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Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth

J. G. Amar·M. N. Popescu
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Abstract

Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett. {\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate analytically the asymptotic scaled capture-number distribution (CND) for one-dimensional irreversible submonolayer growth of point islands. The predicted asymptotic CND is in reasonably good agreement with kinetic Monte-Carlo (KMC) results and leads to a \textit{non-divergent asymptotic} scaled island-size distribution (ISD). We then show that a slight modification of our analytical form leads to an analytic expression for the asymptotic CND and a resulting asymptotic ISD which are in excellent agreement with KMC simulations. We also show that in the asymptotic limit the self-averaging property of the capture zones holds exactly while the asymptotic scaled gap distribution is equal to the scaled CND.

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J. G. Amar, M. N. Popescu. 2003-07-11. Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth. https://doi.org/10.1103/physrevb.69.033401

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