Bandgap Inhomogeneity of a PbSe Quantum Dot Ensemble from Two-Dimensional Spectroscopy and Comparison to Size Inhomogeneity from Electron Microscopy.

Femtosecond two-dimensional Fourier transform spectroscopy is used to determine the static bandgap inhomogeneity of a colloidal quantum dot ensemble. The excited states of quantum dots absorb light, so their absorptive two-dimensional (2D) spectra will typically have positive and negative peaks. It is shown that the absorption bandgap inhomogeneity is robustly determined by the slope of the nodal line separating positive and negative peaks in the 2D spectrum around the bandgap transition; this nodal line slope is independent of excited state parameters not known from the absorption and emission spectra. The absorption bandgap inhomogeneity is compared to a size and shape distribution determined by electron microscopy. The electron microscopy images are analyzed using new 2D histograms that correlate major and minor image projections to reveal elongated nanocrystals, a conclusion supported by grazing incidence small-angle X-ray scattering and high-resolution transmission electron microscopy. The absorption bandgap inhomogeneity quantitatively agrees with the bandgap variations calculated from the size and shape distribution, placing upper bounds on any surface contributions.