Scalable fabrication of hemispherical solid immersion lenses in silicon carbide through grayscale hard-mask lithography

The reliable creation of large-scale, high-aspect-ratio microlens arrays^1–3 can impact several areas of photonics and quantum technology. Microlenses are used, for example, to collimate the outputs of vertical-cavity surface-emitting laser (VCSEL) arrays,^4,5 enhance light collection efficiency from quantum emitters,^6–10 increase the sensitivity of image sensors by boosting coupling to the device active area,^11–13 and increase the efficiency of interconnects for optical transceiver chips.^14–16 

In quantum technology, micrometer-scale solid immersion lenses (SILs) have played a significant role in efficiently extracting single photons from single solid-state quantum emitters in diamond^17–20 and group III–V semiconductors.^21–27 In solid-state matrices, photon collection is usually limited by total internal reflection, which traps most of the emission in the high-index medium. By removing refraction at large angles, SILs can boost collection efficiency by a factor of 10–20, as shown, for example, for the spin/photon interface associated with single nitrogen-vacancy (NV) centers in diamond²⁸ and for quantum dots under Gaussian-shaped SILs.²⁷ Embedding NV centers in micro-fabricated SILs has enabled spectacular breakthroughs such as single-shot projective readout of its electronic spin,²⁰ the first loophole-free Bell test,²⁹ and the realization of a multi-node quantum network of remote solid-state quantum devices.^30,31 More recently, this technology has been extended to similar quantum emitters in other materials with better technological maturity, such as silicon carbide.^32–35 

Conventionally, individual SILs have been fabricated by focused ion beam (FIB) milling.^{18–20,34,36,37} FIB gives exquisite shape control but is very time-consuming and expensive, with several hours required to mill a single microlens. One alternative to FIB milling, typically utilized for larger-scale SIL arrays, is resist reflow. In this lithography-based technique, photoresist pillars are heated past their glass transition temperature so that surface tension rounds the resist into lens-shaped structures. Resist reflow is fast and scalable and has been used to create lenses in several materials, including polymers,^38–43 glasses,^3,44,45 sapphire,^46,47 diamond,^48,49 and silicon carbide.³³ However, since the lens profile is formed through surface tension, shape control is only achievable through varying reflow temperature or duration, the wettability of the surface,^50,51 or the dimensions of the precursor resist pillars.⁴² This imposes serious limitations on the tunability and uniformity of resist reflow-fabricated lenses.¹ Furthermore, only very shallow (low sagitta vs radius) SILs have been demonstrated, thus far, using this technique, possibly due to the collapse of high-aspect-ratio features during reflow.⁵² Densely packed concave lens arrays can also be fabricated using self-assembled microsphere monolayers⁵³ to indent the photoresist during spin coating.

Here, we present a fabrication process utilizing grayscale lithography,^52,54,55 where micrometer-scale structures with precisely controllable heights are created through varying the exposure dose spatially over a low contrast photoresist. We introduce a grayscale hard-mask technique into this process, which decouples the etch chemistry of the resist mask and substrate, enabling increased aspect ratios and process robustness over conventional grayscale lithography. These advances allow us to achieve a large degree of reproducible shape control over fabricated structures, while maintaining the scalability and speed inherent in lithography-based approaches to microlens fabrication.

The devices presented here were fabricated in commercial SiC material (Xiamen PowerWay, $500 μ m$ substrate with $15 μ m$-thick epilayer) diced into $5 × 5 mm$ chips. Prior to photolithography, a $5 μ m$-thick silica (SiO₂) layer was deposited on the chip via plasma-enhanced chemical vapor deposition (STS Multiplex CVD). The fabrication process is outlined in Fig. 1.

Positive grayscale photoresist (micro resist technology GmbH ma-P 1275G) was spin-coated at $3000 rpm$ to achieve $8 μ m$ thickness and soft-baked at up to 100 °C over 50 min. The mechanism for grayscale structures in this resist involves an optical transition from opaque to transparent upon exposure, such that the resist is rendered soluble from the top down as a function of dose. Hence, the height of resist retained is correlated with the exposure dose, and maximum dose is applied in the regions around lenses to wash the resist away.

The resist was exposed using a direct-write laser lithography system (laser writer; Heidelberg Instruments DWL 66+). The exposure beam was stepped over the chip with variable dose, fully exposing the regions around lenses but lens/trench structures themselves with lower dose to allow partial exposure of the resist for spatially variable height after development. The resist was developed using a TMAH-based solvent (micro resist technology GmbH mr-D 526/S) for 5 min and baked to minimize retained solvent at 60 °C for 10 min.

The chip was subsequently loaded into a reactive ion etcher (RIE; Oxford Instruments PlasmaLab 100), where the SiO₂ layer was etched using the grayscale photoresist as a mask with a 25/7/3 CHF₃/Ar/O₂ gas chemistry. In this etching step, the CHF₃ primarily etches the SiO₂, and the O₂ primarily etches the photoresist, allowing for a tunable total selectivity depending on the targeted height of the SiO₂ features. The Ar gas acts as a thermal link to improve chip cooling during etching while providing a small amount of physical etching. The etch proceeds until the SiO₂ layer has been cleared, ideally coinciding with etching through the photoresist mask.

The second RIE step transfers the SiO₂ patterns into the SiC substrate. For this step, a 20/2/5 SF₆/Ar/O₂ chemistry was used, where the Ar again acts as a thermal link, and the O₂ both densifies the plasma⁵⁶ and improves the SiC etch rate through chemical etching of carbon.^57–60 As SF₆ preferentially etches SiC over SiO₂ with a selectivity of ∼5–10,^61,62 this again allows for a high-selectivity etch step, though the selectivity can be tuned through the introduction of CHF₃.

Utilizing a two-step etch process as outlined earlier brings two benefits to our fabrication protocol: first, etching of the photoresist and SiC substrate (which are both more efficiently etched in the presence of oxygen) is decoupled across two different steps, and second, the selectivity of each etch step becomes tunable through controlling the flow rate of CHF₃ gas, which only etches the SiO₂. For further discussion, see the supplementary material.

The total process time to complete all of the above steps is approximately 12 h for a pattern including ∼20 000 lenses. Of this, 8 h is spent on etching, limited by the use of a conventional RIE in our process; in principle, an ICP-RIE can increase the etch rate by up to an order of magnitude.^59,60,63 The only process step that has a dependence on lens number is laser writing, and writing time can also be minimized by careful consideration of the pattern design. Therefore, the process is immensely scalable, and fabrication at wafer scales with reasonable process times is conceivable.

As mentioned earlier, grayscale exposure of the positive photoresist is performed through stepped direct laser writing. During this process, the laser writer is given an array of grayscale pixels corresponding to a chip area, where the brightness of each pixel denotes the desired dose at that location. Since the ma-P 1275G photoresist used is specifically developed for grayscale lithography, this dose variation results in a resist height variation after exposure.

Figure 2 demonstrates the shape control possible through grayscale hard-mask lithography. As the shape of grayscale features, here rounded lenses and trenches etched into the SiC substrate, can be arbitrarily and reproducibly modified within fabrication limitations, it is straightforward to create arrays of differently shaped devices [Fig. 2(a)] and sweep design parameters, e.g., lens width [Fig. 2(b)] and trench curvature [Fig. 2(c)]. Therefore, the desired shape could be achieved through iterative modification of the design profile, benchmarking the target shape to device profiles measured after fabrication, or alternatively through choosing the optimal shape from a parameter sweep. The limitations imposed by fabrication primarily relate to the resolution of the laser writing step, given a particular resist (thicker resists yield lower resolution) and corresponding proximity effects, as well as the fundamental mechanism of grayscale exposure, viz. exposure of the resist from top to bottom, which severely limits undercuts and overhangs needed for fully three-dimensional structures. While it is possible to produce these, e.g., through careful choice of multilayer resist stacks,^64–66 this would significantly complicate the fabrication process.

While grayscale lithography allows reproducible shape control, the relationship between dose and final resist height is not necessarily linear and depends on factors such as the intrinsic resist exposure curve, development parameters, and the pre-exposure baking process. To calibrate the developed resist height, slowly varying slope patterns were exposed in the resist, initially with a linear exposure dose. The slope profiles were then measured using a stylus profilometer (KLA Tencor^TM P-7), both after resist development and after the complete fabrication process. By comparing the targeted height of the profile for each dose value to the actual height achieved, the dose curve could be calibrated. As this procedure yields the universal sensitivity curve of the resist, the same calibration is applied to all shapes fabricated, and additional shape modifications arising from the design, for example, through the local spread of the exposure beam, are addressed through proximity effect correction (PEC).

In electron-beam lithography (EBL), random trajectories of individual electrons in the beam can lead to the exposure of resist regions tens of micrometers away from the beam entry point, affecting the shape of developed resist patterns. PEC is, therefore, routinely applied to EBL patterns to account for this and recover the desired shape. The characteristic distribution of the dose experienced from a point exposure of the resist is captured by a point-spread function (PSF), empirically obtained for every combination of resist, substrate, and exposure parameters.

By substituting Eq. (1) and the desired lens profile [Fig. 3(a), dashed black line] into Eq. (2), the corrected dose profile given a set of experimental parameters (⁠ $α , β , δ , η$⁠) can be obtained [Fig. 3(a), solid gray line]. As shown in Fig. 3(a), the overall effect of the PEC for this profile is to increase targeted resist height (reduce exposure dose, as positive resist is used) in the regions of partial exposure, exaggerating convex features. This is intuitively consistent with shapes fabricated without correction, where hemispherical target profiles yielded conical lens shapes [see, e.g., profiles in Fig. 2(b)], so that correction could be anticipated to involve an increase in the profile curvature.

While PEC optimization is a highly multivariate problem, the physical interpretation of each parameter provides an intuition for how changing it affects the final shape. Through a series of sweeps of the correction parameters, it was possible to achieve hemispherical lens shapes to a high level of fidelity. In Fig. 3(b), a set of lenses with increasing correction strength (η) from left to right is shown. While the lowest correction strength [η = 0, reducing Eq. (2) to $D ( x ) = ( E 0 / K ) P ( x )$] shows low shape fidelity to the desired $5 μ m$ hemisphere, the profile with the strongest correction (η = 6) only meaningfully deviates from being hemispherical at its edges, possibly due to the radius of curvature of the profilometer tip. This clearly demonstrates the importance of PEC for laser writing micrometer-scale profiles with large aspect ratios.

We benchmark SIL performance by studying the enhancement of optical collection efficiency from silicon vacancy (V_Si) centers, one of the leading systems for spin-based quantum technology in SiC.^{32,34,69–72} V_Si centers were generated in the sample through high-energy electron irradiation after lens fabrication, with a fluence of $∼ 1 × 10 13$ electrons/cm² (see the supplementary material for further details).

Photoluminescence from these emitters was measured using a room-temperature optical confocal microscope setup with a 0.95 NA objective, as detailed in the supplementary material. V_Si centers in SiC feature a dipole oriented along the c-axis, i.e., roughly 4° from the sample surface normal. The performance of the lenses in enhancing collected light from single V_Si centers was quantified through comparison of single-emitter optical properties beneath lenses [SIL emitters, see Fig. 4(a)] and in regions without photonic structures [bulk emitters, see Fig. 4(b)].

The first effect of the SIL, i.e., enhancement of light collection, primarily affects the saturated brightness of the emitter, through which the enhancement factor is determined. In the case of the emitters measured for Fig. 4(c), these values for the SIL and bulk emitter are $P L sat , SIL = 21.8 ± 0.1 kcps$ and $P L sat , bulk = 8.1 ± 0.2 kcps$⁠, respectively, leading to an enhancement factor of 2.7 ± 0.1. [Note that as this bulk emitter is brighter than average, this value is underestimated compared to the statistics in Fig. 4(d).]

The second effect of the SIL, the reduction of the beam waist and corresponding increase in intensity, is observed as a reduction in $I sat$⁠. For the SIL and bulk emitters measured in Fig. 4(c), the value of this parameter is $I sat , SIL = 0.38 ± 0.01 mW$ and $P sat , bulk = 1.44 ± 0.08 mW$⁠, respectively, leading to an intensification factor of 3.8 ± 0.2.

In the sample measured for this work, the V_Si centers are created at random locations, and variation in the enhancement factor due to the relative location of SIL emitters beneath lenses can be expected. To quantify this variation, the saturated photoluminescence of 12 bulk and 42 SIL emitters (across 20 different SILs) was measured. The enhancement factor of each SIL emitter was quantified through comparison to the average brightness of all measured bulk emitters, and the statistics for the resulting values was fit to a normal distribution. This yielded a value for the enhancement factor of 4.4 ± 1.0, as seen in Fig. 4(d).

The measured enhancement factor can be compared to simulations carried out by Sardi et al.³³ While shallow emitters could achieve an enhancement factor of up to $∼ 7$⁠, the peak simulated enhancement factor for deeper emitters in a hemispherical SIL was $∼ 4$⁠, which is consistent with our results. A further observation from the simulations by Sardi et al. is that careful choice of the SIL profile and emitter position can lead to much higher enhancement factors, e.g., up to 17 for a rounded conical profile. The shape control of our grayscale hard-mask protocol can allow this degree of freedom to be harnessed to further optimize SIL performance.

For perfectly hemispherical lenses, the enhancement factor obtained is nearly independent of the NA of the objective used. However, as fabrication variations will cause deviations in the SIL shape, it can be expected that the enhancement factor is always to at least some degree NA-dependent, though this effect will be more marked for strongly non-hemispherical lenses. This could contribute to the difference in the enhancement factor obtained between this demonstration (NA = 0.95) and Sardi et al. (NA = 0.85), though the SIL shapes themselves are also significantly different between the works.

SIL performance is anticipated to be similar for emitters in other materials, when changes in refractive index and dipole orientation are accounted for. Furthermore, as the lens profile can be modified almost arbitrarily with the grayscale hard-mask technique presented in this work, improved lens shapes can not only yield better performance than attained here but can be specifically optimized for other materials and emitters.

We have demonstrated a scalable, reproducible process to fabricate hemispherical SILs using grayscale hard-mask lithography, and an optical collection efficiency enhancement factor of 4.4 ± 1.0 for lenses fabricated through this technique. Our approach is much faster than FIB and provides better shape control than other lithographic approaches such as resist reflow.^33,48 We analyzed the SILs' performance on randomly located emitters, not centered on the lens; we expect further improved performance from SILs registered to the emitter position.^18,28

While we have focused here on hemispherical SILs, our grayscale hard-mask lithography protocol can enable the precise fabrication of more complex shapes. Future work could harness optimization of the SIL shape (allowing, e.g., elliptical^7,73 or conical³³ profiles) and adjacent structures, such as trenches, to re-direct light into lower-numerical-aperture collection optics.

Our technique could further be extended to different materials such as diamond, provided one can achieve sufficient etching selectivity using the grayscale hard-mask.

An appealing feature of silicon carbide is the integration of photonic structures with microelectronics, enabling the possibility to control the charge state of emitters,⁷⁴ tune their emission wavelength, and deplete environmental charge traps to minimize the spectral diffusion of the spin-selective atomic-like transitions used for spin-photon interfacing.⁷⁵ As the grayscale hard-mask method is scalable and compatible with standard photolithography and CMOS processes, it is possible to integrate the protocol with electronics workflows, allowing the co-location of photonic and electronic elements on-chip and enabling greater flexibility for hybrid photonic-electronic integrated circuits.^76–78 

See the supplementary material for further details on the grayscale hard-mask process, AFM profilometry of hemispherical lenses, the experimental setup, and characterization performed on the V_Si centers.

We thank Fiammetta Sardi, Matthias Widmann, and Florian Kaiser for helpful discussions. We are grateful to Daniel Andrés Penares and Mauro Brotons i Gisbert for their assistance with building the experimental characterization setup and to Alexander Jones, Maximilian Kogl, Tatyana Ivanova, and Daniel Forbes for their aid in AFM profilometry. We thank Dominique Colle of Heidelberg Instruments for fruitful discussions on grayscale dose calibration.

This work was funded by the Engineering and Physical Sciences Research Council (No. EP/S000550/1), the Leverhulme Trust (No. RPG-2019-388), and the European Commission (QuanTELCO, Grant Agreement No. 862721). C. Bekker is supported by a Royal Academy of Engineering Research Fellowship (No. RF2122-21-129).

C. Bekker and C. Bonato have a patent (UK Patent Application No. 2219798.2) pending based on this work.

Christiaan Bekker: Conceptualization (supporting); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Project administration (supporting); Software (equal); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Brian Gerardot: Supervision (equal); Writing – review & editing (equal). Cristian Bonato: Conceptualization (lead); Funding acquisition (lead); Methodology (equal); Project administration (lead); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (equal). Muhammad Junaid Arshad: Investigation (supporting); Methodology (supporting); Software (supporting); Writing – review & editing (supporting). Pasquale Cilibrizzi: Investigation (supporting); Writing – review & editing (supporting). Charalampos Nikolatos: Investigation (supporting); Software (equal). Peter Lomax: Resources (equal); Writing – review & editing (supporting). Graham S. Wood: Resources (equal); Writing – review & editing (supporting). Rebecca Cheung: Resources (equal); Writing – review & editing (supporting). Wolfgang Knolle: Resources (equal); Writing – review & editing (supporting). Neil Ross: Methodology (supporting); Resources (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.