  We study the relaxation to equilibrium of two dimensional islands containing
up to 20000 atoms by Kinetic Monte Carlo simulations. We find that the commonly
assumed relaxation mechanism - curvature-driven relaxation via atom diffusion -
cannot explain the results obtained at low temperatures, where the island edges
consist in large facets. Specifically, our simulations show that the exponent
characterizing the dependence of the equilibration time on the island size is
different at high and low temperatures, in contradiction with the above cited
assumptions. Instead, we propose that - at low temperatures - the relaxation is
limited by the nucleation of new atomic rows on the large facets : this allows
us to explain both the activation energy and the island size dependence of the
equilibration time.
