Electroelastic Fields for Piezoelectric Threading Dislocation

Defects such as dislocations and v-pits are common in the multiquantum well (MQW) region of the gallium nitride (GaN)-based LED and other electronic devices. Major sources of their formation can be attributed to the lattice mismatch between the film (GaN) and the substrate (sapphire). The misfit dislocations at the interface are formed to release the excessive strain in the film when the film reaches its critical thickness. These misfit dislocations can grow in the film and be converted to threading dislocations. Threading dislocations that are found in large numbers (in the order of 10⁹/cm²) can be formed due to internal defects in the film layers or the misfit dislocations at the interface. These threading dislocations in the multi-quantum well act as non-radiative recombination center, which drastically reduces the optoelectronic performance of the devices. Some of the threading dislocations (~40%) are immobile in the GaN film because of the absence of sufficient gliding force. V-pits are formed in the film at the tip of those threading dislocations which are immovable in the GaN-film.

Electroelastic field components of a single piezoelectric threading edge/screw dislocation have been evaluated numerically for the case of piezoelectric gallium nitride (GaN) thin film deposited on a sapphire substrate. All the growth orientations, the c-plane (polar) growth, the a-plane (non-polar) growth, m-plane (non-polar and semi-polar) growth for GaN layer have been considered. Integral formalism method developed by Barnett (1962) based on Stroh formalism has been utilized to calculate these electroelastic fields. The displacement, electric potential, in-plane and shear strains, electric fields, inplane and shear stresses and electric displacements have been calculated. Numerical investigation of the electroelastic field components of the v-pits in the gallium nitride film have also been carried out. Finally, the electroelastic field solutions for a v-pit at the tip of threading edge dislocation have been obtained by combining both solutions.

Critical thickness required to form the misfit dislocation at the interface of indium gallium nitride (InGaN) film deposited on the gallium nitride (GaN) has also been calculated considering the piezoelectric properties of the InGaN film. The role of individual piezoelectric constants, e₃₁, e₃₃ and e₁₅ on the critical thickness along with the charge of dislocation and the spontaneous polarization also have been investigated.

These results can be utilized to estimate the optoelectronic performance of the device in presence of threading dislocations as well as in performing discrete dislocation dynamics (DDD) simulation of interactions of dislocations in piezoelectric thin film such as gallium nitride (GaN).