OPTICAL interconnects have been used in highperformance

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1 1684 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 9, MAY 1, 2017 Si Photonic Crystal Slow-Light Modulators with Periodic p n Junctions Yosuke Terada, Member, IEEE, Tomoki Tatebe, Yosuke Hinakura, and Toshihiko Baba, Member, IEEE Abstract We theoretically optimized and demonstrated the periodic p n junction in silicon photonic crystal slow-light modulators to balance the efficiency and speed of phase shifters and reduce the power consumption compared with those of previous linear and interleaved p n junctions. In particular, sawtooth and wavy junctions, whose profiles match with the distribution of the slow-light mode, theoretically prove effective in achieving these objectives. However, the sawtooth junction requires a high-resolution process. Therefore, we finally employed the wavy junction and obtained 25- and 32-Gb/s operations in a 200-µm device with extinction ratios of 4 and 3 db, respectively, for an excess modulation loss of 1 db. Index Terms Mach Zehnder modulator, photonic crystal, p n junction, silicon photonics, slow light. I. INTRODUCTION OPTICAL interconnects have been used in highperformance computers and data centers owing to their high transmission capacity and low power consumption. Silicon Si) photonics fabricated using complementary metal-oxide semiconductor CMOS) processes have a great advantage in low-cost manufacturing of high-speed high-performance photonic integrated circuits for optical interconnects. Here, on off keying OOK) carrier-plasma modulators incorporating p n doped Si rib-waveguide phase shifters [1] [12] are used widely for opto-electronic conversion, and the carrier-depletion mode under reverse bias and Mach Zehnder MZ) circuit [2] [10] are particularly popular because of their high speed and wide working spectrum Δλ, enabling a wide temperature tolerance ΔT. Their large size several millimeters) and relatively large power consumption prove to be drawbacks, but those can be addressed by employing Si photonic crystal waveguides PCWs), which generate slow light with a low group velocity large group index n g ) [14], [15], as phase shifters. The schematic and top views of the device fabricated using a 180 nm CMOS process 248 nm KrF exposure) are shown in Fig. 1a) and b), respectively. The device consists of a Si-wire MZ circuit, PCW phase shifters for Manuscript received November 1, 2016; revised January 18, 2017; accepted January 23, Date of publication January 24, 2017; date of current version April 20, This work was supported by New Energy and Industrial Technology Development Organization. The authors are with the Department of Electrical and Computer Engineering, Yokohama National University, Hodogaya-ku, Yokohama , Japan yterada@ynu.ac.jp; tatebe-tomoki-pc@ynu.jp; hinakura-yosukezm@ynu.jp; baba-toshihiko-zm@ynu.ac.jp). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT radio-frequency RF) modulation, and PCW thermo-optic TO) phase tuners for setting the initial phase difference between its two arms. We have already reported a 25 Gb/s error-free operation of the device with a moderately large n g of 20 and a phase shifter length as small as L = 200 μm [2].Wehavealsoused lattice-shifted PCWs LSPCWs) that generate low-dispersion slow light and allow almost uniform modulation performance for Δλ = 16 nm [2] and ΔT = 105 K [3]. In the 25-Gbps modulation, we employed an interleaved p n junction [2], [4], which has a periodic profile and increases the phase shift Δφ [2], [4] [7], [13]. In general, Δφ induced by carrier plasma is almost proportional to the charge accumulated in the junction, Q [11] we usually observe the slight nonlinearity, but neglect it here.) Therefore, Δφ Q = CV C is the junction capacitance and V is the applied voltage). The interleaved junction has a large C because of the junction profile; therefore, a larger Δφ is obtained for constant V or a lower V is allowed for a constant Δφ. The charge and discharge consume a signal bit energy at the resistance around the junction, R pn. Assuming that the modulation signal swings between 0 V pp and eliminating the case where the bit does not transit between 0 and 1, the average energy consumption per bit, W bit,isgiven as W bit = CV 2 pp/4 [16]. If we employ the push pull drive wherein differential signals are applied to the two arms of the MZ circuit, the value of W bit becomes double, i.e., CVpp/2. 2 For target Δφ, V pp 1/C and W bit 1/C; therefore, W bit can be reduced by the interleaved junction. However, in our previous study [2], we revealed that the cutoff frequency, f 3dB =2πR pn C, was reduced by the interleaved junction to less than 18 GHz, which is close to the critical frequency for 25 Gb/s operation. In that study, the junction profile was not optimized so as to balance Δφ and f 3dB. The profile did not match the slow-light mode; therefore, the lack of overlap between the junction and the mode did not contribute to Δφ but increased unnecessary capacitance components. On this condition, the above relations V pp 1/C and W bit 1/C are not completely expected. In this study, we discuss sawtooth and wavy junctions as more optimized periodic junctions and particularly demonstrate high-performing modulation in the latter. In Section II, we review the performance of Si MZ modulators required for optical interconnections. In Section III, we theoretically predict the high performance of the above mentioned two junctions under the assumption of an ideal fabrication condition. In Section IV, we show that the wavy junction can be fabricated more easily and the diffusion of the doping is a serious concern for periodic junctions, which reduces Δφ. InSectionV, we IEEE. 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2 TERADA et al.: SI PHOTONIC CRYSTAL SLOW-LIGHT MODULATORS WITH PERIODIC P N JUNCTIONS 1685 Fig. 2. Δφ required for ER. Fig. 1. Si PCW MZ modulator. a) Schematic. b) Total view of fabricated device and scanning electron micrograph SEM) of p n doped PCW. The latter is colored to show the p n junction boundary. c) Transmission upper) and n g lower) spectra of PCW with neither lattice shifts nor p n doping. demonstrate the measured results of Δφ and Gb/s modulation, which are beyond the previous results obtained using the interleaved junction. II. REQUIREMENTS The requirement for OOK modulators in optical interconnects depends upon the power consumption of the optical transceivers and the total systems. An example of such requirements considered in this study include a bit rate BR 25 Gb/s, an extinction ratio ER 3 db, a phase-shifter length L 1 mm, an on-chip insertion loss Loss 5 db, and a temperature tolerance ΔT 100 K or the corresponding working spectrum Δλ 8 nm). Our PCW slow-light modulator satisfies the requirement for L and ΔT or Δλ). In this study, we fixed L = 200 μm because a longer L increases the insertion loss. The insertion loss is given by the passive loss and the modulation-excess loss, ML. The passive loss is composed of i) scattering loss caused by structural disordering of fabricated PCWs, ii) freecarrier absorption caused by doping, iii) connection loss between the wire waveguide and PCW, and iv) excess loss of two multimode-interference-type 1 2 couplers in the MZ circuit. Fig. 1c) shows the transmission spectrum of the fabricated undoped 200 μm PCW normalized by that of the same-length Si-wire waveguide. From this transmission band, the sum of i) and iii) is estimated to be 1 2 db. This value can be reduced by employing a more advanced CMOS process and optimization of the connection structure. The total excess loss of the two optimized 1 2 couplers is 0.5 db [17]. Thus, the sum of i), iii), and iv) will not be greater than 2 db. Focusing on ii) and ML, which is related to ER, if the initial phase difference between two arms of the MZ circuit is set close to π by using TO phase tuners, we can obtain a large ER with a small Δφ. However, this initial phase difference causes a large ML and degrades the signal-to-noise ratio, S/N. ML should be reduced, while ML = 0 db requires a particularly large Δφ for the target ER. Therefore, minimizing the total loss by adding a moderate ML is a good strategy. Δφ required for a target ER and a given ML in [db] is expressed as ) Δφ = arccos ML+ER) 1 arccos ML 1 ) 1) and calculated, as shown in Fig. 2. Δφ =0.50π is necessary for ER = 3 db and ML = 0 db, whereas Δφ =0.27π is necessary for ML = 1 db. In the previous PCW modulator, ER exhibited a 1 db fluctuation because of the fluctuation in the n g spectrum [2]. This fluctuation can be reduced by optimizing the connection structure and suppressing unwanted internal

3 1686 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 9, MAY 1, 2017 resonance; still ER > 4 db would be desired to compensate for this fluctuation, and Δφ =0.32π is necessary for ML = 1dB. For high-speed modulators, Δφ is limited by f 3dB, which is dominated by the time constant and also affected by the phase mismatch between slow light and RF signal [2]. The phase mismatch becomes severe when the phase shifter is elongated, n g is enhanced, and BR is increased. In the discussion of this paper, we impose the limits L = 200 μm, n g 20, and BR = Gb/ s to neglect the phase mismatch. The equivalent circuit of the modulator is then simplified to a series of internal resistance of pulse-pattern generator PPG), R 0, R pn, and C [see Fig. 3a)]. The capacitance voltage, V C t), for operating the phase shifter is related to the PPG voltage, V 0 t), as dv C t) dt + V Ct) = V 0t) 2) where R = R 0 + R pn. We observed the waveform of the RF signal from the PPG Anritsu MP1800A, MU183020A; the highest BR is 32 Gb/s) actually used in this experiment using a sampling oscilloscope, and the rise and fall of V 0 t) was estimated as { ) }] 3 t V in,rise t) = V 0 [1 exp 3) τ [ ) ] 3 t V in,fall t) = V 0 exp 4) τ where τ = 18 ps. From Eqs. 2) 4), V C,rise t, V C0 )= V 0 [1 exp t +exp t V C,fall t, V C0 ) = exp t )] )[ V C0 V 0 t ) ) ] t 3 exp + t dt τ )[ V C0 + V t 0 { t exp τ ) 3 + t 0 0 5) } ] dt. 6) When the RF signal is a pseudo-random bit sequence PRBS), the above two V C t) form an eye pattern. Assuming Δφ V C t), similar eye patterns are formed in the phase difference between the two arms, φ. Examples of such eye patterns are shown in Fig. 3b) and c). The eye starts to close when the frequency component of the RF signal approaches f 3dB =1/2π. The difference between the local maximum of V C t) for a sequence and the local minimum for gives the value of the eye opening and effective Δφ in the modulation RF Δφ). Fig. 3. Analysis of transient response characteristics. a) Lumped circuit model. b) and c) Transient response of phase at 25 and 32 Gb/s, respectively. d) RF Δφ/DC Δφ calculated with f 3dB. For the timing of the maximum open eye, t m, )) 1 RFΔφ = 1 V C,fall t m,v C,rise BR, 0 V 0 )) 1 DCΔφ V C,rise t m,v C,fall BR,V 0 7)

4 TERADA et al.: SI PHOTONIC CRYSTAL SLOW-LIGHT MODULATORS WITH PERIODIC P N JUNCTIONS 1687 Fig. 4. Studied p n junction profiles. a) Total image including electrodes. b) Linear junction. c) Interleaved junction. d) Sawtooth junction. e) Wavy junction. Fig. 5. a) Average intensity distribution of slow-light mode at k =0.4052π/a). b) e) Distribution of Δn Si for each junction. where DC Δφ is that not including the high-speed response. Fig. 3c) shows the RF Δφ/DC Δφ calculated with f 3dB, indicating that the reduction of f 3dB by excessively increasing C in a deep interleaved junction severely reduces RF Δφ. III. THEORETICAL PERFORMANCE Four types of p n junctions are theoretically analyzed, as shown in Fig. 4, to find the one junction that is well-balanced between DC Δφ and f 3dB, resulting in the highest RF Δφ.Particular attention is given to sawtooth and wavy junctions and they are compared with linear and interleaved junctions. The longitudinal pitch, p, of the interleaved junction is set to a previously determined value, 600 nm. For the sawtooth and wavy junctions, we set p = 400 and 800 nm, respectively, and the junction width, w y, as a free-design parameter. Other parameters are kept similar to those in [4]; the refractive indices of Si and silica cladding are 3.48 and 1.44, respectively; Si thickness is 210 nm; lattice constant of the PCW is a = 400 nm; hole diameter is 2r = 210 nm; doping concentrations are N A acceptor) = cm 3 and N D donor) = cm 3 ; concentration at the p + and n + regions for the ohmic contact is N + A = N + D = cm 3 ; and distance between these regions is W = 4 μm the distance between electrodes is also set at W = 10 μm, but the result is not sensitive to this value). An example slow-light mode distribution, E 2, in the PCW is shown in Fig. 5a). In this study, the distribution is averaged by taking the square of the Fourier transform of the modal time evolution at each position. Large E 2 appears periodically at the center of the waveguide and near the first-row of holes. This figure assumes a propagation constant of k =0.4052π/a), but the distribution does not change much for other values of k in the transmission band. When the reverse bias, V DC, is applied to the junction, the carrier densities are changed by ΔN n,p and the index of Si is locally changed by Δn Si, which is expressed as [18] Δn Si = ΔN n ΔN p 0.8 where ΔN n,p are in units of cm 3. We calculated the distribution of ΔN n,p using a commercial simulator, Lumerical DEVICE, and obtain the distribution of Δn Si for the voltage swing V DC = V, as shown in Fig. 5b) e). Large Δn Si 8)

5 1688 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 9, MAY 1, 2017 Fig. 6. Performance of PCW phase shifter with linear p n junction and n g spectrum. a) DC Δφ. b) Loss. occurs at the edges of the depletion region around the p n junction, and Δn Si =0appears between the edges because the depletion region already exists at V DC =0V. We calculated the change of modal equivalent index, Δn eq, using the following formulas [4]: ΔnSi E 2 dxdydz ΔnSi E 2 dxdy Δn eq = E 2 =Γ slab dxdydz E 2 9) dxdy slab Γ slab = E 2 dxdydz 10) all E 2 dxdydz where Γ slab is the confinement factor of the slow-light mode into the photonic crystal slab, which was calculated as Γ slab = for different k. AlargeΔn eq is expected for the sawtooth and wavy junctions because their profiles overlap with the mode maxima. Δφ is given by Δn eq Δφ =ΔkL = k 0 n g ζl ζ = dn Si n Si dω b 11) n Si dn eq ω b dn Si where k 0 is the wavenumber in vacuum and ω b is the frequency of the photonic band. We slightly modify the definition of ζ from that in [2], [4] for easy calculation; from the photonic band calculation, ζ = is obtained for different k. Since the mode distribution and n g vary with k and corresponding wavelength in the PCW, Δφ also varies. The spectrum of DC Δφ obtained for the linear junction, as an example, is shown in Fig. 6a), with the n g spectrum obtained from the slope of the photonic band [15]. DC Δφ increases with the increase in n g toward the band-edge wavelength. The loss because of free carrier absorption is also shown with n g in Fig. 6b). It Fig. 7. Comparision of performance between four junctions. a) DC Δφ. b) C and W bit.c)f 3dB. d) f) RF Δφ at different BRs. λ = 1564 nm. V DC = 0 3V. increases similarly to DC Δφ, but the increase is also observed at shorter wavelengths exhibiting lower n g. This is because of the increase of mode spreading toward the n + and p + regions. We calculated DC Δφ, C, W bit, f 3dB, and RF Δφ, assuming n g =22 and the push-pull drive, as shown in Fig. 7. The linear junction dashed line) shows high speed and small W bit,butδφ is so small that the eye opening is limited. DC Δφ for V DC = V increases with increasing w y [see Fig. 7a)]. It then decreases for the interleaved and wavy junctions because these junctions particularly overlap with the holes for large w y.atw y = 400 nm, DC Δφ 0.45π is expected for these periodic junctions. According to Fig. 2, this value allows ER = 3 db even with ML < 0.2 db, or ER > 8dB with ML = 1 db. The difference between these periodic junctions is not significantly large; however, the interleaved junction appears to be slightly advantageous compared with others. Regarding C, we calculate Q at the center voltage, V DC = 1.5 V, and apply the relation C = dq/dv DC. Unlike DC Δφ, C definitely decreases for the sawtooth and wavy junctions [see Fig. 7b)]. W bit estimated from CVpp/2 2 for the push pull drive is as small as 0.3 pj/bit for the sawtooth and wavy junctions at w y = 400 nm, which is approximately 70% of that for the interleaved junction and much smaller than that for the conventional rib-waveguide modulators, i.e., 4.2 pj/bit [10]. f 3dB is

6 TERADA et al.: SI PHOTONIC CRYSTAL SLOW-LIGHT MODULATORS WITH PERIODIC P N JUNCTIONS 1689 Fig. 8. Design of p n junction upper) and SEM image of fabricated device in which surface etching occurred at p-type ion implantation lower). a) Interleaved junction. b) Sawtooth junction. c) Zigzag wavy) junction. determined from R pn and C. Compared with the rib-waveguide modulators, the slow-light mode in the PCW penetrates twice as far into the photonic-crystal claddings. To avoid absorption loss, W must be increased appropriately, resulting in increased value of R pn. Actually, R pn =52Ωwascalculated for the aforementioned W and doping concentration. A slightly larger value of R pn is often measured for fabricated devices because of the presence of non-activated dopants near the periphery of the holes [8]; therefore, we assume R pn =60Ω, in this study. Adding the internal resistance of PPG R 0 =50Ω),wesetR = 110 Ω and calculate f 3dB =1/2π [see Fig. 7c)]. The sawtooth and wavy junctions exhibit higher f 3dB, although it is gradually reduced by increasing w y. The interleaved junction exhibits a lower value because of excess capacitance. We finally obtain RF Δφ by setting V pp = 3.0 V and V DC = 1.5 V, which correspond to the values assumed for DC Δφ and f 3dB, and substituting the obtained value of DC Δφ and f 3dB into Eqs. 5) 7). At w y = 400 nm, RF Δφ for the wavy junction shows maximum values of 0.41π 0.37π at Gb/s, which allows ER > 4 db with ML = 0.5 db [see Fig. 7d)]. Regarding RF Δφ, the wavy junction is slightly more advantageous than the interleaved junction particularly for higher BR, owing to the higher values of f 3dB. The sawtooth junction with w y > 500 nm appears to be more advantageous. The next section demonstrates that its structure is not actually fabricated. IV. FABRICATED P N JUNCTION The p n junction profile for the fabricated device diverges in some ways from the designed one. To evaluate the same, we observe irregular device samples in which the p-doped Si surface is etched during ion implantation using SEM. As mentioned earlier, the devices are fabricated using a 180 nm CMOS process. The interleaved and wavy junctions with larger p and figure sizes are fabricated almost similarly to the corresponding designs, although their edges are slightly rounded. In contrast, the sawtooth junction with the smallest p and sharper shape is not fabricated accurately and is much narrower than that Fig. 9. Modeling of fabricated sawtooth and wavy junctions. Model for a) sawtooth and b) wavy junctions. c) Expected lateral depth in fabrication calculated for designed one. Three lines for each junction are obtained for D = 100, 150, and 200 nm. designed because of the resolution limit of the lithography. We model the designed and fabricated profiles of the sawtooth and wavy junctions, as shown in Fig. 9a). The rounded edge is expressed by an arc with diameter D. The fabricated junction width, w y, is obtained by solving the following equations that include the designed width w y : Sawtooth junction) w y = w y + D w y D p + p 1+ 4w y 3p 1+ 4w y ) 2 ) 1 2 ) 2 ) )

7 1690 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 9, MAY 1, 2017 Wavy junction) π w y = w y sin 2 2πb ) + D D p 2 4b 2 13) ) 2 )) 2 p 2π D = 2b 1+ sin πw y p b. 14) For the 180 nm process, D = 200 nm is evaluated from the SEM images in Fig. 8, and w y is obtained, as shown in Fig. 9b). The sawtooth junction with p = 400 nm can be fabricated with a small error only when w y 100 nm. In the calculation shown in the previous section, the sawtooth junction is expected to show a large value of RF Δφ at w y 500 nm, but such a junction is difficult to fabricate, even with D = 100 nm. In contrast, the wavy junction with p = 800 nm can be fabricated using the current process when w y = 400 nm, at which RF Δφ assumes a maximal value. In addition to the accuracy of the lithography, we must also pay attention to the diffusion of dopants after the implantation and subsequent annealing. Let us assume that the doping concentration N A,D x) decays according to the following Gaussian function for the distance from the boundary, x [see Fig. 10a)]: [ x ) ] 2 N A.D x) =N A,D exp 15) σ where σ is the diffusion length. Fig. 10b) and c) show the distribution of calculated N A,D. Since we consider the diffusion of both p- and n-type regions, the dopings are compensated at the boundary and the intrinsic region is formed. The position of the intrinsic region is close to the n region because it is assumed that N A and N D are different from each other. We input these distributions into the DEVICE and calculate the relative change of DC Δφ, as shown in Fig. 10d). DC Δφ for the wavy junction decreases with increasing σ. It is maintained at 90% for σ 25 nm, but degrades to <70% for σ = 100 nm. The decrease in the wavy junction is smaller than that in the interleaved junction. This may be because of a smaller intrinsic region for the same diffusion length, which is expected for the wavy junction with larger p. V. MODULATION CHARACTERISTICS We measure the DC Δφ in the modulator with the wavy junction and test the high-speed modulation. As shown in Fig. 1c), we use a PCW without lattice shifts, with n g changing gradually. We selected a wavelength showing n g =22.In the measurement of DC Δφ, we controlled the TO phase tuner so that the transmission intensity took a minimal or maximal) value; we then changed the intensity by applying the reversebias V DC to the phase shifter and obtained DC Δφ by applying the change to the theoretical response of the MZ circuit. As shown in Fig. 11a), DC Δφ is almost linear for V DC, and those of the two arms are almost equal, suggesting that we can double the value of Δφ using a push pull drive. When V DC is fixed at 3.0 V, DC Δφ is changed with w y, as indicated by circles in Fig. 11b). We evaluate DC Δφ =0.29π with the push pull drive at w y = 320 and 390 nm. This value is approximately Fig. 10. Influence of dopant diffusion. a) Definition of diffusion length. b) and c) Doping concentration distribution in interleaved and wavy junction, respectively. σ is set as 66 nm as an example. d) Relative change in DC Δφ for σ. Fig. 11. DC Δφ measured for wavy junction. a) V DC dependence. b) w y dependence. Solid line shows calculated values assuming σ = 119 nm.

8 TERADA et al.: SI PHOTONIC CRYSTAL SLOW-LIGHT MODULATORS WITH PERIODIC P N JUNCTIONS 1691 Fig. 13. Eye patterns at different BRs observed for wavy junction device. We set the initial phase to obtain ER = 3 and 4 db. the following relationship: Δφ 100.1E R t u n e r 1. cos = 0.1E R t u n e r Fig Gb/s modulation characteristics of wavy junction device. a) Transmission characteristics varied by TO phase tuner with and without PRBS signals applied to phase shifter. b) Eye patterns at different initial phases. Labels correspond to those in a). 70% of the theoretical value in Fig. 7a). One reason for this is the diffusion of dopants, as mentioned above. The solid curve shows the theoretical value by assuming σ = 119 nm, exhibiting behaviors similar to the experimental plots. For this σ, we calculate C to be 39 ff for VDC = 1.5 V and Wbit = 0.17 pj/ bit for Vpp = 3.0 V. For the high-speed modulation, we apply the push pull PRBS signals bit) from PPG to the device. On the PPG, we set Vpp = 1.75 V and VDC = 0.90 V. However, since RF electrodes of this device are not electrically terminated by a 50 Ω load, the signal should be reflected, and considering the RF loss at Rpn, Vpp actually applied to the junction would be 1.7 times larger than the set value. Thus, actual Vpp 3.0 V, which corresponds to the Vpp value assumed in the calculations of Fig. 7 and to the VDC value in Fig. 11. After the light output is amplified by an erbium-doped fiber amplifier and the amplified spontaneous emission is eliminated by a band-pass filter, the eye pattern is observed using sampling oscilloscopes Keysight 86100C and 86109A. The responses of the TO phase tuner with and without 25 Gb/s PRBS signals are shown in Fig. 12a). The maximum ER of the phase tuner, ERtuner, decreases from 25 to 13 db with the PRBS signals, caused by the imbalance between two arms induced by the push pull drive. Δφ and ERtuner have 16) The value of RF Δφ estimated from this equation is 0.3π, and it is close to the measured plots of DC Δφ in Fig. 11, suggesting that f3db is reasonably high. The value of RF Δφ may degrade for the same reason as that for the degradation of DC Δφ, but the value can still yield ER > 3 db with M L = 0.5 db. We set the initial phase differences to be 0.37π [point A in Fig. 12a)] and 0.46π point B) and observed the eye patterns in Fig. 12b). We confirm that ER = 3 db for M L = 0.5 db and ER = 4 db for M L = 1 db, respectively. Either the ER is larger or the ML is smaller than that for the interleaved junction with the same ng [4]. The eye patterns for different BRs are shown in Fig. 13, where the initial phase difference is determined such that ER becomes 3 or 4 db. The clear eye opening with ER = 3 db is maintained up to 32 Gb/s, although ML increases to 1 db. VI. CONCLUSION We optimized the periodic p n junction in the phase shifter of Si PCW MZ modulator to improve the device s overall performance. Theoretically, the sawtooth and wavy junctions show a moderately larger value of RF Δφ and a 60% power consumption compared with those of the previously fabricated interleaved junction. However, fabrication errors for the sawtooth junction were severe when the 180 nm CMOS process was used. The wavy junction could be fabricated by this process with negligible error, making it advantageous in this case. We set Vpp = 1.75 V, VDC = 0.9 V PPG set value) and M L = 1 db in the wavy-junction device showing ng = 22 and obtained the 25 and 32 Gb/s eye openings with ER = 4 and 3 db, respectively. Higher bit-rate operation will be available by higher voltages, but 32 Gb/s may be the upper limit for

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Miller, Energy consumption in optical modulators for interconnects, Opt. Exp., vol. 20, no. S2, pp. A293 A308, [17] S. Kinugasa, N. Ishikura, H. Ito, N. Yazawa, and T. Baba, One-chip integration of optical correlator based on slow-light devices, Opt. Exp., vol. 23, no. 16, pp , [18] R. A. Soref and B. R. Bennet, Electrooptical effects in silicon, IEEE J. Quantum Electron., vol. QE-23, no. 1, pp , Jan Yosuke Terada M 14) received the B.E., M.E., and Ph.D. degrees from the Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan, in 2007, 2010, and 2013, respectively. During his Ph.D. degree, he focused mainly on material physics with special focus on Ge light emitters. In 2013, he joined Yokohama National University, Yokohama, Japan, as a Research Associate. He is currently working toward Si photonic-crystal slow-light modulators. He is a Member of the Japan Society for Applied Physics JSAP). Tomoki Tatebe received the B.E. degree from Yokohama National University in He has studied Si photonic-crystal slow-light modulators. He is currently working on a Si photonic-crystal optical deflector as a Master s student in the same university. He is a Member of JSAP. Yosuke Hinakura received the B.E. degree from Yokohama National University in He has studied Si photonic-crystal slow-light modulators. He is currently working toward Si photonic-crystal optical modulators as a Master s student in the same university. He is a Member of JSAP. Toshihiko Baba M 93) received the Ph.D. degree from Yokohama National University YNU) in Then, he became a Research Associate at the Tokyo Institute of Technology, Tokyo, Japan, in 1990, an Associate Professor at YNU in 1994, and a full-time Professor in He has studied antiresonant reflecting optical waveguides, verical-cavity surface-emitting lasers, photonic crystals, Si photonics, nanolasers, slow light, and biosensing. He is the author and coauthor of more than 180 papers. Dr. Baba is a Member of JSAP, Institute of Electrical, Information and Communication Engineering, and the Optical Society. He has received 17 academic awards, including the IEEE/LEOS Distinguished Lecturer award in 2006/2007.