Finite element modeling of dislocation in solids and its applications to the analysis of GaN nanostructures

Abstract Dislocation is a very important defect in solids and its mechanical behavior could be influenced by the surrounding environment such as surfaces or interfaces. This work introduces an easy and flexible model of implementing the screw dislocation in the finite element analysis, and it could be easily extended to incorporate the surface stress to refine the analysis of nanostructures. Applications to a complete analysis of dislocation dissipation by the image force in GaN nanorods are investigated in this work. Various shaped nanorods are studied, including top chopped nanorods that have not been studied in other literatures. This work demonstrates the dislocation is dissipated towards the free surfaces more effectively in the cap region of nanorods. This dislocation dissipation mechanism agrees well with the phenomena observed in the experiments carried out in this work. Image forces are compared for different shaped nanorods. It is proposed to incorporate surface stress into the current model to refine the stress calculation as it is crucial for nanostructures with dimensions less than 10 nm. This work could contribute to nanostructure design and provide guidance for the fabrication of dislocation-free nanostructures.