## Abstract

A two dimensional photonic crystal (PhC) resonator, based on a recent design concept, entirely embedded in Silica, is fabricated in a CMOS full-process multiproject wafer, including additional steps such as implantation, metalization, Germanium deposition and planarization. A large loaded Q-factor (5.9 × 10^{5}) is achieved without removal of the silica cladding. A statistical analysis over 56 devices leads to an average value for the loaded Q of 4 × 10^{5}, in close agreement with calculations. An upper boundary for the fabrication disorder is estimated to 1.2 nm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Optical resonators, as well as waveguides, interferometers or splitters, are essential ingredients of photonic integrated circuits (PIC). As they allow spectral filtering and wavelength selectivity, they improve the response of modulators and photodetectors and provide the feedback for lasing. The enhancement of the light-matter interaction and, therefore, energy efficiency, is related to the spatial distribution of the electric field and to the quality factor of the cavity, rather than to the physical size of optical cavity. Ultra-low power miniaturized devices such as lasers [1], optical random access memories (RAM) [2] have achieved femtoJoule/microWatt energy/power levels, owing to high-Q small modal volume optical resonators based on two-dimensional Photonic Crystal (PhC) [3]. Moreover, enhanced light-matter interaction allowed by this kind of resonator is the centerpiece of breakthrough research in the field of quantum optics [4], atom optics [5] and also optomechanics [6].

The continuous improvement of both design and fabrication [7] has led to the achievement of a very large Q-factor (> 10^{7}) in wavelength scale mode volumes (*V* ≈ (*λ*/*n*)^{3}) [8]. This combination of large Q-factor and small mode volume is unique, clearly motivating the implementation in a standard photonic foundry, specifically CMOS, in the perspective of the photonic-electronic convergence. The challenge here is the resolution of the lithographic process, compared to the electron-beam writer, which is known to be crucial in sub-wavelength photonic structures [9]. Nonetheless, high-Q (2 × 10^{6}) PhC resonators have been reported [10], still based on a suspended membrane with a 2*μm* air gap underneath. This involves an additional processing step after the CMOS fabrication consisting in removing the Buried Oxide (BOX) through chemical etching. It is however desirable to keep the photonic layer protected by silica, more precisely the planarization layer allowing stacking additional elements, the full CMOS process, or also allowing the hybrid integration of other materials, e.g. active III–V semiconductors. Keeping a truly all-solid cladding structure, without any void, is challenging, but experimental Q-factors ranging between 1 × 10^{5} and 1 million have been achieved [11–14]. We point out that there the e-beam lithography has been used. Full solid cladding PhC cavities fabricated in a CMOS foundry have been demonstrated, with Q-factors about 4.5 × 10^{4} [15] for 1D cavities and 2.2 × 10^{5} [16] for 2D cavities, without removing BOX, meaning that they can be readily integrated into larger photonic circuits.

In this paper we demonstrate a high-Q PhC resonator fabricated through the standard full-process CMOS fabrication line at IMEC Leuven (Belgium). Our devices have been included on the same mask than other functional silicon Photonic Integrated Circuits (PIC) and fabricated within a MultiProject Wafer (MPW) run. Despite numerous additional fabrication steps required by MPW users compared to a PhC-only run, the largest Q-factor (5.9×10^{5}) achieved demonstrates the role of the cavity design. A statistical analysis over 56 resonators has been carried out leading to estimates of the disorder induced losses, which are believed to remain the dominant limitation to the Q-factor.

## 2. Design and fabrication

The Photonic Integrated Circuit containing the PhC cavities (Fig. 1(a)) has been fabricated by IMEC using the iSiPP25G pilot line, within a full-process multi-project wafer run. A 193 nm deep immersion lithography is used to pattern a 220 nm thick silicon slab on a 2 *μ*m thick BOX layer. The wafer also included a variety of photonic devices, both active (Germanium photodiodes, thermo-optic switches, ...) and passive (shallow and deep etched waveguides, MMIs, ...). The full process used here consisted in three etch steps: a complete 220 nm etch, a partial 70 nm etch and another partial 160 nm etch. In our case the deep etch has been used, except for the grating couplers which have been partially etched. As part of a multi-project wafer run, the process flow also included implantation steps, germanium (Ge) growth, planarization, metal deposition and oxide cladding.

The planarizing step is very important. It is normally used to isolate PIC devices from back-end steps, namely metalization levels (vias, PADs, ...). The PhC cavitiy (Fig. 1(b)) has been designed to comply as much as possible with the rules defined for this process. Under these conditions, it is very likely that the holes are entirely filled with Silicon Oxide, which is a necessary condition for achieving high Q-factor, and therefore the PhC structure is as represented in Fig. 1(c).

Embedding a PhC structure in a solid cladding has several implications, which generally tend to increase internal losses, mainly radiative leakage. Radiative leakage is understood when representing the distribution of the field of the mode in the reciprocal space [17] and it is associated with waves with in-plane wavevector |*k*_{//}| < *ωn _{clad}*/

*c*(see Fig. 2(b)). The issue with solid cladding is that a larger fraction of the field is coupled to radiation and therefore radiative losses increase. This can be reformulated as favored leakage by the reduced index contrast. A practical guideline to improve the radiation-limited Q-factor is to avoid as much as possible abrupt changes in the spatial distribution of the field by introducing a suitable tapering of the PhC [18]. It has been shown that tapered1D periodic structures are very effective in this respect, in particular when the index contrast is reduced, such as in diamond PhCs [19] or with all-solid cladding resonators [20].

Here we rather focus on the design of the cavity itself, which is shown on Fig. 2(a). The main idea is to implement an effective photonic potential through a combination of two photonic lattices with slightly different periods [21]. It has been shown theoretically that an arbitrarily large radiation-limited Q-factor can be achieved, yet with a much simpler design. We note that the principle of bichromatic PhC cavities has already been implemented in Silicon suspended membranes [22] and more recently in III–V suspended alloys [23]. Here we use the same cavity design as we used in [23], which is a variation of the original design proposed in [21]. Three parameters are in fact enough to describe the structure: the periods of the two lattices *a* and *a′* (see Fig. 2(a)), as well as the radius of the holes *r*. Here the set of parameters is *a* = 405 nm, *a′* = 0.98*a* = 397 nm and *r* = 134 nm. The cavity is formed by a 35 periods long missing line defect (see Fig. 2(a)) in the main triangular lattice. The photonic potential is obtained here by changing the period *a′* = 0.98*a* of the first row of holes next to the missing line defect. The cavity is then evanescently coupled to two PhC waveguides located symmetrically with respect to the cavity center. The PhC waveguides terminate into a wire waveguide [24] and are finally connected through grating couplers to standard single-mode fibers. This PhC design has been adapted from the suspended InGaP structure in [23] to the embedded Silicon structure by merely adjusting the period and the size of the holes and it has been integrated directly on GDS mask files of the main project.

Using an in-house implementation of the FDTD method with grid resolution *a*/20 = 20 nm and subpixel smoothing, we have calculated the intrinsic Q-factor (radiation limited) for an uncoupled resonator, and found that even for our all solid-cladding structures Q is as large as 1.4 × 10^{7} for the fundamental mode and 6 × 10^{6} for the second order mode. Such large Q denotes minimized out of plane scattering, which is consistent with the mode distribution in the reciprocal space (Fig. 2(b)) [17]. As shown on Fig. 1(a), eight sets of cavities have been fabricated, with varying holes diameter, cavity length and waveguide coupling strength. However only two sets of cavities exhibited measurable resonances, only differing by the waveguide to cavity distance, respectively *m* = 6 and *m* = 7 lattice periods along the *M* direction (see Fig. 2(a)) (Other parameters are identical and mentioned above). We will refer to these two geometries as “strong” and “weak coupling” respectively. The corresponding calculated loaded Q-factor is 3.5 × 10^{5} for coupling strength *m* = 6 and 6 × 10^{5} for *m* = 7, for the fundamental (Fig. 2(c)) mode. With these parameters the expected resonance of the fundamental mode is at 194 THz (1545 nm) and the second order mode is separated by 420 GHz. In the CMOS MPW process, the unit cell (i.e. Fig. 1(a)) has been replicated resulting into 28 nominally identical dies, hence 56 individual measurable resonators.

## 3. Results

The resonances are detected by analyzing the complex transmission spectrum obtained through coherent detection, namely Optical Coherent Tomography (OCT) based on a sweep laser source (Santec TSL 510). We have shown that our implementation of this technique provides a spectral resolution of about 20 MHz [23]. The temperature of the sample is stabilized to 25 °C with a controller providing 0.01 °C accuracy. On Fig. 3(a) we report the narrowest lineshape measured, namely 330 MHz, corresponding to *Q _{exp}* = 5.9 × 10

^{5}. We note that this result exceeds previous reports on all-solid cladding CMOS cavities [14–16] by a factor of 2 to 3.

The resonance follows the expected dependence on the temperature (Fig. 3(b)). Interestingly, we detect a temperature dependence of the frequency separation (the free spectral range FSR). The measurement error is estimated from the deviation from the linear fit *δ* ≈ 30*MHz*, which is consistent with the expected accuracy of our setup. From the same measurements we extract the uncertainty for the Q-factor Δ*Q* = 3 × 10^{4} (hence 5%).

All the 28 dies and 56 resonators (all functional) have been characterized and the results have been analyzed statistically. For each resonator we consider the first two resonances. The distribution of the values of the Free Spectral Range (FSR, *ν*_{1} − *ν*_{0}), shown in Fig. 4(a), is centered at 460 GHz and is approximately following a Gaussian law, as it would be expected if the source of the fluctuations were a random change of the structure, namely because of the surface roughness due to fabrication imperfections. Interestingly FSR and the frequency offset (2*δν* = *ν*_{1} + *ν*_{0} − 〈*ν*_{1} + *ν*_{0}〉) are weakly correlated (Fig. 4(b)). The linear regression gives *FSR* = 458 ± 5GHz+(0.04 ± 0.01)*δν*, hence an increase of the frequency also results into an increase of the frequency spacing. This is an hint that the same mechanism affecting the FSR is also involved in the fluctuations of the center frequency. This point would have been trivial in more conventional multi-mode resonators, such as rings, but it is not obvious here as each mode has a specific field distribution and is therefore sensitive to different areas of the sample. These considerations are of great importance when dealing for example with light-matter interactions such as parametric interactions [23]. It is also very desirable to have a perfect control over the tunability of the resonances when using PhC resonators for filtering. We also note that *δFSR*/*δν* = 0.04 is about an order of magnitude larger than their temperature dependence (0.004), as shown in Fig. 3(b).

The measured FSR strengthen the assumption that holes are completely filled with *SiO*_{2}, as calculations with unfilled holes predict a FSR too small to be consistent. As shown on Fig. 5(a), the frequency offset is correlated to the position of the die on the wafer. This is inherent to the MPW process which replicates the mask over the whole wafer thus scattering our devices all over the wafer. Therefore it has to be accounted that the observation of Fig. 4(b) is also linked to this spatial dispersion of the cavities. We present a map of this dispersion of the resonance frequencies over the wafer on Fig. 5(b). Quantitatively, accounting for this dependence reduces the standard deviation of *ν* from 0.3643 THz to 0.1890 THz. This can be explained by a decrease of the slab thickness (or an increase of the size of the holes) from the center to the edge of the wafer. These inhomogeneities are well known in the CMOS process. It can be taken into account in our simulations and, assuming that the variation is imputable mainly on the slab thickness, it leads to a variation coefficient of −0.176 GHz/nm. The corresponding thickness variation is shown on Fig. 5(a), and is in average around 5 nm, which is consistent with what is expected from this kind of SOI wafer.

We now consider the distribution of the measured Q-factors (see Fig. 6(a) for devices with m=7, similar result is observed for m=6 devices). First of all, we note that we have not found any correlation with the position, contrary to the resonance frequencies. Interestingly, there is a correlation between the Q-factor of the first and second order modes (Fig. 6(b)). Importantly, the Q-factor of the fundamental mode for the resonator with weaker coupling is 4.1 × 10^{5} in average, which is substantially larger than earlier reports [14–16]. This confirms that the standard CMOS process can be used to achieve high-Q nanocavities with a good reproducibility. As a consequence, a sufficiently large amount of cavities is tested and a statistical analysis of the devices can be performed [10,25,26], which is more insightful than a single outstanding device based study.

As shown in [10,25], the statistical fluctuations of the Q-factor provide hint on the structural disorder. Hence we consider the model:

where the measured cavity loss 1/*Q*has two contributions: the former is intrinsic to the design (radiation limited) and the material (absorption) 1/

_{exp}*Q*, while the latter is related to the structural disorder 1/

_{int}*Q*. This latter term is responsible for the fluctuations. We assume that it follows a normal distribution, thus the distribution of $\delta {Q}^{-1}=\frac{1}{{Q}_{\mathit{exp}}}-\u3008\frac{1}{{Q}_{\mathit{exp}}}\u3009$ should be centered on 0, and would have the same shape, as it is representative of the fabrication disorder. This is applied with respect to each mode and coupling (4 data groups) and the resulting

_{dis}*δQ*

^{−1}become then independent of these characteristics. Thus, all the measurements can be aggregated to form an ensemble of 112 independent values of

*δQ*

^{−1}. Results are shown on Fig. 7. We first note that there is no clear correlation with the die, hence with the position (Fig. 7(a)). On the other hand, the histogram of

*δQ*

^{−1}clearly reveals a normal distribution, which provides an a-posteriori justification of our hypothesis (Fig. 7(b)). We now connect the width of the distribution with the structural disorder, following [10]. Namely, using the formula Here the standard deviation is

*δQ*

^{−1}= 5.97 × 10

^{−7}. This term is obtained from the raw data after correcting for the measurement uncertainty itself (

*δQ*

^{−1}= 2.08 × 10

^{−7}, as discussed above). The same proportionality constant

*A*= 2.57 × 10

^{−7}as in [10], could be assumed, on the ground that the PhC structure and the field distribution are very similar. This choice would lead to an estimate of the roughness of about

*σ*= 1.2 nm. There are however many reasons suggesting that the roughness is smaller, consistently with values reported recently characterizing the DUV lithography in the IMEC foundry, namely ≈ 1 nm [9,15, 26], as well as other foundries: 0.84nm [10] and 1.6nm [16].

_{hole}First, the measured *δQ*^{−1} accounts for all kind of fabrication disorder, in particular imperfect filling of the holes. The method followed here, which is based on [10], only considers positional and size disorder of hole radius, leading to an overestimate of the roughness. Moreover, preliminary calculations made on our structure suggest that in our case *A* is about a factor 2 larger, because radiative leakage is more sensitive to disorder in silica cladded structures. This mechanically reduces the estimate for the roughness to a value below 1 nm. This suggests that holes must be perfectly filled, as expected for this process, otherwise disorder would have been much larger. [10,16,26]. The main point, in our view, is that full-process IMEC pilot-line has been used for fabricating 2D PhC nanocavities, and seems suited for these structures, which comes somehow as a surprise. Further work will be devoted to a thorough structural analysis, in particular cross-sectional SEM images as in [10,16,26].

## 4. Conclusions

We have demonstrated high-Q photonic crystal cavities fabricated in a standard silicon photonics full process, within a multi project wafer run. The largest Q-factor observed (*Q* = 5.9 × 10^{5}, table 1) is substantially larger than any other previous report also based on CMOS DUV lithography and all-solid SiO_{2} cladding. This is remarkable, as it is well known that a solid-cladding considerably increases radiative leakage and therefore reduces the Q-factor. This result is about a factor 4 from the best result in suspended membranes, still fabricated with DUV [10]. A “bichromatic” design of the PhC has been used which, besides minimizing radiative losses, almost complies with the design rules of the multiproject wafer process. It is also worth in mentioning that our results are not far away from what has been achieved with all-solid cladding resonators fabricated by e-beam [11–13], in spite of the much lower resolution of DUV. The robustness of our design against fabrication imperfections seems to contribute to the result. The second is that the process used seems to guarantee the filling of the holes with silica, which is important to reduce additional disorder. These results are corroborated by a full statistical analysis over our 56 devices, showing a very good reproducibility of the performances, giving a strong argument in favor of the mass-production. Another important point is that robustness is achieved while preserving a relatively small modal volume (*V* = 2.2(*λ*/*n*)^{3}) which is comparable with other geometries.

We have shown that compact and high-Q resonators can be included in a standard integrated photonic circuit using the most general and relatively less expensive process. These cavities could for instance be used for photonic filtering in complex photonic processing chips, in the context of 5G or microwave applications. Tunability could easily be implemented using integrated heaters. Also, these resonators could be used in the context of the quantum information in integrated circuits.

## Funding

European Union Horizon 2020 research and innovation programme under grant agreement No 780848 (FunComp) and the project “Symphonie” funded by the French Research Agency (ANR).

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