Optical transitions in CdS semiconductor quantum dots (QDs) have been studied by the Monte Carlo method based on probability calculations of the time-dependent Schrodinger equation. It has been demonstrated that excited by a continuous-wave laser, an assembly of CdS QDs, whose radii range from 2 to 5 nm centered at 3.7 nm, shows an emission peak around 2.65 eV in the optical emission spectrum, which corresponds to optical transitions among degenerate sublevels close to the ground sublevels in the conduction and valence bands of a CdS QD having a radius of 3.7 nm. For resonant one-photon excitation, the emission peak is very sharp, while for resonant two-photon excitation, the emission peak becomes blueshifted and broadened. The inclusion of the nonradiative electron-phonon processes makes the two-photon excitation peak significantly sharper and shows a better agreement with experimental work, thus demonstrating the upconversion luminescence of the QDs required for many applications including bioimaging.
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