Nanophotonic enhanced two-photon excited photoluminescence of perovskite quantum dots

All-inorganic CsPbBr3 perovskite colloidal quantum dots have recently emerged as promising material for a variety of optoelectronic applications, among others for multi-photon-pumped lasing. Nevertheless, high irradiance levels are generally required for such multi-photon processes. One strategy to enhance the multi-photon absorption is taking advantage of high local light intensities using photonic nanostructures. Here, we investigate two-photon-excited photoluminescence of CsPbBr3 perovskite quantum dots on a silicon photonic crystal slab. By systematic excitation of optical resonances using a pulsed near-infrared laser beam, we observe an enhancement of two-photon-pumped photoluminescence by more than one order of magnitude when comparing to using a bulk silicon film. Experimental and numerical analyses allow relating these findings to near-field enhancement effects on the nanostructured silicon surface. The results reveal a promising approach for significant decreasing the required irradiance levels for multi-photon processes being of advantage in applications like low-threshold lasing, biomedical imaging, lighting and solar energy.

All-inorganic perovskite lead halide semiconductors in the form of colloidal nanocrystals have recently caused a stir as an excellent class of materials for optoelectronic applications [1,2,3,4,5]. Their advantages range from extremely high photoluminescence efficiencies up to 90%, narrow and tunable emission spectra, facile solution deposition on arbitrary substrates, to the presence of surface-capping ligands for further electronic and optical adjustments. An additional feature of this material family stimulated developments in the field of multi-photon optics: Nanocrystals based on all-inorganic cesium lead bromide (CsPbBr3) perovskite colloidal quantum dots exhibit a large two-photon absorption cross section in the order of 2·10 5 GM [6,7,8,9], inspiring applications on low-threshold multi-photon pumped stimulated emission [6] and lasing [7,10]. However, multiphoton absorption involving virtual energy levels is generally weak compared to single photon processes and scaling in n-th order with excitation intensity, with n being the number of absorbed photons [11]. One strategy to enhance the interaction of light with absorbing and photoluminescent species is taking advantage of high local light intensities using metallic (plasmonic) or dielectric (photonic) nanostructures [12]. For instance, photon upconversion by triplet-triplet annihilation or using lanthanide-doped nanophosphors can be enhanced by plasmonic nanostructures [13,14,15,16], partly also in combination with photonic crystal structures [17]. While plasmonic nanostructures have to be carefully designed in order to avoid plasmonic absorption losses in the relevant spectral windows of the device, high refractive index dielectric photonic nanostructures enable reduced dissipative losses and large resonant enhancements [18,19]. Using twodimensional photonic crystal slabs, for instance, near-field enhancement effects can cause a significant boost of the (linear) photoluminescence emission from colloidal quantum dots [20,21].
As a consequence, such two-dimensional nanostructures have become a widely used platform in the field of biosensing and microscopy [22]. Here, the near-field enhancement originates from the excitation of leaky photonic crystal modes spatially overlapping with the emitters, which were directly attached to the nanostructured surface. This experimental configuration -with the propagation direction of light close to the normal of the photonic crystal slab (and not parallel like in many other photonic crystal applications) -very much resembles the current hot topic of dielectric metasurfaces [19].
In this study, we investigate the two-photon excited photoluminescence of CsPbBr3 perovskite quantum dots with 9.4 nm size interacting with the leaky modes of a silicon photonic crystal slab in hexagonal nanohole geometry with a lattice constant of 600 nm. For fabrication of the silicon nanostructures, we apply scalable techniques involving nanoimprint lithography and thin-film growth methods. CsPbBr3 perovskite quantum dots are synthesized by using a method developed by Kovalenko and co-workers [1,23], and deposited by drop-casting on the silicon nanostructures.
By tuning angle of incidence (0° -50°) and wavelength (900 -1000 nm) of a pulsed near-infrared laser beam we systematically excite resonance modes of the silicon photonic crystal slab. We measure the two-photon pumped photoluminescence of the CsPbBr3 quantum dots deposited on (i) the silicon photonic crystal slab and (ii) a bulk silicon film. Numerical simulations based on the finite element method relate enhanced photoluminescence in case of the photonic crystal slab to near-field enhancement effects on the nanostructured silicon surface. For our experiments on nanophotonically enhanced two-photon excited photoluminescence, we use a glass substrate coated by a silicon thin film with 115 nm thickness exhibiting hexagonally arranged cylindrical air holes, 600 nm lattice constant and 365 nm hole diameter radius. Details on the fabrication process based on nanoimprint lithography, physical vapor deposition of silicon, and thermal solid phase crystallization, allowing for nanopatterning of silicon layers on areas up to 5 × 5 cm 2 , are given in the Methods section as well as in references [24,25,26]. The upper part of Fig. 1a shows a scanning electron microscope image of the silicon nanohole array. White arrows indicate the two high symmetry directions of the hexagonal lattice,  -K and  -M. We recently demonstrated numerically and experimentally that such nanopatterned silicon layers form an excellent platform for nanophotonic enhancement of the linear one-photon excited photoluminescence of lead sulfide quantum dots [21]. The underlying mechanism is the systematic excitation of leaky modes of the nanopatterned silicon film by tuning wavelength and angle of incidence of the exciting beam [27]. These leaky modes can exhibit strongly increased electric field energy densities close to the nanostructure surface. Fluorescent species located within the leaky mode volume, i.e. attached to the surface of the nanostructures, show significantly enhanced emission in this case. The aim of the present study is to use such local field enhancement to increase the two-photon pumped photoluminescence of all-inorganic CsPbBr3 perovskite colloidal quantum dots. As two-photon absorption involving a virtual energy level scales quadratically with intensity, we expect the effect of local field enhancement on the photoluminescence being significantly larger than in the case of linear absorption. We coated the nanopatterned silicon layer by 9.4 nm size CsPbBr3 perovskite colloidal quantum dots by drop-casting from toluene solution (see Fig. 1a, lower part). The quantum dots were prepared by using hot-injection method. A Csoleate solution was injected into PbBr2 solution at 180℃. Figure 1b depicts the cross section of the sample, pointing out that the quantum dot containing layer fills up the holes of the photonic crystal structure and exhibits a thickness around 80 nm on planar areas of the sample. The variation of the thickness when measuring at different positions of the sample is around ±20 nm. Considering a 1-2 nm capping on the quantum dots this corresponds to about 7 monolayers and a concentration of about 5 to 6·10 12 cm -2 . (Please refer to the Methods Section for details on the concentration calculation.) A schematic drawing of the resulting sample geometry is shown in Fig. 1c (not to scale). A stripe of flat silicon at the edge of the sample serves as reference for the photoluminescence measurements. Hence, the bulk silicon film is placed on the same glass substrate, has the same thickness, and has experienced the same processing sequence during fabrication like the nanopatterned film, only the nanohole pattern is missing. Scanning electron microscopy images reveal that the drop-cast CsPbBr3 quantum dot coating is equivalent on both, nanopatterned and bulk, areas of the silicon film and no significant difference of density and thickness is observed (see Fig. S1 in Supporting Information).   Reflectance spectra are commonly used to investigate photonic band structures in periodically patterned media [27,28]. Sharp features in such spectra correspond to the excitation of leaky resonance modes. These leaky modes can couple to external light and can exhibit strong near-field enhancement effects close to the surface of the photonic nanostructures [20,26,21]. Figure 2a shows the experimentally measured reflectance of the silicon photonic crystal slab in hexagonal nanohole geometry with 600 nm lattice constant, coated by a CsPbBr3 quantum dot layer as depicted in the lower part of Fig. 1a, as function of wavelength and angle of incidence. The incident light was linearly polarized normally to the plane of incidence (TE-polarized) and the angle was tilted with respect to the -K direction of the hexagonal lattice up to 50°. In this limited range of incident angles, we do not expect strongly differing extensions of modes out of the photonic crystal plane for TE and TM modes. (The latter can have a larger out-of-plane extension particularly at grazing incidence.) Resonant features in reflectance changing their spectral position for varying incident angle are clearly visible at wavelengths larger than approximately 600 nm. While in near infrared the resonant features are well distinguishable, the density of features becomes higher towards shorter wavelengths. This can be explained by the high density of modes in the photonic band structure at higher energies (i.e. shorter wavelengths). For wavelengths even shorter than 600 nm the sharp angular dependent resonant features vanish and only a broad angularindependent feature remains. As the absorption coefficient of the silicon is already quite high in that spectral region the penetration depth of the light becomes small. For 508 nm, the wavelength of quantum dot emission, the penetration depths is below 1 µm and hence similar to the photonic crystal periodicity. Coherent effects involving many photonic crystal periods are therefore not expected, explaining the missing resonances in the reflectance spectrum. Figure 2b depicts the respective numerical results calculated using a time-harmonic finite-element Maxwell solver (JCMsuite [29]) with plane wave excitation corresponding to the direction of incidence, wavelength and polarization. We numerically describe the sample geometry as shown in Fig. 2d by a hexagonal unit cell consisting of a glass subspace (blue), a silicon nanohole-layer (dark grey), which is conformally covered with a CsPbBr3 quantum dot coating (green) with 80 nm thickness features clearly visible in the simulations, are less pronounced in the experimental data but still discernible and found at similar positions as in the simulations. We hence conclude that the experimental-numerical agreement justifies qualitative numerical predictions. In order to estimate the local near-fields, which are expected to affect the drop-cast CsPbBr3 quantum dots, we defined the quantity E+ describing the local electric field energy enhancement in the vicinity of the silicon nanostructure (Fig. 2c). E+ is determined by integrating the electric field energy density distribution ( ) over the volume of the CsPbBr3 quantum dot coating. The electric field energy density distribution is given by ( ) = The value of E+ can therefore be regarded as quantity for the linear intensity enhancement affecting the drop-cast CsPbBr3 quantum dots located on the silicon nanostructure.
Photonic crystal structures can affect the emission of quantum dots by several mechanisms [31,32]: (i) absorption enhancement of the exciting light, (ii) out-of-plane extraction enhancement of the emitted light, i.e. distinct directions with enhanced light emission [33,3], an effect often discussed in the context of light emitting diodes [3,3], and (iii) changes of the spontaneous emission rate (Purcell effect). In our experiment design, effect (ii) and (iii) are expected to play a minor role because of the above-mentioned high absorption of silicon at the emission wavelength (508 nm). The low penetration depth of light suppresses photonic band structure effects.
Mechanism (i), however, is relevant in our experiments as excitation takes place at near infrared wavelengths with low absorption in the silicon and a penetration depth much larger than the photonic crystal dimensions (dSi, =900nm ~ 50 µm). For more details on ruling out emission/extraction effects please also see Fig. S3 in the Supporting Information showing that the local field energy enhancement E+ does not reach values significantly larger than 1 in the range of the emission wavelength (508 nm). For our experiments, we regard the excitation regime ranging from about 900 nm to 1000 nm as most significant, as for wavelengths larger than 1000 nm the perovskite quantum dots do not evince two-photon-absorption and for wavelengths below 900 nm the absorption of the crystalline silicon becomes noticeable such that leaky mode induced effects like near-field enhancements start decreasing [26]. Therefore, the resonances crossing the excitation regime ranging from about 900 nm to 1000 nm are most relevant for our experiments, e.g. the above mentioned broad resonance starting at a wavelength of 1050 nm at normal incidence and proceeding to smaller wavelengths for larger angles.  The regenerative amplifier is seeded by a femtosecond oscillator (Tsunami, both Spectra Physics).
An example spectrum of the excitation beam from the optical parametric amplifier is shown in  Fig. 3a) even if the sample is rotated. As circumstantiated above and seen in Fig. 2a and Fig. S3, no extraction enhancement effect, i.e. distinct directions with enhanced light emission, is expected in the wavelength regime of photoluminescence around 508 nm. Therefore, we regard the photoluminescence emission of the CsPbBr3 quantum dots on planar and nanotextured silicon films as isotropic in the half space above the silicon surface. Figure 3c shows an example spectrum of the light collected from CsPbBr3 quantum dots on a nanotextured silicon film after excitation at 925 nm with a peak intensity of (17 ± 3) GW/cm 2 . A detailed description of the excitation fluence determination is given in the Methods Section. The photoluminescence peak arising from the CsPbBr3 quantum dots is clearly visible at center wavelength 508 nm with a FWHM of about 20 nm. In order to determine the intensity regime where the photoluminescence signal from the perovskite quantum dots predominantly arises from two-photon-absorption of the excitation laser beam we analyzed the intensity dependence of luminescence. Figure 3d shows the photoluminescence intensity as a function of the excitation laser intensity (exc = 925 nm) on a log-log scale. For peak intensities below 17 GW/cm 2 the slope of the curve is close to 2, i.e. we observe a nearly quadratic intensity dependency as expected for two-photon-absorption processes. The inset illustrates the respective energy level diagram. For higher excitation intensities, however, the photoluminescence increases sub-quadratically with intensity. This is an indication that Auger recombination processes start playing a role. Details on the fitting procedure and setting the upper intensity threshold are given in Fig. S5   We measured the intensity of the CsPbBr3 quantum dot photoluminescence for a fixed excitation fluence corresponding to an intensity of (17 ± 3) GW/cm 2 impinging the sample at normal incidence. The incident angle on the sample was varied from -20° to 50° with respect to the -K direction of the hexagonally nanopatterned silicon film, with 0° corresponding to normal incidence. Figure Figure 4b shows the example photoluminescence spectra of CsPbBr3 quantum dots located on a nanopatterned silicon film (green curve) and on a planar silicon film (black curve) for an excitation at 925 nm at an incident angle of +24°. In this case, we observe an enhancement of two-photon-pumped photoluminescence by a factor of 15 by using a nanopatterned instead of a planar substrate.
In order to explain the experimentally measured photoluminescence enhancements by placing the quantum dots onto a periodically nanostructured surface instead of using a planar substrate, we use the optical simulations as shown in Fig. 2. The two-photon-absorption experiment shown in Fig. 4a can qualitatively be compared to the averaged cut through the wavelength-and angledependent local field energy enhancement E+ map at a certain excitation wavelength with large FWHM (Fig. 2e and 2f). In experiment as well as in simulations, the excitation wavelength is kept fixed, while the angle of incidence is varied. As E+ is a linear measure for the intensity enhancement and the two-photon-absorption pumped photoluminescence depends quadratically on the intensity, absolute enhancement values are not comparable. However, the excitation conditions in terms of wavelength and incident angle for maximum photoluminescence can be predicted. The green circles shown in Fig. 4a depict the photoluminescence intensity at 925 nm excitation, which corresponds to the cut through the field energy enhancement map shown in Fig. 2e. Both, experimentally and numerically, a single peak is observed occurring at an incident angle of 24° (experiment) and 26° (simulation), respectively. Further, the blue squares shown in Fig. 4a, depicting the photoluminescence intensity at excitation with center wavelength 972 nm, qualitatively corresponds to the simulated cut through the electric field energy enhancement map shown in Fig. 2f. Here, the highest measured photoluminescence occurs at an incident angle of 14° while the simulated maximum near-field enhancement is calculated for 16°. Qualitative agreement is hence excellent and excitation conditions (angle of incidence and wavelength) yielding maximum two-photon-pumped photoluminescence can be effectively predicted by our numerical model. Regarding quantitative values, the experimentally measured enhancement factors are lower than the numerical prediction (15 versus 56) but in the same order of magnitude. Summing up, the interaction with leaky photonic modes of a two-dimensional photonic crystal slab can easily enhance two-photon pumped photoluminescence of perovskite quantum dots by more than one order of magnitude.
Photoluminescence intensities could eventually be further increased by specifically tuning of several experimental parameters: (1) A better match of the spectral widths of exciting beam and the photonic leaky mode, e.g. by the use of spectral filters or laser pulses with longer pulse duration and hence a narrower spectrum. (2) Choosing a resonance with strong near field enhancement and optimized spatial overlap of the 3D photonic mode distribution with the CsPbBr3 quantum dots.
Due to the huge parameter space and the high-dimensional output such an optimization task is challenging. A part of the authors recently introduced a machine learning method based on clustering paving the way for such a qualitative design optimization [36]. (3) The use of tailored defect structures in the periodic photonic nanostructure potentially yielding extremely large intensity enhancements [28].
The simplicity and the robustness of the approach makes it an appealing option in many fields of applications. For instance, two-photon absorption processes play a crucial role in advanced biomedical photonics. Photon-upconversion, lanthanide-doped nanoparticles that emit short-wavelength light under near-infrared excitation enable nearly total elimination of autofluorescence and light scattering of the surrounding matrix. Avoidance of this optical background permits a potentially unprecedented sensitivity [3,3,3]. Decreasing the required illumination intensities by the use of nanophotonic structures as described in the present paper might enhance the resolution even further. Additional potential application fields involve low-threshold lasing, bioimaging and biosensing. The choice of an unsophisticated technological platform enabling large-area fabrication opens further possibilities in the solar energy sector. Multi-photon processes enable the shaping of the solar spectrum by up-and down-conversion paving the way to overcome the wellknown limit of single-junction photovoltaic devices [40].
In conclusion, the two-photon pumped photoluminescence yield of perovskite quantum dots could be enhanced by more than one order of magnitude by depositing them on a nanostructured silicon film compared to the use of a planar silicon film only. Optical simulations agree well with the experiments and can explain the observed enhanced photoluminescence by near-field enhancement effects of photonic leaky modes. The simple technological platform and robustness of the approach provide opportunities in many fields of applications involving bio imaging and sensing, low-threshold lasing and solar energy.

Synthesis of CsPbB 3 quantum dots
CsPbBr 3 colloidal nanocrystals (NCs) were prepared by using a method developed by Protesescu et al. [1,23] 0.814 g Cs 2 CO 3 (Sigma-Aldrich, 99%) were mixed with 40 mL 1-octadecene (ODE, Sigma-Aldrich, 90%) and 2.5 mL oleic acid (OA, Sigma-Aldrich, 90%), kept at 120 ℃ and degassed for 1 hour. The mixture was heated up to 150 ℃ for 30 min under N 2 atmosphere. Obtained Cs-oleate was kept in a glove box and heated up to 100 ℃ before using. Next, 0.0689 g PbBr 2 (Sigma-Aldrich, 99.999%) and 10 mL ODE were degassed for 1 hour at 120 ℃, afterwards 0.5 mL dry oleylamine (OAm, Sigma-Aldrich, 80−90%) and 0.5 mL OA were added and heated up to 120 ℃ under N 2 atmosphere. The temperature was increased to 180 ℃, then 0.4 mL Cs-oleate solution was rapidly injected. After injection, the mixted solution was immediately cooled by an ice-water bath. The ice-water cooled crude solution was centrifuged at 6500 RPM for 10 min. After the centrifugation, the supernatant was discarded and the particles were re-dispersed in toluene. In order to obtain narrow size distribution of NCs, the solution was again centrifuged at 2500 RPM for 5 min. After this centrifugation, the supernatant was collected.
We calculated the quantum dot concentration in the NC film drop-cast on the silicon photonic crystal to about 5 to 6·10 12 cm -2 , considering the concentration in the initial solution (0.35 µmol/L), the volume of one droplet for drop-casting (14 µL; diameter of 3 mm) and the area of the nearly circular drop-cast spot on the sample (0.5 cm 2 ; diameter of 8 mm). As cross check, we calculated the amount of NCs in one monolayer to about 8·10 11 cm -2 (considering the NC size of 9.4 nm plus 2 nm capping). The 80 nm thick NC film hence consists of about 7 monolayers, yielding a NC concentration of about 5 to 6·10 12 cm -2 , which is consistent with the value above.

Fabrication of silicon photonic crystal slabs
We fabricate crystalline silicon photonic crystal slabs in hexagonal nanohole geometry on glass substrates on an initial area of 5 x 5 cm 2 by a process sequence comprising nanoimprint-lithography as well as silicon thin-film deposition and crystallization techniques. Starting point is a nanoimprint template written into a silicon wafer with hexagonally arranged nano-columns exhibiting a period of 600 nm, a column diameter of 300 nm and a column height of 500 nm by Eulitha AG, Switzerland, serving as master structure. A soft nanoimprint stamp is prepared as mold for the replication process by pouring poly-(dimethyl) siloxane (PDMS) onto the template and subsequent curing at 70°C.
We replicate the columnar template structure by imprinting this PDMS-stamp onto glasses coated by an organicinorganic sol-gel consisting of a mixture of methyl-tri-methoxy-silane and tetra-methoxy-ortho-silicate [41]. The following broadband UV-curing for 5 minutes andafter having peeled off the PDMS soft stamp -thermal annealing for 60 minutes at 600°C removes organic residues and yields a silica replica of the original template considering a shrinkage of the columnar features of about 50%. The resulting hexagonally arranged silica nano-columns on glass substrates exhibit a period of 600 nm and a column height of 230 nm. We use these high-temperature stable

Angular resolved reflectance measurements
Angular resolved reflectance was measured using a Lambda 1050 UV/Vis Spectrophotometer by Perkin Elmer with automated reflectance/transmittance analyzer (ARTA) supplement [42]. The sample is mounted on a rotatable holder with the rotation axis exactly on the sample surface. When the sample is rotated, i.e. when angle of incidence is varied, the detector movement is coordinated such that the detector position always corresponds to the specularly reflected beam. Rotation angles close to normal incidence (-10° <  < +10°) are omitted, because the detector cannot be moved directly in front of the light entrance port in this case.

Excitation fluence determination
For determination of the intensity impinging on the sample surface at normal incidence we considered a circular Gaussian beam profile with diameter FWHM = (500 ± 10) µm measured using a profile sensor (S9132, Hamamatsu) made by Pascher Instruments AB, a pulse length  p = (80 ± 10) fs and a temporal Gaussian pulse shape, a repetition rate of  rep = 1 kHz and a mean beam power P mean measured using a thermal effect-based power meter (Model 1918-C, Newport). We calculated the peak power of the optical pulse P peak by P peak = 0.94• P mean / rep • p ), as well as the peak intensity I peak by I peak = P peak /(w 2 /2) with w = 0.8495•FWHM.

Numerical simulations
For computing reflectance spectra and field energy enhancement we model the structure as a periodic array, with a hexagonal unit cell as depicted in Fig. 2d. In accordance with the experimental setup, the periodicity length is 600 nm, the height of the Si layer is 116 nm, the diameter of the pores in the Si layer is 367 nm, and the height of the conformal QD layer is 80 nm. For SiO 2 , a refractive index of n = 1.53, and for Si, tabulated data (E.D. Palik) is used. The timeharmonic Maxwell equations are solved using an adaptive finite-element method implemented in the commercial solver JCMsuite [29]. The unit cell of the periodic array is meshed with about 1600 prismatoidal mesh elements with sidelengths between 25 nm and 70 nm. Second order finite-elements [29] are used for the FEM discretization of the computed fields. With this numerical setting, the computation time on a standard desktop computer for a single, timeharmonic simulation is about 15 seconds. We have checked numerical accuracy by both, refining the spatial meshing as well as increasing the polynomial order of the FEM discretization in convergence test simulations. In order to obtain angle-and wavelength-dependent spectra, the wavelength and angle of incidence of the plane-wave excitation is varied in a series of computations. Reflectance and field energy enhancement are obtained from the near fields using fieldintegration post-processes.

ASSOCIATED CONTENT
The manuscript is accompanied by Supporting Information containing -Scanning electron microscopic image of the CsPbBr3 coating on bulk and nanotextured parts of the silicon layer.
-Simulated angular resolved reflectance data for a wide range of effective refractive indices of the quantum dot containing effective medium.
-Simulated electric field energy enhancement in the 80 nm thick CrPbBr3 quantum dot containing layer at short wavelengths (500 nm) -Photonic crystal design: Simulated angular resolved reflectance data for a wide range of thicknesses of the silicon photonic crystal slab -Fitting details for the determination of the upper intensity threshold -Details on the (cos  characteristic of photoluminescence signal dependent on the incident angle 