Excitonic states in spherical layered quantum dots

Abstract

The properties of excitons formed in spherical quantum dots are studied using the k⋅p method within the Hartree approximation. The spherical quantum dots considered have a central core and several concentric layers of different semiconductor materials that are modeled as a succession of potential wells and barriers. The k⋅p Hamiltonian and the Coulomb equations for the electron–hole pair are solved using a self-consistent iterative method. The calculation of the spectrum of the empty quantum dot and the electron–hole pair is performed by means of a very accurate numerical approximation. It is found that the exciton binding energy as a function of the core radius of the quantum dot shows a strong non-linear behavior. In particular, for quantum dots with two potential wells, the binding energy presents a large steep change. This last behavior is explained in terms of the polarization charges at the interfaces between different materials and the matching conditions for the eigenfunctions.