Island size distribution with hindered aggregation

A General Solution to the Continuum Rate Equation for Island-Size Distributions: Epitaxial Growth Kinetics and Scaling Analysis

The nucleation and growth of surface islands in the pre-coalescence stage has previously been studied by different methods, including the rate equation approach and kinetic Monte Carlo simulations. However, full understanding of island growth kinetics and the scaling properties of their size distributions is still lacking. Here, we investigate rate equations for the irreversible homogeneous growth of islands in the continuum limit, and derive a general island-size distribution whose shape is fully determined by the dynamics of the monomer concentration at a given size dependence of the capture coefficients. We show that the island-size distribution acquires the Family-Viscek scaling shape in the large time limit if the capture coefficients are linear in size for large enough islands. We obtain analytic solutions for the time-dependent monomer concentration, island density, average size and island-size distribution, which are valid for all times, and the analytic scaling function in the large time limit. These results can be used for modeling growth kinetics in a wide range of systems and shed more light on the general properties of the size distributions of different nano-objects.

Epitaxial growth in one dimension

The final structure and properties of layers grown by epitaxy techniques are determined in the very early stage of the process. This review describes one-dimensional models for epitaxial growth, emphasizing the basic theoretical concepts employed to analyze nucleation and aggregation phenomena in the submonolayer regime. The main findings regarding the evolution of quantities that define the properties of the system, such as monomer and island densities, and the associated island size, gap length, and capture zone distributions are discussed, as well as the analytical tools used to evaluate them. This review provides a concise overview of the most widely used algorithms for simulating growth processes, discusses relevant experimental results, and establishes connections with existing theoretical studies.

Colloidal model of two-step protocol for epitaxial growth in one dimension

We explore the application of a two-step growth protocol to a one-dimensional colloidal model. The evolution of the system is described in terms of the time-dependence of both monomer and island densities,N₁andN, while its structure is characterized by using distributions of the gap length, the capture zone, the inter-island distance, and the island length. Analytical results obtained from rate equations are compared with these from molecular dynamics simulations. Since the two-step growth protocol deals with nucleation and aggregation processes in two completely separated time regimes, it makes possible to gain better understanding and control on the island formation mechanism than the standard one-step protocol. The predicted features and advantages of the two-step process could be experimentally tested using deposition of colloidal spheres on pattern substrates.

Island Growth of Poly(chloro-p-xylylene) Coatings

Abstract

The evolution of the morphology of island poly(chloro-p-xylylene) films formed on silicon substrates by vapor deposition polymerization is investigated by atomic force microscopy. The dependences of the effective thickness of the island coating, the number density of polymer islands, and their average size on the surface coverage are studied. The maximal density of polymer islands and the surface coverage corresponding to the transition to the coalescence regime are estimated. Within the framework of the theory of dynamic scaling, the size distribution of islands and the size distribution of their “capture zones” are analyzed. It is shown that, at low degrees of filling of the substrate, before the coalescence of islands, these distributions are described by scaling functions corresponding to the model of reaction-limited aggregation. The size of the critical nucleus is estimated from the size distributions of the “capture zones” of polymer islands.

Two-step unconventional protocol for epitaxial growth in one dimension with hindered reactions

We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of the monomers to the occupied sites of the lattice. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, N_{1} and N. We also calculate the gap length, the capture zone and the island distributions. For all the sets of barriers considered, the results given by the proposed analytical model are compared with those from kinetic Monte Carlo simulations. We found that the behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol allows more control and understanding on the island formation mechanism because it intrinsically separates the nucleation and aggregation processes in different time regimes.