Exciton states and optical transitions in colloidal CdS quantum dots: Shape and dielectric mismatch effects

We present a theoretical investigation of electron-hole and exciton energy spectra as well as oscillator strengths of optical transitions in colloidal CdS quantum dots (QD's) with spherical and tetrahedral shape. The Coulomb potential energy of the electron-hole system is treated taking into account the dielectric mismatch at the QD boundaries. Calculation of electron-hole energy spectrum and Coulomb potential energy in tetrahedral QD's is carried out using the finite difference method. It is shown that the bulk Coulomb potential energy with the dielectric constant of QD leads to lower exciton energy levels as compared to the Coulomb potential, which includes electron-hole interaction and self-action energies. The Coulomb potential changes the electron-hole pair energies without dielectric confinement contributions in such a way that the exciton ground state becomes active for optical transitions in dipole approximation for both tetrahedral and spherical QD's while the lowest electron-hole pair energy level is active for tetrahedral and passive for spherical QD's. The exciton binding energy in both types of QD's is enhanced by a factor of 2 in the presence of the dielectric mismatch. It is proven that the inclusion of the real QD shape and dielectric mismatch is important not only for the quantitative analysis but also for the qualitative description of optical properties of colloidal CdS QD's.