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

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 for nucleation and aggregation in one dimension: Accessing the interaction parameters

Through a one-dimensional colloidal model for epitaxial growth, we characterize the nucleation and aggregation processes occurring in a gap between adjacent islands. The timescales associated with deposition, diffusion, aggregation, and nucleation inside the gap are studied in terms of the parameters defining the interaction between colloidal particles. Numerical results from molecular-dynamics (MD) simulations are compared with analytical models and good agreement is found between both data sets. The results for the timescales are used to calculate the associated rates to generate kinetic Monte Carlo (KMC) simulations, which allow exploring larger systems and longer timescales in comparison with MD simulations. The KMC simulations reproduce the global behavior of the densities of islands and monomers as well as the gap length distribution between adjacent islands.

Island density scaling in reversible submonolayer growth with attachment barriers

Island nucleation and growth play an important role in thin-film growth. One quantity of particular interest is the exponent χ, which describes the dependence of the saturation island density N_{sat}∼(D_{h}/F)^{-χ} on the ratio D_{h}/F of the monomer hopping rate D_{h} to the deposition rate F. While standard rate equation (RE) theory predicts that χ=i/(i+2) (where i is the critical island size), more recently it has been predicted that in the presence of a strong barrier to the attachment of monomers to islands, a significantly larger value χ=2i/(i+3) may be observed. While this prediction has recently been tested using kinetic Monte Carlo simulations for the case of irreversible growth corresponding to i=1, it has not been tested for the case of reversible island growth corresponding to i>1. Here we present a mean-field self-consistent RE method which we have used to study the dependence of the effective value of χ on D_{h}/F and barrier-strength for i=1,2,3, and 6. Both the no-nucleation-barrier case in which there exists a barrier for monomers to attach to islands larger than the critical island size (but not to smaller islands) and the nucleation-barrier case in which there is a barrier for monomers to attach to islands of all sizes are studied. In all cases, we find that the existence of attachment barriers significantly increases the effective value of χ for a given barrier strength. In addition, for i=1 we find good agreement between our extrapolated asymptotic value of χ and the theoretical strong-barrier prediction both with and without a nucleation barrier. In contrast, for i>1 the value of χ is significantly larger in the presence of a nucleation barrier than in its absence. In particular, while an asymptotic analysis of our results for i>1 also leads to excellent agreement with the strong barrier prediction in the presence of a nucleation barrier, in the absence of a nucleation barrier the asymptotic values are significantly lower.

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.

Island size distribution with hindered aggregation

We study the effect of hindered aggregation on the island formation processes for a one-dimensional model of epitaxial growth with arbitrary nucleus size i. In the proposed model, the attachment of monomers to islands is hindered by an aggregation barrier, ε_{a}, which decreases the hopping rate of monomers to the islands. As ε_{a} increases, the system exhibits a crossover between two different regimes; namely, from diffusion-limited aggregation to attachment-limited aggregation. The island size distribution, P(s), is calculated for different values of ε_{a} by a self-consistent approach involving the nucleation and aggregation capture kernels. The results given by the analytical model are compared with those from kinetic Monte Carlo simulations, finding a close agreement between both sets of data for all considered values of i and ε_{a}. As the aggregation barrier increases, the spatial effect of fluctuations on the density of monomers can be neglected and P(s) smoothly approximates to the limit distribution P(s)=δ_{s,i+1}. In the crossover regime the system features a complex and rich behavior, which can be explained in terms of the characteristic timescales of different microscopic processes.