Measuring surface diffusion from nucleation island densities

We present a critical view of the analysis of experimental island densities acquired as a function of temperature in terms of barriers and prefactors for tracer diffusion at surfaces. We investigate the achievable precision for methods ranging from simple application of scaling laws, via integration of mean-field rate equations within various approximations for the capture rates, to kinetic Monte Carlo simulations that account for the various island shapes realized on square and hexagonal lattices. The discussion of theoretical models will be accompanied by variable temperature STM data for the nucleation of Ag on a Pt~111! surface. We introduce experimental methods to test for dimer diffusion and dissociation, as well as for transient mobility of monomers. Density scaling is analyzed in the presence of post-deposition mobility and easy adatom attachment to islands and other monomers. From extended kinetic Monte Carlo simulations we establish density scaling for the various island shapes on square and hexagonal lattices for coverages up to percolation, which is particularly relevant for methods working in reciprocal space. @S0163-1829~99!01231-X#