Dielectric polarization in axially-symmetric nanostructures: A computational approach

A computational scheme to evaluate exactly the effects of the dielectric mismatch in semiconductor nanostructures with axial symmetry is presented. It is based on the numerical computation of the image charges induced by the carriers at the dielectric interface. Strategies enabling an efficient convergence in the calculation of the self-polarization potential are detailed. Illustrative calculations on exciton and image potential states properties of semiconductor nanorods reveal the need of the developed tool. We show that, contrary to spherical nanostructure geometries, the optical band gap of nanorods is blueshifted as the dielectric constant of the surrounding medium decreases. As for image potential states, we find a strongly anisotropic distribution of the surface electron density, which is a consequence of the variable curvature of the dielectric interface.