  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.
