Island nucleation inside a one-dimensional gap with hindered aggregation

Abstract

The island formation process inside a one-dimensional gap with length L is studied. In the model i + 1 monomers are required to form an stable island. The aggregation of monomers to the islands at the ends of the gap is hindered by an additional attachment barrier Ea which reduces the hopping rate of the monomers to the island. Depending on Ea there are different regimes: zero and weak barriers, large but finite barriers and infinite barriers. The probability of nucleation at position n inside a gap with length L, , and the nucleation rate ω are studied. Both, and ω, are calculated by using two different analytical methods: exact master equation for the time evolution of i + 1 monomers deposited simultaneously and mean field approximation. In all cases the results are compared with Kinetic Monte Carlo simulations to explore the range of applicability of both methods.