Beyond-Mean-Field Treatments of Island Formation during Submonolayer Deposition: Island Size Distributions for Large Cri
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Beyond-Mean-Field Treatments of Island Formation during Submonolayer Deposition: Island Size Distributions for Large Critical Sizes Maozhi Li1,3, Maria C. Bartelt4,*, and J.W. Evans2,3 1 Institute of Physical Research & Technology, 2Department of Mathematics, and 3 Ames Laboratory, Iowa State University, Ames Iowa 50011 4 Department of Chemistry and Materials Science, Lawrence Livermore National Laboratory, Livermore, California 94550 ABSTRACT Kinetic Monte Carlo (KMC) simulation of atomistic models reveals the failure of mean-field treatments of the island size distribution (ISD) for islands formed by homogeneous nucleation during submonolayer deposition on perfect surfaces. KMC also facilitates analysis of scaling properties of the ISD, although here some misperceptions persist which we attempt to clarify. However, KMC becomes inefficient for highly reversible island formation (e.g., for large values of a critical size, i, above which islands are stable) due to the high density of diffusing adatoms on the surface. This reduced efficiency is quantified here with results for CPU time versus i. This feature has motivated development of alternative beyond-mean-field coarse-grained approaches which should be more efficient for large i. We provide results for the ISD for a range of i = 1, 2, 3, and 6 using one such approach, a stochastic geometry-based simulation (GBS) strategy.
INTRODUCTION Island formation during deposition is of both fundamental and technological interest. Traditional mean-field (MF) rate equation approaches have been used effectively since the mid1960’s to analyze experimental island density behavior [1]. In the early 1990’s, Kinetic Monte Carlo (KMC) simulation of simple but realistic atomistic models revealed the failure of MF theory to predict island size distribution for homogeneous nucleation mediated by adatom diffusion [2,3]. One of the authors of this paper, Maria C. Bartelt*, in whose memory this Fall 2004 MRS Symposium is dedicated, was widely recognized not just for her role in this discovery of the breakdown of MF treatments, but also for numerous key contributions to the subsequent development of a beyond-mean-field understanding of island formation during deposition. Early treatments did recognize some subtle aspects of the island formation process, although not the origin of the above MF failure. It was quickly appreciated that island distribution was not spatially random, nearby pairs of islands being rare due to depletion of the adatom density (and thus nucleation rate) nearby existing islands [1]. This depletion effect was already incorporated into self-consistent MF analyses of island size dependence of “capture numbers”, which describe the propensity of an island to capture diffusing atoms [1,4]. The MF analysis assumed that the environment of an island is independent of size. We note that these capture numbers are the key input to the (inadequate) MF rate equations. It was also recognized long ago that aggregation can be described geometrically in terms of “capture zon
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