Correlated island nucleation in layer-by-layer growth

Temporal correlations of nucleation events in layer-by-layer growth are studied by simulating a one dimensional model. In order to focus on fluctuations due to the nucleation process, deposition and diffusion are treated deterministically. The correlations decay algebraically with effective exponents depending on the order of the nucleations in a layer. The autocorrelation function of all nucleation events decays as t(-1.35) with time t. In spite of these correlations, the corresponding randomness in the growth process does not lead to a roughening of the surface. The reason is that stochastic nucleation implies only conserved current fluctuations.