Effects of short-range attachment barriers on island nucleation in irreversible growth

A variety of effects can lead to short-range attachment barriers in submonolayer growth. While it has been predicted that the exponent χ describing the dependence of the island density on deposition rate F crosses over from the diffusion-limited (DL) value i/(i+2) (where i is the critical island size) in the absence of a barrier to the attachment-limited (AL) value 2i/(i+3) for a strong attachment barrier, this prediction has not been confirmed. Furthermore the dependence of the effective value of χ on barrier strength and ratio R = D/F (where D is the monomer hopping rate) has not been studied. Here we present the results of kinetic Monte Carlo (KMC) simulations for the case of deposition on a 2D substrate and irreversible growth corresponding to i = 1. In particular, we have studied the case of a barrier to island nucleation and attachment as well as that of a barrier to island attachment only. In both cases the effective value of χ increases with increasing R to a peak value χ_pk(R_pk) larger than 1/3 before decreasing very slowly towards the DL value. In addition, both χ_pk and R_pk increase with increasing barrier strength. A self-consistent rate-equation approach is also presented and good agreement is found with our KMC simulations for all values of barrier strength and D/F.