Pattern formation and localized structures in monoatomic layer deposition

We study the nonlinear robust behaviors of a model for the deposition of a monolayer of molecules on a surface which takes into account the interactions of the adsorbed molecules. The transport properties of the model lead to non Fickian diffusion. It is shown that we have generically Turing structures coexisting with uniform concentrations and consequently localized structures through the pinning mechanism. The characteristic lengths are in the nanometer region in agreement with recent experiments.