Self-Consistent Study of the Electronic Properties of a Single Exciton in Nanoscopic CdSe Quantum Dots

The electronic and excitonic properties of a single exciton confined in nanoscopic CdSe quantum dots with different geometries are investigated using a self-consistent Schrödinger-Poisson approach within the effective mass and Hartree approximations. Box, cylindrical, ellipsoidal, and square-based pyramidal quantum dots are considered, keeping their volume and cross-sectional area equal to isolate geometrical effects. The results show that increasing either the longitudinal (Lz) or transverse (L) dimension reduces the carrier confinement energies and produces a redshift of the exciton transition, with a stronger effect when the transverse dimensions are increased. The electron-hole Coulomb interaction decreases as the carrier wave functions become more spatially extended and remains strongly dependent on the quantum-dot geometry. Notably, the pyramidal structure exhibits the most pronounced geometry-dependent behavior, while the cylinder and ellipsoid show similar exciton transition energies because the energy associated with the strong confinement in the xy plane dominates over that associated with the weaker confinement along the z direction as the longitudinal parameter is increased. Similarly, the box and cylinder exhibit comparable exciton transition energies as the transverse parameter is increased. These results demonstrate that the shape and aspect ratio of nanoscopic quantum dots provide effective parameters for controlling their excitonic and optical properties.