1. Introduction

Three-dimensional (3D) photonic crystals (PhCs) are artificial dielectric structures with 3D periodic refractive index modulation in the light wavelength scale [1–3]. 3D PhCs have photonic bandgaps in all directions [3–6], referred to as complete photonic bandgaps, which can be used as an efficient 3D mirror for selected wavelengths [7–9]. These 3D PhC mirrors have wide applications, such as antennas [10], solar cells [11], and display filters [12]. 3D PhCs have been traditionally demonstrated by stacking two-dimensional (2D) PhC slabs [13–18]. However, these types of 3D PhCs require challenging fabrication processes, such as wafer surface treatments, wafer fusions, and accurate pattern alignments. Recently, silicon 3D PhC structures have been demonstrated by one-time oblique dry etching using a tetrahedron Faraday cage, which enables simultaneous 3D ion etching [19–21].

Diamond is physically and chemically stable and has the highest thermal conductivity of all materials (2000 Wm⁻¹K⁻¹), thereby enabling high-power laser control [22]. Its wide transparent window from UV to mid-IR is a significant advantage for various optical device applications [23]. In addition, the point defect represented by the nitrogen-vacancy (NV) center in the diamond can be used as a single-photon source [24], which is utilized in the field of quantum sensors and quantum computing devices [25,26]. Despite these advantages, diamond 3D PhCs have not been reported because of their challenging fabrication process. Meanwhile, several studies have been conducted on the fabrication of membrane nanostructures on single-crystal diamond surfaces using Faraday cages [27–29].

By taking advantages of the above nano-fabrication techniques, we demonstrate two 2D PhC layers in single-crystal diamond surfaces by one-time angled etching using a tetrahedron Faraday cage. The two 2D PhC layers compose a quasi-3D PhC structure, and the wavelength-dependent vertical reflections are measured. By adjusting the lattice constant of the PhCs, the reflected wavelength spectra and colors are changed. Furthermore, the doubled collection efficiency from the NV center light emission in the diamond surface with the PhC structure is achieved.

2. Device fabrication

A schematic of the PhC structure and the selectively reflected light spectrum is shown in Fig. 1(a). The photonic bandgap from the PhC structure in the diamond surface reflects the specific wavelength bands based on the PhC lattice constant. For the 3D photonic bandgap, we adopt a face-centered cubic (FCC) or cubic closest packing (CCP) structure (A-B-C-A), as shown in Fig. 1(b) [2]. This structure has three-fold rotational symmetry around the z-axis and can be realized by three cylindrical holes, which have a tilting angle of 35^° from normal [Fig. 2(e)]. Owing to advanced nano-fabrication techniques, these holes and the crystal structure can be fabricated by simple one-time angled etching, which reduces the fabrication time and costs [20,21]. Figure 1(c) shows the photonic bandgap simulation results of the structure using the Lumerical 3D FDTD tool. In this simulation, the cylindrical air hole radius is set to 0.38a, where a is the lattice constant.

 

Fig. 1. (a) Schematic of diamond 3D PhC reflector. The frequency range corresponding to the crystal bandgap (orange in here) is selectively reflected. (b) FCC or CCP structure with lattice constant of a. (c) Simulated photonic band diagram of 3D PhC made of diamond with a refractive index of 2.4. A complete photonic bandgap appears at the frequencies of 0.504–0.526 (c/a).

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Fig. 2. Schematics of the diamond PhC fabrication process. (a) SiN etching mask deposition on the diamond surface. (b) E-beam lithography and preparation of SiN hard mask. (c) Simultaneous three-directional angled dry etching using a tetrahedron Faraday cage (blue triangle cup). (d) The final PhC device after removal of SiN mask. (e) The formation of CCP structure by three directional angled etching. The cylinders show the etching directions, which are 35° from normal and 120^° away from each other. Not to scale.

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In the case of diamond, owing to its relatively low refractive index of 2.4, a narrow bandgap is formed at high frequencies ranging from 0.504 to 0.526 (c/a), where c is the speed of light. The light in this range can be reflected by 100% regardless of the direction. The L3 direction, which is the vertical (z) direction of the structure, shows a wide bandgap ranging from 0.421 to 0.526 (c/a), which can be used as a wide bandwidth reflector. If the lattice constant (a) is 350 nm, for example, 665.4–694.4 nm wavelength light is reflected from all directions, while the broadband of 665.4–831.4 nm wavelength is reflected for vertical light.

To fabricate 3D PhC diamond, we prepare 500 μm-thick bulk chemically vaporized deposition (CVD) single crystal diamond from Element 6. Approximately 50 nm of silicon nitride (SiN) is deposited on the diamond surface using plasma-enhanced chemical vapor deposition (PECVD) [Fig. 2(a)]. After an e-beam lithography and inductively coupled plasma reactive ion etching (ICP-RIE) process, 2D hexagonal PhC structures are patterned into the 50 nm-thick SiN as a hard mask for diamond dry etching [Fig. 2(b)]. The lattice constant (a) of the pattern is designed at 10 nm intervals from 270 nm to 420 nm to investigate the bandgap dependence on the crystal lattice.

The bulk diamond under the SiN hard mask is etched via inductively coupled plasma – reactive ion etching (ICP-RIE) using a Faraday cage, which enables angled dry etching and 3D PhC formation, as shown in Fig. 2(c). The homemade aluminum Faraday cage is a triangular pyramid shape with three window holes at each surface. The surface angle of the cage is 35^° from the bottom, and the rectangular window holes are perpendicular to the cage surface. The size and depth of the holes are chosen to be 0.5 mm × 2 mm and 3.6 mm, respectively, to maximize the etching directionality. Then, the accelerated plasma ions travel through the holes to meet at the diamond surface, resulting in simultaneous three-directional etching.

After etching the diamond using a mixture of oxygen and chlorine gases for 40 min, multiple holes in the diamond surface are obtained, creating the 3D PhC structure [Fig. 2(d)]. The etching condition is a pressure of 10 mTorr, an ICP power of 700 W, a bias power of 30 W, and a gas flow rate of 45/5 sccm (O₂/Cl₂). The SiN hard mask on the final sample is removed using hydrogen fluoride (HF). Figure 2(e) shows how the angled etching generates air spheres that compose the CCP structure. The cylinders represent the etching directions that are normal to the Faraday cage surface and correspond to the edges of the regular tetrahedron. The holes in the first layer are formed by the SiN hard mask under dry etching, and a second layer hole is produced by the three cylinders from the three holes in the first layer. In principle, the third and additional layers can be fabricated in the same way, resulting in a 3D PhC structure.

Figure 3(a) shows the top view of the diamond PhC generation process under the Faraday cage. The oxygen and chlorine etching ions are injected through the Faraday cage window perpendicular to the cage surface and etch the first and second layers in sequence, as explained above. The SEM images of the fabricated structure are shown in Fig. 3(b). From the top view, the hexagonal second layer pattern (yellow dashed circles) is observed through the holes of the first layer, indicating the 3D geometry of the sample. To study the etching depth or the PhC thickness, we cut the sample using the focused ion beam (FIB) and checked the cross-section [inset of Fig. 3(d)]. It is shown that our sample has approximately two 2D PhC layers owing to the limited selectivity to diamond when angled etching is performed. A thin layer of platinum (Pt) is used to protect the sacrificial diamond device during the cutting process using a FIB.

 

Fig. 3. (a) Top view of the crystal structure formation process using the Faraday cage. The plasma ions from three directions etch through the first layer holes and make second layer holes underneath. (b) SEM image of the diamond PhC top view. (c) Simulation results of reflectance (black) and transmittance (red) of 3D PhC structure with seven crystal layers. (d) The reflectance simulation depends on the number of 2D PhC layers. Inset: SEM image of the diamond PhC structure cross-section: Pt, platinum.

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We expect that additional layers are possible by deeper etching using a metal hard mask, an optimally designed Faraday cage, and etching conditions. Specifically, a larger hole size of the Faraday cage can increase the diamond etching rate; however, it also decreases the directionality of the etching ions. Double or multiple layered holes may solve this issue. By changing the hole size, shape, and aspect ratio, we expect to find an optimized Faraday cage for deep etching in the near future. In terms of etching condition optimization, higher etching selectivity is critical, either using another strong etching mask or an improved dry etching recipe. Unlike conventional vertical etching, the oblique etching method limits the thickness of the etching mask to less than 50 nm owing to the shadowing effect. In this study, we use a SiN hard mask with a selectivity of 1:10 to diamond in the current vertical etching condition. Considering the low etching rate and selectivity in the hole during angled etching, which is the main limitation of the current method, aluminum or nickel metal hard masks are good candidates for angled dry etching with high selectivity [30]. In addition, we plan to attempt other etching recipes with different gas ratios and RF power, which could maximize the etching rate and selectivity by sacrificing the surface roughness.

While ideal 3D PhCs have infinite periodicity in any direction with 100% reflectance, actual devices do not. Thus, it is necessary to calculate the reflectance according to the number of layers in the case of quasi-3D structures. Figure 3(c) shows the simulated reflectance and transmittance of the 3D PhC diamond from the vertical (L3) direction. In this simulation, seven 2D PhC layers with a lattice constant of 350 nm are used. The bandgap is opened very close to the 665.4–831.4 nm wavelength region corresponding to the L3 direction bandgap, as shown in Fig. 1(c). Owing to the limited number of PhC layers, up to 99% of the vertically incident light is reflected at the center of the bandgap. As the number of layers decreases, the reflectance in the bandgap decreases, as shown in Fig. 3(d). The reflectance here is the maximum value at the center of each bandgap with a different number of layers. The structure with two PhC layers, as in our case, has approximately 25% maximum reflectance at a 575 nm wavelength from vertical light [Fig. 3(d)].

3. Measurement and characterization

For optical characterization of the fabricated device, a home-built lens system with two beam splitters is used [Fig. 4(a)]. Continuous (CW) single-frequency lasers are employed for reflection tests at fixed wavelengths of each PhC with different lattice constants. A 40x magnification objective lens with 0.95 NA is used to reduce the focal spot size to less than 20 μm, which is the size of the diamond PhC structures. The lens is also employed to measure most of the reflected light from the diamond PhC samples. The structure size can be increased as large as 500 μm, which is currently limited by the Faraday cage size and the etching equipment specification. First, we observe the microscopic image of the diamond PhC samples using a white light background source (not shown in the setup).

 

Fig. 4. (a) Measurement set-up for the reflection spectrum in PhC diamond. (b) Microscope image of the diamond PhC and (c) color distribution using simulation spectra data. (d) Simulated reflectance spectra of two samples (a = 320, 400 nm). (e–f) Experimental (red) and simulated (black) reflectance at 532 and 660 nm wavelengths. CW, continuous wave; SMF, single-mode fiber; CCD, charged-coupled device; BS, beam splitter; DUT, device under test (diamond PhC); MMF, multi-mode fiber; PD, photodetector.

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Figure 4(b) shows the rainbow colors from sixteen samples with different lattice constants, implying that each crystal structure reflects the selected wavelength band corresponding to the photonic bandgap. The color is determined by the spectrum, which can be obtained by simple simulation. Using the Lumerical 3D FDTD, the reflection spectra of each sample with two layers of PhC and different lattice constants are simulated and converted to colors using the chromaticity diagram method, as shown in Fig. 4(c). For simplicity, only the first ordered bandgap is considered in this simulation. Both the experimental and simulation results show a bluish color at small sample numbers and a reddish color at large sample numbers, which indicates the wavelength bandgap redshift due to the increased sample number or lattice constant. The detailed design and measured lattice parameters are shown in Table 1. A portion of the discrepancy between the designed and measured hole parameters is due to SEM calibration and measurement errors, which are approximately 10 nm. Even with consideration of these errors, the fabricated hole size is measured to be smaller than the designed one owing to the fabrication error in the current device, such as e-beam writing dose, resist developing and dry etching.

Table 1. Designed and measured lattice parameters of 16 diamond PhC samples.

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The reflectance spectra simulations of two representative samples (nos. 6 and 14) are shown in Fig. 4(d). As mentioned above, the sample with a small lattice constant (no. 6) has a bandgap near 532 nm, and the sample with a long lattice constant (no. 14) shows a bandgap near the 660 nm wavelength. This bandgap shift could be measured by simple experiments using single-frequency lasers. We used green (MGL-FN-532) and red (MLL-FN-660) lasers with wavelengths of 532 nm and 660 nm, respectively, and we measure the reflection of each sample, as shown in Figs. 4(e) and 4(f) after calibration using a broadband mirror. These green and red lasers have an approximately 1 nm bandwidth, which is negligibly small considering the broad bandgap. The red and black points represent the experimental and simulation results, respectively. The simulation and experimental mismatch is mainly due to the imperfect fabrication. When etching ions pass through the Faraday cage windows, some of them are reflected, which causes the etching angle dispersion [19,21]. Even with limited reflectivity, the fabricated diamond PhC structures show a finely controllable bandgap in the visible wavelength region.

As a PhC application example, we use the structure to increase the collection efficiency of the emission light from the diamond NV centers. Diamond point defects, represented by the NV centers, could be used as a single-photon light source that emits specific wavelengths [24]. To increase the collection efficiency of the photons, various nanostructures, such as nano-pillar [31], nano-cone [32], grating [33], and lens [34] have been reported. In addition to the previous structures, our PhC can be added under the light source to extract more single-photons through the diamond surface. Figure 5(a) visualizes the light emissions from the NV centers in the surface without the structure (left) and with the structure (right) underneath. Although our sample has low reflection in the normal direction owing to the insufficient number of 2D PhC layers, the angled light rays experience more layers and could be more notably reflected. For example, the ray tilted at 35° from the normal see three layers [Fig. 1(b) and Fig. 2(e)] and have approximately 70% reflection in this structure [Fig. 3(d)]. Therefore, a reasonable portion of omnidirectionally emitted single-photons are reflected from the PhC structure, resulting in increased collection efficiency. Generally, the NV centers are approximately 10 nm beneath the surface; thus, the PhC structure can be considered under the NV centers.

 

Fig. 5. (a) Schematics of light collection from the diamond surface NV center with no structure (left) and 3D PhC (right). (b) Magnified image of sample no. 16, and confocal images of the NV centers on the crystal structure (A) and non-structure (B). Single NV center on the structure (X on A) shows higher emission than the NV center on bare diamond (Y on B). Scale bar is 500 nm. (c)–(d) g⁽²⁾ measurements of the NV centers at X and Y, respectively. (e) Photoluminescence spectra of NV centers on the structure (red curve) and non-structure (black curve). (f) Emission photon counts of single NV centers on A (red curve) and B (black curve), which are dependent on input laser power. (g) Saturated count rates of NV centers with PhC (red) and without PhC (black). (h) Simulated collection efficiency of NV center emission with a structure (red curve, two 2D layers) and without a structure (black curve, bulk). These efficiency data are collected by varying the NV center position. Grey area is the standard deviation.

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For the sample preparation, N+ ions are implanted in the diamond surface at an energy of 10 keV and a density of 2×10⁸ /cm². Next, annealing at 800 °C for 2 h is conducted to form the NV center layer in the diamond surface. Thereafter, the PhC structure is fabricated in the diamond surface. Sample 16, which has a reflection band near the 700 nm wavelength with NV centers, is shown in Fig. 5(b). The light emission from NV centers using a 532 nm wavelength excitation laser on the structure (A) and non-structure (B) are measured using a homemade confocal setup with a numerical aperture of 0.95. The detected number of photons per second from the NV centers on spot X at A is approximately twice as high as that on spot Y at B owing to the PhC structure under the NV center.

Figures 5(c) and 5(d) show the second-order correlation function g⁽²⁾(τ) measurement results of the NV centers using an excitation power of 0.5 mW at X and Y, respectively. They demonstrate the single-photon source characteristics and prove that each X and Y spot contains one point defect [24]. The data is fitted with an equation, g⁽²⁾(τ) = 1 − (1 + a) exp(− |τ |/τ₁) + a exp(−|τ |/τ₂) [35], without background correction. The measured photoluminescence spectra of the NV center at the X and Y spots are shown in Fig. 5(e). The black curve (Y) is the typical NV center spectrum on a bare diamond; the red curve (X) is the increased spectrum of the NV center with the PhC structure. Figure 5(f) shows the single-photon emission count versus 532 nm excitation laser power. We use a saturation growth-rate equation for fitting the curves, p = k₁x/(x + k₂) + k₃x, where p is the count rate, x is the input laser power, k₁ denotes the rate at the saturation level of x, and k₂ is the half-saturation constant. k₃ represents the background slope parameter of various origins, such as Raman scattering, stray light, and imperfectly blocked laser. In the case of the NV centers in the PhC (red) and bulk (black) diamond in Fig. 5(f), the background slopes are 13.14 and 4.67 kcps/mW, respectively. Both single-photon sources show saturation curves at sufficiently high input power with an enhanced count rate on the PhC structure. For statistical analysis, the photon count rate at a saturated power from five NV centers is measured for bulk and PhC diamond of the same sample [Fig. 5(g)]. As shown in the figure, the saturated photon count rate on PhC is 186.76 ± 25.08 kcps, which is twice higher than that of bulk diamond (90.12 ± 7.53). The low saturation power from the PhC sample is presumably due to the excitation power reflection from the PhC structure.

In addition, we simulate the collection efficiency of NV center emission of sample no. 16 with and without the PhC structure [Fig. 5(h)]. Based on the simulation, up to 2% of emitted photons from NV center in bulk diamond can be detected by the high NA objective lens through the diamond surface. In the simulation, to estimate the maximum achievable value via experiment, we use NA of 1. In the wavelength range of interest, three- to four-fold enhanced collection efficiency is estimated, which supports the above measurement results. The grey area is the standard deviation of the red reflection curves owing to the different NV center dipole locations. The increased collection efficiency in the wavelength region not on the bandgap could be due to the direct out-coupling to the free space from the nanostructure.

4. Conclusion

In summary, we fabricate two layers of 2D PhCs in single-crystal diamond surfaces by using a simultaneous three-directional angled etching method. The method enables creation of a quasi-3D CCP photonic crystal structure with a partial bandgap. Various reflection spectra and colors from blue to red are observed by adjusting the lattice constants, thereby indicating the bandgap shift. In addition, the PhC structure doubles the collection efficiency of the NV center single-photon sources in the diamond surface. The wide bandgap of the device can cover various single-photon sources with different wavelengths. These advantages can be applied in the fields of quantum information, quantum sensing, and quantum computing. We expect that a deep structure with a full bandgap can be demonstrated in the near future. This capability will enable the 3D waveguide, mirror, and cavity to be available for wide applications, such as high-power, nonlinear, and quantum photonics.