  A variational model for epitaxially-strained thin films on rigid substrates
is derived both by {\Gamma}-convergence from a transition-layer setting, and by
relaxation from a sharp-interface description available in the literature for
regular configurations. The model is characterized by a configurational energy
that accounts for both the competing mechanisms responsible for the film shape.
On the one hand, the lattice mismatch between the film and the substrate
generate large stresses, and corrugations may be present because film atoms
move to release the elastic energy. On the other hand, flatter profiles may be
preferable to minimize the surface energy. Some first regularity results are
presented for energetically-optimal film profiles.
