Calculus of Variations and Geometric Measure Theory

M. Goldman - B. Zwicknagl

Scaling law and reduced models for epitaxially strained crystalline films

created by goldman on 31 Oct 2012
modified on 29 Nov 2013


Accepted paper

Inserted: 31 oct 2012
Last Updated: 29 nov 2013

Journal: SIAM J. Math. Analysis
Year: 2013


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.