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

Abstract

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.

Distributional fixed-point equations for island nucleation in one dimension: The inverse problem

“…We note here that our f kM C results are similar to the nucleation probabilities for i = 1, 2 and 3 shown in a recent publication by González, Pimpinelli and Einstein [6].…”

“…Island nucleation and growth during submonolayer deposition is a topic of continuing research, with ongoing development of theoretical models to describe the scaling properties of the island sizes and spatial distribution [1]. Over the past two decades, the focus has tended to move from the problem of obtaining the correct form of the island size distribution (ISD) to finding the capture zone distribution (CZD) [2][3][4][5][6]. An island's capture zone is defined as the region on the substrate closer to that island than to any other.…”

“…An alternative approach, of the type we adopt here, treats the process using fragmentation equations. An island nucleation means the creation of a new capture zone and the size reduction of the zones that were previously occupying that region of the substrate; so the parent capture zones are fragmented to create the daughter capture zone [5,6,[9][10][11][12][13].…”

“…Aside from these analytical models, when looking only at the functional form of a simulated or experimentally obtained CZD in the scaling regime, the semi-empirical Gamma distribution function has been used frequently as * hrvojka.krcelic@strath.ac.uk † m.grinfeld@strath.ac.uk ‡ paul.mulheran@strath.ac.uk a fitting model, both in two [6,[14][15][16][17] and in one dimension [18]. Similarly, Einstein and Pimpinelli proposed a Generalized Wigner surmise [19] as a model function for the CZD, relating it back to a fragmentation process.…”

Tasas de difusión y de deposición en un modelo de epitaxia coloidal

“…Con tal fin se determinaron las tasas de difusión D y de deposición Ƒ en un modelo de suspensión coloidal bidimensional mediante el empleo de un modelo analítico basado en la ecuación de Fokker-Planck y el desarrollo de simulaciones de dinámica molecular (DM). El sistema planteado está motivado por el interés en el crecimiento controlado de estructuras unidimensionales que ha sido objeto de numerosos estudios recientes tanto desde la perspectiva teórica como experimental (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28) .…”