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, truncated-cone, 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.