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 ∼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.