Size-Dependent Optical Properties of Colloidal PbS Quantum Dots

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 ε increases with the Qdot volume d³ 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 ε in this spectral range, and it provides an accurate method to calculate the Qdot concentration. Around the band gap, ε only increases with d^1.3, and values are comparable to the ε 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 τ is calculated from f_if. We find values ranging between 1 and 3 μs, 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.