Abstract
A fully self-consistent rate-equation approach to irreversible submonolayer growth is presented. This approach explicitly takes into account the correlation between the size of an island and the corresponding average capture zone. It is shown that this leads to capture numbers which depend explicitly on the island-size, and excellent agreement with experimental and Monte Carlo results is found for this size-dependence. Consequently, the predictions for the island-size distributions are in very good agreement with Monte Carlo simulation results over the whole range of coverages in the pre-coalescence regime.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Tsao, J.Y. (1993) Material Fundamentals of Molecular Beam Epitaxy. Academic Press, Boston.
Stroscio, J.A., Pierce, D.T. and Dragoset, R.A. (1993) Homoepitaxial growth of iron and a real space view of reflection-high-energy-electron diffraction, Phys. Rev. Lett. 70, pp. 3615–3618; Stroscio, J.A. D.T. Pierce, D.T. (1994) Scaling of diffusion-mediated island growth in iron-on-iron homoepitaxy, Phys. Rev. B 49, pp. 8522-8525; Chambliss D.D. and Wilson, R.J. (1991) Relaxed diffusion limited aggregation of Ag on Au(111) observed by scanning tunneling microscopy, J. Vac. Sci. Technol. B 9, pp. 928-932; Chambliss D.D. and Johnson, K.E. (1994) Nucleation with a critical cluster size of zero; Submonolayer Fe inclusions in Cu(100) Phys. Rev. B 50, pp. 5012-5015; Tsui, P., Wellman, J., Uher, G. and Clarke, R. (1996) Morphology Transition and Layer-by-Layer Growth of Rh(111) Phys. Rev. Lett. 76, pp. 3164-3167.
Venables, J.A., Spiller, G.D. and Hanbücken, M. (1984) Nucleation and growth of thin films, Rep. Prog. Phys. 47, pp. 399–459; Venables, J.A. (1973) Rate equation approach to thin film nucleation kinetics, Phtios. Mag. 27, pp. 697-738; Venables, J.A. (1987) Nucleation calculations in a pair-binding model, Phys. Rev. B 36, pp. 4153-4162.
Zinsmeister, G. (1968) Theory of thin film condensation. Part B: solution of the simplified condensation equation, Thin Solid Films 2, pp. 497-; ibid 4, 363 (1969); Zinsmeister, G. (1971) Theory of thin film condensation. Part D: influence of a variable collision factor, Thin Solid Films 7, pp. 51-.
Amar, J.G. Family F. and Lam, P.M. (1994) Dynamic scaling of the island-size distribution and percolation in a model of submonolayer molecular-beam epitaxy, Phys. Rev. B 50, pp. 8781–8797; Amar J.G. and Family, F. (1995) Critical cluster size: Island morphology and size distribution in submonolayer epitaxial growth, Phys. Rev. Lett. 74, pp. 2066-2069; Amar J.G. and Family, F. (1996) Kinetics of submonolayer and multilayer epitaxial growth, Thin Solid Films 272, pp. 208-222.
Bartelt M.C. and Evans, J.W. (1992) Scaling analysis of diffusion-mediated island growth in surface-adsorption processes, Phys. Rev. B 46, pp. 12675–12687; Bartelt M.C. and Evans, J.W. (1994) Nucleation and growth in metal-on-metal homoepitaxy—rate equations, simulations and experiments, J. Vac. Sci. Tech. A 12, pp. 1800-1808.
Bales G.S. and Chrzan, D.C. (1994) Dynamics of irreversible island growth during submonolayer epitaxy, Phys. Rev. B 50, pp. 6057–6067.
Bales G.S. and Zangwill, A. (1997) Self-consistent rate theory of submonolayer homoepitaxy with attachment/detachment kinetics, Phys. Rev. B 55, pp. R1973–R1976; Popescu, M.N., Amar, J.G. and Family, F. (1998) Self-consistent rate-equation approach to transitions in critical island size in metal (100) and metal (111) homoepitaxy, Phys. Rev. B 58, pp. 1613-1619.
Bartelt M.C and Evans, J.W. (1996) Exact island-size distributions for submonolayer deposition: Influence of correlations between island size and separation, Phys. Rev. B 54, pp. 17359–17362 (1996).
Bartelt, M.C. Schmid, A.K. Evans, J.W. and Hwang, R.Q. (1998) Island size and environment dependence of adatom capture: Cu/Co islands on Ru(0001, Phys. Rev. Lett. 81, pp. 1901–1904.
Mulheran P.A. and Blackman, J.A. (1995) The origins of island size scaling in heterogeneous film growth, Philos. Mag. Lett. 72, pp. 55–60.
Blackman, J.A. and Mulheran, P.A. (1996) Scaling behavior in submonolayer film growth: A one-dimensional model, Phys. Rev. B 54, pp. 11681–11692; Mulheran, P.A. and Blackman, J.A. (1997) Simulation and theory of island growth on substrate steps, Surf. Sci. 376, pp. 403-410.
von Smoluchowski, M. (1916) Drei vorträgeüber diffusion Brownische bewegung und koagulation von koHoidteilchen, Z. Phys. Chem. 17, pp. 557–585; (1917) Versuch einer mathematischen theorie der koagulationskinetik kolloidaler 31ösungen ibid 92, pp. 129-168.
Blackman J.A. and Wilding, A. (1991) Scaling theory of island growth in thin films, Europhys. Lett. 16, pp. 115–120; Ratsch, C, Zangwill, A., Smilauer, P. and Vvedensky, D.D. (1994) Saturation and scaling of epitaxial island densities, Phys. Rev. Lett. 72, pp. 3194-3197.
Amar, J.G., Popescu, M.N. Family, F. (2001) Rate-equation approach to island capture zones and size distributions in epitaxial growth, Phys. Rev. Lett. 86, pp. 3092–3095; (2001) Self-consistent rate-equation approach to irreversible submonolayer growth in one dimension, Surf. Sci. 491, pp. 239-254.
Popescu, M.N., Amar, J.G. and Family, F. (2001) Rate-equation approach to island-size distributions and capture numbers in submonolayer irreversible growth, Phys. Rev. B 64, art. no. 205404.
The interpretation of the self-consistency conditions is one of the major differences between the one-and two-dimensional growth. Eq. (13) is identically satisfied in the case of one-dimensional growth, while Eq. (12) leads to corrections (due to spatial fluctuations) in the mean-field expression of the average capture number σav
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Popescu, M.N., Family, F., Amar, J.G. (2002). Capture-Numbers and Island Size-Distributions in Irreversible Homoepitaxial Growth: A Rate Equation Approach. In: Kotrla, M., Papanicolaou, N.I., Vvedensky, D.D., Wille, L.T. (eds) Atomistic Aspects of Epitaxial Growth. NATO Science Series, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0391-9_9
Download citation
DOI: https://doi.org/10.1007/978-94-010-0391-9_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0675-3
Online ISBN: 978-94-010-0391-9
eBook Packages: Springer Book Archive