Study of island formation in epitaxially strained films on unbounded domains

Peter Bella (1) , Michael Goldman (1) , Barbara Zwicknagl (2)

1 MPI-MiS - Max Planck Institute for Mathematics in the Sciences
2 Instutute for Applied Mathematics [Bonn]

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.

Domaines: Equations aux dérivées partielles [math.AP]

Peter Bella, Michael Goldman, Barbara Zwicknagl. Study of island formation in epitaxially strained films on unbounded domains. Archive for Rational Mechanics and Analysis, 2015. ⟨hal-00947595v2⟩