Derivation of built-in polarization potentials in nitride-based semiconductor quantum dots

We present a simple analytical approach for the calculation of the built-in strain-induced and spontaneous potentials in nitride-based semiconductor quantum dots. We derive the built-in potentials and electric fields in terms of volume or surface integrals. We describe using a number of simplifying assumptions the general properties of piezoelectric and spontaneous fields in GaN/AlN and InN/GaN quantum dots and obtain analytic solutions to the potential along and close to the axis of symmetry in spherical, cylindrical, cuboidal, truncatedcone, and ellipsoidal dots. We show that the potential distribution in a hexagonal quantum dot is well represented by that of an equivalent dot with circular symmetry. We demonstrate that the built-in electric fields in nitride dots can provide a strong additional lateral confinement for carriers localized in the dot. This additional lateral confinement strongly modifies the electronic structure and optical properties of nitride-based quantum dot structures.