Two-step Unconventional Protocol for Epitaxial Growth in One Dimension with Hindered Reactions

We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step (rather than the conventional one-step) growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of monomers to occupied sites. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, N₁ and N. We also calculate the gap length, capture zone, and island-size distributions. For all sets of barriers considered, we compare the results from this analytical model with those from kinetic Monte Carlo simulations. The behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol gives more control and understanding of the island formation mechanism by intrinsically separating the nucleation and aggregation processes into different times regimes. We discuss experimental implications