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Self-Consistent Rate-Equation Approach to Nucleation and Growth in Point/Extended Island Models of 1-D Homoepitaxy

Published online by Cambridge University Press:  10 February 2011

Jacques G. Amar ,
Mihail N. Popescu  and
Fereydoon Family
Jacques G. Amar
Affiliation:
Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606
Mihail N. Popescu
Affiliation:
Department of Physics, Emory University, Atlanta, GA 30322
Fereydoon Family
Affiliation:
Department of Physics, Emory University, Atlanta, GA 30322
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Abstract

A self-consistent rate equation (RE) approach to submonolayer growth on a one-dimensional surface is presented. This approach explicitly takes into account the existence of gaps between clusters and can successfully predict the coverage dependence of the average densities of monomers N1, and clusters, N. It also implies an unusual dependence for the monomer-monomer capture number σ1 as a function of monomer density. To obtain the island size-distribution, a second set of mean-field equations is used describing the evolution of the size-dependent capture zones and leading to explicit size- and coverage-dependent capture numbers. The solution of this fully self-consistent RE approach is then compared with kinetic Monte Carlo results

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 570: Symposium V – Epitaxial Growth , 1999 , 3
Copyright
Copyright © Materials Research Society 1999

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References

REFERENCES

[1] Tsao, J.Y., Material Fundamentals of Molecular Beam Epitaxy, World Scientific, Singapore, (1993)Google Scholar
[2] Mo, Y.W., Kleiner, J., Webb, M.B., Lagally, M.G., Phys. Rev. Lett. 66, 1998 (1991).Google Scholar
[3] Ernst, H.J., Fabre, F., and Lapujoulade, J., Phys. Rev. B 46, 1929 (1992).Google Scholar
[4] Hwang, R.Q., Schroder, J., Gunther, C., and Behm, R.J., Phys. Rev. Lett. 67, 3279 (1991); R.Q. Hwang and R.J. Behm, J. Vac. Sci. Technol. B 10, 256 (1992).Google Scholar
[5] Li, W., Vidali, G., and Biham, O., Phys. Rev. B 48, 8336 (1993).Google Scholar
[6] Kopatzki, E., Gunther, S., Nichtl-Pecher, W., and Behm, R.J., Surf. Sci. 284, 154 (1993).Google Scholar
[7] Rosenfeld, G., Servaty, R., Teichert, C., Poelsema, B., and Comsa, G., Phys. Rev. Lett. 71, 895 (1993).Google Scholar
[8] Stroscio, J.A., Pierce, D.T., and Dragoset, R.A., Phys. Rev. Lett. 70, 3615 (1993); J.A. Stroscio and D.T. Pierce, Phys. Rev. B 49, 8522 (1994).Google Scholar
[9] Zuo, J.-K. and Wendelken, J.F., Phys. Rev. Lett. 66, 2227 (1991); J.-K. Zuo, J.F. Wendelken, H. Durr, and C.-L. Liu, ibid., 72, 3064 (1994).Google Scholar
[10] Chambliss, D.D. and Wilson, R.J., J. Vac. Sci. Technol. B 9, 928 (1991); D.D. Chambliss and K.E. Johnson, Phys. Rev. B 50, 5012 (1994).Google Scholar
[11] Jiang, Q. and Wang, G.C., Surf. Sci. 324, 357 (1995).Google Scholar
[12] Tsui, F., Wellman, J., Uher, C., and Clarke, R., Phys. Rev. Lett. 76, 3164 (1996).Google Scholar
[13] Venables, J. A., Spiller, G.D., and Hanbucken, M., Rep. Prog. Phys. 47, 399 (1984); J. A. Venables, Philos. Mag. 27, 697 (1973); Phys. Rev. B 36, 4153 (1987).Google Scholar
[14] Blackman, J.A. and Wilding, A., Europhys. Lett. 16 (1), 115 (1991).Google Scholar
[15] Mulheran, P.A. and Blackman, J.A., Philos. Mag. Lett. 72, No. 1, 55 (1995).Google Scholar
[16] Blackman, J.A. and Mulheran, P.A., Phys. Rev. B 54, 11681 (1996).Google Scholar
[17] Mulheran, P.A. and Blackman, J.A., Surf. Sci. 376, 403 (1997).Google Scholar
[18] Family, F. and Meakin, P., Phys. Rev. Lett. 61, 428 (1988).Google Scholar
[19] Ratsch, C., Zangwill, A., Smilauer, P., and Vvedensky, D.D., Phys. Rev. Lett. 72, 3194 (1994).Google Scholar
[20] Amar, J.G., Family, F. and Lam, P.M., Phys. Rev. B 50, 8781 (1994).Google Scholar
[21] Amar, J.G. and Family, F., Phys. Rev. Lett. 74, 2066 (1995).Google Scholar
[22] Bartelt, M.C. and Evans, J.W., Surf. Sci. 344, 1193 (1995).Google Scholar
[23] Bartelt, M.C. and Evans, J.W., Phys. Rev. B 54, R17359 (1996).Google Scholar
[24] Amar, J.G. and Family, F., Thin Solid Films 272, 208 (1996).Google Scholar
[25] Bales, G.S. and Chrzan, D.C., Phys. Rev. B 50, 6057 (1994).Google Scholar
[26] Popescu, M. N., Amar, J. G. and Family, F., Phys. Rev. B 58, 1613 (1998)Google Scholar
[27] Gates, A. D. and Robins, J. L., Surf. Sci. 191, 499 (1987).Google Scholar
[28] Gates, A. D. and Robins, J. L., Surf. Sci. 116, 188 (1982).Google Scholar
[29] Gates, A. D. and Robins, J. L., Surf. Sci. 191, 492 (1987).Google Scholar
[30] Kallabis, H. and Wolf, D.E., e-print archive, cond-mat/9806140, and references thereinGoogle Scholar
[31] Smoluchowski, M. von, Z. Phys. Chem. 17, 557 (1916); ibid., 92, 129 (1917).Google Scholar
[32] Zinsmeister, G., Thin Solid Films,4, 363–386, (1969)Google Scholar