Sub-single exciton optical gain threshold in colloidal semiconductor quantum wells with gradient alloy shelling

Colloidal semiconductor quantum wells have emerged as a promising material platform for use in solution-processable lasers. However, applications relying on their optical gain suffer from nonradiative Auger decay due to multi-excitonic nature of light amplification in II-VI semiconductor nanocrystals. Here, we show sub-single exciton level of optical gain threshold in specially engineered CdSe/CdS@CdZnS core/crown@gradient-alloyed shell quantum wells. This sub-single exciton ensemble-averaged gain threshold of (Ng)≈ 0.84 (per particle) resulting from impeded Auger recombination, along with a large absorption cross-section of quantum wells, enables us to observe the amplified spontaneous emission starting at an ultralow pump fluence of ~ 800 nJ cm−2, at least three-folds better than previously reported values among all colloidal nanocrystals. Finally, using these gradient shelled quantum wells, we demonstrate a vertical cavity surface-emitting laser operating at a low lasing threshold of 7.5 μJ cm−2. These results represent a significant step towards the realization of solution-processable electrically-driven colloidal lasers.


Supplementary Note 1: Synthesis of core/crown@gradient-alloyed shell CdSe/CdS x Zn x S colloidal quantum wells
Preparation of cadmium myristate: Cadmium myristate was prepared according to a previously reported recipe 1 . 1.23 g of cadmium nitrate tetrahydrate was dissolved in 40 mL of methanol and 3.13 g of sodium myristate was dissolved in 250 mL of methanol. When both the powders were completely dissolved, the solutions were mixed and stirred vigorously for 1 h.
Cadmium myristate was formed as a precipitate, which was then removed by centrifugation and washed by redispersing in methanol to remove any unreacted and/or excess precursors. After repeating the washing step for at least three times, the precipitated part was completely dried under vacuum overnight.
Synthesis of the 4ML thick CdSe core NPLs: We followed the recipe reported previously with slight modifications 1 . 170 mg of cadmium myristate, 12 mg of Se and 15 mL of ODE were loaded into a three-neck flask. After degassing the mixture for 1 h at room temperature, the solution was heated to 240 °C under argon atmosphere. When the solution turns bright orange (generally around 190-200 °C), 80 mg of cadmium acetate dihydrate was swiftly added to the reaction solution. After reaching 240 °C, the solution was cooled to room temperature and 0.5 mL of OA was injected. CdSe NPLs were precipitated by adding acetone and dispersed in hexane. Size-selective precipitation using centrifugation at different speeds was used if any additional sizes of NPLs were formed.

Preparation of anisotropic growth solution for CdS crown:
A previously reported procedure was followed with slight modifications 1 . For the preparation of cadmium precursor, 480 mg of cadmium acetate dihydrate, 340 μL of OA, and 2 mL of ODE were loaded in a beaker. The 3 solution was sonicated for 30 min at room temperature. Then, it was heated to 160 °C in ambient atmosphere under continuous stirring and alternating sonication until the formation of whitish color homogeneous gel. After the cadmium precursor was prepared, it was mixed with 3 mL of 0.1 M S-ODE stock solution and used for the CdS crown coating.
Synthesis of CdSe/CdS core/crown NPLs: A typical core-seeded synthesis method reported previously was used with slight modifications 1 . A portion of the 4 ML core synthesis in hexane and 15 mL of ODE were loaded in a three-neck flask. The solution was degassed at 100 °C for the complete removal of hexane. Then, the solution was heated to 240 °C under argon flow and a certain amount of anisotropic growth mixture for CdS crown was injected at the rate of 12 mL/h.
After obtaining the desired crown size by adjusting the injection amount, the resulting mixture was further annealed at 240 °C for 5 min. After that, the solution was cooled down to room temperature and the core/crown NPLs were precipitated using ethanol. The NPLs were cleaned three times with ethanol and methanol to remove any traces of unreacted precursors, which was crucial for the shell growth step using c-ALD. Lastly, they were then dispersed in hexane to be used for the shell deposition.

Synthesis of CdSe/CdS@Cd 1-x Zn x S core/crown@shell NPLs:
We used a modified procedure of our c-ALD recipe reported previously 2, 3 . 1 mL of core/crown NPL seeds in hexane (having first absorption peak at 514 nm) were kept for use such that 100 µL of these NPLs dissolved in ~3 mL hexane had an optical density of ~2 at 370 nm. For cation precursors we used 0.4 M cadmium nitrate tetrahydrate (Cd-nitrate) and 0.4 M zinc nitrate hexahydrate (Zn-nitrate) solutions in NMF. For sulfur precursor we used 40-48 wt% solution of ammonium sulfide in water. Specifically, for the first sulfur shell growth, we added 40 µL of ammonium sulfide in 4 mL NMF and under vigorous stirring added 1 mL of CdSe/CdS core/crown seeds, which we had 4 prepared separately. After 2 minutes of stirring when all the NPLs had entered the NMF phase from hexane, the reaction was stopped by quickly adding acetonitrile and excess toluene to precipitate the NPLs via centrifugation. This cleaning step was repeated once more by redispersing the NPLs in NMF and precipitating them using acetonitrile and excess toluene to remove any remaining sulfur precursor. Finally, the NPLs were dispersed in 4 mL of NMF for the next cation deposition step. Next, we added 1 mL of solution having a mixture of X% Cdnitrate and (100-X)% Zn-nitrate in NMF by volume for the cation step. The X (volume percentage of Cd precursor) value was varied as 50, 10, 5, 2, 1 and 1 from first to the sixth Cd 1- x Zn x S shell layers. The reaction was allowed to continue by stirring for at least 45 min in ambient atmosphere and under room light, after which the NPLs were precipitated out by adding acetonitrile and excess toluene for centrifugation. The cleaning step similar to the previous one was repeated once more to remove all excess precursors. The growth cycle of sulfur and cation where m z is the effective mass of electron (hole), V(z) is the potential arising from conduction (valence) band offsets, and Ψ(z) is the wave function of electron (hole). We assumed the even parity for the symmetry of first excited states and solved the TISE for > 0. Then, because of the symmetry, we reflected the obtained solution to < 0.
To solve the problem, we divided the right half of the potential well into five regions, as indicated in Supplementary Figure 1, and write the general solutions for each region: Region I, by assuming even symmetry:  Then, we solved the equations for electron (hole) by using the following boundary conditions: To do so, "A" assumed to be 1 for finding the general solution, and then it was obtained by applying the normalization condition: In our calculations, for the value of effective masses and band offsets, we used the data that are given in Supplementary References 3.

At the interface between Region I-II ( = ):
From ~96% where a close-packed solid film of CQWs is sandwiched between them. c, Schematic of vertically-pumped CQW-VCSEL wedge which provides a variable cavity length. To eliminate any residual excitation beam, we used a long-pass filter. The output laser beam was collected with a spectrometer.

Polarization measurements of output laser beam:
To characterize the polarization state of the laser emission, a linear polarizer was placed between the cavity output and spectrometer. By varying the angle of the polarizer, the signal was collected at the spectrometer. The luminescence intensity of the cavity is depicted as function of the detection angle in Figure S6, where the polarization factor was found to be 0.82.