A higher-order extended finite element method for dislocation energetics in strained layers and epitaxial islands

This paper presents a higher-order method for modeling dislocations with the extended finite element method (XFEM). This method is applicable to complex geometries, interfaces with lattice mismatch strains, and both anisotropic and spatially non-uniform material properties. A numerical procedure for computing the J-integral around a dislocation core to determine the energy release rate for a virtual advance of the dislocation line is described. Several examples in three dimensions illustrate the applicability of this method to material interfaces and semiconductor heterostructures, specifically the computation of the energetics of systems of dislocations in SiGe islands deposited on pure Si substrates.