Using the density functional theory and the generalized gradient approximation, we calculated the atomic structure, the density of electronic states, and the optical absorption spectra of CdS quantum dots containing intrinsic defects — a cadmium vacancy VCd and an interstitial sulfur atom SI, and substitutional impurities — zinc and copper in place of the atom cadmium — ZnCd and CuCd, respectively. The calculations were performed for the Cd33S33 cluster corresponding to the so-called “magic” size of the quantum dot. This size has a minimum of dangling bonds at the surface and allows the using of such a cluster without the passivation. The structural relaxation during the formation of such defects and the distribution of the wave function of the state corresponding to the top of the valence band are analyzed in details. It has been shown that the cadmium vacancy forms local states in the band gap of CdS nanocrystals, and can serve as centers of radiative recombination. Other defects form energy levels in the depths of the valence band or near its top, but whose energy positions do not correspond to the band maxima in the experimental photoluminescence spectra of CdS quantum dots, both undoped and doped with zinc. The calculated optical absorption spectra demonstrate a strong peak in the region of fundamental absorption of CdS for a cluster containing a substitutional impurity of CuCd, in contrast to other systems where no such peaks are observed. In addition, the replacement of the cadmium atom with copper leads to a decrease in the number of chemical bonds to three and, accordingly, to the largest relaxation among the systems studied. This feature is caused by the crystal structure inhomogeneity of copper sulfide CuxS, which, depending on stoichiometry, can be either a semiconductor or a metal.
Size-dependent single-particle energy levels and interparticle Coulomb interactions in CdSe quantum dots measured by scanning tunneling spectroscopy
