  We consider a variational model for the formation of islands in
heteroepitaxial growth on unbounded domains. We first derive the scaling
regimes of the minimal energy in terms of the volume of the film and the
amplitude of the crystallographic misfit. For small volumes, non-existence of
minimizers is then proven. This corresponds to the experimentally observed
wetting effect. On the other hand, we show the existence of minimizers for
large volumes. We finally study the asymptotic behavior of the optimal shapes.
