A new method for calculation of island-size distribution in submonolayer epitaxial growth

Petrov, Petar; Miller, W.; Rehse, U.; Fornari, R.

doi:10.1016/j.apm.2010.09.010

Cited by 7 publications

(1 citation statement)

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“…Islands smaller than i + 1 are unstable, i.e., the monomers belonging to such islands can di↵use away with di↵usion constant D. For the sake of simplicity, we adopt the point island model, where the size of an island is just the number of monomers which have attached to it but all are on the same lattice site; for more information see Refs. [23,28,33,[41][42][43][44][45][46][47][48][49].…”

Section: Model Descriptionmentioning

confidence: 99%

Fragmentation approach to the point-island model with hindered aggregation: Accessing the barrier energy

2017

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We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length l_{a}. For l_{a}=0 the islands behave as perfect sinks while for l_{a}→∞ they behave as reflecting boundaries. For intermediate values of l_{a}, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and l_{a}. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and l_{a}). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of l_{a} and i=1, 2, and 3.

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