Triangular cross-section grating couplers for integrated quantum nanophotonic hardware in silicon carbide

Quantum networks require a medium that can store quantum information for a long time and provide an interface to transfer the information reliably over long distances. Photons are excellent quantum information carriers as they experience low loss and less decoherence when transmitted through optical fiber networks, making it easier to integrate quantum networks into existing infrastructure Kimble (2008); Monroe (2002); Azuma et al. (2023). Color centers, luminous defects in wide band gap semiconductors Norman et al. (2021), have sparked interest within the quantum community due to their spin-photon interface where the electron or nuclear spin acts as a stationary qubit and spin-entangled photon acts as a flying qubit Hensen et al. (2015). For quantum networks and distributed quantum information processing (QIP), color centers in silicon carbide (SiC) are particularly interesting as they generate spin-entangled photons near telecom band wavelengths Majety et al. (2022) with seconds long spin coherence times Anderson et al. (2022) and ultra-narrow inhomogeneous broadening Cilibrizzi et al. (2023). Moreover, compatibility with silicon-based device fabrication processes and availability of high-purity wafer-scale substrates make SiC a potential platform for scalable QIP hardware.

Color centers are required to be integrated with nanophotonic devices to perform on-chip QIP Castelletto et al. (2022); Majety et al. (2022). In this regard, suspended photonics paves the way for higher optical confinement due to maximum refractive index contrast with the surrounding medium. Previous efforts in fabricating color center integrated SiC suspended devices either limited the performance of color center optical coherence Lukin, Guidry, and Vučković (2020) or encountered scaling issues Majety et al. (2022). As color centers exhibit excellent spectral stability in bulk substrates Udvarhelyi et al. (2019), the angle-etching method has emerged as a promising technique to fabricate bulk freestanding nanostructures for color center integration. Angle-etching can be implemented either by a Faraday cage or by ion beam etching (IBE). In this method, ions are directed at an angle toward the substrate to undercut the nanophotonic structures which results in a triangular cross-section profile. SiC color center photonics and spintronics in this non-conventional triangular geometry have demonstrated robust performance for QIP applications Majety et al. (2021); Babin et al. (2022); Majety et al. (2023); Saha, Majety, and Radulaski (2023); Majety et al. (2024a).

Recently, we have developed a reactive ion beam etching (RIBE) process for wafer-scale integration of triangular cross-section photonic devices with color centers in SiC Majety et al. (2024b). An on-chip wafer-scale testing mechanism is required for characterizing color center interaction with triangular shaped nanophotonic hardware. Although edge couplers offer highly efficient coupling over a large bandwidth, they do not support wafer-level testing and have complex post-fabrication steps with limited access to the circuits Cheng et al. (2020); Marchetti et al. (2019). Vertical grating coupler (GC) is a convenient choice for flexible integration with other photonic elements on the same chip, consequently, allowing for wafer-scale testing. Fiber-based GCs exhibit excellent coupling efficiency at the cost of large footprints and precise fiber alignment Marchetti et al. (2019). As cryogenic environment is required for color center characterization Norman et al. (2024), free-space GCs in combination with microscope objective have proven to be a very practical solution Faraon et al. (2008); Zhou et al. (2018). Typical microscopy systems have a higher numerical aperture (NA) compared to optical fibers and provide wider bandwidth Zhu et al. (2017). Moreover, due to the absence of mode mismatch issues between the fiber core and the GC, free-space GCs can be optimized for a compact layout.

In this work, we conduct a thorough study on free-space SiC triangular cross-section suspended GC in light of color center quantum nanophotonics. Fig. 1(a) shows a perspective illustration of color center coupling characterization with integrated GC. First, we describe the important parameters of the GC and evaluate their performance using Finite-Difference Time-Domain (FDTD) simulations. As we intend to utilize the wafer-scale RIBE process for device fabrication, we incorporate the fabrication constraints in our design. Next, we optimize the design to maximize the collection efficiency from color center emission through a microscope objective and discuss coupling dynamics in the triangular geometry. In the end, we demonstrate the fabrication of the triangular cross-section GC using the RIBE process.

In this section, we analyze the design parameters for triangular cross-section suspended GC in SiC. Our triangular cross-section GC consists of (i) a triangular waveguide, (ii) an adiabatically tapered region, and (iii) a fishbone like grating structure. We choose the fishbone grating design in accordance with the fabrication compatibility of the RIBE process to produce wafer-scale triangular cross-section devices. Fig. 1(b) shows the top view schematic of the GC with waveguide width $w_{\mathrm{1}}$, etch angle (half angle at the apex) $\alpha$, taper angle $\theta_{\mathrm{taper}}$, taper length $L_{\mathrm{taper}}$, maximum taper width $w_{\mathrm{2}}$, grating period $a$, and the central bone width $w_{\mathrm{bone}}$. The refractive index of SiC is kept $n_{\mathrm{SiC}}=2.6$ throughout the analysis. We parameterize the scales w.r.t. wavelength of interest $\lambda_{\mathrm{0}}$ to make the design scalable for the variety of color centers SiC hosts. We optimize each component individually to achieve the most efficient design.

The GC design optimization is focused on enhancing the collection efficiency from color center integrated nanophotonic devices for characterizing light-matter interaction. Fig. 3(a) shows the side view of the 3D FDTD simulation setup for calculating the collection efficiency. We use a mode source to inject the f-TE mode of the waveguide (width $w_{\mathrm{1}}$) at $\lambda_{\mathrm{0}}$ into the grating. A field and power monitor is placed above the triangular cross-section GC at a $\lambda_{\mathrm{0}}/2$ distance for measuring the fraction of power going in the upward direction. As we are interested in maximizing the light collection through a microscope objective, we add another field and power monitor very close to the top surface of the GC to calculate the far field radiation pattern and subsequently the fraction of power collected by an objective with a given NA (0.65 in this work). The collection efficiency is obtained by multiplying the power fractions calculated from these two monitors. We use a field and power monitor before the source to check the amount of light reflected back into the waveguide.

For a given design, the collection increases with the number of gratings and saturates for 5 unit cells. As a result, we use 5 grating periods for all the GCs in our analysis. Fig. 3(b) exhibits the collection efficiencies ($C_{\mathrm{fTE}}$) from the injected f-TE waveguide mode with variation in $DC$ and $a$. We observe that reflection decreases with the increase in $C_{\mathrm{fTE}}$. The maximum $C_{\mathrm{fTE}}$ is $\sim 29\%$, acquired from a design with $DC=0.2$ and $a=0.742\lambda_{\mathrm{0}}$. The obtained $C_{\mathrm{fTE}}$ value is comparable to another compact GC design realized in silicon nitride platform for microscope objective collection where the theoretical coupling efficiency reaches up to $40\%$ ($60\%$ with a reflective mirror coating on the substrate) Zhu et al. (2017). Notably, the most efficient design does not satisfy the phase matching condition which can stem from the broken symmetry of the triangular profile compared to rectangular structures. This phenomenon is observed in another theoretical work with triangular cross-section GCs in gallium nitride Hadden et al. (2022). Fig. 3(c)-(d) shows the far field radiation pattern and side view cross-section of electric field intensity ($|\mathrm{E}|^{2}$) distribution, respectively, at $\lambda_{\mathrm{0}}$ for the most efficient design. We also simulate the collection efficiency of the optimized design as a function of normalized wavelength $\lambda/\lambda_{\mathrm{0}}$. The collection efficiency for the f-TM mode at $\lambda_{\mathrm{0}}$ is $\sim 13\%$, lower than half of $C_{\mathrm{fTE}}$, which is expected. Conventional 1D grating couplers have to deal with bandwidth issues Andreani et al. (2016); Vitali et al. (2023) whereas the triangular cross-section GC broadband response appears flat, meaning the same design can be utilized for studying different zero-phonon line (ZPL) emissions from a color center in SiC. To characterize the incoupling efficiency of the optimized design, we employ a Gaussian source focused from above by an objective with 0.65 NA and a power monitor in the waveguide region as shown in Fig. 4(b). For higher incoupling, the source needs to be focused on the first grating period. Focusing on other unit cells results in lower incoupling as a large amount of light readily couples to the guided mode of the adiabatic taper as seen in Fig. 4(d). The s-polarized Gaussian beam mostly couples to the f-TE mode while the p-polarized beam couples mostly to the f-TM mode. Although we observe some initial coupling to high-order modes, they diminish as the incoupled light propagates through the waveguide. Fig. 4(c) illustrates the broadband response for the incoupling efficiency of the optimized design. The incoupling efficiency is much lower than outcoupling as our optimization technique prioritizes the collection efficiency.

Non-uniform GCs have proven to be very effective in enhancing the overall efficiency Marchetti et al. (2019); Ding, Ou, and Peucheret (2013); Lee et al. (2016). Non-uniformity is generally introduced by linearly apodizing the $DC$ or $a$ along the direction of propagation. In search of the most optimized design, we opt for a similar technique. Keeping $a=0.742\lambda_{\mathrm{0}}$ constant, we linearly change the $DC$ of each unit cell with the following equation: $DC_{i}=DC_{\mathrm{0}}\pm r\times i$, where $r$ is the apodization factor, $DC_{\mathrm{0}}=0.2$, and $i=0,1,2,3,4$. However, we observe the $C_{\mathrm{fTE}}$ slowly decreasing for both cases with variation in $r$ from 0 to 0.02. On the other hand, we linearly change $a$ for each grating section, with constant $DC=0.2$, by the following equation: $a_{i}=a_{\mathrm{0}}(1\pm f\times i)$, where $f$ is the aperiodic factor, $a_{\mathrm{0}}=0.742\lambda_{\mathrm{0}}$, and $i=0,1,2,3,4$. Fig. 5(a) demonstrates that $C_{\mathrm{fTE}}$ gradually increases (decreases) with increasing (decreasing) $a$ and starts to decrease (increase) after reaching an inversion point. We notice that even for the most optimized aperiodic design, with $f=0.07$, $C_{\mathrm{fTE}}$ only increases by $\sim 2\%$. However, we observe a significant change in the broadband response, Fig. 5(b), and the far field radiation pattern, Fig. 5(d), of the aperiodic GC. The far field radiation appears less dispersive compared to the periodic design. While collection and incoupling efficiencies for the f-TM mode remain invariant for the aperiodic optimization, the broadband response for the f-TE mode becomes a normal distribution. Based on the specific application requirement, one can adopt either the periodic or the aperiodic design as both designs exhibit comparable collection efficiencies.

Designed grating couplers can readily be implemented with the wafer-scale quantum nanophotonic fabrication processes. As illustrated in Fig. 1(a), we envision fabricating a suspended triangular waveguide with grating couplers positioned on both ends. One coupler is used to direct the laser into the waveguide and stimulate the color center with off-resonant excitation. The other one couple both the excitation light and the color center emission out into a microscopy system where the excitation beam is selectively filtered out. With this mechanism, light-matter interaction in the triangular geometry can be experimentally characterized for all the suspended active and passive photonic devices.

We test the key step in the fabrication of the studied GC designs in SiC with the RIBE process. In this method, a collimated and uniform beam of high energy reactive and inert gas ions are directed toward a substrate holder that can be rotated and tilted at an angle. The tilt of the substrate holder defines the $\alpha$ of the triangular cross-section and the rotation ensures a uniform device undercut. The presence of physical etch, due to the inert gas ions, reduces the mask etch selectivity as well as causes higher re-deposition from the sputtered material which makes the etching process slower. Hence, we have considered these constraints in our designs as explained in Section II.

We choose $\lambda_{\mathrm{0}}=1243$ nm, one of the ZPL emissions from NV center in 4H-SiC, for both the periodic and aperiodic GC fabrication. Fig. 6(a) shows the nanofabrication process flow. We use electron beam lithography for defining the GC patterns on 4H-SiC substrate. Then, we deposit 120 nm thick nickel as a hard metal mask using electron beam evaporation and transfer the GC patterns on to the mask through a lift-off process. The triangular cross-section waveguides and GCs are then fabricated by the RIBE process using SF₆, O₂, and Ar gas ions. During the etching process, we deliberately set the substrate tilt angle to $60^{\circ}$ for obtaining $\alpha=45^{\circ}$ Majety et al. (2024b). The SEM images of the fabricated GCs are presented in Fig. 6(b)-(e). We observe that the undercut in these devices are $\sim 250$ nm, after an hour of etching, which can be a bottleneck for experimental characterization as a significant amount of light can couple to the bulk. This issue can be resolved by performing a prolonged etch. However, a practical robust solution can be the inclusion of inductively coupled plasma-reactive ion etching (ICP-RIE) in the fabrication process flow. The etch rate for ICP-RIE, with the same SF₆ and O₂ chemistry, is much higher compared to the RIBE process. As a result, performing a vertical etch with ICP-RIE, before the angle-etching step, can result in a deeper undercut essential for experimental characterization of the fabricated devices.

Triangular cross-section photonic devices can be fabricated at a wafer-scale in SiC with the RIBE process. This process preserves color center optical properties which facilitates the implementation of on-chip QIP with integrated quantum photonic mesh architecture. With the addition of the proposed GCs on the same chip, wafer-level testing can be executed on the fabricated devices. Our simulation results show that the triangular cross-section fishbone grating design can yield high collection efficiency ($\sim 31\%$) for studying the color center coupling with the integrated nanophotonic devices and initial fabrication results demonstrate the feasibility of producing the optimized designs with the RIBE process.

The data that support the findings of this study are available upon reasonable request from the corresponding author Pranta Saha ([email protected]).