Capture numbers and island size distributions in models of submonolayer surface growth

Abstract

The capture numbers entering the rate equations (RE) for submonolayer film growth are determined from extensive kinetic Monte Carlo (KMC) simulations for simple representative growth models yielding point, compact, and fractal island morphologies. The full dependence of the capture numbers σs(Θ, Γ) on island size s, and on both the coverage Θ and the Γ = D/F ratio between the adatom diffusion coefficient D and deposition rate F is determined. Based on this information, the RE are solved to give the RE island size distribution (RE-ISD), as quantified by the number ns(Θ, Γ) of islands of size s per unit area. The RE-ISDs are shown to agree well with the corresponding KMC-ISDs for all island morphologies. For compact morphologies, however, this agreement is only present for coverages smaller than Θ ≃ 5% due to a significantly increased coalescence rate compared to fractal morphologies. As found earlier, the scaled KMC-ISDs nss 2 /Θ as a function of scaled island size x = s/s approach, for fixed Θ, a limiting curve f∞(x, Θ) for Γ → ∞. Our findings provide evidence that the limiting curve is independent of Θ for point islands, while the results for compact and fractal island morphologies indicate a dependence on Θ.

Competing growth processes induced by next-nearest-neighbor interactions: Effects on meandering wavelength and stiffness

“…These fractal fingers cease to grow; thereafter decreasing the meandering wavelength. This reasoning is confirmed by recent work on island size distributions in models of submonolayer surface growth [33]. The latter showed that fractal morphologies exhibit lower coalescence rate than compact ones caused by the fact that fingers of two approaching fractal islands typically first avoid each other, which subsequently leads to a screening effect and a slowing down of further growth of these fingers.…”

Submonolayer growth study using a solid-on-solid model for 2 × 1 reconstructed surfaces of diamond-like lattices

“…The island size distribution (ISD) in the aggregation regime for the case of irreversible growth is expected to follow the generalized scaling form [15,[35][36][37][38] (s/b s N). The form of the master function f(x) depends on the details of the kinetics.…”

“…The size of an island s is the total number of atoms in the island. Following the typical description of submonolayer growth [15,[35][36][37][38], we calculate the island size distribution N s and the island density ρ. N s is defined as the number of islands of size s. In general, it depends on the coverage θ. The length and width of an island is calculated by measuring the total number of bonds in the two horizontal directions along the perimeter of the island.…”

Analytic scaling function for island-size distributions

“…Of course, the results of Refs. [7,8,14,19,20] reveal only approximate size linearity of the capture rates and only for certain sizes, which is why our simplified model might not be suited to describe physical reality. However, in this model situation we are able to derive an explicit solution in the form of a modified Beta distribution.…”

“…N onanalytic ISD shapes have been obtained within the m ean-field approxim ation for the capture rates w here islands are considered isolated [6,15,16,22,23,28], This approach fails in the scaling lim it o f high adatom diffusivities because neigh boring islands always com pete for the diffusion flux [1][2][3][4], A nalyses o f tw o-dim ensional (2D) island growth based on the Voronoi tessellation for the mean capture zones [7,8] and direct KM C sim ulations [14,19,20] reveal the com m on feature o f the capture ra te s-a linear increase o f as w ith s at large enough s. The coefficient in this linear correlation is alm ost independent o f 0 for com pact islands but changes w ith increasing 0 for point and fractal islands [14], This property is distinctly different from the m ean-field situation and shows that larger islands have larger capture zones surrounding such islands and that the strength o f a given island to capture adatom s is roughly proportional to its surface area [7,14], A ccording to the current view [14], the REs can quantitatively reproduce the scaled ISDs but only w ith the correct self-consistent determ ination o f the capture rates crs( 0 ) . However, analytic scaling functions proposed previously, e.g., by A m ar and Fam ily for the ISDs [9] or Pim pinelli and Einstein for the distribution o f capture zones [21], are based on sem iem pirical considerations rather than direct solutions to the REs.…”