Unravelling the ultrafast charge dynamics in PbS quantum dots through resonant Auger mapping of the sulfur K-edge

There is a great fundamental interest in charge dynamics of PbS quantum dots, as they are promising for application in photovoltaics and other optoelectronic devices. The ultrafast charge transport is intriguing, offering insight into the mechanism of electron tunneling processes within the material. In this study, we investigated the charge transfer times of PbS quantum dots of different sizes and non-quantized PbS reference materials by comparing the propensity of localized or delocalized decays of sulfur 1s core hole states excited by X-rays. We show that charge transfer times in PbS quantum dots decrease with excitation energy and are similar at high excitation energy for quantum dots and non-quantized PbS. However, at low excitation energies a distinct difference in charge transfer time is observed with the fastest charge transfer in non-quantized PbS and the slowest in the smallest quantum dots. Our observations can be explained by iodide ligands on the quantum dots creating a barrier for charge transfer, which reduces the probability of interparticle transfer at low excitation energies. The probability of intraparticle charge transfer is limited by the density of available states which we describe according to a wave function in a quantum well model. The stronger quantum confinement effect in smaller PbS quantum dots is manifested as longer charge transfer times relative to the larger quantum dots at low excitation energies.

XRD was recorded using a PANalytical XPert PRO diffractometer with Cu Kα radiation at room temperature.

Additional Details Regarding RAS maps:
The Pb 4f core level were recorded in parallel to the Auger signal in order to note any sample degradation visible through formation of metallic Pb 1 . The Pb 4f core level remained stable for most of the samples, except for the PbS 2 nm, where a metallic lead Pb 4f signal accumulates over time (about 3 %, Figure S8). As this amount is not significantly larger than previously reported for the 3 nm PbS-PbI2 QD sample 1 , we do not expect this to have a significant effect on the results. However, it is the only sample in the series that formed the metallic lead.
All spectra from the resonant maps were analyzed using least squares cure fitting in IGOR using the SPANCF macros. The Auger peaks were fitted to a Doniach-Šunjić 3 spectral line shape, while the Raman peaks were fitted to a Voigt line shape. The spectral background was fitted to a Shirley function. 4 This fitting model was acquired through iterations by changing parameters when necessary. As the goal is to fit the areas of the dispersing and constant kinetic energy features over the whole excitation energy range we used two peaks for the Raman (dispersing) features. The normal Auger spectrum taken far above threshold provided positions for the constant kinetic energy signals.
The position of first and second Raman peaks were adjusted to the best fit (at a selected photon energy, e.g. 2475 eV, where the feature was still intense, but not significantly overlapping with Auger peaks), and after the fit was achieved, they were set to a constant BE distance to each other which was used in fitting all PbS resonant maps. Their absolute BE position was moved by the photon energy step in spectrum-by-spectrum fitting. The evolutions of the fitting parameters are plotted in the Supporting information ( Figure S9). The small 3 P2,0 transition always had the same width and asymmetry parameters as the main 1 D2 transition.

Surface-volume ratio calculations
The surface to volume ratio was calculated according to: where 23 is the radius of QD.
The surface/bulk ratio was calculated as: where the radius for (8)8%*) is 23 + : 1 , where : 1 is the ionic radius of I -.

Supplementary Tables
Table S1 Fit parameters and calculated positions for exciton peak from absorption spectra, as well as the average size calculated from the width of three strongest peaks in XRD diffraction. The error of the size determined by XRD is the standard deviation of the calculation. The standard deviation of the absorption (σABS) is calculated from the Gaussian fit of the exciton peak. The exciton peak position plus/minus σABS is used to estimate the size distribution given in the main paper.  Binding energy is calibrated to external Au reference. Figure S3. Content of S 2p (red) and I 4d (blue) in relation to total amount of Pb in differently sized PbS samples. Figure S4. High resolution HAXPES spectra of the PbS samples: S1s, (left) O1s (middle), and C1s (right), calibrated against external gold reference mounted on the manipulator and normalized to S 1s (S 1s) and S 2s (O 1s and C 1s). Binding energy calibrated against external Au reference.