Island sizes and capture zone areas in submonolayer deposition: Scaling and factorization of the joint probability distribution

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 23, 2002, Pages 1-12

  Evans, J W ^a   Bartelt, M C ^b  

^a IOWA STATE UNIVERSITY   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85038917103     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.235410     Document Type: Article

References (34)

1. S. Stoyanov and D. Kashchiev, Curr. Top. Mater. Sci. 7, 69 (1981);
2. J. A. Venables, Philos. Mag. 27, 693 (1973).
3. M. C. Bartelt and J. W. Evans, Phys. Rev. B 46, 12 675 (1992).
4. G. S. Bales and D. C. Chrzan, Phys. Rev. B 50, 6057 (1994).
5. The mean-field treatment does account for spatial correlations in the island distribution, specifically the low population of near-by pairs of islands. This feature reflects the depleted adatom density, and thus nucleation rate, near island edges, which constitute sinks for diffusing adatoms.
6. M. C. Bartelt and J. W. Evans, Phys. Rev. B 54, R17359 (1996).
7. J. A. Venables and D. J. Ball, Proc. R. Soc. London, Ser. A 322, 331 (1971).
8. P. A. Mulheran and J. A. Blackman, Phys. Rev. B 53, 10 261 (1996) inappropriately equates island size and CZ area distributions, and proposes that no scaling with θ occurs for irreversible island formation.
9. J. W. Evans and M. C. Bartelt, in Morphological Organization in Epitaxial Growth and Removal, edited by Z. Zhang and M. G. Lagally (World Scientific, Singapore, 1998), p. 50.
10. Note the typographic error in the (formula presented) equation. The general strategy of a rate equation approach for analyzing CZ areas was suggested by G. S. Bales at ACCG-10, 1996.
11. J. W. Evans and M. C. Bartelt, Phys. Rev. B 63, 235408 (2001).
12. P. A. Mulheran and D. A. Robbie, Europhys. Lett. 49, 617 (2000).
13. J. G. Amar, M. N. Popescu, and F. Family, Phys. Rev. Lett. 14, 3092 (2001).
14. M. N. Popescu, J. G. Amar, and F. Family, Phys. Rev. B 64, 205404 (2001).
15. M. C. Bartelt, A. K. Schmid, J. W. Evans, and R. Q. Hwang, Phys. Rev. Lett. 81, 1901 (1998);
16. M. C. Bartelt, C. R. Stoldt, C. J. Jenks, P. A. Thiel, and J. W. Evans, Phys. Rev. B 59, 3125 (1999).
17. M. C. Bartelt and J. W. Evans, Surf. Sci. 298, 421 (1993).
18. See alsoK. J. Caspersen, A. R. Layson, C. R. Stoldt, V. Fournee, P. A. Thiel, and J. W. Evans, Phys. Rev. B 65, 193407 (2002).
19. APFs treatment yields (formula presented) Here, (formula presented) is the inverse function of (formula presented) and (formula presented) for (formula presented) and (formula presented) for (formula presented)
20. J. W. Evans, J. B. Hannon, M. C. Bartelt, and G. L. Kellogg, Bull. Am. Phys. Soc. 45, 363 (2000).
21. Implicitly, in our formulation, we assume that existing CZ boundaries are not modified outside the CZ of the just nucleated island. This is exactly true for VCs and ECs, and likely a good approximation for DCs.
22. For notational simplicity, in this paper, we drop (formula presented) on these P’s appearing in Ref. 9.
23. Application of (formula presented) to (8) yields terms of the form (formula presented) (formula presented) thus generating “correction terms” (formula presented)
24. Equation (12) implies that (formula presented)
25. Note that (formula presented) for (formula presented) if (formula presented) and (formula presented) (Refs. 5 and 9).
26. This value of the integrand is (formula presented)
27. F. G. Gibou, C. Ratsch, M. F. Gyure, S. Chen, and R. E. Caflisch, Phys. Rev. B 63, 11 505 (2001).
28. Phys. Rev. BSeeC. Ratsch, M. F. Gyure, S. Chen, M. Kang, and D. D. Vvedensky, 61, R10 598 (2000);
29. Phys. Rev. BD. D. Vvedensky, 62, 15 435 (2000) for other relevant work of this group.
30. L. H. Tang, J. Phys. (Paris) 3, 935 (1993).
31. J. G. Amar and F. Family, Phys. Rev. Lett. 74, 2066 (1995);
32. H. Brune, Surf. Sci. Rep. 31, 121 (1998).
33. M. C. Bartelt and J. W. Evans, Surf. Sci. Lett. 314, L835 (1994).
34. In physical terms, islands of size s with CZ area A are created when CZs of just-nucleated islands overlap CZs of existing islands of size s with larger area of (formula presented) Suppose (formula presented) so (formula presented) The factor of (formula presented) is needed in (formula presented) since there are typically two initial (discrete) CZ areas (formula presented) which will produce a final (discrete) CZ area A.