  Thin film growth is investigated in two types of lattice gas models where
substrate and film particles are different, expressed by unequal interaction
energy parameters. The first is of solid-on-solid type, whereas the second type
incorporates desorption, diffusion in the gas phase above the film and
re-adsorption at the film (appropriate for growth in colloidal systems). The
difference between particle-substrate and particle-particle interactions plays
a central role for the evolution of the film morphology at intermediate times.
The models exhibit a dynamic layering transition which occurs at generally
lower substrate attraction strengths than the equilibrium layering transition.
A second, flattening transition is found where initial island growth transforms
to layer-by-layer growth at intermediate deposition times. Combined with the
known roughening behavior in such models for very large deposition times, we
present four global growth scenarios, charting out the possible types of
roughness evolution.
