1. Introduction

Photonic crystal (PC) nanocavities can confine light within extremely small volumes on the order of the cubic wavelength, thus providing an intense interaction of the light and embedded emitters. This light-matter interaction has lead to the observation of a number of quantum electrodynamic (QED) phenomena, such as Rabi-splitting [1,2] (in the strong coupling regime) and the Purcell enhancement of spontaneous emission [3, 4] (in the weak coupling regime). The latter effect can be exploited, e.g., for the realization of low-threshold nanolasers [5,6] and efficient single photon sources [7, 8].

Most of the reports on PC nanocavities and their coupling to emitters have concentrated on material systems with high refractive indices, such as Si or GaAs, which operate in the near infrared spectral region [9–16]. Extending these experiments into the visible range of the spectrum poses a number of challenges, above all the need for a transparent material featuring a relatively high refractive index to provide sufficient optical confinement. (Al,In,Ga)N-based material systems are one possibility, allowing the fabrication of devices emitting in the ultra violet to green region [17–19]. Red laser emission from AlGaInP/GaInP PC membranes has also been demonstrated [20]. However, the fabrication of these III/V semiconductor devices is expensive and still technologically challenging (especially concerning free-standing structures) and a direct integration with standard CMOS technology is not possible. Using organic materials is another possibility [21], allowing an easy doping of the PC material with a large number of different emitters (e.g., dye molecules or colloidal quantum dots), but usually suffering from relatively small refractive indices.

Recently, Makarova et al. [22] investigated the emission from Si nanocrystals in Si-rich SiN PC membranes, demonstrating the potential of these structures as photonic building blocks in the yellow to red wavelength range. In comparison to III/V semiconductors the fabrication process of SiN PCs is fully compatible with standard CMOS technology, making the fabrication (even of free-standing structures) easy and cost-effective. Furthermore, SiN-based PCs are fully bio-compatible, paving the way for a number of bio-photonic applications. However, the cavity quality factors obtained so far were quite modest (200–300) [22]. If the full spectrum of cavity QED effects is to become accessible with these kinds of structures, the quality factor has to be further optimized.

Here we report on studies of the well-known L3 cavity in SiN PC membranes. In Ref. 22 the large ratio of the hole radius r to the lattice constant a (r/a=0.4) allowed only to observe higher ordermodes, which are usuallymore lossy than the fundamentalmode and exhibit a smaller free spectral range. Therefore, we focus our attention on the fundamental cavity mode, optimizing the cavity design with respect to the quality factor, both theoretically and experimentally. Dye molecules, spin-cast on top of the membranes, are used as broadband light emitters which probe the mode structure of the cavities at room temperature and allow an easy determination of the corresponding quality factors. Using external emitters instead of intrinsic ones has the advantage that the full spectrum of emitters available in the corresponding wavelength range can be applied. Furthermore, different emitters can be used subsequently or in combination to cover different wavelength ranges.

The paper is organized as follows: A theoretical analysis of the quality factor of an optimized L3 cavity design is presented in Sec. 2. In Sec. 3 the fabrication procedure and preparation of the samples is described, also analyzing occurring fabrication imperfections. Furthermore, experimental details of the fluorescence measurements are given. In Sec. 4.1 a mode analysis based on the fluorescence measurements is performed, comparing the experimental peak positions of a simple L3 cavity to the predicted ones. This is followed by a detailed study of the quality factors of the optimized cavities in Sec. 4.2, including a discussion of the observed discrepancies to the simulation. Finally, Sec. 5 concludes our paper.

2. Numerical analysis

The L3 cavity, which basically consists of three missing holes in a row, is one of the most extensively studied types of PC cavities. This is mainly due to the fact that it supports a spectrally well separated fundamental mode with small mode volume (on the order of the cubic wavelength), whose quality factor can easily be optimized to relatively high values (>5×10⁴ in Si-based PCs) by simply adjusting the surrounding holes of the cavity [23, 24]. However, this optimization was performed for high-index material systems and its applicability to low-index materials has to be justified. We therefore carried out a number of numerical simulations using a three-dimensional finite-difference time-domain (FDTD) algorithm. A schematic representation of the simulated cavity is shown in Fig. 1(a). The radius of the holes and the thickness of the PC membrane were r=0.3a and t=1a, respectively, where a is the lattice constant. The membrane itself was made of SiN for which a refractive index of n=2.01 was assumed. The lateral size of the whole PC structure was 28a×14√3a. It has to be noted that the dimension of the computational domain should not be chosen considerably smaller than that, since lateral losses are much more significant in such a low-index system compared to high index PCs due to the weaker lateral confinement. In our case, the applied dimensions coincide with those of the fabricated structures discussed later in this article.

 

Fig. 1. (a) Schematic representation of the cavity geometry. The surrounding holes of the L3 cavity have a reduced radius r ^′ (left and right holes, light red) and r ^″ (upper and lower holes, light green), respectively. Additionally, the left and right holes are displaced outwards by a distance d. (b) Absolute value of the electric field of the fundamental cavity mode in the central plane of the PC membrane. (c) Calculated quality factor for various values of r ^′ and d for a cavity with r=0.3a, t=1a, and r ^″=0.3a. (d) Calculated quality factor as a function of r ^″ for the same cavity with fixed r ^′ and d.

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We have investigated three different approaches to optimize the quality factor Q of the fundamental mode (Fig. 1(b)). First, the radius r ^′ of the left and right boundary holes was reduced and second, the holes were shifted outwards by a distance d. The impact on the quality factor can be seen in Fig. 1(c). A nearly five-fold enhancement of Q occurs for r ^′=0.2a and d=0.2a. Further decrease of r ^′ or increase of d does not improve the quality factor significantly. Besides, too small hole radii or too large shifts can be problematic since a reliable and reproducible fabrication becomes more challenging. We therefore used these values (r ^′=0.2a, d=0.2a) as a starting point for further optimization. Shifting the neighbor and next-neighbor holes to the left and right of the cavity (as had been done, e.g., in Ref. 24) did not lead to any significant improvement in our simulations. Instead, as a third approach, we altered the radius r ^″ of the upper and lower boundary holes of the cavity. The result is shown in Fig. 1(d). Obviously, an additional boost of Q by more than a factor of 2 can be achieved by slightly reducing r ^″ to about 0.25a, leading to a maximum quality factor of Q≈4700. The observed improvement of the quality factor results from the shift of the cavity boundaries away from the points of high field intensity. This leads to a smoother decay of the cavity mode into the surrounding PC structure and therefore to lower vertical losses. In the wave vector picture this is equivalent to the fact that the fraction of k vectors lying in the leaky region, i.e. those which are not confined by total internal reflection, is reduced [24].

According to the Purcell effect [25] the spontaneous emission rate of an emitter, which is spectrally and spatially aligned with respect to the field maximum of the cavity mode, is enhanced by a factor

where λ is the peak wavelength of the mode, n=√ε is the refractive index of the membrane, and V is the mode volume. The latter can be calculated from

with ε($\overrightarrow{r}$ ) and $\overrightarrow{E}$ ($\overrightarrow{r}$ ) being the local dielectric constant and electric field, respectively. With a quality factor Q=4700 and a mode volume V=1.32(λ/n)³, as is calculated from our simulations, a maximum enhancement of the spontaneous emission rate of nearly 270 would be possible for an emitter placed at the center of the membrane. However, in our experiments emitters are located at the surfaces of the membrane, where the electric field intensity |$\overrightarrow{E}$ ($\overrightarrow{r}$ )|² reaches only values of about 20% of the value |$\overrightarrow{E}$ ($\overrightarrow{r}$ )|² max in the central plane. This reduces the possible Purcell factor to ≈50. Furthermore, the experimentally observed Purcell enhancement is usually only a fraction of the predicted one, as slight spatial and spectral misalignments can significantly reduce the coupling between cavity and emitter. Nonetheless, the numerical results are encouraging and suggest that cavity QED effects investigated in high-index PCs can also be achieved in such a low-index system. We thus fabricated and studied a series of L3 cavities and the coupling of emitters to them, as is presented in the following sections.

3. Sample fabrication and experimental setup

The PC structures were fabricated using low pressure chemical vapor deposited silicon nitride with a core thickness of 300 nm or 230 nm. As a carrier, 4 inch silicon h100i wafers with a 1.6 µm and 2.2 µm thick SiO₂ cladding layer were used, respectively. The fabrication of the resonators occurred by means of electron beam lithography (EBL) and reactive ion etching (RIE). EBL was performed using a LEO 1560 equipped with a Nanomaker® pattern generator from Interface Company (Moscow). A single layer of 2.2M polymethylmethacrylate (thickness 150 nm) was patterned using a 30 kV electron beam, followed by 10 s development using AR 600-50 (Allresist, Berlin) and subsequent IPA rinse. For etching of the photonic structures a hard metallic mask was used, obtained by evaporating a 20 nm thick Ni layer and dissolving the resist using N,N-dimethylformamid. RIE was performed using an OXFORD Plasmalab 80 Plus RIE etcher. The etching process involved the use of fluorine-based radio frequency and inductively coupled plasma. A gas mixture of C₄F₈ and SF₆ was used to vertically etch both the nitride and the oxide layers while simultaneously passivating the etched sidewalls. In order to achieve good thermal contact with the ground electrode, the substrates were glued (AZ MIR 701) to a 4 inch wafer. After RIE the remaining Ni mask was removed using a 10% solution of HCl. The final fabrication step involved the selective wet etching of the underlying oxide layer using a 50% solution of pure HF.

An example of a fabricated cavity with a lattice constant a=270 nm is shown in Fig. 2(a). From scanning electron microscope (SEM) images before and after the final etching process we conclude that the SiN is slightly etched by the HF solution, resulting in larger hole radii and smaller membrane thicknesses. Thus, starting from 300 nm and 230 nm thick SiN layers, the final structures had thicknesses of t≈270 nm and t≈200 nm, respectively. From the close-up image in Fig. 2(b) it can be seen that the holes have different radii at the top and bottom of the membrane, respectively, indicating a slightly conical shape. Thereby, the tilt of the hole walls (relative to the vertical direction) increases with decreasing hole radius, ranging from 4° to 8° throughout the samples. The impact of this type of fabrication imperfection will be discussed in Sec. 4.2.

 

Fig. 2. (a) SEM image of one of the fabricated SiN PC cavities. (b) A close-up view of the membrane holes. The conical shape of the holes, which gets more pronounced with decreasing hole radius, can clearly be seen.

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After rinsing the samples in a 50:50 H₂O₂/H2SO₄ mixture for several hours a solution of NileRed molecules (Molecular Probes) in ethanol (concentration ~10^-6 M) was spin-cast on the membranes at 2000 rpm. The dye acts as a broadband emitter in the range between 600 nm and 750 nm. For excitation of the photoluminescence (PL) the 514 nm line of an Ar⁺ laser was used. The excitation light was focused onto the cavities through a 100×/0.9 NA microscope objective, forming a sub-micrometer spot on the sample surface. The excitation power was approximately 1 µW. The PL light was collected through the same objective and spatially filtered by a 100 nm pinhole. The light was than dispersed by a spectrograph (Acton SpectraPro 2500i) and detected with a liquid nitrogen cooled charge coupled device (Roper Scientific).

4. Experimental results and discussion

4.1. Mode analysis

We have fabricated a large variety of different PC structures, varying the hole radii r, r ^′, and r ^′, the hole shift d (see Fig. 1(a)), and the membrane thickness t. First, we analyze the general mode structure of the L3 cavity as seen in our experiments and compare it to the numerical simulations, before a detailed analysis of the corresponding quality factors is presented in Sec. 4.2. For simplicity we start with the simple L3 geometry, i.e. without any additional modifications. A number of PL spectra for different lattice parameters is shown in Fig. 3(a)–(d). Several peaks are observed in the detected emission spectrum, which shift to smaller wavelengths as r is increased or t is decreased. This clearly indicates the coupling of the dye molecules to the cavity modes. The peak corresponding to the fundamental mode (highlighted in red) can principally be tuned through the entire visible spectrum above 550 nm, although we have limited our studies to the wavelength range between 600 nm and 700 nm. As not all of the molecules were aligned in position and orientation to the cavity field to couple efficiently, a large background emission remained which closely resembles the unaltered reference spectrum (gray lines). Note that in our experiment we always determine the optical properties of the dye-loaded cavities, not the bare cavities. However, if we used lower dye concentrations (down to 10^-8 M) the observed changes in the spectral position of the resonances were always below 0.1% and also the quality factor did not change within the accuracy of the measurement. Thus, we deduce that the influence of the dye on the optical properties of the cavity can be neglected for the present analysis.

 

Fig. 3. (a)–(d) PL spectra (black) from simple L3 cavities coated with NileRed. The lattice constant is a=270 nm. For clarity, the fundamental mode (TE_y1) is highlighted in red. Corresponding reference spectra (gray) were recorded on the PC membrane away from the cavity and scaled to match the long wavelength part of the cavity spectrum. (e) Absolute value of the electric field of the first four cavity modes in the central plane of the PC membrane. (f) Comparison of the calculated peak wavelength of the cavity modes (lines) with the experimentally observed values (symbols). The lattice parameters are a=270 nm and t=1a.

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To get a deeper insight into the observed mode structure we have compared the experimental peak positions to those of the calculated modes. In the FDTD simulation we found four modes lying within the TE bandgap of the PC membrane, two of them dominantly polarized in x-direction (denoted as TE_x1 and TE_x2) and y-direction (denoted as TE_y1 and TE_y2), respectively. The corresponding mode patterns are displayed in Fig. 3(e). In Fig. 3(f) the theoretical behavior of these four modes is shown as a function of r together with the experimentally obtained peak positions. Note that the indicated value of r for the fabricated structures is an effective hole radius, as the holes are in fact conical. Contrary to this, our simulations were carried out assuming perfect cylinders. However, simulations with conical holes indicate that the resulting mode structure can well be described by an effective hole radius. This assumption is supported by the excellent agreement between the experimental and theoretical data shown in Fig. 3(f).

It should be mentioned that apart from the resonances depicted in Fig. 3(f) several other peaks occur in some of the spectra. The most prominent one can be seen adjacent to the fundamental mode in Fig. 3(a) and Fig. 3(b). The origin of this resonance is currently unknown. It was not observed on the bare PCmembrane (i.e. away fromthe cavity) and thus seems to be linked to the cavity. An interesting feature of this resonance is its quality factor Q~800, usually exceeding that of all other modes except for the best optimized cavities (see Sec. 4.2). It exhibits a clearly y-polarized emission, as is seen from polarization-selected PL measurements. We were not able to reproduce the unidentified resonance in our numerical simulations. Even if the conical shape of the holes is taken into account no additional modes occur that match the observed one. We were also able to rule out higher order slab modes as well as an influence of the dye, since the resonance seems to be independent of the dye concentration and is reproducible even if well separated dye-doped polystyrene beads (20 nm diameter) are used as emitters instead of a homogeneous film of molecules. Measurements on other types of cavities (L1 and L2) showed a similar phenomenon. Further investigations on the nature of this unidentified resonance are necessary, since it may provide an interesting alternative to the well-known cavity modes, once its origin and properties are understood.

4.2. Optimization of the quality factor

The quality factor of the fundamental mode can be determined from the measured spectra by fitting a Lorentzian to the experimental data. For the simple L3 geometry the obtained values are limited to Q~300–350. Based on the results of the numerical simulation we fabricated and measured a series of optimized L3 cavities by varying the hole radius r ^′ and the hole shift d. The results are shown in Fig. 4(a). As expected, the quality factor increases with decreasing r ^′ and growing d. Further improvement can be achieved by reducing the hole radius r ^″, as is seen from measurements on another series of cavities (Fig. 4(b)). The error bars in both figures result from uncertainties in the determination of d and r ^″ from SEM images, respectively. The best quality factor obtained so far was Q=1460. The corresponding PL spectrum is shown in Fig. 4(c), together with two polarization-selected measurements, clearly demonstrating the dominant linear polarization of the emission from the different cavity modes. If we assume that the fundamental mode has indeed a mode volume of V≈1.3(λ/n)³ (see Sec. 2), a quality factor of Q=1460 would give rise to a maximum Purcell factor of 17 for an emitter at the surface of the PC membrane. However, this only holds for emitters with an emission linewidth comparable to or smaller than the width of the cavity resonance. This is certainly not fulfilled in the experiments shown here due to the broadband emission of the dye molecules. Consequently, in future experiments emitters with a much narrower emission width should be employed to achieve more pronounced cavity QED effects.

The obtained quality factors are considerably smaller than the calculated ones (see Fig. 1(c) and Fig. 1(d)), most likely due to imperfections of the fabricated structures. If we decompose the measured Q _total into two components, namely Q _ideal of the idealized, simulated structure and Q _loss being composed of all additional losses, then Q _loss can be determined from the calculated and measured values using Q ^-1 _loss=Q ^-1 _total-Q ^-1 _ideal. Assuming Q _loss to be independent of r ^′, d, and r ^″ we have plotted a corrected theoretical estimation of the quality factor in Fig. 4(a) and Fig. 4(b) (dashed lines), showing reasonable agreement with the experimentally observed behavior.

From previous studies it is known that the main contributions to additional cavity losses are distortions of the hole shape, surface roughness, and absorption of the emitters [26]. We have performed FDTD simulations of PC structures based on SEM images of our samples to study the influence of distortions of the circular shape of the holes. From comparison with ideally circular structures we find that the contribution of this kind of imperfection to the observed Q _loss is negligible. Contrary to this, the influence of the conical shape of the holes is much more severe, as can be deduced from simulations of membranes with tilted hole walls. For example, a tilt of 5° (relative to the vertical direction) leads to a drop of the quality factor from Q=4700 to Q=1950. The reason for this is found in the vertical asymmetry, which leads to a coupling of the confined TE-like modes to propagating TM-like modes [27,28]. This results mainly in an increase of the losses in horizontal direction. Together with the losses due to surface roughness and dye absorption this easily explains the observed discrepancy between measurement and calculation. Consequently, the best route for a further optimization of the quality factor would primarily involve a better control of the tilt of the hole walls. Recently, we managed to fabricate structures with almost perfectly cylindrical holes by improving the fabrication parameters. Thus, we believe that quality factors of Q~3000 can be reached with our PC cavity design.

 

Fig. 4. (a) Experimentally obtained quality factors (symbols) of the fundamental mode for a series of L3 cavities with a=270 nm, r=0.29a, t=1a, and various values of r ^′ and d. The dashed lines represent the corresponding theoretical predictions. (b) Achieved quality factors for another series of L3 cavities with a=270 nm, r=0.3a, and t=0.74a, where r ^″ has been modified in addition to r ^′ and d. (c) PL (black) and reference (gray) spectra from the cavity displaying the best quality factor in (b). The two lower spectra were recorded with polarization filtering, clearly demonstrating the dominant polarization of the different cavity modes. The inset shows the TE_y1 peak and a corresponding Lorentzian fit.

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5. Conclusions

In conclusion, we have investigated the spontaneous emission from dye molecules on SiN photonic crystal nanocavities, probing the mode structure and quality factor of the cavities. A mode analysis yields good agreement between the calculated and observed spectral positions of the modes, but reveals also some unknown high-Q resonance which still needs to be identified. Theoretically, quality factors as high as 4700 are predicted after optimization of the cavity geometry, while experimentally Q values of nearly 1500 were achieved. The main source of the discrepancy between experiment and simulation is found in the tilt of the hole walls, leading to additional cavity losses. Improvements in the fabrication procedure may thus lead to a further boost of the quality factor.

Keeping in mind that these photonic crystal cavities can operate in the entire visible wavelength range above 550 nm, they provide a powerful tool to carry recent experiments on cavity QED effects into the visible spectrum. This is particularly appealing since a large number of different types of emitters exists in this spectral region, e.g. dye molecules, colloidal quantum dots, or color centers in diamond nanocrystals. Especially the latter are promising single photon sources [29] whose efficiency could be greatly enhanced once coupling to a nanocavity is achieved. As was already pointed out, the fabrication of SiN photonic structures is fully compatible with existing CMOS technology, making a cost-effective integration into complex optoelectronic devices feasible.