Excitons in spherical quantum dots revisited: analysis of colloidal nanocrystals

The problem of exciton states in spherical semiconductor quantum dots is revisited, employing the finite element method to numerically solve the system of differential equations for the center of mass and relative motion of the interacting electron-hole pair. This process is performed within the effective mass and parabolic bands approximations. The use of a finite confinement together with a parabolic description of the conduction and valence band profiles prevents the two equations from uncoupling. The allowed energies are reported as functions of the quantum dot radius. A comparison of theoretically determined fundamental photoluminescence peak energies with available experimental reports in the cases of CdS, CdSe and CdTe is presented and discussed, showing a good agreement between calculated and measured results.