Physical origin of thickness-controlled sequential phase formation during reactive diffusion: Atomistic modeling

Abstract

Experimental studies of reactive diffusion during annealing of a film deposited on a substrate reveal that the phase formation proceeds either simultaneously or sequentially depending on the film thickness and that its time dependence exhibits a linear-to-parabolic time-dependence transition. This surprising behavior is investigated here theoretically at the atomistic scale via kinetic Monte Carlo simulations based on an Ising energetic model that preserves the main thermodynamic properties of the model system under study, namely, a $B$ substrate with an fcc structure on which a thicker or thinner $A$ film is deposited and annealed at a given temperature. We show that the phase growth linear time dependence is related neither to an interface effect nor to diffusion asymmetry but results from the first stage of phase formation in a local composition close to the phase stoichiometry, whereas the following parabolic time dependence is due to the need for atom transport before phase nucleation. In addition, the thickness-controlled sequential phase formation is attributed to the existence of an asymmetric interdiffusion profile that results, even in the case of symmetric diffusion kinetics, from the respective finite and semi-infinite nature of the film and of the substrate.