Limitations of the thermodynamic Gibbs-Thompson analysis of nanoisland decay

Abstract

The interpretation of island-within-island decay experiments is commonly based on a quasiequilibrium analysis with the island evaporation rate related to the inverse of its curvature, i.e., the Gibbs-Thompson chemical potential $\ensuremath{\mu}(r)$, where $r$ is the island size. However, it has been suggested that the quasiequilibrium analysis fails for sufficiently small island sizes because the distribution of atoms, with different coordination and detachment barriers at the island perimeter controls the evolution. With realistic Monte Carlo simulations that use calculated barriers for Ag(111), published in the literature and consistent with measured equilibrium island shapes, we have examined the island decay law. Deviations of the decay law of an adatom island from the expected quasiequilibrium analysis for the case of diffusion-limited kinetics are observed $N(t)={({N}_{0}\ensuremath{-}ct)}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}1$ (instead of the expected $\ensuremath{\alpha}\ensuremath{\approx}2∕3$). In addition, the decay of a corresponding vacancy island for the same island-within-island geometry (without a step edge barrier), which is expected to be the same as the adatom island decay (in the quasiequilibrium analysis) is found to be faster. This also signals independently the failure of the quasiequilibrium analysis.