Silicon Nitride Photonic Crystal Free-Standing Membranes: A Flexible Platform for Visible Spectral Range Devices

2.1. The closing band-gap for low refractive index materials

A system composed by a quantum light emitter coupled to a resonant optical mode can be modeled as two interacting oscillators. The strength of this interaction can lead to two different coupling regimes known as strong and weak coupling. In weak coupling regime, the free-space spontaneous emission rate (Γ₀) is modified by the so-called Purcell effect: the coupled system emits with a rate Γ_C=FΓ₀, where F = 3/(4π²)Q/V (λ/n)³ is called Purcell Factor (Q and V are the quality factor and the modal volume of the photonic mode, respectively). When the system is instead in the strong coupling regime, the confined excitons and photons coherently exchange energy with a coupling strength, g, inversely proportional to V, i.e. g ∝ 1/ √ V. Thus the properties of the photonic mode and, in particular, the electromagnetic field confinement in both time and spatial domains strongly affect the dynamic of the coupled system.

At visible wavelengths, these phenomena have been observed by means of several optically confined systems [28,29], but 2D-PhCs represent the most promising structures, since they give the best control on the optical properties of the resonators. To date, PhC cavities for visible spectral range are based on various geometries [6,11,21] and on higher-order modes of the widely studied H1 defect [30] (sketched in Fig. 1(a), inset). This resonator consists of a missed hole in a triangular PhC lattice, and it allows two orthogonally polarized resonant modes in the photonic band gap (hereafter referred to as x- and z-pole modes, on the base of the orientation of the wave vector).

The cross polarization of x- and z-pole modes and the absence of higher-order states represent non-negligible advances for applications in quantum optics [31,34]. Moreover, the H1 cavity presents the lowest V among PhC point defects, thus enhancing quantum electrodynamic (QED) phenomena in both strongly and weakly coupled systems. However, obtaining small V at visible wavelengths is a challenging goal, because of the low refractive index of transparent materials in this spectral range, which reduces the effectiveness in localizing the optical modes. Nevertheless, the aforementioned advantages, together with the increasing interest toward the realization of efficient emitting devices in the visible spectral range, foster theoretical and experimental studies to find alternative routes to improve light confinement in low-index H1 systems.

In the following, we consider a resonator consisting of a point defect H1 in a triangular lattice of air holes (period a, radius r) realized in a silicon nitride slab having refractive index n=1.93 and a thickness t. Plane-Wave Expansion (PWE) and 3D Finite Difference Time Domain (FDTD) algorithms [32] were used to investigate the electromagnetic response of such structure. All the calculations were restricted to modes with non-negligible components of the electric field along x and z and a non-negligible component of the magnetic field along y (hereafter referred to as TE- like modes).

One way to realize ultrasmall-volume PhC cavities while keeping high Q- factors in the visible range and preserving the dipole-like shape of the modes is the so-called closing band-gap technique [33], involving PhC slab thickness (t) optimization. As shown in Fig.1(a), the x-pole mode Q-factor has a maximum for t = 1.55a, while it is almost constant for t < 1.2a. The Photonic Band-Gap (PBG) existing for t = 0.7a disappears when t is increased to 1.55a (see Figs. 1(b) and 1(c)). In agreement with the closing band-gap principle [33], this effect is assigned to a new nature of the electromagnetic confinement in the xz plane: it is not still due to the PBG, but it has to be assigned to the momentum space mismatch between the cavity mode and the second guided mode in the PhC slab. The increased thickness of the slab leads to slight variations of the x- and z-pole modal profiles along y, thus leading to a wider modal volume, as shown in Fig. 1(a). However, these variations of V are negligible with respect to the increase in Q, since the modal extension in the xz plane is preserved. Indeed the Purcell factor [Fig. 1(d)] follows the Q-factor behavior: for t = 1.55a, F is maximized to F ∼ 78 with V ∼ 0.68 (λ/n)³ and Q ∼ 700. A similar trend has been found for the z-pole mode.

2.2. Modal selective tuning

The x- and z-pole modes engineering would foster many applications based on H1 nanocavities operating at visible wavelengths. For instance, the degeneracy of x- and z-pole modes may be useful for entangled photon generation [34]. Other applications, such as single-photon sources or PhC-based optical read out of lab-on-chip devices [27], require well-defined and linearly polarized non-degenerate resonances. Several solutions have been reported in past years to break the energy degeneracy of the optical modes or to recover it [30,35-37]. A promising strategy to obtain a control on x- and z-pole modes is displayed in Fig. 1(e): by acting on two cavity neighboring holes, the resonant frequency of the x-pole mode (f_x) can be significantly modified while keeping constant the z-pole mode one. This finding can be ascribed to the selective modification of the wavevector k = (k_x, k_y, k_z) along a specific axis. Indeed x- and z-pole modes have the strongest component of k oriented along the x and z axes, respectively. If two holes are moved one toward each other along the x axis (S<0, see Fig. 1(l) for definition), k_x is modified without affecting k_z. As a consequence, f_x increases while f_z does not change. In the same way f_x decreases for S > 0, while keeping f_z constant. Figures 1(f-i) display x- and z-pole modal profiles for S = 0 and S = 0.2a: the electric field component along x (E_x) of the z-pole mode profile remains unchanged when the holes are moved far from the center [Figs.1(g) and 1(i)]. The shift instead results in the elongation of the x-pole modal function along x [Figs. 1(f) and 1(h)], thus modifying its resonant frequency.

It is important to notice that such alterations of field distributions modify the modal Q factors [Fig. 1(e)]: when S < 0, abrupt changes are introduced near the electric field maximum of the z-pole mode function, resulting in an increase in radiation losses and in a smaller Q factor (Q ∼ 557 for S = −0.057a) [38]. In contrast, if S > 0 these abrupt variations are avoided, the radiative energy in the light-cone minimized, and the Q-factor of the z-pole mode enhanced together with almost preserved V and f_z. The optimized Q-factor turns out to be Q ∼ 810 for S = 0.075a, and the Purcell factor is assessed as F ∼ 90.

These findings are confirmed by the analysis in the z-pole momentum space, obtained by using a 2D Fourier Transform (2DFT), reported in Figs 2(a) and (b) for S = −0.1a and S = 0.2a, respectively. The white circle of Figs 2 (a) and (b) delimits the leaky region, defined by the light cone [38-40]: the stronger the components within this area, the higher the radiation losses along y. For S = −0.1a (Figs. 2(a) and (e)) a sharp peak is present at the center of the leaky region, affecting the value of Q; instead if S = 0.2a (Figs. 2(b) and (f)), the 2DFT is almost constant inside the light cone.

As demonstrated in [38], the Q-factor depends also on the shape of the two peaks outside the light cone. A Gaussian shape typically leads to higher Q-factor, giving a direct measure of the energy not coupled with the radiation mode. Figs. 2(c) and (d) show a zoom of Figs. 2(a) and (b), respectively: the behavior for S = −0.1a is far from a 2D Gaussian function. For S = 0.2a (Fig. 2(d)), it is instead clear that by moving two holes far from the center, a 2D Gaussian function for these peaks is obtained, as also confirmed by the 1D gaussian fitting of the cross section of these lobes reported in Fig. 2(g). Therefore, by increasing the z-pole Q-factor, a positive S does not substantially affect the position, modal volume and resonant frequency of the z-pole electric field main lobe, leading to a straightforward increase of the Purcell factor of microresonators.

This therefore verifies that momentum space engineering, a strategy exploited to improve the confinement of defect states localized within the PBG [11,38,42], can also be efficient for cavity resonances without PBG.

4.1. Nanoemitters deposited on top of the cavity

A micromolar solution (10⁻⁶mol/l) of DRs in toluene was prepared by using the synthesis procedure described in [43] by L. Carbone and co-workers and drop-casted on the realized microcavities. Figure 3(b) displays three resonances for three different values of a. The resonant peaks are well fitted by a Lorentzian function [Fig. 3(b), inset] and result in a maximum Q ∼ 620 for an unmodified H1 cavity (a ∼ 265 nm).

To explore the mode shifting over a wide spectral range, an organic fluorophore (Cy3) with broad emission spectrum was immobilized on the device. The μPL spectra for different values of S reported in Figures 3(c-f) show that the z-pole mode is almost unaffected by holes shifting, while x-pole resonant wavelength can be broadly tuned by means of S. Polarization-resolved measurements were carried out to identify the two modes, and their resonant wavelengths (λ_x and λ_z) as a function of S are displayed in Fig. 3(g). In agreement with the theoretical results of Fig. 3(e), the x-pole mode is tunable over a range ∆λ_x ∼ 40 nm. Small discrepancies between experimental results and theoretical calculations have been observed in terms of slight variations of λ_z and weak nonlinearity of λ_x; since these variations do not show a clear dependence on S, they could be reasonably attributed to unavoidable fabrication imperfections. The theoretical findings about the influence of the holes position on the z-pole Q-factor have been confirmed by the experiments. For S = 15 nm Q ∼ 750 has been measured, while for S = −20 nm the z-pole Q-factor falls down to a value of ∼ 200.

4.2. Colloidal nanocrystals localized in the maximum of the electric field distribution

It is well known that in 2D-PhC slabs the in-plane confinement (xz) is due to the photonic band gap produced by the PhC periodicity, while in the out-of-plane direction (y) the confinement is due to the total internal reflection. As already mentioned, in the xz plane the electromagnetic field is localized in the center of the cavity (see figures 1(f-i)); FDTD simulations show also that along y the main lobe of the confined radiation is in the center of the slab (see Fig. 4).

The coupling reported in section 4.1 is thus not optimized, as the nanocrystals and the organic molecules are deposited on top of the cavities.

A viable strategy to approach the maximum allowed Purcell factor is to localize the nanoemitters in the center of the slab. This has been done with colloidal dot-in-rod nanocrystals using the same fabrication process described in section 3 and splitting the growth procedure of the Si₃N₄ slab in two steps. Figure 5(a) shows a sketch of the fabrication procedure. First of all, a 200 nm thick Si₃N₄ slab was grown on a Si substrate. A thin layer of colloidal DRs, with a molar concentration of ∼ 10⁻⁶mol/l was then spin-coated on it with a rotating speed of 500 rpm, thus obtaining a thickness lower than 10 nm as assessed by SEM inspection. After solvent evaporation, a second 200 nm thick layer of Si₃N₄ was grown on top of the sample. We verified the uniformity of the deposited layer by exploiting both the morphological characterization and the photoluminescence maps collected by a confocal microscope. A SEM cross-section of the resulting sandwiched structure is shown in Fig. 5(b). The nanocavities were then realized through electron beam lithography and dry and wet etching processes by following exactly the fabrication procedure reported in paragraph 3 (Fig. 5(c)).

Also in this case, the optical measurements of the nanocavities were carried out by the OLYMPUS FluoView 1000 confocal laser scanning microscope, with a spatial resolution of 200 nm. A CW laser diode emitting at wavelength λ_ex = 405 nm was used as excitation source. In Fig. 5(d) are reported the photoluminescence spectra collected from the 2D-PhC H1 nanocavities with different lattice constants a. Superimposed to the broad emission spectrum (FWHM ∼ 30 nm) of NCs uncoupled to the cavity, sharp peaks with a quality factor of about 600 are clearly detected, assessing the modulating effects of the PhC nanocavity on the emission of NCs coupled to the optical mode localized in the defect. Moreover, the normalized frequency a/λ of the experimental results was found to be about a/λ ∼ 0.46 against the expected value of a/λ of ∼ 0.431. As already suggested in case of the modal selective tuning, this slight difference can be mainly attributed to the effects of fabrication imperfections, inducing unavoidable uncontrolled variations in the optical properties of the PhC nanocavities [45].

The efficient coupling between the semiconductor nanocrystals layer and the dielectric cavity is due to the fact that the nanocrystals layer can be precisely positioned in the maximum of the confined electric field in the vertical direction. Indeed, in this case the Purcell effect results optimized [46] and the spontaneous emission rate strongly increased, leading to the possibility to measure a better Q-factor [47]. At the same time it is noteworthy to point out how the introduction of a guest material, embedded in two Si₃N₄ layers, does not affect the optical properties of the nanocavity as shown by the good match of the calculated and measured Q-factors (equal to 680 and 600, respectively).

5.1. Working principle

PhC nanocavities can be embedded in a two-dimensional array, to realize an improved optical detection system of a miniaturized assay for genomic and proteomic analyses, (DNA or protein microarray). Fig. 6(a) is a three-dimensional sketch of the biochip architecture including different nanocavities, each having a different resonant wavelength. Moreover, a one-to-one correspondence is also preserved between a cavity and a group of specific bio-molecules (probes) immobilized on the surface (as shown in the expanded view of Fig. 6(a)). The as-realized chip can be exposed to a biological solution containing unknown target species, or analytes; conjugation between the analytes and their complementary probes takes place on the device surface [51]. Since the target analytes are typically labeled with fluorescent markers, the binding events can be revealed through optical inspection of the biochip readout area, thus allowing a complete compositional analysis of the assay [52].

The recourse to a microarray configuration already allows the simultaneous analysis of a certain number of analytes thanks to spatial discrimination [52,53]. Here we upgrade the allowed degree of parallelization by assigning a peculiar spectral signature, given by the resonating behavior of each cavity, to each bioprobe immobilized on the surface. This gives the possibility to distinguish the spectral response of each target analyte bound to the corresponding probe, albeit a single common fluorophore is used for the labeling of the whole unknown solution. Fig. 6(b) exemplifies a possible spectral scan of the signal collected from the whole readout area. Different peaks can be observed on the emission spectrum of the fluorescent marker, each revealing the presence of a specific target analyte in the investigated assay. Besides the spatial discrimination implemented in microarray configurations, in this case the spectral distinction contributes substantially to the parallelization of the device. We also expect a beneficial effect given by Purcell effect, which increases the radiative emission rate of emitting materials interacting with quantum confined systems [54, 55]. Hence, a significant increase in the luminescence intensity of the markers coupled to the PhC cavities is envisioned, leading to a significant improvement of the signal-to-noise ratio and of the overall sensitivity of the biochip detection.

5.2. Experimental results

PhC nanocavities resonating in the visible spectral range were fabricated in Si₃N₄ membranes on a Si substrate, exploiting the modified single defect H1 nanocavity described in section 2 [33,43,47,57]. Several chips were fabricated, each containing an array of optimized H1 resonators with variable lattice constant a, thus tuning the corresponding resonant wavelengths. We tested the proposed architecture both with single-stranded DNA (ss-DNA) and antibody probes immobilized on the Si₃N₄ surface of two different devices. Complementary DNA targets or specific secondary antibodies, labeled with cyanine 3 (Cy3) and rodhamine (TRITC) fluorophores, respectively, were then allowed to recognize the immobilized probes, thus obtaining a uniform fluorescent monolayer of the biomolecular species.

The effects of fluorescence enhancement and peak sharpening in resonant conditions are clearly observed in the emission spectra reported in Fig. 7(a) for PhC nanocavities treated with TRITC-labeled proteins and in Fig. 7(b) for DNA-functionalized nanocavities (five uppermost lines, compared to the lowest spectrum corresponding to the emission of Cy3- DNA strands without photonic resonators). In both cases it is evident that the change of the lattice period a of the photonic crystal resonator leads to the modification of the spectral response coming from target analytes conjugated by the same broad emitting organic dye: a specific spectral feature is thus attributed to the target analytes captured on different cavities. The best measured Q-factor obtained in the PhC-nanocavities DNA-chip prototype is ∼ 725, corresponding to a full-width at half maximum of ∼ 0.9 nm. Taking into account the spectral resolution limits, a conservative estimate suggests the possibility to distinguish up to 150 different resonant peaks within the 150nm bandwidth of the Cy3 emission spectrum. This means that up to 150 parallel analyses can be simultaneously performed with one single spectral scan of the readout area of the biochip, thus drastically decreasing the time required for a complete compositional identification.

By confocal microscopy it is also possible to visualize the effects of emission enhancement in resonant conditions, as reported in the photoluminescence maps reported in Fig. 7(c). In this array of five different nanocavities, functionalized with ss-DNA and hybridized with Cy3-labeled complementary DNA sequences we have performed a spectral scanning of the acquisition wavelength with a resolution of 2 nm. When the detection wavelength matches one of the five resonating wavelengths of the nanocavities, marked from λ₁ to λ₅ in Fig. 7(b), it is possible to distinguish a bright spot in the center of each nanocavity.

In order to quantify the enhancement effect of each photonic crystal pattern, in Fig. 8 it is reported a three-dimensional intensity profile collected on a Cy3-labeled DNA functionalized nanocavity in resonant conditions. The central bright spot corresponding to the H1 defect cavity reveals a signal improvement as high as 160 as compared to the luminescence coming from unpatterned Si₃N₄ surface. A major role of the Purcell effect [54,55] can be envisioned, by virtue of the strong optical quantum confinement performed by the H1-shifted nanocavities.

Noteworthy, the photonic crystal pattern itself causes an improvement of fluorescence emission as compared to the surrounding unpatterned Si₃N₄ layer, although the immobilization and hybridization processes have been homogeneously performed on the whole sample surface. In this case, an enhancement of ~ 20 times is achieved. This behavior may be ascribed to the combination of two effects. First, the free-standing membrane layer makes available a larger surface area to the probes immobilization (about a factor of 4 more than the unpatterned layer), resulting in a higher number of immobilized Cy3-labeled analytes in the PhC regions. Second, in 2D-PhC patterns an efficient transfer channel between externally radiated light and energy trapped in the membrane is represented by the so-called leaky modes [48,57,58]. The coupling of such modes with the absorption or emission bands of neighboring emitters may lead to a significant increase of their luminescence. Although the photonic crystal pattern has not been specifically optimized to maximize such effect, the role of leaky modes localized on the PhC pattern for the further increase of the luminescence experimentally observed is not negligible.

The insertion of PhC cavities in classical biochip architectures leads, therefore, to a huge increase of the emission intensity of fluorescent markers, thus providing higher sensitivity, and allowing detection of very small amounts of target biomolecules in the investigated solution. In addition, the nanocavities attribute peculiar spectral features to the target analytes captured by their surface, so that the presence of specific species in the solution can be inferred by a simple spectral analysis of the optical response of the read-out region. This enables parallel detection of multiple elements, thus accelerating the analysis time.