On the elastic field and image force of dislocations in anisotropic solids and its application to GaN nanostructures

The determination of the elastic field and image force of dislocation in anisotropic media is a nontrivial problem. This work revisits Eshelby’s sextic anisotropic elasticity theory to obtain the stress field of a screw dislocation in an infinite anisotropic solid. The image force of a dislocation in an anisotropic nanowire is then derived by using the concept of ‘image dislocation’. Moreover, this work proposes to study the image force of nanorods by approximating the three-dimensional shape effect as a height-dependent shape function, which could be obtained through curve fitting of the finite element data. The analytical solution is applied to analyse image forces on different dislocations in GaN nanorods oriented along polar (c-axis) and nonpolar (a, m-axis) directions. The result shows the dislocation dissipation could be more effective in a-GaN but less in m-GaN by comparing with the standard growth of c-GaN. The approach developed in this work is applicable to other material systems. Therefore, it could contribute to a wide range of nanostructure design and fabrication for dislocation-free devices.