Methods of depositing a film on a substrate surface include surface mediated reactions in which a film is grown over one or more cycles of reactant adsorption and reaction. In one aspect, the method is characterized by the following operations: (a) exposing the substrate surface to a first reactant in vapor phase under conditions allowing the first reactant to adsorb onto the substrate surface; (b) exposing the substrate surface to a second reactant in vapor phase while the first reactant is adsorbed on the substrate surface; and (c) exposing the substrate surface to plasma to drive a reaction between the first and second reactants adsorbed on the substrate surface to form the film.