Rate-equation approach to island size distributions and capture numbers in submonolayer irreversible growth

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 20, 2001, Pages

  Popescu, Mihail N ^a   Family, Fereydoon ^a   Amar, Jacques G ^b  

^a EMORY UNIVERSITY   (United States)

^b UNIVERSITY OF TOLEDO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ANALYTIC METHOD; ARTICLE; CALCULATION; CORRELATION FUNCTION; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MONOLAYER CULTURE; PERCEPTION; PREDICTION; QUANTITATIVE ASSAY; SYSTEM ANALYSIS;

EID: 0035890536     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.205404     Document Type: Article

References (60)

1. J Y. Tsao, Material Fundamentals of Molecular Beam Epitaxy (World Scientific, Singapore, 1993).
2. Y W. Mo, J. Kleiner, M B. Webb, M G. Lagally, Phys. Rev. Lett.66, 1998 (1991).
3. J A. Stroscio, D T. Pierce, and R A. Dragoset, Phys. Rev. Lett.70, 3615 (1993)
4. J A. Stroscio and D T. Pierce, Phys. Rev. B49, 8522 (1994).
5. H J. Ernst, F. Fabre, and J. Lapujoulade, Phys. Rev. B46, 1929 (1992).
6. R Q. Hwang, J. Schroder, C. Gunther, and R J. Behm, Phys. Rev. Lett.67, 3279 (1991)
7. R Q. Hwang and R J. Behm, J. Vac. Sci. Technol. B10, 256 (1992).
8. W. Li, G. Vidali, and O. Biham, Phys. Rev. B48, 8336 (1993).
9. E. Kopatzki, S. Gunther, W. Nichtl-Pecher, and R J. Behm, Surf. Sci.284, 154 (1993).
10. G. Rosenfeld, R. Servaty, C. Teichert, B. Poelsema, and G. Comsa, Phys. Rev. Lett.71, 895 (1993).
11. J.-K. Zuo and J F. Wendelken, Phys. Rev. Lett.66, 2227 (1991)
12. Phys. Rev. Lett.J.-K. Zuo, J F. Wendelken, H. Durr, and C.-L. Liu, 72, 3064 (1994).
13. D D. Chambliss and R J. Wilson, J. Vac. Sci. Technol. B9, 928 (1991)
14. D D. Chambliss and K E. Johnson, Phys. Rev. B50, 5012 (1994).
15. Q. Jiang and G C. Wang, Surf. Sci.324, 357 (1995).
16. F. Tsui, J. Wellman, C. Uher, and R. Clarke, Phys. Rev. Lett.76, 3164 (1996).
17. T R. Linderoth, S. Horch, E. Laegsgaard, I. Stensgaard, and F. Besenbacher, Phys. Rev. Lett.78, 4978 (1997).
18. J A. Venables, G D. Spiller, and M. Hanbucken, Rep. Prog. Phys.47, 399 (1984)
19. J A. Venables, Philos. Mag.27, 697 (1973)
20. J A. VenablesPhys. Rev. B36, 4153 (1987).
21. F. Family and P. Meakin, Phys. Rev. Lett.61, 428 (1988).
22. J G. Amar and F. Family, Phys. Rev. Lett.74, 2066 (1995).
23. J G. Amar, F. Family, and P M. Lam, Phys. Rev. B50, 8781 (1994).
24. J G. Amar and F. Family, Thin Solid Films272, 208 (1996).
25. J G. Amar and F. Family, Surf. Sci.382, 170 (1997).
26. G S. Bales and D C. Chrzan, Phys. Rev. B50, 6057 (1994).
27. G S. Bales and A. Zangwill, Phys. Rev. B55, 1973 (1997).
28. J A. Blackman and A. Wilding, Europhys. Lett.16, 115 (1991).
29. P A. Mulheran and J A. Blackman, Philos. Mag. Lett.72, 55 (1995).
30. J A. Blackman and P A. Mulheran, Phys. Rev. B54, 11 681 (1996)
31. P A. Mulheran and J A. Blackman, Surf. Sci.376, 403 (1997).
32. P A. Mulheran and D A. Robbie, Europhys. Lett.49, 617 (2000).
33. C. Ratsch, A. Zangwill, P. Smilauer, and D D. Vvedensky, Phys. Rev. Lett.72, 3194 (1994).
34. M C. Bartelt and J W. Evans, Phys. Rev. B46, 12 675 (1992).
35. M C. Bartelt and J W. Evans, J. Vac. Sci. Technol. A12, 1800 (1994).
36. M C. Bartelt and J W. Evans, Surf. Sci.344, 1193 (1995).
37. M C. Bartelt and J W. Evans, Phys. Rev. B54, R17 359 (1996).
38. M C. Bartelt, A K. Schmid, J W. Evans, and R Q. Hwang, Phys. Rev. Lett.81, 1901 (1998).
39. J G. Amar, M N. Popescu, and F. Family, Surf. Sci.491, 239 (2001).
40. M N. Popescu, J G. Amar, and F. Family, Phys. Rev. B58, 1613 (1998).
41. J G. Amar, M N. Popescu, and F. Family, Phys. Rev. Lett.86, 3092 (2001).
42. M. von Smoluchowski, Z. Phys. Chem., Stoechiom. Verwandtschaftsl.17, 557 (1916)
43. Z. Phys. Chem., Stoechiom. Verwandtschaftsl.M. von Smoluchowski92, 129 (1917).
44. G. Zinsmeister, Thin Solid Films2, 497 (1968)
45. Thin Solid FilmsG. Zinsmeister4, 363 (1969)
46. Thin Solid FilmsG. Zinsmeister7, 51 (1971).
47. V. Halpern, J. Appl. Phys.40, 4627 (1969).
48. E M. Hendricks and M H. Ernst, J. Colloid Interface Sci.97, 176 (1984).
49. N V. Brilliantov and P L. Krapivsky, J. Phys. A24, 4787 (1991).
50. The exact term to account for the monomer-monomer collision rate in Eqs. (678) is (formula presented) that leads to a nonlinear diffusion equation which may be solved numerically (see Ref. 41). In order to obtain a linear equation the mean-field approximation (formula presented) is used (see also Ref. 20).
51. A K. Myers-Beaghton and D D. Vvedensky, Phys. Rev. B42, 5544 (1990).
52. M N. Popescu, J G. Amar, and F. Family (unpublished).
53. The A dependence of (formula presented) can be neglected because it is much smaller than that due to the terms depending on (formula presented)
54. P A. Mulheran and J A. Blackman, Phys. Rev. B53, 10 261 (1996)
55. Phys. Rev. BM C. Bartelt, C R. Stoldt, C J. Jenks, P A. Thiel, and J W. Evans, 59, 3125 (1999).
56. Coalescence effects (see Fig. 22) are also important starting at coverages around 0.18. While the KMC simulations naturally include coalescence, the rate equations do not include terms to account for such effects.
57. The condition (formula presented) is required by the definition of the average capture number along with the normalization of the island-size distribution function.
58. A decreasing value of (formula presented) with increasing coverage for irreversible growth of extended islands has been seen previously experimentally (Ref. 3) as well as in KMC simulations. (Ref. 16).
59. Summing Eq. (36) over all (formula presented), without any correction to ensure that the normalization condition (formula presented) is satisfied, one obtains (formula presented), where (formula presented) is the Heaviside step function. While this distribution satisfies the normalization condition (formula presented), it has very little resemblance to the correct Voronoi-area distribution and leads to a divergent average Voronoi area.
60. D D. Vvedensky, Phys. Rev. B62, 15 435 (2000).