of Maryland, College Park, MD 20742, U.S.A.
Get access

Abstract

We study theoretical aspects of step fluctuations on vicinal surfaces by adding conservative white noise to the Burton-Cabrera-Frank model in one spatial dimension. We consider material deposition from above, as well as entropic and elastic-dipole step repulsions. Two approaches are discussed: (i) the linearization of stochastic equations when fluctuations are small, which captures correlations; and (ii) a mean field approach, which leaves out correlations but captures nonlinearities. Comparisons to kinetic Monte-Carlo simulations are presented.

Keywords

epitaxydiffusionsimulation
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1318: Symposium SS/TT/UU/VV – Advances in Spectroscopy and Imaging of Surfaces and Nanostructures , 2011 , mrsf10-1318-uu07-04
Copyright
Copyright © Materials Research Society 2011

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. Cohen, S. D., Schroll, R. D., Einstein, T. L., Métois, J. J., Gebremariam, H., Richards, H. L., and Williams, E. D., Phys. Rev. B 66, 115310 (2002).Google Scholar
2. Hamouda, A. BH., Pimpinelli, A., and Einstein, T. L., Europhys. Lett. 88, 26005 (2009).Google Scholar
3. Burton, W. K., Cabrera, N., and Frank, F., Phil. Trans. Roy. Soc. 243, 299 (1951).Google Scholar
4. Jeong, H. C. and Williams, E. D., Surf. Sci. Rep. 34, 171 (1999).Google Scholar
5. Margetis, D., J. Phys. A: Math. Theor. 43, 065003 (2010).Google Scholar
6. Patrone, P. N., Einstein, T. L., and Margetis, D., Phys. Rev. E, accepted for publication.Google Scholar
7. Marchenko, V. I. and Parshin, A. Ya., Sov. Phys. JETP 52, 129 (1980).Google Scholar
8. Patrone, P. N., Wang, R., and Margetis, D. (unpublished).Google Scholar
9. Gruber, E. E. and Mullins, W. W., J. Phys. Chem. Solids 28, 875 (1967).Google Scholar