  he properties of excitons formed in spherical quantum dots are studied using the $\mathbf{k}\cdot\mathbf{p}$ 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 $\mathbf{k}\cdot\mathbf{p}$ 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 behaviour. In particular, for quantum dots with two potential wells, the binding energy presents a large steep change. This last behaviour is explained in terms of the polarization charges at the interfaces between different materials and the matching conditions for the eigenfunctions. 
Excitonic states in spherical layered quantum dots