Determining the Absorption Bandgap Inhomogeneity of PbSe Quantum Dots

Quantum Dots
Fig. 1. (a) GISAXS image obtained on an ensemble of PbSe nanoparticles dispersed on SiO2 support. The arrows indicate scattering from nanosized objects. (b) After optical excitation, 2-D spectra show transient changes in sample transmission as a function of both excitation and detection frequencies. The 2-D spectrum shows contours like a topographic map. The solid contours are at 10% intervals of the maximum positive signal (green to red fill colors). Dashed 10% contours show negative signals (blue fill colors). The dotted black line is the diagonal, with equal excitation and detection frequencies. The nodal line that separates positive and negative is shown in pink. The slope of the nodal line determines the optical bandgap inhomogeneity, which is important for many applications of quantum dots. Adapted with permission from S. D. Park et al., Nano Lett. 17, 762−771 (2017). Copyright 2017 American Chemical Society.

Scientists using the U.S. Department of Energy’s Advanced Photon Source (APS) have developed a novel means of determining the absorption bandgap inhomogeneity of colloidal lead selenide (PbSe) quantum dots (QDs) using femtosecond two-dimensional (2-D) Fourier transform spectroscopy. The simple analysis promises to be applicable to solutions and arrays of many other quantum-confined materials as well.

For instance, due to their size-tunable optical and electronic properties, quantum-confined semiconductor nanocrystals have shown great potential in many emerging optoelectronic applications including light-emitting diodes, lasers, solar cells, and photodetectors. However, these and other applications require very stringent control over the line width of the first exciton (electron-hole) transition of the QDs.

Line width broadening has contributions from dynamic broadening mechanisms arising within each nanocrystal and static inhomogeneous broadening arising from differences between nanocrystals in an ensemble, such as size and shape dispersion. These two broadening mechanisms have different impacts on transport in nanocrystal arrays. In particular, it is the energetic disorder from the static inhomogeneity of the first quantum-confined exciton bandgap that must be tightly controlled for optimal transport.

Initial attempts to compare the absorption bandgap inhomogeneity of the QDs obtained from 2-D spectroscopy to the value calculated from the size and shape distribution of the QDs led to inconsistencies when standard methods based on transmission electron microscopy (TEM) were used to determine the sizes and shapes. The researchers from the University of Colorado, Boulder, and Argonne National Laboratory resolved the conflicts in part by using new 2-D histograms that correlate major and minor TEM image projections, revealing the elongated structure of the nanocrystals, a result that was supported by measurements using high-resolution TEM and grazing incidence small-angle x-ray scattering (GISAXS), the latter at X-ray Science Division beamline 12-ID-C of the APS, an Office of Science user facility at Argonne. Because the bandgap inhomogeneity calculated from the size and shape distribution didn’t include impacts from surface effects, but that measured from 2-D spectroscopy did, the comparison revealed that no more than ~41-meV of the broadening came from surface contributions.

In 2-D spectroscopy, a sample is excited by light, and transient changes in its spectrum are measured as a function of two frequency dimensions. These 2-D spectra have positive signals from reduced ground state absorption, positive signals from excited state stimulated emission, and negative signals from excited state absorption. The researchers showed that the absorption bandgap inhomogeneity of the ensemble was robustly determined by the slope of the nodal line separating the positive and negative peaks in the 2-D spectrum around the bandgap transition (Fig. 1b). That is, it was shown that the slope of the nodal line provides a robust, single-parameter determination of the absorption bandgap inhomogeneity for the entire quantum dot ensemble, which was shown to reveal the dynamic absorption line shape as well.

This was the first application of 2-D spectroscopy to the determination of nanoparticle size distributions. Since the 2-D spectra indicated a new analysis of TEM images was needed, the researchers wanted to connect to an established determination of nanoparticle size and shape. Like 2-D spectroscopy, GISAXS would also probe more of the ensemble than the thousands of nanoparticles that could be analyzed by TEM. Using the GISAXS technique, a large area (100-mm × 0.55-mm strip) of the sample surface with many millions of nanoparticles could be probed. The GISAXS technique has the advantage of determining both the lateral size and the height of the nanoparticles. The analysis of the 2-D GISAXS images, as shown in Fig. 1a, revealed prolate particles with axes 4.4 nm and 3.4 nm long (within an accuracy of ± 0.2 nm), lying on the surface along their longer axis and validated the new TEM analysis techniques.  — Vic Comello

Source : Advanced Photon Source (APS)