Silicon nitride nanobeam enhanced emission from all-inorganic perovskite nanocrystals

Optically active perovskite nanocrystals have shown considerable promise for a myriad of applications, such as single photon source, light-emitting diodes and nanophotonics. Coupling those nanocrystals to photonic microand nanostructures will offer additional degrees of freedom to manipulate their optical properties. Herein, we demonstrate the coupling of perovskite nanocrystals to a mechanically robust, poly(methyl-methacrylate) (PMMA)-encapsulated silicon nitride nanobeam photonic crystal cavity at room temperature. As determined from the time-resolved photoluminescence decay measurements, we observed enhanced spontaneous emission from the perovskite nanocrystals by a factor of 1.4, consistent with finite difference time domain simulation. In addition, by varying the concentration of the perovskite nanocrystal in the PMMA layer, the effective index of the layer can be modified, allowing us to tune the cavity mode resonance. Our results show that solution-processable perovskite nanocrystals hold a promising prospect for applications such as on-chip light sources, optoelectronic devices and photonic integrated circuits. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Halide perovskites, as a class of material, have been garnering significant attention among the research communities on their fundamental properties, as well as prospects for practical applications [1][2][3][4][5]. In particular, semiconductor lead halide perovskites are found to be promising for optoelectronic applications, including on-chip light sources [6][7][8]. The interest in lead halide perovskites partly lies in their chemical composition: YMZ 3 where Y could be an organic compound such as methylammonium or formamidinium or a cesium cation (Cs + ); M being the lead cation (Pb 2+ ); and Z is the halide anion namely chloride (Cl -), bromide (Br -), iodide (I -) or a mixture, forming a typical perovskite crystalline structure. Such a chemical structure allows for wide-band emission tunability via composition stoichiometry, enabling the coverage of the whole visible spectrum. As such, lead halide perovskite could compensate for the "green gap" of conventional semiconductor such as the III-nitride and III-phosphide [4,9,10]. Colloidal perovskite nanocrystals are also superior to their traditional II-VI colloidal counterparts which tend to be difficult to synthesize and suffer from poor optical properties on the blue side of the visible spectrum [11,12].
Lead halide perovskites also exhibit several favorable properties for light emitting devices, including high photoluminescence (PL) quantum yield attributed to the low densities of defects [13,14], which reduce the nonradiative loss via carrier trapping. The large stokes shift in the emission of these perovskites also reduces the carrier loss to detrimental reabsorption [15]. Combined with the large exciton binding energy, indeed, there have been many demonstrations of perovskite light emitting devices such as LED and lasers capable of operating at room temperature [16][17][18][19][20][21][22][23][24][25].
Efforts to utilize perovskite in devices to manipulate their optical properties inevitably involve the tweaking the dimensionality of the perovskite sample [26][27][28][29], patterning of micro/nanostructures onto perovskites [30][31][32] or coupling the perovskites to micro/nanostructures [33][34][35]. For example, the coupling of perovskite nanocrystals to a nanobeam photonic crystal (PhC) cavity is promising as the localization of waves in the small mode volume cavity could enable the miniaturization of light source or photonic devices useful for integrated photonic circuits. However, the conventional air-suspended nanobeam suffers from the lack of mechanical stability which hampers a more widespread adoption.
To circumvent this problem, we design and fabricate a silicon nitride (SiN) nanobeam which sits on top of an oxide substrate [36] as opposed to the conventional air-suspended configuration. This enables us to spin-coat a layer of poly(methyl-methacrylate) (PMMA) mixed with all-inorganic CsPbBr 3 perovskite nanocrystals to encapsulate the nanobeam (Fig.  1) -a step which could damage the air-suspended nanobeam. We demonstrate a facile way to tune the cavity mode resonance: by varying the concentration of the perovskite nanocrystal in the PMMA layer, the effective index of the layer can be modified, allowing us to tune the cavity mode resonance. We then verify the coupling of the perovskite nanocrystals to the cavity at room temperature and observed the enhancement of the spontaneous emission from the perovskite nanocrystal by a factor of ~1.4, consistent with expectations based on numerical simulations. Our results highlight the prospects of using solution processable perovskite nanocrystal for a mechanically robust on-chip photonic device with a small footprint.

Silicon nitride photonic crystal cavity
As described in our previous works [36,37], to design the nanobeam resonators, we first simulated the photonic band structure using the MIT Photonic Bands (MPB) software package and then optimized the characteristics of the optical cavity via finite difference time domain (FDTD) calculations with Lumerical FDTD solutions. The calculations here were carried for a SiN (index, n = 2) nanobeam completely surrounded by a material of n = 1.45 of effectively infinite thickness above and below the nanobeam. The optimized design of the SiN nanobeam resonators consist of elliptical holes with a period, a = 157 nm, major and minor diameters being 202 nm and 100 nm respectively, with 40 such holes forming the Bragg region on each side of the nanobeam. The cavity is formed by linearly tapering both the period and the major axis of the 10 holes approaching the center from each side, as shown schematically in Fig. 2(a). The innermost elliptical holes have a minimum period and major diameter of 146 nm and 150.4 nm respectively. The minor diameter of the holes is kept constant throughout the nanobeam. The edge-to-edge gap of the two innermost holes is 78.3 nm. The nanobeam has a thickness of 220 nm and a width of 450 nm. We obtained the fundamental mode -which is the mode of interest -with resonant wavelength, λ cav~5 20 nm at which the CsPbBr 3 perovskite nanocrystals tend to exhibit the most intense PL. The simulated electric field intensity distribution of the fundamental mode is shown in Fig. 2 The simulated cavity Q-factor is about 200,000 with a mode volume of ~3(λ/n) 3 . However, to accommodate two grating couplers and their associated tapers within the field of view within the confocal microscope for the initial characterization of the cavity mode, the overall resonator size is reduced such that each Bragg region consist of 20 holes instead of 40. This results in a reduced Q-factor of ~9000 while keeping a similar resonant wavelength and mode volume.
The nanobeam PhC cavities were fabricated using a 220 nm thick SiN membrane (refractive index ~2.0) grown via LPCVD on thermal oxide of silicon. A layer of roughly 400 nm thick Zeon ZEP520A resist is deposited onto the SiN membrane with a spin-coater. The resist was also coated with a thin layer of Pt/Au which served as a charge dissipation layer. This is followed by the patterning of the resist using a JEOL JBX6300FX with an accelerating voltage of 100 kV. The pattern was then transferred to the SiN by reactive ion etching using CHF 3 /O 2 . More specific details of the fabrication and characterization of such nanobeam PhC cavities can be found in our previous work [36].

Coupling perovskite nanocrystal to encapsulated SiN nanobeam PhC cavity
The CsPbBr 3 Perovskite nanocrystals were dispersed in toulene and were synthesized following the procedures described in [38]. The perovskite nanocrystal solution was then mixed with PMMA formulated in anisole (MicroChem 950PMMA A4). We prepared solutions of perovskite nanocrystals with different concentrations. We injected a varying amount of anisole (Aldrich, anhydrous 99.7%) -0 ml, 5 ml and 10 ml -to a fixed 10 ml of PMMA solution before mixing with about 0.1 ml of perovskite nanocrystal solution. With increasing volume of anisole, the solution becomes more dilute and the concentration of perovskite nanocrystals in PMMA is reduced. To couple the perovskite to the cavity, the solution was then spin-coated on the nanobeam sample at 4000 rpm for 1 minute, which effectively places the nanocrystals on the cavity and at the same time encapsulating the nanobeam. Taking the thickness of the PMMA layer to be the length from the surface of the substrate to the top of the PMMA layer, the thickness is expected to be about 400 nm in accordance to the manufacturer data sheet. Figure 2(c) shows the scanning electron micrograph (SEM) of the PMMA encapsulated nanobeam. Optical experiments on the samples were carried out in a confocal microscopy system at room temperature. For the time-averaged measurements, a continuous wave He-Cd laser excitation at 442 nm was focused (100 × objective lens, NA = 0.90) onto the sample. The emission spectra were measured with a Horiba HR Evo spectrometer with a focal length of 800 mm together with a 300 lines/mm grating and a liquid nitrogen cooled Si CCD detector. For time-resolved decay measurements, a Ti:sapphire femtosecond-pulsed laser with ~100 fs pulses at 80 MHz was used. The emission of the laser was frequency doubled to output 400 nm pulses. The emission from the sample was detected with an avalanche photon detector (Micro Photon Devices) connected to a single photon counting module (PicoHarp 300). The overall temporal resolution of the time-resolved setup was measured to be about 22 ps. Figure 3(a) shows a series of spectra corresponding to PMMA layers with decreasing perovskite nanocrystal concentration. The PL emission of the CsPbBr 3 perovskite nanocrystals is centered at 520 nm. The spectra also show the narrow cavity mode resonances at longer wavelengths relative to the perovskite nanocrystal emission as indicated by the arrows above the peaks. The background PL in the spectra can be attributed to emission from the perovskite nanocrystals which are not coupled to the cavity as well as the scattered light off the nanobeam.
To further study the coupling between the perovskite nanocrystal with the encapsulated nanobeam, we spin-coated the PMMA mixed with perovskite solution of different concentrations. As the perovskite nanocrystal in the PMMA layer decreases, we found that cavity mode resonance becomes increasingly blue-shifted. We attribute the blue-shift of the mode resonance to the change in the effective index of the encapsulating PMMA. Decreasing concentration of CsPbBr 3 (refractive index ~2.6) in PMMA (refractive index~1.49) will result in the overall decrease in the effective index of the encapsulating layer of the nanobeam, and blue-shift the cavity mode. By peak fitting, we could also extract the mode wavelength, λ cav and the linewidth at full-width half-maximum (Δλ FWHM ) to determine the experimental Q = λ cav /Δλ FWHM of the cavity modes. The extracted Q-factors for the spectra increases from ~900 to ~1500 with decreasing perovskite concentration. The experimental Q-factors are smaller than that obtained in the simulations, which we attribute to the fabrication imperfection due to the small nanobeam feature sizes necessary for operation in the 500 nm wavelength regime. To explain the experimental observations, we carried out further FDTD simulations with MEEP [39] software package in which we model a nanobeam being encapsulated by a layer of PMMA with a finite thickness ( Fig. 1(b)) as in the experiments. We simulated the change in the concentration of perovskite nanocrystals in the PMMA layer by varying the index value of the top PMMA layer encapsulating the nanobeam structure. The holes of the nanobeam are taken to be filled with material of the same index as that of the PMMA layer. The main simulation results are summarized in Fig. 3(b). Indeed, the simulated mode resonance wavelength exhibits a monotonic decreasing trend with the reduction of the effective index of the PMMA layer, consistent with experimental observation. Furthermore, the simulated Qfactor increases with the decrease of the effective index of the PMMA layer supporting our experimental observations. The decrease of the effective index of the PMMA layer raises the index contrast between the layer and the nanobeam, thus the higher Q-factor.
The dilution of PMMA with additional anisole (lowering the concentration of perovskite nanocrystal) could also reduce the thickness of the PMMA layer. To rule out the possibility that the change in the cavity mode resonant wavelength is due to the change in the PMMA thickness, we performed simulations for PMMA layer thicknesses of 250 nm, 400 nm and 600 nm. Figure 4 summarizes the cavity mode wavelength and the Q-factor of the simulation results. Overall, for all values of the effective index, the cavity mode wavelength increases with a thicker PMMA layer. The increase in the mode wavelength with thickness is more significant at larger effective index. Given the values of the Q-factors, the shift of the mode wavelength with changing thickness should be larger or comparable to its linewidth and thus would be observable spectrally. Nonetheless, the variation in the mode wavelength due to PMMA thickness is well within 10 nm for most values of the effective index of the PMMA layer such that it could not account for the large shift observed in the experiments. Therefore, we attribute the experimentally observed shift in the mode wavelength mainly to the varying effective index of the encapsulating PMMA layer.
Instead of changing the effective index of the PMMA layer by diluting the PMMA solution, one could also dilute the perovskite nanocrystal solution while keeping a fixed PMMA concentration. With the same spin coating conditions, one would get consistent PMMA layer thicknesses regardless of its effective index and could thus eliminate the effect of layer thickness on the cavity mode wavelength. It is worth highlighting that measurements were performed on the same nanobeam resonator. Aside from the changing Q-factor because of the varying effective index of the PMMA layer, the cavity showed no significant degradation despite having undergone multiple rounds of sonication with acetone and spin coating of the PMMA layer, proving that the nanobeam PhC cavity is structurally robust. This tuning method of the mode resonance via the effective index around the cavity environment could be useful for the coupling of other colloidal quantum emitters to cavities, possibly with other types of capping layer beside PMMA.
To verify the spontaneous emission enhancement of the perovskite nanocrystal coupled with the cavity, we measured the time-resolved PL decay of the perovskite emission. The PL decay curves of the perovskite emission from the coupled and uncoupled cases are presented in Fig. 5. The perovskite nanocrystal PL exhibits a multiexponential decay due to a distribution of the nanocrystal parameters such as size and nonradiative decay rate [40]. Assuming that the perovskite nanocrystals ensemble consists of 3 main subpopulations, each with a characteristic decay behavior, the decay curves were most accurately fitted with a three exponential decay function: where I(t) is the PL intensity at time t, I 0 is the background intensity, t 0 is the temporal offset relative to 0 when the decay begins and t i (A i ) with i = 1, 2, 3 being the three decay time constant (amplitude). We take the shortest decay time t 1 as the representation radiative lifetime since the fractions of the amplitude, A 1 /(A 1 + A 2 + A 3 ) is close to 1 in both the coupled and uncoupled cases, implying that the subpopulation of the nanocrystal with characteristic decay time t 1 is dominant. The t 1 times are extracted to be 0.65 ± 0.04 ns and 0.46 ± 0.03 ns respectively for the coupled and uncoupled cases, consistent with previous report [41]. Taking the ratio of t 1 of the uncoupled case to that of the coupled case, we obtained a Purcell factor of 1.4 ± 0.8, indicating the enhancement of spontaneous emission. where λ cav is the mode resonant wavelength, n is the refractive index of SiN, Q e is the Q-factor of the emitter and V mode being the mode volume. In consideration of the local density of states, one would also need to factor in the local electric field intensity expressed as where r is the position of the emitter. We note that this model of Purcell factor is appropriate for our experiments since the emitter emission linewidth is larger than that of the cavity mode linewidth. In this case, the Purcell factor depends on the Q-factor of the emitter and not that of the cavity. By performing multiple peak fit to the spectra of the uncoupled case, the full-width at half-maximum linewidth of the perovskite nanocrystal emission was found to be 20 nm and thus giving a Q-factor of about 26. From the FDTD simulations, V mode was found to be ~3(λ/n) 3 . Assuming that the emitter is located at the center of the nanobeam cavity on the surface gives 2 | | local E = 0.26. The resulting Purcell factor is obtained to be 1.34 consistent with experimental results.

Conclusions
We have demonstrated the coupling of perovskite nanocrystal to a PMMA encapsulated SiN nanobeam PhC cavity at room temperature, enhancing the spontaneous emission from the perovskite by a factor of 1.4. The Purcell factor could be further increased by improving the design of the cavity to obtain lower mode volumes and/or enhancing the electric field at the surface where the emitters are coupled. In addition, we showed the effective tuning of the cavity mode resonance by changing the effective index of the encapsulating PMMA layer via varying the concentration of perovskite nanocrystal. This method of tuning could be useful for other types of colloidal quantum emitters and cavities. Combined with the mechanically robust encapsulated nanobeam, our results show that solution processable perovskite nanocrystals could prove to be a viable alternative to the commonly used epitaxially grown light emitting materials for applications such as on-chip light source, optoelectronic devices and photonic integrated circuits. Furthermore, the coupling of perovskite nanocrystal to an encapsulated nanobeam cavity could be a promising platform to study solid-state quantum electrodynamics in the strong light-matter interaction regime.