Quantum size effects on excitonic Coulomb and exchange energies in finite-barrier semiconductor quantum dots

The size dependence of the one-particle band gap and the Coulomb and exchange excitonic corrections of spherical quantum dots are calculated using the effective-mass approximation with finite confining potentials. Full analytical expressions are found for the three magnitudes, and it is shown that the Coulomb and exchange excitonic corrections are in good qualitative and quantitative agreement with available state-of-the-art calculations (for Si, GaAs, and CdSe) and experiments (for InP).