Surface integral determination of built-in electric fields and analysis of exciton binding energies in nitride-based quantum dots

We present a simple analytical approach to calculate the built-in strain-induced and spontaneous piezoelectric fields in nitride-based quantum dots (QDs) and then apply the method to describe the variation of exciton, biexciton and charged exciton energy with dot size in GaN/AlN QDs. We first present the piezoelectric potential in terms of a surface integral over the QD surface, and confirm that, due to the strong built-in electric field, the electrons are localised near the QD top and the holes are localised in the wetting layer just below the dot. The strong localisation and smaller dielectric constant results in much larger Coulomb interactions in GaN/AlN QDs than in typical InAs/GaAs QDs, with the interaction between two electrons, Jee, or two holes, Jhh, being about a factor of three larger. The electron–hole recombination energy is always blue shifted in the charged excitons, X− and X+, and the biexciton, and the blue shift increases with increasing dot height. We conclude that spectroscopic studies of the excitonic complexes should provide a useful probe of the structural and piezoelectric properties of GaN-based QDs.