Adatom capture by arrays of two-dimensional Ag islands on Ag(100)

Abstract

We examine the capture of diffusing Ag adatoms by arrays of two-dimensional Ag islands subsequent to deposition on Ag(100) at room temperature. This is achieved by a combination of scanning tunneling microscopy experiments, kinetic Monte Carlo simulations, and diffusion equation analyses. The dependence of the capture rates on Ag-island size is shown to reflect larger island-free regions surrounding the larger islands, i.e., a strong correlation between island sizes and separations. This feature, and the influence of the local environment of the islands on capture, are elucidated by introducing suitable tessellations of the surface into "capture zones" for each island. We show that a Voronoi-type tessellation based on the distance from the island edges accurately reflects adatom capture. However, a tessellation exactly describing adatom capture is only obtained from a solution of the steady-state equation describing adatom deposition, diffusion, and capture by an array of islands distributed as in experiment. The stochastic nature of adatom capture is also quantified by analysis of the dependence on the deposition location of the probability for diffusing adatoms to be captured by a specific island. The experimental island size dependence of adatom capture is found to be entirely consistent with that obtained from a "canonical" model for the irreversible nucleation and growth of square islands. Disciplines Mathematics | Physical Chemistry CommentsThis article is from Physical Review B 59, no. 4 (1999) We examine the capture of diffusing Ag adatoms by arrays of two-dimensional Ag islands subsequent to deposition on Ag͑100͒ at room temperature. This is achieved by a combination of scanning tunneling microscopy experiments, kinetic Monte Carlo simulations, and diffusion equation analyses. The dependence of the capture rates on Ag-island size is shown to reflect larger island-free regions surrounding the larger islands, i.e., a strong correlation between island sizes and separations. This feature, and the influence of the local environment of the islands on capture, are elucidated by introducing suitable tessellations of the surface into ''capture zones'' for each island. We show that a Voronoi-type tessellation based on the distance from the island edges accurately reflects adatom capture. However, a tessellation exactly describing adatom capture is only obtained from a solution of the steady-state equation describing adatom deposition, diffusion, and capture by an array of islands distributed as in experiment. The stochastic nature of adatom capture is also quantified by analysis of the dependence on the deposition location of the probability for diffusing adatoms to be captured by a specific island. The experimental island size dependence of adatom capture is found to be entirely consistent with that obtained from a ''canonical'' model for the irreversible nucleation and growth of square islands.

Smoluchowski ripening of Ag islands on Ag(100)

“…31 Simulations appropriate for this scenario show that f 0 (x) has the characteristic monomodal form: It has a maximum value at xϭx max Ϸ1.1 of f 0 (x max )Ϸ0.78, decreasing to a minimum of about 0.30 at x decreases to xϷ0.02 ͑before increasing slightly at xϭ0), and a variance of 2 Ϸ0.24. 29 With this initial distribution, we find that the variance, (t) 2 , at first decreases slightly ͑to just below 0.2͒ before slowly increasing. However, we shall see below that experimentally observed minimum values for 2 are around 0.1, but with a large uncertainty ͑cf.…”

“…There have been extensive studies 2 of the initial shape of the size distribution, f (x,0)ϭ f 0 (x), produced by the nucleation and growth process, although its form was only recently understood. 28,29 Such distributions have a significant population of small islands ͑compared with the average size͒, 27 particularly for irreversible island formation, which applies for the Ag/Ag͑100͒ system at room temperature. 31 Separate theoretical studies of coarsening have demonstrated that a distinct shape, determined by the details of the coarsening process, is selected for long times.…”

“…͑In fact, the form produced by the nucleation and growth process has only been understood very recently. [27][28][29] ͒ Thus, we characterize the initial shape evolution in this paper. To this end, we find it instructive to consider the variance of the scaling function ͑as opposed to the dispersion of the size distribution considered previously, 15,16 the behavior of which is driven by the increase in the mean island size͒.…”

Nucleation, Growth, and Relaxation of Thin Films: Metal(100) Homoepitaxial Systems

“…20 This geometric interpretation of deviations from MFT is most directly confirmed by performing a standard Voronoi tessellation of the surface based on the island centers. [32][33][34] A Voronoi tessellation is simply a means of partitioning the surface into cells, such that points within a Voronoi cell (VC) associated with a given island are closer to the center of that island than to the centers of other islands. See Figure 4a.…”

“…23,24 See Figure 3c. Here, we use a value of ≈ 0.87 (i.e., s av ∼ θ 0.87 ) reflecting an enhanced tendency for saturation of the density of islands of finite extent, 34 N av ∼ θ/s av ∼ θ 0.13 , relative to "point islands" where 38 ≈ 2/3 (i.e., s av ∼ θ 0.66 ) and N av ∼ θ 1/3 . The experimental island size distribution, shown in Figure 3d, is roughly consistent with theory allowing that some smaller islands are necessarily lost due to coarsening before STM imaging (see section 4.3), or are not resolved.…”