Effects of short-range attachment barriers on submonolayer growth

Abstract

A variety of effects can lead to short-range attachment barriers in thin-film growth. While it has been predicted that the exponent χ which describes the dependence of the island density N on deposition rate F in the submonolayer regime (where N∼Fχ) crosses over from the diffusion-limited value i/(i+2) (where i is the critical island size) in the absence of an attachment barrier to the attachment-limited 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 the barrier strength and ratio R=D/F (where D is the monomer hopping rate) has not been studied. Here we consider the effects of attachment barriers in irreversible growth (i=1) for both the case of a barrier to island nucleation and attachment as well as that of an island attachment barrier but no nucleation barrier. Our results indicate that in both cases the effective value of χ increases with increasing R to a maximum value χmax(Rmax) which depends on barrier strength before decreasing very slowly toward the diffusion-limited value. In addition, both χmax and Rmax increase as the barrier strength increases. The results of self-consistent rate-equation calculations are also presented and good agreement is found with our simulations. We also present a scaling analysis for the dependence of Rmax on the barrier strength for arbitrary critical island-size i and good agreement is found with our simulation results for the case in which there is both a nucleation barrier and a barrier to island attachment.