Analytical model to predict the dislocation at different interfaces in thin-film multilayer: Application to LED multi-quantum well (MQW)

Abstract

The analytical model to predict the density of misfit dislocations at different interfaces in a piezoelectric multilayer with two thin-film layers deposited on a thick substrate has been formulated considering the two-stage relaxation with the aim to generalize further for the multilayer system in future. Different lattice parameters of the film layers and the substrate give rise to high misfit strain. Misfit dislocation formation at the interface releases excessive misfit strain. The internal energy of the piezoelectric thin film at the critical thickness and after relaxation through ‘n’ number of misfit dislocations together with the energy of the misfit edge dislocation have been utilized to develop the formulation. This formulation has been used to estimate dislocation density at the interface of the gallium nitride film layer with various cases of misfit strains. It has rightly predicted higher dislocation density for higher misfit strain cases as well as for greater film thickness. It will be used to predict the dislocation densities at the gallium nitride–indium gallium nitride interface and the sapphire–gallium nitride interface of the LED device in future. The theoretical model developed in this work can be beneficial in estimating the optoelectronic performance of the LED devices correctly in the presence of defects. The model can also be helpful in developing strategies to reduce the dislocation density by accurately predicting them for the given misfit strain in the film.