1. Introduction

The creation of three-dimensional (3D) photonic nanostructures with complex 3D designs is a key challenge for the complete control of photons in three dimensions. 3D photonic crystals [1–17], which are composed of wavelength-scaled periodic arrangements of dielectric materials in three dimensions, are particularly promising structures for the achievement of this goal. Various milestones in the manipulation of photons have been gradually reached over recent years; for example, arbitrary 3D light guiding [7], control of emission [2,5,10], and the use of surface-related phenomena [6] have been demonstrated. However, the accurate fabrication of such 3D photonic structures has been difficult, which has inhibited more rapid progress. The stacking of two-dimensional (2D) patterns [1–7] is one important method of construction, but it requires complicated and time-consuming processing. Although a template-based deposition method [8–12] represents an alternative approach, the formation of unexpected defects in the template or during the deposition is still an issue to be overcome.

Fabrication methods based on high-aspect ratio etching [13–17] are expected to be beneficial for the simpler fabrication of 3D structures. Thus far, focused ion beam (FIB) etching, chemically assisted ion beam etching (CAIBE), and reactive ion etching (RIE) have been used in 3D fabrication, where the etching has been applied in two or three steps. Nevertheless, none of these methods have yet been optimized. For example, although three-step sequential etching led to the creation of a 3D photonic crystal [13], it was observed that the experimental performance was degraded compared with that expected from the design parameters, suggesting the shape deformation as a consequence of the sequential etching of holes, which intersect each other. In the case of a recently proposed method based on double sequential etching [15,17], the etched holes were designed not to cross each other, allowing a well-defined structure to be created. However, the highly precise alignment of the positions of each etched hole required in this method makes the processing severe.

In this work, we develop a new way for creating 3D photonic structures by ‘single-step’ plasma etching, where troublesome fine alignment or unanticipated deformation of the etching shape due to sequential processing can be avoided. By applying three-directional simultaneous etching, we demonstrate the fabrication of 3D photonic crystals and discuss the differences between structures fabricated by simultaneous and sequential etching. We measure the optical characteristics to reveal that a complete photonic bandgap is created at optical communication wavelengths. The demonstration of 3D photonic crystals with various lattice intervals also shows the photonic bandgap effect in a wide wavelength range including 0.6 to 1.1 μm, suggesting that our method can be conveniently applied to 3D photonic crystals in the range of the near-visible wavelengths that requires finer structures.

2. Method

Figure 1(a) shows a schematic image of our simultaneous multi-directional etching concept. Positive ions, which play the main role in RIE process, are simultaneously irradiated to a semiconductor wafer from multiple directions. Etching is performed through a mask with a desired 2D pattern, and a 3D structure is simply formed in one step. This method essentially enables various types of 3D structures to be formed simply by changing the initial 2D pattern and/or the angles of the ion-irradiation paths. To perform such simultaneous multi-directional etching in conventional RIE equipment, the ion trajectory is controlled. Thus far, to obtain etching in one oblique direction to the surface normal of the substrate, we developed a method to control ion trajectory by modifying the ion sheath [17]; by simply placing a metal plate on the substrate, where the plate possesses a trench designed to adequately control the form of the ion sheath or the distribution of the equi-potential plane, the ions are guided in a direction parallel to the trench, allowing their trajectory to be modified as desired.

 

Fig. 1 Schematic picture of multi-directional etching technique for fabricating 3D photonic nanostructures. (a) Schematic image of multi-directional simultaneous etching process. After the preparation of an etching mask with the necessary 2D patterns, multi-directional plasma etching is performed through the etching mask. (b) Schematic view of ion-sheath control plate for three-directional, simultaneous etching. At the bottom face of ion-sheath control plate, three trenches overlap in one area.

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We extend such a mechanism to obtain multi-directional, simultaneous etching. The ion-sheath control plate design that we consider is shown in Fig. 1(b). We formed trenches in three different directions on one metal plate. Since these trenches overlapped with each other at the bottom face of the plate, we expect to realize multi-directional etching in this area. In this work, we used single-crystalline silicon as a constituent material and etched it using RIE equipment with an inductively coupled plasma source with a mixture of SF₆ and O₂ gas at cryogenic temperature [17]. We determined the shape of the trenches in the ion-sheath control plate by considering the plasma condition, particularly the thickness of the ion sheath [17]. We set the height of the trench apertures and the length of the trenches to 0.5 and 5.8 mm, respectively. Since the feature sizes of such an ion-sheath control plate are of the order of mm, we simply prepared it by aluminum using a conventional metal processing technique.

3. Results and discussions

We now demonstrate our simultaneous, multi-directional etching technique by fabricating 3D photonic crystals with the structure shown in Fig. 2(a). This structure was previously theoretically proven to possess a complete photonic bandgap under an azimuthal-angle interval of 120° and an elevation angle of 35.3° [18]. In this structure, the unit in thickness direction a_z is defined as a_z = $\sqrt{6}$a_x, where a_x is the in-plane lattice interval. We prepared aluminum etching masks with 2D triangular-lattice hole arrays and subsequently etched in three directions through the mask. Here, the rotational alignment of the angle between the 2D lattice pattern in the etching mask and the ion-sheath control plate is important. For it, we prepared alignment markers, which indicate the position of the ion-sheath control plate, on the wafer at the same time as forming the 2D mask patterns. The estimated rotational error was less than 0.5°. Figures 2(b) and (c) show top-view and cross-sectional scanning electron microscope (SEM) images of the fabricated structure; the lattice interval a_x was set to 530 nm and the radius of the air holes was set to 0.35a_x. We aimed to obtain the thickness of 1a_z as a fundamental structure. The area of one photonic-crystal domain was set to 75 μm × 75 μm. It is obvious from Fig. 2(b) that the triangular-lattice pattern was accurately transferred during the three-directional etching process. Furthermore, Fig. 2(c) demonstrates that the expected 3D structure was successfully formed to a depth of ~1.3 μm, which corresponds to ~1a_z.

 

Fig. 2 Demonstration of 3D photonic-crystal fabrication. (a) Schematic structure of fabricated 3D photonic crystal. Etching is performed through an etching mask with a triangular-lattice air-hole pattern. (b) Top-view and (c) cross-sectional SEM images of fabricated 3D photonic crystal. The 3D structure is formed to a depth of 1.3 μm (~1a_z).

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Next, we compare the effectiveness of our simultaneous etching method with that of sequential etching from the viewpoint of the optical characteristics. Figure 3(a) shows the measured reflection spectrum of the structure in Fig. 2(b) that was obtained by normalizing the reflection spectrum of the 3D photonic crystal with that of a gold mirror. We observed high reflectance of more than 80% in the wavelength ranging from ~1.2 to ~1.7 μm, which suggests the formation of a photonic bandgap in the surface-normal direction and the successful formation of the desired 3D structure. For comparison, we also fabricated a sample by using the same etching mask but by performing sequential etching in three steps, and measured its optical properties. The first etching step was performed while covering two trenches of the ion-sheath control plate shown in Fig. 1(b), and the same procedure was repeated in different directions for the other two etching steps. The inset of Fig. 3(b) shows a top-view SEM image of this sample. We see that the obtained 3D structure was changed from that fabricated by simultaneous etching [see the inset of Fig. 3(a)]. This difference of the structure critically affects the optical performance as shown in Fig. 3(b). The reflectance was no more than 45%. Considering that the reflectance at the interface between air and silicon is ~40%, the photonic bandgap effect appears to be absent in the structure formed by sequential etching. This suggests that during the second or third etching steps, the existing holes disturb the etching condition, thus the shape of the subsequently etched holes will differ from that expected. Here, note that the structure, which was designed to avoid the overlap of etching holes, was successfully demonstrated using a sequential etching process [17]. These results indicate that simultaneous etching is a key method, particularly for accurately creating structures where the etching holes intersect each other inside 3D structures.

 

Fig. 3 Comparison between 3D structures fabricated by simultaneous and sequential etching processes. (a), (b) Reflection characteristics of 3D structures formed by simultaneous and sequential etching, respectively. The insets show top-view SEM images. The high reflectance shown in (a) implies that the photonic bandgap effect is realized. No significant increase in reflectance was measured in (b).

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We now focus on the detailed optical characteristics of 3D photonic crystals fabricated by simultaneous three-directional etching. By increasing the etching time, we increased the etching depth to ~2 μm, which corresponds to ~1.5a_z, and examined both the transmittance for various incident angles and the reflectance for normal incidence. Transmittance was obtained by normalizing the transmission spectra of the photonic-crystal sample with those of the flat area without photonic crystals. Here, a_x was 530 nm and the radius of the holes was set to 0.38a_x. A top-view SEM image of the fabricated structure is shown in Fig. 4(a). The inset in Fig. 4(a) shows the measured directions in transmission measurements. The measurement results are shown in Fig. 4(b), where it is apparent that the reflectance exceeded 95% and the transmittance was less than −15dB at wavelengths around 1.3 μm. The attenuation of the transmittance (< −10dB) was obtained in common for all incident angles in the wavelength ranging from ~1.2 to 1.4 μm, suggesting the formation of a complete photonic bandgap in such a wavelength range. These results were consistent with the calculated reflectance and transmittance in the surface-normal direction obtained by finite-difference time-domain calculations [Fig. 4(c)]. Here we discuss the quality of our 3D structures from the viewpoint of the attenuation of the transmittance for angled incidents. In previous works [1,4,6,7,17], the attenuations of the transmittances in common to all the measured incident angles were −8~-15dB per period in the vertical direction (1a_z). Our structure demonstrated −15-dB attenuation by 1.5a_z: attenuation of −10dB/a_z. This suggests that our structure exhibited high-quality photonic bandgap comparable to previous works, although the fabrication process was significantly simplified and straightforward.

 

Fig. 4 Optical properties of 3D photonic crystal fabricated by simultaneous three-directional etching. (a) SEM image of fabricated sample with the etching depth of ~2 μm (~1.5a_z). The inset shows the measurement directions of transmittance. (b) Measured and (c) simulated reflectance and transmittance spectra.

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Finally, in order to demonstrate the flexibility of our simple processing technique, we fabricated 3D photonic crystals with various lattice intervals a_x. At first, we demonstrated the control of the photonic bandgap range within the communication wavelengths by fabricating 3D photonic crystals with lattice intervals ranging from 530 to 650 nm on a wafer. We utilized identical ion-sheath control plate and etching condition. The etching depths were estimated to be ~2 μm, which corresponds to 1.5~1.3a_z for a_x of 530~650 nm. Figure 5(a) shows top-view SEM images of 3D crystals with different lattice intervals. In the reflectance and transmittance shown in Fig. 5(b), the high-reflectance and low-transmittance bands, which were formed owing to the photonic bandgap effect, shifted to long wavelength with increasing lattice intervals. These results demonstrate that our method is applicable to a wide range of 3D photonic structures. We then produced 3D photonic crystals to possess photonic bandgaps in a shorter wavelength range. Since this requires smaller lattice intervals, the creation becomes difficult in the other methods previously discussed. For example, in the sequential twice-etching method [17], the alignment accuracy of the positions of the first and second etching should increase as the lattice interval becomes smaller. In contrast, simultaneous etching does not require such a delicate process. We prepared 2D patterns with lattice intervals ranging from 315 - 450 nm as etching masks and performed etching using the same ion-sheath control plate and the same etching condition. The etching depths were set at about 1 μm; this corresponds to a thickness of 0.9~1.1a_z. Figure 6(a) shows top-view SEM images of the 3D photonic crystals. Clearly, all of these structures were fabricated as expected. We measured their reflectance, which was obtained by normalizing the reflection spectra of the sample with those of silver mirror. We did not measure the transmittance because the structures were prepared on the top of the single-crystalline silicon wafer with a thickness of about 500 μm, which mostly absorbs light in a wavelength below 1.1 μm. In the reflectance spectra shown in Fig. 6(b), we see high-reflectance bands depending on lattice intervals a_x; high reflectance (>~80%) was obtained in the wavelength range around 1.0 μm for a_x = 450 nm, 0.95 μm for a_x = 405 nm, 0.75 μm for a_x = 360 nm, and 0.60 μm for a_x = 315 nm. Although relatively high reflection (40~50%) was seen in the wavelength around 1.1 μm for a_x = 360 nm and 0.95 μm for a_x = 315 nm, we assume that they originated from Fabry-Perot interference. The obtained high-reflectance exceeding ~80% suggests the formation of a photonic bandgap even in such a short wavelength range of 0.6~1.1 μm. Note that the reflectance remained high (>~80%) despite the inherent material absorption of Si due to the band-to-band transition in the wavelength below 1.1 μm. The influence of such an absorption nature on the optical characteristics of the Si-based 3D photonic crystals will be described elsewhere.

 

Fig. 5 Demonstration of 3D photonic crystals in optical communication wavelengths range. (a) Top-view SEM images for lattice intervals ranging from 530 to 650 nm, (b) measured transmittance and reflectance of structures shown in (a).

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Fig. 6 Demonstration of 3D photonic crystals in wavelengths below 1.1 μm. (a) Top-view SEM images for lattice intervals ranging from 315 to 450 nm, (b) measured reflectance of structures shown in (a).

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5. Conclusion

We have developed and demonstrated a technique for creating 3D photonic nanostructures by simultaneous multi-directional etching. We showed that this method can be used to fabricate 3D photonic-crystal structures on single-crystalline silicon wafers using a single etching step. The fabricated structures exhibited optical properties consistent with the formation of a photonic bandgap in optical communication wavelengths range, implying that the 3D photonic structures were successfully formed as expected. We also demonstrated that the lattice intervals of 3D structures can be varied by simply changing the mask pattern, demonstrating the bandgap effect in wavelengths ranging from 0.6 to 1.1 μm, which requires finer structures. We expect to apply our method to thicker 3D photonic structures by extending the etching time while tuning the etching conditions and the ion-sheath control plate. The formation of various types of 3D structures in a variety of materials would be realized by further developing the design of the ion-sheath control plate, depending on the etching materials and mask patterns. Because our method enables even the batched processing of 3D structures with complex designs, it will promote further progress in research on 3D photonic nanostructures.