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We report superior spectral characteristics of silicon-nanowire-based 5th-order coupled resonator optical waveguides (CROW) fabricated by 193-nm ArF-immersion lithography process on a 300-mm silicon-on-insulator wafer. We theoretically analyze spectral characteristics, considering random phase errors caused by micro fabrication process. It will be experimentally demonstrated that the fabricated devices exhibit a low excess loss of 0.4 ± 0.2 dB, a high out-of-band rejection ratio of >40dB, and a wide flatband width of ~2 nm. Furthermore, we evaluate manufacturing tolerances for intra-dies and inter-dies, comparing with the cases for 248-nm KrF-dry lithography process. It will be shown that the 193-nm ArF-immersion lithography process can provide much less excess phase errors of Si-nanowire waveguides, thus enabling to give better filter spectral characteristics. Finally, spectral superiorities will be reconfirmed by measuring 25 Gbps modulated signals launched into the fabricated device. Clear eye diagrams are observed when the wavelengths of modulated signals are stayed within almost passband of the 5th-order CROW.
© 2013 Optical Society of America
1. Introduction
Constantly increasing interconnect bandwidth across the entire system requires extremely compact and low energy consumptive optical interconnection technologies. Silicon (Si)-based optical interconnects are believed to provide higher bandwidth and lower power consumption than those for electrical Cu-wiring interconnections [1,2]. Considering high-performance computer and high-end server applications that requires ever-increasing input/output (I/O) bandwidth of central processing units, wavelength division multiplexing (WDM) technology can be one of promising solutions for coping with enhancement of the aggregate bandwidth and potential reduction of the assembly cost for connecting to optical fibers [3,4].
Usually, WDM system normally requires WDM filters which are desirable to be configured with Si-nanowire waveguide structures, from the viewpoint of the monolithic integration with compact and energy-efficient Si-nanowire based optical modulators [5]. In many cases, since almost WDM filters can work with the help of the lightwave interference phenomena based on the splitting and remixing at multiple optical paths, their operational performances strongly depend on the controllability of the relative phase relation between all of the split optical paths [6,7]. The aforementioned phase behavior is generally governed by the refractive index variation caused by waveguide width fluctuation during fabrication process. Usually, the phase of the optical signal propagating in the Si-nanowire waveguide randomly changes along the propagation direction, which leads to, needless to say, degraded spectral characteristics for any type of WDM filters such as microring resonators (MRRs) [8–16], delayed Mach-Zehnder interferometers (DMZIs) [7,17] or arrayed waveguide gratings (AWGs) [6,18]. To overcome these drawbacks, the shallow rib waveguides [6,15] or the intentionally widened channel waveguides [17,18] have been introduced for MRRs, DMZIs and AWGs to alleviate the degree of random phase variation according to the identical waveguide width fluctuation during fabrication process. Although these ways are fairly effective to compensate for relative low fabrication accuracy, they are not a fundamental solution. Moreover, the aforementioned approaches are difficult to be applied to coupled resonator optical waveguides (CROW) [8–13] which normally require Si-nanowire channel structures, because the previously reported ways may cause considerable excess losses at the microring by radiating the fundamental mode or by exciting the higher-order modes.
Recently, for pure Si-nanowire waveguides, S. K. Selvaraja et al reported low loss property and accurate phase controllability of the Si-nanowire-based waveguide components fabricated by 193-nm ArF-dry lithography on a 200-mm SOI wafer [19] and by 193-nm ArF-immersion lithography on a 300-mm SOI wafer [20]. Especially, from the viewpoint of production yield and phase accuracy for future operational complexity of several kinds of photonic devices, transition to 300-mm wafer scale process would be promising, together with high resolution photomask and processing technologies.
In this work, as a feasibility study of ArF-immersion lithography process, we designed and fabricated Si-nanowire 5th-order CROW and characterized their spectral characteristics and uniformities on a 300-mm SOI wafer. First, the device configuration of 5th-order CROW is explained with analytic formulae. Then, we experimentally demonstrate flat-topped channel dropping spectral response with an excess loss of only 0.4 ± 0.2 dB, and a high out-of-band rejection ratio of >40dB, together with good spectral uniformities for intra-dies and inter-dies. In order to specify the degree of excess phase errors by fabrication process, the 5th-order CROW with the exactly same parameters are also fabricated by 248-nm KrF-dry lithography process and are quantitatively compared with the results for the ArF-immersion lithography. Finally, spectral superiority over the ArF-immersion lithography process will be reconfirmed by evaluating the eye diagrams of 25 Gbps non-return to zero (NRZ) modulation signals whose wavelength is within almost passband range of the fabricated 5th-order CROW.
2. Test device design
2.1. Configuration of device
Figure 1 shows schematic diagrams of a 5th-order CROW. We assume the CROW is configured with Si-nanowire channel waveguides with 440-nm-wide and 220-nm-thick, as shown in Fig. 1. It has been well known that the CROW provides a flattened drop channel response with steep roll-off and high out-of-band rejection ratio [8–16]. Such CROW can be analytically treated by employing the coupling modes with complex propagation constants [8].
Fig. 1 Schematic diagram of a 5th-order coupled resonator optical waveguide (CROW) (a) and the cross-sectional area of a Si-nanowire waveguide (b).
The spectral response at the drop channel of the CROW is flat-topped by optimizing the coupling strengths between serially coupled microrings [21]. In many cases, the coupling strengths can be optimally set by adjusting the gaps of microrings with identical dimensions. First, we analytically calculated the drop channel spectra for the 5th-order CROW, under the assumption of the parameters indicated in Table 1. Actually, we calculated spectral characteristics for the 5th-order CROW with several parameters that are not identical to those shown in Table 1. It should be noted that the parameters shown in Table 1 was obtained by fitting the calculated spectra to the measured ones that will be shown in the section 3.
Table 1. Parameters used in analytic calculations shown in Fig. 2
Based on the analytic formulae reported in [8], we have the following two relations
where β indicates a propagation constant. LM/2 represents the half of the optical path length of each microring except the equivalent coupling length between microrings. α stands for an excessive round-trip loss within each microring. Overall, the spectral response for 5th-order CROW can be given by multiplying each transfer matrix at each microring section as follows.where XSubscript and YSubscript represent the transfer matrices for identifying coupling behaviors between the microrings and optical delays within each microring. aSubscript and bSubscript indicate electric field distribution at each point. We can assume that the input light is launched from the input port only (a0 = 1, and aN + 1 = 0). Thus, the thru ( = b0/a0) and drop ( = bN + 1/a0) channel response can be given by The matrix components shown in Eqs. (1)-(3) include several losses concerned with the Si-nanowire waveguide propagating and the optical coupling (κ1 ~κ3) between the multiple microrings. In addition, considering excess phase change terms together with a propagation constant β at the Si-nanowire microrings, we can theoretically evaluate the degree of spectral degradation for the 5th-order CROW. That is, the matrix formation shown in Eq. (2) can be rewritten bywhere δϕA and δϕB are random phase errors occurring at each half of microring. In this case, each value is assumed to be normally-distributed in which the standard deviation of random phase error is represented by σ(δϕ) [6]. As a matter of course, other Y matrix parameter can be treated in the same manner, assuming the normal distribution of δϕ. Figure 3 shows the calculated drop channel spectra for the 5th-order CROW with (a) no phase error [σ(δϕ) = 0], (b) σ(δϕ) = 0.03π radian, and (c) σ(δϕ) = 0.20π radian. In the calculation, we assumed that each coupling ratio (κ1, κ2 and κ3) are set to the values shown in Table 1. In Figs. 3(b) and 3(c), we iteratively calculated the spectral response by five times, and superimposed each result.Fig. 3 Calculated drop channel resonance spectra for the 5th-order CROW with (a) σ(δϕ) = 0, (b) σ(δϕ) = 0.03π radian, and (c) σ(δϕ) = 0.20π radian.
It is important to note that δϕ at each microring was statistically determined on the assumption of the designated σ(δϕ). The propagation loss of the Si-nanowire waveguide was set to 2 dB/cm. Also, round-trip excess loss indicated by α in Eqs. (2) and (5) was set to 0.04 dB/round-trip. In Fig. 3(a), 5th-order CROW shows flatband and sharp roll-off spectral response if there is no excess phase error. Meanwhile, as shown in Figs. 3(b) and 3(c), excess phase error causes the degradation of spectral response in terms of insertion loss, spectral flatness and center wavelength uniformity. It is evident that the degree of spectral degradation directly depends on the magnitude of δϕ. As can be clearly seen in Fig. 3(b), the drop channel response tends to maintain box-like spectral shape without accompanying severe excess loss. But, as σ(δϕ) increases by more than 6 times [see Fig. 3(c)], considerable spectral degradation is unavoidable. In this case, the relative phase change of 0.03π radian for the currently used Si-nanowire waveguides corresponds to the length variation of ~10 nm. Namely, in order to attain the desired drop channel response, the fabrication process must be able to control the optical path length by at least less than ~10 nm.
3. Experimental Results
3.1. Fabrication of the device
Based on the analytic calculations, the 5th-order CROWs were fabricated on a 300-mm SOI wafer with a 0.22-μm-thick Si core layer and a 2-μm-thick buried oxide layer in an AIST fabrication process (193-nm ArF-immersion lithography equipment manufactured by Nikon, NSR-610C). Figure 4 shows the top views of the fabricated 5th-order CROW based on Si-nanowire channel waveguides (440-nm-wide and 220-nm-thick). Total chip area was 50 μm (width) × 150 μm (length). The devices were diced and polished with a 3-mm-length in order to perform optical fiber based butt-coupling measurements.
The gap parameters for the fabricated devices are shown in Table 2. As seen in Table 2, we set the gap parameters centro-symmetrically (i.e. Gap 1 = Gap 6). Theoretically, if there is no excess phase error, the drop channel response keeps nearly constant within the range of parameter variation (Gap 2 & Gap 5). Other parameters including the curvature radius (R) and the coupling length (LDC) within the microrings are shown in Fig. 4. Basically, these parameters are the same as those used in the calculation shown in Table 1.
Table 2. Gap parameters used in the fabricated 5th-order CROW.
In this work, for a reference, we also fabricated the 5th-order CROW on a 200-mm SOI wafer with a 0.22-μm-thick Si core layer and a 2-μm-thick buried oxide layer in a foundry process (248-nm KrF optical scanner, 180-nm CMOS process). The design parameters of the device are exactly same as the case for Table 2.
3.2. Characterization of static filter spectral response
We characterized optical transmission characteristics of the fabricated chips. As a broadband light source, a super luminescent light emitting diode (SLED) was used. The input polarization state was adjusted to be a linearly polarized TE-mode through a polarization controller. The input light was butt-coupled to the input port of the device through a polarization maintaining lensed fiber. The output light was also butt-coupled to a single-mode lensed fiber and measured with a spectrum analyzer.
First, we characterized the transmission characteristics of Si-nanowire straight waveguides. The propagation loss of the Si-nanowire waveguides is measured to ~2dB/cm by cut-back method. Figure 5 shows the measured transmission spectra for the fabricated device named as CROW-3 in Table 2. The value of transmittance was normalized by that of a 3-mm-long straight waveguide mainly for excluding the coupling losses between optical fibers and two Si waveguide facets. Figure 5 depicts the spectra in the 80-nm-wide spectral range (a), and magnified at around 1556 nm in wavelength (b).
Fig. 5 Measured transmission spectra for the fabricated device: (a) Entire spectral view and (b) magnified view at around 1556 nm
As clearly shown in Fig. 5(a), we were able to observe clear resonance spectra based on serially-coupled microrings at thru and drop channels. The spectral widths for each channel tend to increase as the wavelength becomes longer. This is because the optical coupling ratio between the multiple microrings becomes higher. Meanwhile, the out-of-band rejection ratio for the drop channel was measured to be >40dB within a very wide spectral range, although this ratio is limited by experimental setups. The deterioration of the out-of-band rejection ratio towards the longer-wavelength range is due to the severe power reduction of SLED source.
Initially, the center wavelength of the 5th-order CROW was designed to be ~1560 nm. But, through the fabrication process, the waveguide width was slightly narrower than expected. We believe that the reduced equivalent refractive index of the Si nanowire waveguide causes the blue shift of the center wavelength by ~4 nm. The free spectral range (FSR) was estimated to be ~9.6 nm at around λ = 1556 nm. Based on the measured FSR, the group index of the Si-nanowire waveguide was estimated to be ~4.45. As can be seen in Fig. 5(b), very clear flat-topped spectral response was observed. The flatband width was ~2 nm. It should be noted that the excess loss at the passband and the magnitude of spectral ripple were very low. The excess loss and ripple were as low as 0.2 dB at the center of passband and 0.4 dB within the passband of drop channel response, respectively. Through the analytic calculations to fit the excess loss in the 5th-order CROW to the measured results, the round-trip loss within the ring was estimated to be <0.04dB/ring.
In this work, spectral characteristics for TM-mode input were not characterized. Usually, silicon nanowire waveguides have strong birefringence and polarization dependent dispersion properties, which makes it difficult to satisfy the specific requirements for several coupling coefficients at each gap (Gap-1~Gap-6) for TM mode input in the 5th-order CROW. Consequently, the spectral response for TM mode would be accompanied with considerable insertion loss and less spectral periodicity, as is reported in [16].
We also characterized the intra-chip distribution. Figure 6 shows (a) the CAD image for 5th-order CROWs and (b) superimposed drop channel spectral response. As seen in Fig. 6(a), the devices are located at the equal spacing of 50 μm. Consequently, as shown in Fig. 6(b), although there was some spectral discrepancy with each other due to the difference in the gap parameters shown in Table 2 and unavoidable random phase errors during the fabrication process, no significant spectral deterioration was observed for all devices. It is important to note that the deviation of center wavelengths was less than <0.4 nm within the distance of 200 μm. Moreover, the measured filter spectral shape tends to be very similar to the calculation result shown in Fig. 3(b), which specifies the resolution of ArF-immersion lithography might be as low as σ(δϕ) ~0.03π rad. Subsequently, inter-die distribution was evaluated. Figure 7 shows (a) the top view of the 300-mm SOI wafer, and (b) superimposed drop channel spectra for each CROW-3 located in the areas shown in Fig. 7(a).
Fig. 6 Intra-die distribution: (a) CAD image for evenly aligned five 5th-order CROWs and (b) superimposed drop channel spectra (CROW-1~5)
Fig. 7 Inter-die distribution: (a) top view of the 300-mm SOI wafer and (b) superimposed drop channel spectra for each CROW-3 located in the areas shown in Fig. 7(a).
As can be seen in Fig. 7(a), the total size of photomask (shot size) was set to 26 mm × 33 mm. The same multiple patterns were drawn by the lithography, thus enabling to obtain 64 shots on the 300-mm SOI wafer. In this case, the identically designed devices are separated by ~3 cm. To evaluate inter-chip distribution, we characterized the CROWs located in the areas indicated in Fig. 7(a). As shown in Fig. 7(b), all the measured spectra exhibited clear flat-topped drop channel response without remarkable spectral degradation. The measured center wavelengths for all tested chips were deviated by up to ~3.6 nm although the devices were separated by >15 cm. In this case, we can understand that the deviation of center wavelengths is caused by the additional refractive index change due mainly to the sidewall roughness of Si-nanowire waveguide (Δw). Here, we can simply estimate Δw through the following relation,
where Δλ, NGr, and (dNEq/dw) stand for the deviation of the measured center wavelengths, the group index of Si-nanowire waveguide and the equivalent index change in accordance with waveguide width change. When we use the following parameters shown in Table 3, Δw was estimated to be ± 2.1 nm, which is comparable to the measured value (~< ± 3 nm) of line width roughness for Si-nanowire waveguides fabricated by our 193-nm ArF-immersion lithography.Table 3. Parameters used in the analytic estimation in Eq. (7)
It is important to note that the aforementioned Δλ is influenced not only by Δw but also by the surface morphology of the 300-mm SOI wafer. Thus, it is essential to consider the Si-core thickness distribution across the SOI wafer to accurately discuss inter-die distribution. In this experiment, the Si-core thickness distribution we characterized in this work was far less than 1 nm, which is good enough to be able to discuss that Δλ is mainly governed by Δw. Overall, we can conclude that the ArF-immersion lithography assures very low phase noise, thus enabling to achieve high performance filter spectral response with low excess loss and low crosstalk.
Subsequently, in order to experimentally evaluate the resolution capability of optical lithography on the filter spectral response, we have also fabricated the 5th-order CROWs through the 248-nm KrF-dry lithography process. The device parameters are the exactly same as those shown in Table 2. Figure 8 shows the superimposed drop channel spectra: (a) Intra-die and (b) Inter-die distributions where each chip is separated by ~3cm. In contrast to the results by the ArF-immersion lithography, all measured spectra tend to be distorted with the abrupt increase in the insertion loss. Furthermore, the degree of spectral distortion was unpredictable. As theoretically investigated in Fig. 3(c), current KrF-dry optical scanner might give at least 6 times larger σ(δϕ) in the Si-nanowire waveguides, which leads to severely distorted filter spectral response.
Fig. 8 Measured drop channel response for the 5th-order CROWs fabricated by 248-nm KrF-dry lithography process on a 200-mm SOI wafer: (a) Intra-die and (b) Inter-die distributions where each chip is separated by ~3cm.
It should be noted that the random phase errors caused by waveguide sidewall roughness depend not only on the resolution of optical lithography but also on other factors relating to fabrication process such as the optical resist for patterning and the mask formation for etching the Si core. Thus, the results shown in Fig. 8 are not the general case for utilizing the 248-nm KrF dry process. In addition, to alleviate the degree of random phase error without improving the resolution of lithography, one should absolutely make the refractive index change per waveguide width fluctuations less sensitive. The best way to realize such schemes will be introducing shallow etched rib structures [6,15,16]. Mounting thermo-optic micro heaters for compensating for excess phase errors could be an alternative way [11,12], although these approaches are accompanied by the restriction of device design and somewhat complexity of fabrication process.
3.3. Characterization of eye diagrams by launching 25 Gbps NRZ modulation signal
In order to investigate the signal transmission in the 5th-order CROW, dynamic signal waveforms were characterized by sending 25 Gbps NRZ modulation signals (Pseudo-random binary sequence: 215–1) to the device fabricated by ArF-immersion lithography process. A CW tunable laser was used as the optical source. The signal pulse stream was generated by a pulse pattern generator with a modulation rate of 25 Gbps and a commercially available lithium-niobate (LN) Mach-Zehnder modulator (MZM). The generated signal was butt-coupled to the input port of the device with a linearly polarized TE-mode. The transmitted light was measured by a sampling oscilloscope. A Bessel electric filter was not used when we measured eye pattern diagrams. First we measured eye diagram when 25 Gbps modulation signal was incident on the LN-MZM only. As a result, the extinction ratio (ER) and jitter were measured to be ~7.4dB and ~4.2ps, respectively.
Figure 9 shows the measured eye diagrams of 25 Gbps signals whose wavelengths are located in the vicinity of passband of 5th-order CROW, together with the measured drop channel spectrum. It should be noted that the spectral response of the device used in this experiment was the same as that shown in Fig. 5. The static spectrum was re-measured by a tunable laser diode and was plotted in a linear scale. We confirmed that there were no discrepancies between the data measured by a SLED or a tunable laser diode.
Fig. 9 Measured eye pattern diagrams for each 25 Gbps modulation signal wavelength within the passband of 5th-order CROW, together with the linearly plotted drop channel spectrum
We were able to observe clear eye openings when the optical signal wavelengths are stayed at the passband range designated from a4 to c3. Within almost passband range, the measured eye diagrams tend to keep the ER of >6dB and the additional jitter of <2 ps nearly constant. Meanwhile, at the outside of the passband (a1~a3, d1~d3), the eye diagrams were nearly closed as the optical loss becomes larger. It should be noted that a specific degradation of the eye pattern is observed at the longer-wavelength-side edge of the passband (c4) even if there is no significant signal attenuation. This is most likely due to strongly enhanced group delay dispersion at each passband edge. We believe why such an eye opening reduction was more clearly observed at the longer-wavelength side is that the group delay was enhanced only at the longer-wavelength side in accordance with the excess phase error during fabrication process.
Overall, 25 Gbps modulation signal transmission was successfully implemented within almost passband wavelength range of the fabricated 5th-order CROW, which is based on the marked reduction of spectral ripple and low excess loss by the 193-nm ArF-immersion lithography and optimizing fabrication process.
4. Discussion
Table 4 compares the performances of CROWs from the viewpoint of the excess loss at the drop channel, the degree of spectral flatness and the out-of-band rejection ratio. The Si-core thickness for all examples shown in Table 4 was 220 nm. Basically, it is evident that highly accurate phase controllability over the Si-nanowire waveguides is prerequisite for achieving lower excess loss, better spectral flatness and higher out-of-band rejection ratio. As seen in Table 4, the resolution of lithography tends to play an important role in obtaining good phase controllability. In case of 248-nm KrF-dry lithography technology, it seems to be difficult to get low phase errors in the Si-nanowire channel waveguides with 220-nm-thick Si-core. To overcome this drawback, external phase tuning by thermo-optic micro heaters at each coupled microring [11] or relaxation of excess phase errors by leveraging rib waveguides [15,16] were reported. But, these approaches are traded off with additional power consumption, control complexity of device operability, larger device size, and higher excess loss etc. Among several kinds of higher-order CROWs, our device exhibited lower excess loss of 0.4 ± 0.2 dB and higher out-of-band rejection ratio >40dB, together with fairly good spectral uniformity for all fabricated chips, as discussed in section 3.2.
Table 4. Performance comparison for CROWs from the viewpoint of excess loss, spectral flatness, and out-of-band rejection ratio
Overall, although conventional 248-nm KrF lithography process has the potential to exhibit high performance characteristics as reported in [16], 300-mm SOI wafer scale ArF-immersion lithography process would be one of best choices for improving fabrication accuracy and production yield, which will be very promising to accomplish compact and highly efficient WDM multiplexers / demultiplexers based on any of waveguide architecture such as microring resonators, delayed interferometers or arrayed waveguide gratings without using any external phase compensation.
5. Summary
We theoretically analyzed and experimentally demonstrated the Si-nanowire-based 5th-order CROWs. By using the coupled mode theory and transfer matrix method, spectral characteristics of the 5th-order CROW was analytically discussed. The spectral degradation was also numerically evaluated by assuming statistical random phase errors in the Si-nanowire waveguides. Based on the calculation results, the device was fabricated and characterized. The device dimension was 50-μm-wide and 150-μm-long. After fabrication, the devices were diced and polished to a 3-mm length.
Throughout the characterization, it was experimentally confirmed that advanced patterning technology based on 193-nm ArF-immersion lithography and dry etch process showed extremely low phase errors even for Si-nanowire channel waveguides. The fabricated 5th-order CROW exhibited clear resonance spectra both for thru and drop channels, together with low excess loss of <0.2dB and high out-of-band rejection ratio of >40dB at the drop channel without any external phase control. Furthermore, fairly good spectral uniformity for all the fabricated devices was found both in intra-dies and inter-dies. The center wavelengths for box-like drop channel responses of five devices spaced by 50 μm were distributed within 0.4 nm in the die. This tendency was kept nearly constant for other dies on the 300-mm SOI wafer. In the case of the inter-die distribution where each die is spaced by ~3cm, the deviation of the center wavelengths was as low as ± 1.8 nm between the dies separated by up to ~15 cm.
For comparison to investigate the dependence of the resolution of lithography on the filter spectral response, the 5th-order CROWs with identical device parameters were also fabricated by 248-nm KrF-dry lithography process, and was experimentally confirmed that noticeable spectral degradation was unavoidable when we use the Si nanowire channel waveguide in the 5th-order CROW. We analytically verified that the remarkable spectral discrepancy originates from the magnitude of random phase errors for Si-nanowire waveguides. The degree of random phase errors for the ArF-immersion process was theoretically expected to be at least 6 times less than that of the KrF-dry process.
The spectral superiority was reconfirmed by measuring the waveforms of 25 Gbps modulation signals launched into the device. Clear eye openings were observed as long as the optical signal wavelengths are stayed within the flat-topped passband of the 5th-order CROW except at around the longer-wavelength side edge.
We believe these high-precision fabrication technologies based on 300-mm SOI wafer scale ArF-immersion lithography are promising for several kinds of WDM multiplexers / demultiplexers having much complicated configurations and requiring much finer phase controllability. For making the WDM technology more practical in the on-chip optical interconnection, our efforts will go to realize low loss and low crosstalk WDM devices without sacrificing optical functionalities, and eventually to realize compact monolithic integrated WDM optical transceiver for high bandwidth and cost-effective optical interconnections.
Acknowledgment
This research is partly supported by New Energy and Industrial Technology Development Organization (NEDO). Authors thank to Professor Yasuhiko Arakawa, The University of Tokyo, for his continuous encouragement.
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