Electroelastic fields for a piezoelectric threading dislocation in various growth orientations of gallium nitride

Linear piezoelectric formulations were employed to analytically evaluate the electroelastic fields generated by a single threading edge/screw dislocation in piezoelectric gallium nitride (GaN) thin film. All possible growth orientations, namely c-plane (polar), a- and m-planes (non-polar), and (112¯2)-plane (semi-polar) of GaN layers were considered for the analysis. Single piezoelectric threading edge and screw dislocations were also modeled by a commercial finite element analysis code, ABAQUS 6.14. The edge dislocation was modeled by invoking one-dimensional thermal strain analogy to effectively introduce an extra plane of atoms. The screw dislocation was modeled by creating a slip in opposite surfaces by applying opposite displacements of magnitude equal to half the Burgers vector parallel to the direction of the dislocation line. We also evaluated the Peach-Kohler force acting on a piezoelectric dislocation as well as the material force calculated by the J-integral. The effects of piezoelectricity and the line charge on electroelastic fields induced by a single dislocation were investigated for various growth orientations. We also evaluated the role of spontaneous polarization along c-direction in the presence of electroelastic fields generated by the dislocation. These results can be utilized in studying the influence of piezoelectric strains and electrical fields on the optoelectronic performance of GaN-based devices in the presence of dislocations. They can also be helpful in understanding the mechanics of misfit dislocations that form between the substrate and the film.