Size-dependent extinction coefficients of PbS quantum dots.

We report here on a detailed study on PbS colloidal quantum dots. A characterization via X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM) allowed us to reliably determine the diameter and the shape of the nanocrystals. These data, together with second-derivative analysis of the absorption spectra, allowed us to determine the size dependence of seven transitions in the absorption spectrum; some of these transitions were identified on the basis of their normalized confinement energy. The size dependence of the first excitonic transition was best modeled by a four-band envelope approach which considers the anisotropy of the band edges (Andreev, A. D.; Lipovskii, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 15402-15404). The extinction coefficients were calculated using concentrations obtained from inductively coupled plasma atomic emission spectrometry (ICP-AES), and their size dependence was found to follow a power law with exponent equal to approximately 2.5. In contrast with what was expected from the effective mass approximation, the per particle absorption cross section of the lowest transition was found to be strongly dependent on the particle size.