Island nucleation and growth with attachment barriers

Island nucleation and growth play an important role in thin-film growth. One quantity of particular interest is the exponent χ which describes the dependence of the island-density N ~ (D/F)^−χ on the ratio of the monomer diffusion rate D to the deposition rate F. While scaling arguments lead to the standard prediction that χ = i/(i + 2), where i is the critical island-size, it has been predicted by Kandel that in the presence of strong barriers to the attachment of monomers to stable islands, a significantly larger value χ = 2i/(i + 3) may be observed. Here, we present the results of self-consistent rate-equation calculations for i = 1, 2, 3 and 6 and kinetic Monte Carlo simulations for i = 1 and 2 which we have carried out to test this prediction. For the case of barriers to both stable island growth and island nucleation our results for i = 1-3 indicate agreement with the Kandel prediction in the asymptotic limit of strong barriers and large D/F. However, in the absence of nucleation barriers, we find that for i > 1, the asymptotic value of χ is significantly lower – although still larger than the standard prediction. A scaling argument is presented which may explain these results.