Scaling law and reduced models for epitaxially strained crystalline films

Michael Goldman (1) , Barbara Zwicknagl (2)

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

A variational model for the epitaxial deposition of a film on a rigid substrate in the presence of a crystallographic misfit is studied. The scaling behavior of the minimal energy in terms of the volume of the film and the amplitude of the misfit is considered, and reduced models in the various regimes are derived by Gamma-convergence methods. Depending on the relation between the thickness of the film and the amplitude of the misfit, the surface or the elastic energy contribution dominate, and in the critical case the two contributions balance. In particular, the formation of islands is proven if the amplitude of the misfit is large compared to the volume of the film.

Mots clés: Epitaxial growth; scaling law; Gamma convergence; elasticity

Domaines: Equations aux dérivées partielles [math.AP]; Matériaux

Michael Goldman, Barbara Zwicknagl. Scaling law and reduced models for epitaxially strained crystalline films. SIAM Journal on Mathematical Analysis, 2014. ⟨hal-00747644v2⟩