Computing the equilibrium configuration of epitaxially strained crystalline films. (English) Zbl 1001.49017

Bonnetier, E.; Chambolle, A.

SIAM J. Appl. Math. 62, No. 4, 1093-1121 (2002).

Summary: We study a model for shape instabilities of heteroepitaxial crystalline films. Lattice misfits between the substrate and the film induce elastic stresses in the film, which adjusts the shape of its free surface to reduce its total energy, sum of an elastic and a surface energy. We give a precise framework that guarantees the existence of solutions to this variational problem. We show that equilibrium states can be approximated using a two-phase model for representing the surface energy. Numerical results, obtained via this approximation, are presented.

MSC:

49J45	Methods involving semicontinuity and convergence; relaxation
74N20	Dynamics of phase boundaries in solids

Keywords:

\(\Gamma\)-convergence; epitaxially stressed films; shape instabilities; morphological instabilities; stress driven rearrangement instabilities