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Abstract
Here, we report on the increase of the quality-factors of photonic crystal nanocavities fabricated by a CMOS-compatible process. We fabricated nanocavities with the same cavity design but used either a binary photomask or a phase-shift photomask in the photolithography step to assess the impact of the photomask-type on the fabrication accuracy of the air holes. We characterized 62 cavities using time-resolved measurements and the best cavity had a quality-factor of 6.65 × 106. All cavities exhibited a quality-factor larger than 2 million and the overall average was 3.25 × 106. While the estimated magnitude of the scattering loss due to the air hole variations in the 33 cavities fabricated with the phase-shift photomask was slightly lower than that in the 29 cavities fabricated with binary photomask, the phase-shift photomask did not provide a significant improvement in the fabrication accuracy. On average, the scattering loss in these samples is more than 3 times larger than that of nanocavities fabricated using electron-beam lithography, which indicates room for further improvement.
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1. Introduction
It has been shown that photonic crystal (PC) nanocavities with a heterostructure design can achieve quality-factor (Q) values larger than several hundred thousand and small modal volumes (V) on the order of one cubic wavelength of light [1–5]. Various applications such as optical buffer memories [6–8], nonlinear optical devices [9–12], and ionized-air sensors based on Raman Si lasers [13] have been proposed. A larger Q value leads to a longer photon-storage time (which is important for optical buffer memories) and a stronger nonlinear optical effect. Cavities with Q values of 2.2 million [8], larger than 3.0 million [11], and 1.2 million [13] have been utilized to demonstrate these applications. Although various applications with Q values less than 0.1 million have been proposed (for example, wavelength filters [14] and highly sensitive environmental sensors [15–17]), it is important to note that a higher Q value leads to a lower radiation loss in the direction normal to the surface when these devices are incorporated in planar optical circuits including PC waveguides [18–20]. Therefore, with respect to various applications, it is important to increase the experimental Q (the experimental Q is hereafter referred to as Qexp, in order to distinguish it from the Q determined by the design, Qdes). Because the Qdes values of heterostructure nanocavities are usually much larger than the Qexp values [21,22], we should improve the fabrication process.
In general, the ability of fabricating high-Q nanocavities in large quantities is important for applications [23–28]. In 2018, we investigated the Qexp values of 30 nanocavities fabricated by a CMOS-compatible process, and the highest Qexp among these samples was 2.5 × 106 [29]. However, this value is still 4.4 times lower than that of another previously reported nanocavity fabricated by electron-beam (EB) lithography [30]. The Qexp values of PC nanocavities are smaller than Qdes mainly due to scattering (by structural imperfections) and absorption [21,31]. For the realization of further increases in the Qexp of CMOS-compatible PC nanocavities, it is important to clarify which of these losses governs the decrease of Qexp in such nanocavities. In addition, it should be clarified whether using a phase-shift mask (which is able to form fine patterns by controlling the phase of light) in the lithography step can reduce scattering losses.
In this study, we investigate 84 PC heterostructure nanocavities with the same cavity design but fabricated with different types of photomasks. The use of an improved CMOS-compatible fabrication process compared to the previous study allows us to reduce the scattering and absorption losses. The cavities were characterized using time-resolved measurements and the Qexp of the best sample among the 62 measurable samples is 6.65 × 106, which is 2.7 times higher than the best value reported previously. We estimate that the magnitude of the scattering loss of our CMOS-compatible nanocavities is on average more than three times larger than that of nanocavities fabricated by EB lithography. We find that the magnitude of the scattering loss cannot be reduced dramatically by using a phase-shift photomask.
2. Cavity design and fabrication process
Figure 1(a) shows the multi-heterostructure nanocavity design used in this work. Figures 1(b) and 1(c) show scanning electron microscope (SEM) images. The basic PC has a triangular lattice structure in which air holes with an average radius (r) of about 115 nm are periodically arranged with a lattice constant (a) of 410 nm. This heterostructure nanocavity design uses a line defect consisting of 23 missing air-holes and the following shifts in the PC lattice constant at the center of the cavity: the lattice constant in the x-direction is increased in two steps of 5 nm from 410 nm to 420 nm, as shown by the different gray levels. The width in the y-direction is W1 = 710 nm. The waveguide used for excitation of the high-Q nanocavity mode is located six rows away from the cavity and is 10% wider than the nanocavity. A detailed description of the high-Q resonance mode in such a cavity can be found in previous studies [1].
Fig. 1. (a) The used heterostructure nanocavity design including the excitation waveguide. (b) Top view SEM image of the fabricated PC. (c) Cross-sectional SEM image of the fabricated PC.
The Qdes value of the resonance mode is 1.35 × 107, which was determined by a three-dimensional finite-difference time-domain (3D-FDTD) calculation including the effect of coupling to the excitation waveguide. This Qdes value is lower than that of the cavity design used in [29]. The x-direction shown in Fig. 1(a) corresponds to a crystal direction equivalent to [100] of crystalline silicon (Si) [32]. The cavities used in the previous research were fabricated along the [110] direction [29]. However, this difference in the crystallographic orientation does not affect Qexp.
The Qexp value can be determined from Qdes and the non-ideal properties of the sample as follows:
Figure 2 shows the process flow chart. We used a 300-mm-wide Si-on-insulator (SOI) wafer consisting of a 225-nm-thick top Si layer, a 3-µm-thick buried oxide (BOX) layer, and a supporting Si substrate (775 µm). An immersion scanner (Nikon NSR-S610C, 193-nm ArF excimer laser) was used to form the PC pattern [33]. This scanner allows us to install two photomasks and project the two patterns of the photomasks separately on different areas of the same SOI substrate. We prepared one binary mask and one phase-shift mask. Both masks use the same cavity design for all cavities. For the binary mask, the PC patterns are formed in a chromium film with 0% transmittance. On the other hand, for the phase-shift mask, the patterns are formed in a semi-transparent film (transmittance: 6%) that reverses the phase of light. The nanocavities fabricated by using the binary mask are hereafter referred to as BM cavities, and the other nanocavities are referred to as PM cavities. It is expected that the phase-shift mask results in a higher accuracy and thus should reduce 1/Qscat [34]. It is noted that PM cavities were also used in our previous studies [29,35].
The size of the photomask pattern projected onto the SOI wafer was 26 mm × 33 mm. The pattern for the BM cavities was drawn above the wafer center on the right side as shown in the figure, and that for the PM cavities was drawn above the wafer center on the left side. The dry-etching procedure used to form the air holes was not the same as that in the previous work; we improved it in order to reduce the random variations in the air-hole structure and to obtain air-hole sidewalls that are more vertical. The cross-sectional SEM image in Fig. 1(c) indicates an average sidewall angle of about 88.0° for the PM cavities, which is an improved value compared to our previous results, where angles of 87.0° ∼ 87.5° were obtained [29,35]. This improvement leads to a smaller 1/Qtilt (theoretically predicted Q values including the loss due to the tilt are shown in Appendix A1). We confirmed that the average sidewall tilt of the BM cavities is similar to that of the PM cavities. The above process steps were done in the 300-mm pilot line at AIST.
After the Si etching step, the wafer was separated into small chips (800 µm × 2000 µm) by stealth dicing. A chip fabricated with the binary mask contains 44 BM cavities, while a chip fabricated with the phase-shift mask contains 40 PM cavities. The surfaces of two chips were cleaned by a standard process, and a thermal oxidation process at about 500 C° was added (thermal oxidation was not used the in the previous study) [29]. The thermal treatment should improve the crystallinity, which deteriorates during the CMOS process, and therefore should reduce 1/Qabs. Finally, the BOX layer was selectively removed using 48% hydrofluoric acid (HF) to form an air-bridge structure. After a water rinse, the chip surface was dried under a nitrogen stream. It is noted that the chip with the PM cavities was dropped during drying due to a handling error. This made the hydrogen-termination on the Si surface incomplete and may have resulted in an increase in 1/Qabs [31].
3. Experimental results
To accurately estimate a Qexp of several millions, we chose to perform time-resolved measurements because they are not affected by temperature fluctuations. The measurement setup is described in Appendix A2. For the measurement, each chip was placed in a nitrogen-purged chamber (within 5 minutes after the HF treatment) to prevent water from adhering to the surface [31]. Laser pulses with a rectangular temporal profile and a duration of 10 ns were injected at the edge of the excitation waveguide, and the cavity emission in the direction normal to the slab was measured by time-correlated single-photon counting. The intensity of the excitation pulse was less than the power where nonlinear effects appear [36,37]. Further details of this measurement method can be found in a previous report [38].
We were able to measure the temporal profiles of 29 BM cavities (the emission from the remaining 15 BM cavities was too weak due to weaker coupling between the excitation waveguide and the cavity). Figure 3 shows the time-resolved data of the nanocavity with the highest Qexp and a resonance wavelength (λ) of 1567.1 nm (cavity #13 in Fig. 4). A photon lifetime (τ) of 5.54 ns can be estimated from the decay rate of the cavity emission as shown by the red dashed curve. The estimated Qexp is 6.65 × 106 according to the relation Qexp = ωτ. This Qexp value is about 2.7 times higher than that in the previous report [29].
Fig. 3. The decay curve for photons in the nanocavity with the highest Qexp. This figure plots the photon counts on a logarithmic scale.
Fig. 4. (a) The Qexp values of 29 BM cavities and (b) the corresponding resonance wavelengths. The red solid lines indicate the average, and the dashes lines the standard deviation.
Figures 4(a) and 4(b) show the Qexp values and the λ values of the 29 BM cavities, respectively. The Qexp values are randomly distributed between 2.22 × 106 and 6.65 × 106, and the average is 3.44 × 106. The average λ is 1566.25 nm with a standard deviation (σλ) of 0.53 nm. Figures 5(a) and 5(b) show the data of 33 PM cavities (we were not able to observe the emission from the remaining 7 PM cavities). The maximum and average Qexp values are 4.62 × 106 and 3.08 × 106, respectively. The average λ is 1568.31 nm and σλ = 0.54 nm, which are values similar to those of the BM cavities.
All 62 cavities in Figs. 3 and 4 exhibit a Qexp larger than 2 million, and the overall average Qexp is 3.25 × 106, which is 1.7 times larger than that reported in the previous study [29]. Furthermore, the Qdes of the cavity design used in the previous study is 3.31 × 107, which is more than two times larger than the Qdes in this study (1.35 × 107). Thus, the observed significant increase in the average Qexp by 1.7 times is due to improvements in the fabrication process. In the following, we consider that these improvements resulted in smaller loss factors 1/Qscat, 1/Qabs, and 1/Qtilt. The average 1/Qexp for the 62 cavities is 3.08 × 10−7 while that for the previous study is 5.29 × 10−7 [29]. Thus, the magnitude of the reduction of the total experimental loss is 2.21 × 10−7. The FDTD simulation results shown in Appendix A1 indicate that the magnitude of the reduction due to the achieved improvement in the sidewall tilt is 0.17 × 10−7, i.e., 8% of the total reduction. We attribute the remaining 92% to improvements in 1/Qscat and 1/Qabs (the measurement method used to investigate the Qexp in Ref. [29] is different from that used in this paper, and therefore we were not able to determine the individual contributions of these two factors in Ref. [29]).
The average Qexp of the PM cavities is 10% smaller than that of the BM cavities although the phase-shift mask should improve the accuracy. We explain this result with the fact that the 1/Qabs for the PM cavities is larger than the 1/Qabs for the BM cavities, which is confirmed later. Despite the increase in Qexp, the σλ values of the two types of cavities are similar to the σλ reported in another previous work [35]. This tendency of σλ is consistent with previous studies related to EB lithography [39,40]. The reduction of σλ is a future task.
4. Discussion and future prospects
The average Qexp values for both types of cavities are smaller than the average of 7.69 × 106 reported for the cavities fabricated using EB lithography [30]. A comparison of the magnitudes of the four loss factors in Eq. (1) is useful to elaborate methods for further enhancement in Qexp. Therefore, we estimated the magnitudes of 1/Qscat and 1/Qabs for the 62 cavities.
Figures 6(a) and 6(b) show the histograms of 1/Qexp for the BM cavities and the PM cavities, respectively. The corresponding average values of 1/Qexp, Avg.(1/Qexp), are 3.07 × 10−7 and 3.34 × 10−7, respectively. The corresponding standard deviations, S.D.(1/Qexp), are 6.85 × 10−8 and 5.94 × 10−8, respectively. We now estimate the 1/Qscat and the 1/Qabs values by comparing the S.D.(1/Qexp) values with FDTD simulation results [39,41]. We assume that 1/Qscat is determined by the random deviations of the air-hole positions and radii from the design parameters (the variation in the sidewall tilt around the angle of 88° is included in these random deviations). Previous FDTD simulations including random deviations have predicted the following relationships [30]:
Fig. 6. Histograms of 1/Qexp for nanocavities fabricated with (a) the binary mask and (b) the phase-shift mask. (c) The values of 1/Qdes, 1/Qscat, 1/Qabs, and 1/Qtilt for the two types of CMOS-compatible nanocavities and those for nanocavities fabricated using EB lithography.
Table 1 summarizes the values of the loss factors (1/Qdes, 1/Qscat, 1/Qabs, and 1/Qtilt) and σhole. The right column shows the values for 8 nanocavities fabricated using EB lithography, which were extracted from Ref. [30]. Figure 6(c) compares the 1/Qdes, 1/Qscat, 1/Qabs, and 1/Qtilt values. The sum of the four loss factors represents the total loss and is equal to Avg.(1/Qexp). The approximate contributions of 1/Qdes, 1/Qscat, 1/Qabs, and 1/Qtilt to 1/Qexp are 24%, 56%, 10%, and 10% for the BM cavities, while they are 22%, 45%, 24%, and 9% for the PM cavities.
Table 1. Comparison of the four loss factors and the σhole values of the considered types of PC nanocavities
We thus found that scattering constitutes the largest loss for the high-Q nanocavities fabricated by our CMOS-compatible process. The Avg.(1/Qscat) values of both cavity types are more than three times larger than those of the nanocavities fabricated using EB lithography. Therefore, the most important issue at the moment is to decrease σhole by further improving the fabrication process. To some degree, it will also be helpful to improve the tilt of the sidewalls in order to remove the loss of 1/Qtilt (0.31 × 10−7).
The 1/Qabs value of the BM cavities is smaller than that of the nanocavities fabricated using EB lithography, and thus reducing absorption losses has not the highest priority for improvements at the moment. The 1/Qabs value of the PM cavity is 161% larger than that of BM cavity, probably because of the above-mentioned handling error during the HF treatment and the subsequent drying process. We consider that the use of vapor HF to selectively remove the BOX layer could enhance the reproducibility of the hydrogen-termination on the Si surface.
The experimental results show that the Avg.(1/Qscat) of the PM cavities is smaller than that of the BM cavities by 2.2 × 10−8. This difference corresponds to a decrease in σhole by 0.03 nm. Hence, the improvement in 1/Qscat achieved by using a phase-shift mask was not very dramatic for the current samples. This suggests two possibilities: either the effect of using a phase-shift mask is not large for circular air holes with a diameter of 230 nm, or at least one of the process steps used to fabricate the air holes (photolithography, development, hardmask etching, Si etching, and the wet process used to remove the mask) reduce the benefit of a phase-shift mask. This is an issue that should be clarified in the future.
Finally, the 1/Qdes of the cavity design in Fig. 1(a) is three times larger than that of the nanocavity in Ref. [22]. A nanocavity design with a 1/Qdes smaller than 1.00 × 10−8 has been developed by using the machine learning [40]. A photomask with such a cavity pattern can be prepared, and thus it is possible to decrease the 1/Qdes for nanocavities fabricated by a CMOS-compatible process.
5. Conclusion
We have shown that scattering is the dominant loss mechanism in the high-Q nanocavities fabricated by our CMOS-compatible process. Therefore, we consider that the improvement in the accuracy of the air-hole fabrication is important to further increase the Qexp of nanocavities fabricated by a CMOS-compatible process. While the use of a phase-shift mask in the lithography step can lead to a reduction of the scattering loss, this approach did not lead to a dramatic improvement in the current samples. Furthermore, additional CMOS process steps could be added in order to electrically control the properties of the nanocavity (here, we consider process steps such as doping, activation annealing, deposition, and vapor HF etching [42–44]). However, the sequence of these processes needs to be carefully selected to avoid a reduction of the Qexp value.
Appendix
A1. Ideal Q values for different sidewall angles
Figure 7 shows the results of the ideal Q value in the case that the air holes of the cavity are tilted, 1/(1/Qdes + 1/Qtilt), calculated by 3D FDTD simulations. The Q achieved for holes with perfect sidewalls at 90° is equal to Qdes = 1.35 × 107, while the Q is 9.48 × 106 in the case of sidewalls at 88°. The magnitude of 1/Qtilt for 88° is calculated to be 0.31 × 10−7.
A2. Experimental setup
Figure 8 shows the used measurement system. The excitation light entered the chamber through an optical fiber that has an end facet with a lens shape. The position of the optical fiber was controlled by a xyz-stage driven by actuators. The details of the time-domain measurements used to evaluate the lifetime τ of the photons trapped in the nanocavities can be found in [31,38].
Funding
Japan Society for the Promotion of Science (21H01373, 22H01988); Japan Science and Technology Agency (JPMJST2111).
Acknowledgments
Masaaki Katsura and Yuji Ota were supported by a fellowship from the ICOM Foundation.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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