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We quantitatively investigate the size-dependent optical properties of colloidal PbS nanocrystals or quantum dots (Qdots) by combining-the Qdot absorbance spectra with detailed elemental analysis of the Qdot suspensions. At high energies, the molar extinction coefficient epsilon increases With the Not volume d(3) and agrees with theoretical calculations using the Maxwell-Garnett effective medium theory and bulk values for the Qdot dielectric function. This demonstrates that quantum confinement has no influence on E in this spectral range, and it provides an accurate method to calculate the Qdot concentration. Around the band gap, epsilon only increases with d(1.3), and values are comparable to the epsilon of PbSe Qdots. The data are related to the oscillator strength f(if) of the band gap transition and results agree well with theoretical tight-binding calculations, predicting a linear dependence of f(if) on d. For both PbS and PbSe Qdots, the exciton lifetime tau is calculated from f(if). We find values ranging between 1 and 3 mu s, in agreement with experimental literature data from time-resolved luminescence spectroscopy. Our results provide a thorough general framework to calculate and understand the optical properties of suspended colloidal quantum dots. Most importantly, it highlights the significance of the local field factor in these systems

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One of the important factors limiting solar-cell efficiency is that incident photons generate one electron-hole pair, irrespective of the photon energy. Any excess photon energy is lost as heat. The possible generation of multiple charge carriers per photon (carrier multiplication) is therefore of great interest for future solar cells 1 . Carrier multiplication is known to occur in bulk semiconductors, but has been thought to be enhanced significantly in nanocrystalline materials such as quantum dots, owing to their discrete energy levels and enhanced Coulomb interactions 1-3 . Contrary to this expectation, we demonstrate here that, for a given photon energy, carrier multiplication occurs more efficiently in bulk PbS and PbSe than in quantum dots of the same materials. Measured carriermultiplication efficiencies in bulk materials are reproduced quantitatively using tight-binding calculations, which indicate that the reduced carrier-multiplication efficiency in quantum dots can be ascribed to the reduced density of states in these structures.Carrier multiplication is the process in which the absorption of a single, high-energy photon results in the generation of two or more electron-hole pairs. The excess energy of the initially excited electron is used to excite a second electron over the bandgap, rather than being converted into heat through sequential phonon emission. Carrier multiplication is important for the operation for high-speed electronic devices 4 , but is especially relevant for solar cells 1 , because relaxation of hot carriers through phonon emission is a common loss mechanism in bulk semiconductor solar cells. In this context, semiconductor quantum dots are promising building blocks for future solar cells 1 . In addition to the size-tunability of the quantum-dot optical properties, the carrier-multiplication efficiency in quantum dots was reported to be much higher than in bulk materials, where the process is generally referred to as impact ionization. It has been argued that carrier multiplication is more efficient in nanostructured semiconductors owing to quantum-confinement effects causing (1) a slowing of the phonon-mediated relaxation channel 1 and (2) enhanced Coulomb interactions 2 , resulting from forced overlap between wavefunctions and reduced dielectric screening at the quantum-dot surface 3 . In recent years, several femtosecond spectroscopy studies have revealed highly efficient carrier multiplication in PbSe and PbS (refs 2, 5-9) (refs 18, 19) quantum dots. In initial studies, carrier-multiplication efficiencies may have been overestimated owing to several experimental complications, including too high excitation fluences (generating multiple carriers by sequential absorption of multiple photons), lack of stirring of quantum-dot suspensions (causing photo-induced charging) and sample-to-sample variability 19 . Furthermore, recent tight-binding calculations 20 suggest carrier multiplication in quantum dots is not only not enhanced relative to bulk, but is actually lower. Answering the...

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