2003/07/11 by Jacques G. Amar, J. G. Amar, Mihail N. Popescu +1 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevb.69.033401
4 pages, 1 figure, submitted to Phys. Rev. B
arxiv created 2003/07/11 · openalex publication_date 2004/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a set of approximate evolution equations [J. G. Amar et al., Phys. Rev. Lett. 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 nondivergent asymptotic scaled island size distribution (ISD). We then show that a slight modification of our analytic form leads to analytical expressions 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 scaled average gap distribution is identical to the scaled CND and thus demonstrate that in this limit, the self-averaging property of the capture zones holds exactly.