  When thin films are grown on a substrate by chemical vapor deposition, the
evolution of the first deposited layers may be described, on mesoscopic scales,
by dynamical models of the reaction-diffusion type. For monoatomic layers, such
models describe the evolution of atomic coverage due to the combined effect of
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 triggers the formation of nanostructures corresponding
to regular spatial variations of substrate coverage. Patterns wavelengths and
symmetries are selected by dynamical variables and not by variational
arguments. According to the balance between reaction- and diffusion-induced
nonlinearities, a succession of self-assembled structures including hexagonal
arrays of dots, stripes and localized structures of various types may be
obtained. These structures may initiate different types of growth mechanisms,
including Volmer-Weber and Frank-Van der Merwe type of growth. The relevance of
this approach to the study of different types of deposited monolayers is
discussed.
