Revision of single atom local density and capture number varying with coverage in uniform depletion approximation and its effect on coalescence and number of stable clusters

doi:10.1088/1674-1056/20/8/086803

Abstract In vapour deposition, single atoms (adatoms) on the substrate surface are the main source of growth. The change in its density plays a decisive role in the growth of thin films and quantum size islands. In the nucleation and cluster coalescence stages of vapour deposition, the growth of stable clusters occurs on the substrate surface covered by stable clusters. Nucleation occurs in the non-covered part, while the total area covered by stable clusters on the substrate surface will gradually increase. Carefully taking into account the coverage effect, a revised single atom density rate equation is given for the famous and widely used thin-film rate equation theory, but the work of solving the revised equation has not been done. In this paper, we solve the equation and obtain the single-atom density and capture number by using a uniform depletion approximation. We determine that the single atom density is much lower than that evaluated from the single atom density rate equation in the traditional rate equation theory when the stable cluster coverage fraction is large, and it goes down very fast with an increase in the coverage fraction. The revised equation gives a higher value for the 'average' capture number than the present equation. It also increases with increasing coverage. That makes the preparation of single crystalline thin film materials difficult and the size control of quantum size islands complicated. We also discuss the effect of the revision on coalescence and the number of stable clusters in vapour deposition.

Keywords: single atom density coverage uniform depletion approximation coalescence

Received: 01 December 2009
Revised: 14 March 2011
Accepted manuscript online:

PACS:	68.55.A-	(Nucleation and growth)
	68.43.Jk	(Diffusion of adsorbates, kinetics of coarsening and aggregation)
	81.15.Aa	(Theory and models of film growth)
	81.16.Rf	(Micro- and nanoscale pattern formation)

Fund: Project supported by the Natural Science Foundation of Fujian Province of China (Grant No. A0220001).

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Shao Qing-Yi(邵庆益) and Zhang Juan (张娟) Revision of single atom local density and capture number varying with coverage in uniform depletion approximation and its effect on coalescence and number of stable clusters 2011 Chin. Phys. B 20 086803

[1]	Zhang Z Y and Lagally M G 1997 Science 276 377
[2]	Aizenberg J, Black A J and Whitesides G M 1998 Nature 394 868
[3]	Brune H 1998 Sur. Sci. Rep. 31 121. In this paper, the sentences from the thirty-ninth to fourty-fourth line on page 137 reads: “The mean-field approach assumes that the mean density of monomers sufficiently far away from the island takes on a constant value, no matter what the local environment of the island looks like. The first consequence is that, although average island sizes are predicted correctly, as are island densities, the island size distributions are far from being realistic. As a second consequence, coalescence cannot be described very accurately.” This implies that present rate theory yields reliable results only for varTheta le varTheta_sat and for average quantities (see the sentence of the first and second lines on page 138).
[4]	Brune H, Bales G S, Jacobsen J, Boragno C and Kern K 1999 Phys. Rev. B 60 5991
[5]	Amar J G, Family F and Lam P M 1994 Phys. Rev. B 50 8781
[6]	Ratsch C, Zangwill A, vSmilauer P and Wedensky D D 1994 Phys. Rev. Lett. 72 3194
[7]	Venables J A, Spiller G D T and Hanbrm ddot ucken M 1984 Rep. Prog. Phys. 47 399
[8]	Reichelt K 1988 Vacuum 38 1083
[9]	Venables J A and Price G L 1975 Epitaxial Growth (New York: Academic) Part B, Chap. 4
[10]	Lewis B and Anderson J C 1978 Nucleation and Growth of Thin Films (New York: Academic)
[11]	Zinsmeister G 1966 Vacuum 16 529
[12]	Zinsmeister G 1968 Thin Solid Films 2 497
[13]	Zinsmeister G 1969 Thin Solid Films 4 363
[14]	Zinsmeister G 1970 Kristall. Tech. 5 207
[15]	Zinsmeister G 1971 Thin Solid Films 7 51
[16]	Shao Q Y, Fang R C, Wang G Z, Zhang Q F, Xu B X, Zhang G M, Zhao X Y, Liu W M, Wu J L and Xue Z Q 2000 Proceedings of the 5th Annual Joint Workshop on Modern Electronic Technology and Aapplications, School of Electronic & Electrical Engineering in Kyungpook National University, Korea and Department of Electronics in Peking University, China, November 9—12, Taegu, Korea pp. 193—196
[17]	Shao Q Y, Fang R C, Liao Y and Han S J 1999 Chin. Phys. 8 1509
[18]	Shao Q Y, Zhang Q F, Fang R C, Zhu K G, Xu B X, Liu W M, Zhao X Y, Wu J L and Xue Z Q 2001 Chin. Phys. 10 140
[19]	Shao Q Y, Fang R C, Wang G Z and Xue Z Q 2000 Prog. Cryst. Growth 40 221
[20]	Kashchiev D 1982 J. Chem. Phys. 76 5098
[21]	Venables J A 1973 Phil. Mag. 17 697
[22]	Venables J A 1987 Phys. Rev. B 36 4153
[23]	Lewis B 1970 Surf. Sci. 21 273
[24]	Lewis B 1970 Surf. Sci. 21 289
[25]	Stowell M J and Hutchinson T E 1971 Thin Solid Films 8 41
[26]	Stowell M J 1972 Phil. Mag. 26 349
[27]	Sigsbee R A 1971 J. Appl. Phys. 42 3904
[28]	Bales G S and Chrzan D C 1994 Phys. Rev. B 50 6057
[29]	Robins J L, Donohoe A J and Usher B F 1974 Jpn. J. Appl. Phys. Suppl. 21 559
[30]	Usher B F and Robins J L 1976 Thin Solid Films 32 195
[31]	Kyuno K and Ehrlich G 2000 Phys. Rev. Lett. 84 2658
[32]	Li G J, Wang Q, Li H T, Wang K and He J C 2008 Chin. Phys. B 17 3343
[33]	Zhang L, Li W and Wang S Q 2010 Chin. Phys. B 19 073601
[34]	Ke J H, Chen X S and Lin Z Q 2010 Chin. Phys. B 19 026802
[35]	Bartelt M C, Schmid A K, Evans J W and Hwang R Q 1998 Phys. Rev. Lett. 81 1901

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Revision of single atom local density and capture number varying with coverage in uniform depletion approximation and its effect on coalescence and number of stable clusters

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