General Expression for the Size-Dependent Optical Properties of Quantum Dots.

While initial theories on quantum confinement in colloidal quantum dots (QDs) led to analytical band gap/size relations or sizing functions, numerical methods describe size quantization more accurately. However, because of the lack of reliable sizing functions, researchers fit experimental band gap/size data sets using models with redundant, physically meaningless parameters that break down upon extrapolation. Here, we propose a new sizing function based on a proportional correction for nonparabolic bands. Using known bulk parameters, we predict size quantization for groups IV, III-V, II-VI, and IV-VI and metal-halide perovskite semiconductors, including straightforward adaptations for negative-gap semiconductors and nonspherical QDs. Refinement with respect to experimental data is possible using the Bohr diameter as a fitting parameter, by which we show a statistically relevant difference in the band gap/size relation for wurtzite and zinc blende CdSe. The general sizing function proposed here unifies the QD size calibration and enables researchers to assess bulk semiconductor parameters and predict the size quantization in unexplored materials.

The Impact of Partial Carrier Confinement on Stimulated Emission in Strongly Confined Perovskite Nanocrystals.

Semiconductor lead halide perovskites are excellent candidates for realizing low threshold light amplification due to their tunable and highly efficient luminescence, ease of processing, and strong light-matter interactions. However, most studies on optical gain have addressed bulk films, nanowires, or nanocrystals that exhibit little or no size quantization. Here, we show by means of a multitude of optical spectroscopy methods that small CsPbBr3 nanocrystals (NCs) exhibit a progressive red shift of the band-edge transition upon addition of electron-hole pairs, at least one carrier of which occupies a 2-fold degenerate, delocalized state in agreement with strong confinement. We demonstrate that this combination results in a threshold for biexciton gain, well below the limit of one electron-hole pair on average per NC. On the other hand, both the luminescent lifetime and the optical Stark effect of 4.7 nm CsPbBr3 NCs indicate that the oscillator strength of the band-edge transition is considerably smaller than expected from the band-edge absorption. We assign this discrepancy to a mixed confinement regime, with one delocalized and one localized charge carrier, and show that the concomitant reduction of the oscillator strength for stimulated emission accounts for the surprisingly small material gain observed in small NCs. The conclusion of mixed confinement aligns with studies reporting small and large polarons for holes and electrons in lead halide perovskite nanocrystals, respectively, and creates opportunities for understanding multiexciton photophysics in confined perovskite materials.

Optical gain and lasing from bulk cadmium sulfide nanocrystals through bandgap renormalization.

Strongly confined colloidal quantum dots have been investigated for low-cost light emission and lasing for nearly two decades. However, known materials struggle to combine technologically relevant metrics of low-threshold and long inverted-state lifetime with a material gain coefficient fit to match cavity losses, particularly under electrical excitation. Here we show that bulk nanocrystals of CdS combine an exceptionally large material gain of 50,000 cm-1 with best-in-class gain thresholds below a single exciton per nanocrystal and 3 ns gain lifetimes not limited by non-radiative Auger processes. We quantitatively account for these findings by invoking a strong bandgap renormalization effect, unobserved in nanocrystals to date, to the best of our knowledge. Next, we demonstrate broadband amplified spontaneous emission and lasing under quasi-continuous-wave conditions. Our results highlight the prospects of bulk nanocrystals for lasing from solution-processable materials.

Cyan Emission in Two-Dimensional Colloidal Cs2CdCl4:Sb3+ Ruddlesden-Popper Phase Nanoplatelets.

Metal halide perovskites are one of the most investigated materials in optoelectronics, with their lead-based counterparts being renowned for their enhanced optoelectronic performance. The 3D CsPbX3 structure has set the standard with many studies currently attempting to substitute lead with other metals while retaining the properties of this material. This effort has led to the fabrication of metal halides with lower dimensionality, wherein particular 2D layered perovskite structures have captured attention as inspiration for the next generation of colloidal semiconductors. Here we report the synthesis of the Ruddlesden-Popper Cs2CdCl4:Sb3+ phase as colloidal nanoplatelets (NPs) using a facile hot injection approach under atmospheric conditions. Through strict adjustment of the synthesis parameters with emphasis on the ligand ratio, we obtained NPs with a relatively uniform size and good morphological control. The particles were characterized through transmission electron microscopy, synchrotron X-ray diffraction, and pair distribution function analysis. The spectroscopic characterization revealed most strikingly an intense cyan emission under UV excitation with a measured PLQY of ∼20%. The emission was attributed to the Sb3+-doping within the structure.