Effects of cluster diffusion on the island density and size distribution in submonolayer island growth

TL;DR

This study investigates how cluster diffusion influences island density and size distribution during submonolayer growth, revealing deviations from mean-field predictions and proposing a generalized scaling form for different diffusion regimes.

Contribution

It introduces a detailed model of cluster diffusion with power-law decay and compares results across various diffusion exponents, highlighting deviations from theoretical predictions.

Findings

For mu=1/2, the island-size distribution follows a power-law with a higher exponent than predicted.

The crossover island size scales with the average island size with an exponent higher than mean-field theory.

Scaling of the island-size distribution is limited for mu >= 1, especially at higher ratios of diffusion rate to deposition flux.

Abstract

The effects of cluster diffusion on the submonolayer island density and island-size distribution are studied for the case of irreversible growth of compact islands on a 2D substrate. In our model, we assume instantaneous coalescence of circular islands, while the cluster mobility is assumed to exhibit power-law decay as a function of island-size with exponent mu. Results are presented for mu = 1/2, 1, and 3/2 corresponding to cluster diffusion via Brownian motion, correlated evaporation-condensation, and edge-diffusion respectively, as well as for higher values including mu = 2,3, and 6. We also compare our results with those obtained in the limit of no cluster mobility corresponding to mu = infinity. In agreement with theoretical predictions of power-law behavior of the island-size distribution (ISD) for mu < 1, for mu = 1/2 we find Ns({\theta}) ~ s^{-\tau} (where Ns({\theta}) is the number of islands of size s at coverage {\theta}) up to a cross-over island-size S_c. However, the value of {\tau} obtained in our simulations is higher than the mean-field (MF) prediction {\tau} = (3 - mu)/2. Similarly, the value of the exponent {\zeta} corresponding to the dependence of S_c on the average island-size S (e.g. S_c ~ S^{\zeta}) is also significantly higher than the MF prediction {\zeta} = 2/(mu+1). A generalized scaling form for the ISD is also proposed for mu < 1, and using this form excellent scaling is found for mu = 1/2. However, for finite mu >= 1 neither the generalized scaling form nor the standard scaling form Ns({\theta}) = {\theta} /S^2 f(s/S) lead to scaling of the entire ISD for finite values of the ratio R of the monomer diffusion rate to deposition flux. Instead, the scaled ISD becomes more sharply peaked with increasing R and coverage. This is in contrast to models of epitaxial growth with limited cluster mobility for which good scaling occurs over a wide range of coverages.