Reaction–diffusion approach to nanostructure formation during thin-film deposition

Abstract

It is shown that coverage evolution during atomic deposition on a substrate may be described, on mesoscopic scales, by dynamic models of the reaction–diffusion type. Such models combine reaction terms representing adsorption–desorption and chemical processes and nonlinear diffusion terms which are of the Cahn-Hilliard type. This combination may lead, below a critical temperature, to the instability of uniform deposited layers. This instability leads to the formation of nanostructures which correspond to regular spatial variations in substrate coverage. Patterns’ wavelengths and symmetries are selected by the dynamics and not by variational arguments. For increasing coverage, one should observe, in layers with isotropic atomic diffusion, a succession of structures going from hexagonal arrays of high-coverage dots, to stripes and finally to hexagonal arrays of low-coverage dots. For anisotropic diffusion, stripes perpendicular to the high-mobility direction should be selected. The relevance of this approach to the study of deposited Al, Ti and TiN monolayers is discussed.