Fractalization of silicon islands at a coverage close to 0.5 monolayers Zeev Olami a , Yishay Manassen b, * , N. Ramesh Rao b , Rami Dana b a Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel b Department of Physics and the Ilse Katz Center for Nanometer Scale Science and Technology, Ben Gurion University, P.O. Box 653, Be’er Sheva 84105, Israel Received 23 January 2002; accepted for publication 8 August 2002 Abstract Fractal islands are normally observed when the growth is a result of many random coalescence events of small islandsoratomswiththegrowingcluster.Inthispaper,weshowthatfractalizationcanbeobservedalsoforgrowing islandsatacoveragewhichiscloseto0.5monolayers.ThiswasshownforaSi(111)surfacecoveredby0.53monolayer ofsilicon.ThisfractalizationisexplainedbythesimpleconservativeIsingmodel,wherethediffusionofasingleatomis simulated by a single spin flip. In this model, fractal islands are observed over a finite scaling range where smaller islandshaveadimensionof2andlargeronesarefractal.Thefractaldimensionandthescalingrangearedependenton thefraction(equivalenttocoverage) p ofspinup(ordown).Boththedimensionandrangeincreaseas p approaches0.5. We show that the growth of the clusters is in agreement with a classical t 0:33 law [Phys. Rev. B 34 (1986) 7845]. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Scanning tunneling microscopy; Growth; Monte Carlo simulations; Silicon; Dendritic and/or fractal surfaces 1. Introduction The diffusion of atoms or clusters and their coalescence may sometimes give ramified islands with distinct fractal dimension. These ramified fractal islands were investigated many times with scanning probe microscopy on different surfaces [2–6]. This normally happens when the growth of the islands happens according to the scenario de- scribedbythediffusionlimitedaggregation(DLA) and related models. In the past the possibility of getting domains of fractal structure in systems whereadynamicphaseseparationofamixtureof two phases occurs (Ostwald ripening) was dis- cussed. It was claimed that in the case where the two phases are comparable, the early stage mor- phology is fractal [7]. Ostwald ripening [8–10] is the non-equilibrium dynamicsofatwophasesystemafteraquenchto astateinwhichitisnolongeratequilibrium.The nucleation starts with a creation of small clusters and their on-going non-equilibrium dynamics is theissuewhichisunderconsideration.Thisisone oftheclassicalproblemsincondensedmatterphys- ics. If the coarsening is dominated by atomic dif- fusionbetweenislandsthedrivingforcetodomain * Corresponding author. Tel.: +972-7-6472-153; fax: +972-7- 6472-904. E-mail address: manassen@bgumail.bgu.ac.il (Y. Manas- sen). 0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0039-6028(02)02270-7 Surface Science 520 (2002) 35–42 www.elsevier.com/locate/susc