Templated‐Assembly of CsPbBr3 Perovskite Nanocrystals into 2D Photonic Supercrystals with Amplified Spontaneous Emission

Abstract Perovskite nanocrystals (NCs) have revolutionized optoelectronic devices because of their versatile optical properties. However, controlling and extending these functionalities often requires a light‐management strategy involving additional processing steps. Herein, we introduce a simple approach to shape perovskite nanocrystals (NC) into photonic architectures that provide light management by directly shaping the active material. Pre‐patterned polydimethylsiloxane (PDMS) templates are used for the template‐induced self‐assembly of 10 nm CsPbBr3 perovskite NC colloids into large area (1 cm2) 2D photonic crystals with tunable lattice spacing, ranging from 400 nm up to several microns. The photonic crystal arrangement facilitates efficient light coupling to the nanocrystal layer, thereby increasing the electric field intensity within the perovskite film. As a result, CsPbBr3 2D photonic crystals show amplified spontaneous emission (ASE) under lower optical excitation fluences in the near‐IR, in contrast to equivalent flat NC films prepared using the same colloidal ink. This improvement is attributed to the enhanced multi‐photon absorption caused by light trapping in the photonic crystal.


CsPbBr 3 nanocrystals synthesis and purification [1]
: The synthesis is performed by weighting 1 mmol Cs2CO3 and 3 mmol of PbBr2 powders and put it into a 20 mL glass bottle. Afterwards, 10 mL 1-octadecene, followed by 1.5 mL oleic acid and 1.5 mL oleylamine were added. The obtained reaction mixture was immediately put into a tip sonicator (SONOPULS HD 3100, BANDELIN) using a power of 30 W kept for 30 min.
Eventually, the obtained deep yellow reaction mixture was taken out of the tip sonicator and cooled down to room temperature by ambient atmosphere. Finally, the dispersion was centrifuged (Eppendorf Centrifuge 5810 R) at a speed of 6000 rpm for 15 min. The supernatant was discarded and the thus obtained precipitate was redispersed in 3 mL of hexane to obtain a very dense nanocube dispersion. For the purification following the synthesis, 25 ml hexane, 0.1 mL oleic acid and 0.1 mL oleylamine were added to 0.25 mL of the nanocube dispersion. This way, large aggregates of nanocubes formed during the synthesis are disassembled partly into separated nanocubes. This diluted dispersion is afterwards centrifuged two times and each time the precipitate is discarded. The first centrifugation is performed with a speed of 1000 rpm for 10 min and the second centrifugation with 12000 rpm for 10 min. Afterwards, 15 mL of the resulting dispersion was equally split into 10 centrifuge tubes and centrifuged (Eppendorf miniSpin plus) with 14000 rpm for 60 min. The supernatant was discarded for all tubes and the precipitate was dispersed in 0.1 mL hexane. The thus obtained 10 samples were merged to a 1 mL final sample which was used for the assembly of photonic crystals.

PDMS Mold Preparation:
Patterned molds of PDMS were obtained by the replication of silicon masters engraved with the original pattern. Composite PDMS molds were utilized in this work to obtain high fidelity replicas. [2] The silicon masters were functionalized with PFOTS (see materials) by vapor phase silanization using 10 l PFOTS in a sealed vessel. Upon complete evaporation after 30 minutes under vacuum, the excess of PFOTS on the silicon surface was removed by rinsing the master with abundant isopropanol and heating up to 130 ºC for 20 minutes. Briefly, a thin h-PDMS film was firstly used to replicate the nanostructure followed by drying for an hour and 60 °C curing for another hour. Then, a thick supporting soft-PDMS layer of around 5 mm of thickness is added to the h-PDMS to allow handling and to confer flexibility. Soft-PDMS was used by pouring a 10:1 mixture of prepolymer and curing agent. The mixture was previously mixed and degassed under vacuum in a desiccator to remove the trapped air to achieve homogeneous density. Finally, soft-PDMS was cured at 80 °C for 2 hours and the mold is gently detached from the master. The templates obtained by this procedure present the same dimensions of the original silicon masters. [3] The details of the available nanostructures are listed below.  Atomic Force Microscopy profile of the patterned surface of the PDMS mold was obtained with an Agilent 5100.

Suppression of the Coffee-Ring effect
The main challenge regarding pattern formation upon evaporation [4] is to overcome the formation of the so-called coffee-ring effect (CRE), [5] which is originated from the outwards flows that arise to replenish the evaporated solvent at the pinned liquid-air contact line. Such flows of solvent can carry most of the particles to the rim of the wetted area giving rise to an inhomogeneous distribution of material and producing uneven surfaces.
In this work, the self-assembly process has been optimized so no modifications of the surface chemistry are needed to overcome the coffee-ring effect. The inhomogeneous distribution of NCs that CRE could cause was counterbalanced by two facts: i) first by applying pressure on top of the PDMS mold immediately after drop casting. This way, the dispersion was homogeneously spread along the substrate since the beginning of the process. And ii) the infiltration of hexane into PDMS [6] provides an alternative drying route and therefore further preventing the formation of CRE during evaporation, keeping the initial distribution constant.

Finite Differences Time Domain (FDTD) simulations: Numerical calculations were
performed using Lumerical FDTD solutions (www.lumerical.com). A polarized plane wave source impinging at normal incidence to different NC clusters was modeled in a square unit cell with periodic boundaries. The refractive index and the dispersive extinction coefficient of CsPbBr3 are obtained from literature. [7] The glass substrate is set with a refractive index of nglass = 1.43.
For the Figure  For L=600 nm and a thickness of the residual layer of t= 300 nm the diffraction grating is coupled with an electric field waveguide order for λ~800 nm.

Relationship between absorption and intensity of the incident light:
The absorption per unit volume for monochromatic waves with frequency, can be calculated from: where E and D are the electric field and the electric displacement, respectively.
If we consider only dissipative processes in the expression for D, the first term involving describes a linear absorption. The even-order susceptibilities like, (2) , (4) etc, do not make a contribution to the dissipative processes in our case.
Therefore, the lowest-order non-linear absorption will be described by the imaginary part of (3) , which corresponds to two-photon absorption. From Eqs. (1) and (2) if we define I as the intensity of light and is defined as = | | 2 , it should be noted that the energy absorption in this non-linear absorption process is not linearly but quadratically dependent on the light intensity.

CsPbBr3 nanocrystals characterization
The NCs obtained by ligand-assisted ultrasonication are highly monodisperse with an average size of 10.7 nm. The colloidal dispersion was purified by centrifugation to obtain perovskite NC ink redispersed in hexane at a 100 mg/mL concentration. The perovskite NCs exhibited green photoluminescence (PL) with a maximum at 513 nm with a Gaussian FWHM of 21 nm.   Presence of excess ligands render the films more insulating and harder to image by SEM.
Therefore, it is important to remove the excess ligands from CsPbBr3 colloidal solution followed by concentration by centrifugation to obtain the photonic crystals shown in Photoluminescence obtained from a flat NC film under 800 nm excitation and fluence of 13mJ/cm -2 . No ASE was observed.