  We investigate the equilibrium properties of arrays of coherent strained
islands in heteroepitaxial thin films of bidimensional materials. The model we
use takes into account only three essential ingredients : surface energies,
elastic energies of the film and of the substrate and interaction energies
between islands via the substrate. Using numerical simulations for a simple
Lennard-Jones solid, we can assess the validity of the analytical expressions
used to describe each of these contributions. A simple analytical expression is
obtained for the total energy of the system. Minimizing this energy, we show
that arrays of coherent islands can exist as stable configurations. Even in
this simple approach, the quantitative results turn out to be very sensitive to
some details of the surface energy.
