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Stochastic Models of Epitaxial Growth

  • Dionisios Margetis (a1), Paul N. Patrone (a2) and T. L. Einstein (a2)

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.

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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).
2. Hamouda, A. BH., Pimpinelli, A., and Einstein, T. L., Europhys. Lett. 88, 26005 (2009).
3. Burton, W. K., Cabrera, N., and Frank, F., Phil. Trans. Roy. Soc. 243, 299 (1951).
4. Jeong, H. C. and Williams, E. D., Surf. Sci. Rep. 34, 171 (1999).
5. Margetis, D., J. Phys. A: Math. Theor. 43, 065003 (2010).
6. Patrone, P. N., Einstein, T. L., and Margetis, D., Phys. Rev. E, accepted for publication.
7. Marchenko, V. I. and Parshin, A. Ya., Sov. Phys. JETP 52, 129 (1980).
8. Patrone, P. N., Wang, R., and Margetis, D. (unpublished).
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Keywords

Stochastic Models of Epitaxial Growth

  • Dionisios Margetis (a1), Paul N. Patrone (a2) and T. L. Einstein (a2)

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