Radiative Lifetime Modification of LaF₃:Nd Nanoparticles Embedded in 3D Silicon Photonic Crystals

The photonic density of states (DOS) of a silicon inverse photonic crystal is probed using the radiative emission of LaF3:Nd nanoparticles. These emitters are embedded as a thin planar defect within the interior of photonic crystals with varying silicon filling fractions. The alignment of the narrow emission of the particles with the high and low photonic DOS regions is achieved. The time-resolved measurements reveal that the radiative lifetime of the embedded Nd3+ is strongly influenced by the surrounding DOS provided by the silicon inverse opals. Control of spontaneous emission (SE) is central to many applications involved with photon management including light emitting sources,1-3 solar energy4, 5 and quantum information processing.6, 7 For example, control of the direction of SE may facilitate more efficient light extraction in optical display devices. Spectral redistribution of SE may permit more photons to couple into useful optical modes in optical cavity devices (e.g. lasers). According to Fermi's golden rule, the rate of SE is governed by the number of available electromagnetic modes and the coupling between the electric field and the emission dipole at the location of the emitter, namely, local density of states (LDOS).8 Therefore, key to the manipulation of SE is full control of the photonic DOS. Photonic crystals (PhCs), materials with periodically varying refractive index on a length scale comparable to the wavelength of light, provide an excellent means to modify the photonic DOS.4, 9 In analogy to Bragg diffraction of electrons in atomic crystals, photons with a specific range of energies (the so called stopgap) cannot propagate along certain directions in the PhC.10 If the refractive index contrast between the two materials is large enough, stopgaps can exclude a substantial solid angle in the crystal, which results a decreased DOS at these photon energies.11 In extreme cases, where a full photonic band gap (PBG) arises, light is forbidden to travel in all directions and the DOS vanishes at the PBG.12-14 However, because the integrated number of photonic states over photon energies is conserved, the DOS is strongly enhanced at the edges of PBG and highly depleted within the PBG.15 Thus, PhCs can be used to suppress SE within the PBG and enhance SE at the edge of PBG. Compared to 1D and 2D PhCs, which inherently cannot control SE in all three directions, 3D PhCs hold promise for complete control over SE. While various methods have been developed to realize 3D PhCs,16 self-assembled 3D PhCs (so-called artificial opals), constructed by close-packed spheres in a face-centered cubic lattice, are attractive owning to their ease of fabrication and because their optical properties can be tuned simply by varying the sphere diameter.17 Artificial opals made of polystyrene or silica can also be used as sacrificial templates for inversion of materials with high refractive index (e.g. TiO2, Si, GaAs, etc.) to increase their photonic strength.18, 19 In recent years, SE control by colloidal crystals and TiO2 inverted opals has been demonstrated.20-25 However, little work on SE has been conducted on silicon or other high refractive index contrast inverse opal PhCs that exhibit strongly modified photonic DOS.14, 26 The emitters commonly used in the previous SE control studies were either organic dyes or colloidal quantum dots. Although these materials exhibit high quantum emission efficiency, these emitters are not ideal for several reasons: (i) generally the homogeneously-broadened emission of dyes does not allow investigation of sharp DOS features in an opal PhC;23 (ii) both dyes and colloidal quantum dots often suffer from photo oxidation and bleaching;27, 28 (iii) and perhaps most importantly, they are generally introduced into opal PhCs by infiltration and thus randomly infill the PhCs, including the near-surface and surface of the PhC where of course their optical properties are not influenced as much by the PhC. In this communication, we demonstrate incorporation of LaF3:Nd nanoparticles at well-defined locations in a silicon inverse opal. We probe the sharp DOS features of a silicon inverse opal PhC by studying the stable narrow emission of the embedded Nd3+ at 1052 nm as a function of silicon filling fractions and find that the radiative lifetime of the embedded particles is strongly correlated to photonic DOS. Accurate PhC SE studies require that the emitter be stable and have high quantum efficiency as well as a narrow emission linewidth relative to the DOS features. Neodymium-doped lanthanum fluoride is an excellent candidate in these respects. The emission of Nd ion arises from parity forbidden transitions between energy levels of 4f electrons and thus has very narrow (∼20 nm) emission bands.29 The LaF3 host provides protection and also endues the Nd ions with high quantum yield.30 One of the outstanding difficulties in studying SE manipulation in PhCs is an approach to place the emitters at well-defined locations within the three dimensional structure. In our procedure, as summarized in Figure 1, a thin layer of LaF3:Nd particles is introduced into the self-assembled colloidal crystal as a planar defect parallel to the <111> opal crystal plane by spin coating (Figure 1a and Figure 1b). The second crystal grew epitaxially on the first crystal, as the thin nanoparticle layer (<100 nm) preserved the surface morphology of the first opal film and thus was able to direct the growth of the second crystal (Figure 1c). The resulting sample was carefully cut lengthwise into 4 pieces; these pieces were then exposed to a different number of Al2O3 deposition cycles via atomic layer deposition (ALD) (Figure 1d). This Al2O3 layer served to reduce the amount of silicon deposited in the next step by chemical vapor deposition (CVD) (Figure 1e) and thus provided fine control over the spectral position of the optical features. Both silica and alumina were etched away in a diluted HF bath leaving behind a silicon inverse opal with an embedded LaF3:Nd nanoparticle layer (Figure 1f). To ensure the same chemical environment for all 4 samples, they were put in and taken out of HF solution together. The final result were emitter-embedded silicon inverse PhCs of 20.8%, 19.7%, 17.9%, 16.6% silicon filling fractions, starting from the assumption that 22.4% is the maximum filling fraction for an inverse opal;31 these values are extracted from calculations as will be discussed. A cross section SEM image of the sandwich silicon inverse opal is presented in Figure 2a and b provides a closer look at the LaF3:Nd nanoparticle layer. Schematic illustration of steps to incorporate LaF3:Nd nanoparticles into silicon inverse opals: (a) silica colloidal crystals were self-assembled on sapphire substrates; (b) a thin corrugated layer of LaF3 particles was spin coated on top of the first crystal; (c) the second colloidal crystal was epitaxially deposited on the particle layer; (d) the sample was cut into 4 pieces and coated with a varying amount of Al2O3, limiting the amount of silicon deposited by CVD (e); (f) both silica and alumina were etched away in a diluted HF solution. Scanning electron micrograph (SEM) images of (a) the cross section of the emitter-embedded silicon inverse opal and (b) an enlarged view of the embedded LaF3:Nd nanoparticle layer (rough appearing region in the middle of the SEM image). The reflectance and transmittance spectra of the sandwich silicon inverse PhCs with varying silicon filling fractions (SFF) are given in Figure 3. The reflectance plots show intense peaks arising from the Γ-L stopgap, evidence of a highly ordered opal lattice throughout the first and second crystals, as well as secondary lobes due to Fabry-Perot interference. The reflectance peaks of the four samples manifest similar maximum values, which is consistent with the fact that they were originally cut from the same opal crystal and went through identical fabrication procedures except for the number of ALD cycles. The Γ-L stopgap is also evident in the transmittance measurements corresponding to dips in spectra. On the blue side of the stopgaps, the low transmittance is due to increasing light scattering and absorption by silicon through the thick opal crystals (∼14 layers). As the alumina coating is increased from 10 cycles to 40 cycles, the filling fraction of silicon inversion is reduced from 20.8% to 16.6%, causing the stopgap of the silicon inverse PhCs to blue-shift about 0.05 in reduced frequency units (a/λ, where a = 625 nm, is the lattice constant of the opal crystal), corresponding to a 100 nm wavelength shift, which allows finely tuning the relative spectral position between the stopgap and the 1052 nm Nd3+ emission line (green dashed line). Reflectance (red line) and transmittance (blue line) spectra of emitter-embedded silicon inverse opals with decreasing SFF from bottom to top. The dashed green vertical line represents the 1052 nm center wavelength of the emission of the LaF3:Nd nanoparticles; in green is the nanoparticle emission spectrum. The emission spectrum is shown in arbitrary units. All spectra are plotted in both wavelength and reduced frequency, where lattice constant a = 625 nm. Both spectral and time-resolved experiments were performed to study the influence of silicon inverse PhCs on the spontaneous emission of the sandwiched LaF3:Nd nanoparticles. The samples were excited at 796 nm by a Ti: Sapphire CW laser (see supporting information for experimental details). Silicon also absorbs at this excitation and exhibits a weak photoluminescence (PL); however, as displayed in the Figure 4a, the PL spectra were dominated by emission from the Nd3+. The PL spectra suggest that the PL intensity was modified by different photonic environments; to confirm this, time-resolved measurements were used to extract quantitative conclusions. PL intensity alone is not sufficient to draw conclusions since the PL measurements were performed over finite collection angles and it has been reported that the emission out of the photonic structures has a strong angular dependence.25, 32 The time-resolved data (Figure 4b), measured at a center wavelength of λ = 1052 nm with a 50 nm spectral resolution, provide direct evidence of emission manipulation by PhCs through the differences in the radiative lifetime. All decay curves were fitted by a double exponential function and the averaged decay times were calculated as reported previously (see supporting information for curve fitting details).33, 34 The averaged luminescence decay times for the silicon inverse opals with a = 625 nm are 352 ± 13 μs (20.8% SFF), 418 ± 15 μs (19.7% SFF), 565 ± 20 μs (17.9% SFF) and 501 ± 15 μs (16.6% SFF). To qualitatively determine the effect of photonic crystals on SE control, a reference system, e.g., a photonic crystal with a smaller lattice parameter in which the emission is on the red side of the stopgap, has been previously utilized.23-25, 35 We constructed a similar reference structure with embedded emitters from 240 nm silica spheres (a = 340 nm) which was subsequently coated using 10 cycles of alumina ALD and filled with Si via CVD. The ALD and Si infilling procedure was applied to ensure the nanoparticles in the reference sample were in a similar chemical environment as the other samples and to ensure all samples had been similarly processed. The SFF value and lifetime of the reference were found to be 20.0% and 390 ± 16 μs. Compared with this reference sample, the emission is enhanced for the inverse opal with a = 625 nm and 20.8% SFF and is suppressed for the samples with 17.9% SFF and 16.6% SFF, and about the same as the 19.7% SFF sample. (a) Emission spectra and (b) emission decay profiles measured at a center wavelength of 1052 nm for LaF3:Nd nanoparticles embedded in silicon inverse opals fabricated with different SFF. In the opal sandwich structures, the thin LaF3:Nd particle layer that has a refractive index different from the surrounding materials, which introduces a planar defect within the PhC. It has been shown that such a structural defect can create a spectral defect state in PBGs, manifesting itself as a dip (spike) within Bragg peaks in reflectance (transmittance) spectra.36, 37 The spectral position of the state is determined by the refractive index and thickness of the defect material and the optical properties of the surrounding PhC. Regardless of the thickness of the planar defect, a defect state will always be produced in any PBGs and periodically sweeps the entire PBG as the thickness of the defect layer increases.38, 39 For our samples, the defect state is not apparent in the reflectance and transmittance spectra. It might overlap with the tail of the Bragg peak on the high energy side given the fact that the ratio of the emitter layer thickness to the lattice constant is small (∼0.1).38 Most important for this work, the defect mode does not overlap with the Nd3+ emission spectrum. Thus, we can neglect the influence of the defect state on the SE of the emitters and approximate the sandwich structure as a perfect infinite silicon inverse opal PhC in the band structure and DOS calculations. Figure 5 shows the evolution of the calculated DOS for structures (a = 625 nm) with varying SFF and the PL spectrum of Nd3+. As the SFF decreases, while the shape of the DOS curves remains the same, the sharp DOS features gradually migrate to the high energy side, enabling the Nd emission to probe different DOS regions. For example, the PL (centered at a/λ = 0.59) lines up with the high DOS peak near the Γ-L band edge for the case of 20.8% SFF, which is consistent with the enhanced emission (short lifetime) observed experimentally for this sample. For the samples of 17.9% SFF and 16.6% SFF, in which inhibited emission (long lifetimes) were observed, the PL falls within the strongly depleted DOS region of the stopgap. The difference in the measured lifetime for those two cases suggests a variation in the photonic strength within the stopgap, where the former presents a lower DOS than the latter according to the simulation. Simulated DOS of silicon inverse opals (a = 625 nm) fabricated with decreasing SFF from bottom to top (black lines). The shadowed areas refer to the simulated Γ-L gap positions for each case. The dashed green vertical line represents the 1052 nm center wavelength of the emission of the LaF3:Nd nanoparticles; in green is the nanoparticle emission spectrum (shown in arbitrary units). Since structural fluctuations among inverse opals of different batches during the fabrication (e.g. crystal thickness, location of emitters and density of crystal defects) might affect the optical measurements, a quantitative analysis is directly performed among these samples with a = 625 nm that were cut from the same photonic crystal and went through identical fabrication procedures together; the only difference between the samples is the amount of Al2O3 deposited in the intermediate step and the resulting SFF. To examine the influence of the Al2O3 ALD on Nd3+ emission (although Al2O3 was completely removed in the oxide etching step for the sample studies), time-resolved emission measurements were performed on two control samples with similar SFF but different amount of ALD. The Nd3+ emission from the two samples showed similar lifetime suggesting that the different ALD processing times did not alter the emission properties of LaF3:Nd particles (see supporting information for details). In order to study the relative changes of emission rates and DOS due to SFF, the sample with 19.7% SFF is used as a reference because its emission is the least modified according to the small lattice reference (a = 340 nm). Table 1 displays the measured emission rates (inverse lifetime) and the corresponding DOS values (integrated over the emission spectrum of Nd3+) for various SFF normalized by 19.7% SFF data. The emission rate and DOS for each sample are highly correlated: the change of the relative emission rate ranges from 19% SE enhancement (20.8% SFF) to 26% SE inhibition (17.9% SFF); the relative DOS changes for these two cases are a 77% increase and 68% reduction, respectively. To examine if the photonic crystal effect is responsible for the SE change rather than differences in the effective refractive index of each sample due to the variation in SFF, we modeled the PhC as a homogeneous medium (HM) with the effective refractive index obtained from the band structure calculations, and the SE rate in such a homogeneous medium is proportional to the refractive index.40, 41 We estimated the change of the emission rate due to the variation in the SFF, which is found to decrease monotonically in a very small magnitude (≈2% per 1% SFF), e.g. the emission rate in a HM increases 2.0% when SFF increases from 19.7% to 20.8% and decreases 4.3% and 7.0% as SFF is reduced from 19.7% to 17.9% and 16.6%. A much larger change of emission rate was experimentally observed among these samples, indicating the decisive factor for controlling SE was the photonic crystal. Although the general trends in the experimental SE data and the DOS calculations agree, the magnitude of the SE rate change is less than the variation of the DOS. This is due to various non-idealities in the experiment: the self-assembled PhCs contain defects which degrade their photonic strength; the double exponential decay of the emission suggests the presence of a non-radiative decay process, and the experimental samples have finite thickness. In conclusion, we have demonstrated that the photonic band structure of silicon inverse PhCs can be specifically and finely tailored using ALD at an intermediate step between template fabrication and silicon inversion. This is coupled with the incorporation of rare earth nanoparticle emitters into the silicon inverse PhCs at a well-defined location provided by a simple experimental procedure. We utilize the narrow emission linewidth of rare earth nanoparticles and the filling fraction tuning enables to study the effect of the photonic DOS on spontaneous emission. Time-resolved experiments reveal that the emission rate of embedded emitters can be strongly manipulated by the stopgap of silicon inverse opals; up to a 61% change of emission decay rate is observed between the enhanced and the inhibited SE. Synthesis of LaF3:Nd Nanoparticles: LaF3:Nd nanoparticles were synthesized following a modified version of van Veggels's procedure.42 The synthesis was carried out at 90 °C rather than 75 °C to increase the particle size. After formation of the LaF3:Nd nanoparticles, an extra 7 nm of LaF3 was grown on the shell to increase the luminescence yield.43 After purification, the resulting nanoparticles could be dispersed in isopropanol, and have an average diameter of 50 nm, and appear to generally be in small aggregates of a few nanoparticles (the particle was in so that their small aggregates are larger than the by opal spheres and thus spin coating the surface of the opal can be on the top of the opal It is that the Nd3+ quantum efficiency increases as the Nd is We find that Nd LaF3 is into both quantum and of The fabrication of the emitter embedded photonic crystals with the growth of a silica colloidal crystal on a sapphire by The was in a 15 which a silica of nm diameter silica spheres in at 32 the was leaving behind a colloidal crystal of The emitter layer was by the nanoparticle solution on top of the first colloidal crystal by at °C for to the nanoparticles and the first opal film from in the during the second opal A second colloidal crystal film was grown over the nanoparticle layer using the same growth for the first crystal. The sample was cut lengthwise in 4 each of which was exposed to and 40 cycles of respectively. In each ALD the and times were 0.05 and by The was at °C during the deposition ALD deposited ± alumina over the The 4 pieces were subsequently with silicon by means of chemical vapor deposition at °C for 5 using opal presented an of indicating that the of the templates had been colloidal crystals were The silicon was then removed by ion etching as previously and the silica and alumina were removed by the samples in HF HF in a for by in and at DOS The photonic band structures and density of states were calculated using the Photonic The Γ-L stopgap for each PhC was fitted to their reflectance peak (Figure by within the experimental the thickness of silicon coating and the of between two opal The effective refractive index was from the of the first photonic band to the The fitted served as to the corresponding photonic DOS which was carried out using that were in the and carefully The silicon filling fraction was calculated by the silicon inverse structures using with the fitted and over the silicon is available from the or from the and to this The to of the at of for experimental This work was by the of in the for a of to are as are but not or are made available as by the The is not responsible for the or of any supporting information by the than be to the corresponding for the