Method to improve the linearity of the silicon Mach-Zehnder optical modulator by doping control

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24641 Method to improve the linearity of the silicon Mach-Zehnder optical modulator by doping control JIANFENG DING, SIZHU SHAO, LEI ZHANG, XIN FU, AND LIN YANG* State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, P. O. Box 912, Beijing 100083, China * oip@semi.ac.cn Abstract: We optimize the linearity performance of silicon carrier-depletion Mach-Zehnder optical modulator through controlling the doping concentration. The optical field distribution in the waveguide is a Gaussian-like distribution. As the doping concentration increases, the dynamic depletion width of the PN junction under the same modulation signal will decrease, and the integration width of the overlap between the Gaussian-like optical field distribution and the depletion region will become smaller. Therefore the modulated signal has less nonlinear components. Our simulation results proved this analysis. We also fabricated different devices with different doping concentrations. By adopting a ten times doping concentration, the spurious free dynamic range (SFDR) for third-order intermodulation distortion (TID) increases from 109.2 db.hz2/3 to 113.7 db.hz2/3 and the SFDR for second harmonic distortion (SHD) increases from 87.6 db.hz1/2 to 97.5 db.hz1/2 at a driving frequency of 2 GHz. When the driving frequency is 20 GHz, the SFDRs for TID and SHD distortions are 110.3 db.hz2/3 and 96 db.hz1/2, respectively. 2016 Optical Society of America OCIS codes: (250.3140) Integrated optoelectronic circuits; (250.7360) Waveguide modulators. References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. R. Soref and B. Bennett, Electrooptical effects in silicon, IEEE J. Quantum Electron. 23(1), 123 129 (1987). R. A. Soref, The past, present, and future of silicon photonics, IEEE J. Sel. Top. Quantum Electron. 12(6), 1678 1687 (2006). H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, A continuous-wave Raman silicon laser, Nature 433(7027), 725 728 (2005). A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, Electrically pumped hybrid AlGaInAs-silicon evanescent laser, Opt. Express 14(20), 9203 9210 (2006). A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor, Nature 427(6975), 615 618 (2004). Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Micrometre-scale silicon electro-optic modulator, Nature 435(7040), 325 327 (2005). A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, High-speed optical modulation based on carrier depletion in a silicon waveguide, Opt. Express 15(2), 660 668 (2007). R. Ding, Y. Liu, Y. Ma, Y. Yang, Q. Li, A. E.-J. Lim, G.-Q. Lo, K. Bergman, T. Baehr-Jones, and M. Hochberg, High-speed silicon modulator with slow-wave electrodes and fully independent differential drive, J. Lightwave Technol. 32(12), 2240 2247 (2014). X. Tu, T. Y. Liow, J. Song, M. Yu, and G. Q. Lo, Fabrication of low loss and high speed silicon optical modulator using doping compensation method, Opt. Express 19(19), 18029 18035 (2011). D. J. Thomson, F. Y. Gardes, Y. Hu, G. Mashanovich, M. Fournier, P. Grosse, J. M. Fedeli, and G. T. Reed, High contrast 40Gbit/s optical modulation in silicon, Opt. Express 19(12), 11507 11516 (2011). M. Geng, L. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. Liu, Four-channel reconfigurable optical adddrop multiplexer based on photonic wire waveguide, Opt. Express 17(7), 5502 5516 (2009). M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kärtner, H. I. Smith, and E. P. Ippen, Reconfigurable multichannel second-order silicon microring-resonator filterbanks for on-chip WDM systems, Opt. Express 19(1), 306 316 (2011). R. Ji, L. Yang, L. Zhang, Y. Tian, J. Ding, H. Chen, Y. Lu, P. Zhou, and W. Zhu, Five-port optical router for photonic networks-on-chip, Opt. Express 19(21), 20258 20268 (2011). N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, Optical 4x4 hitless slicon router for optical networks-on-chip (NoC), Opt. Express 16(20), 15915 15922 (2008). #275143 Journal 2016 http://dx.doi.org/10.1364/oe.24.024641 Received 2 Sep 2016; revised 6 Oct 2016; accepted 10 Oct 2016; published 14 Oct 2016

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24642 15. D. Ahn, C. Y. Hong, J. Liu, W. Giziewicz, M. Beals, L. C. Kimerling, J. Michel, J. Chen, and F. X. Kärtner, High performance, waveguide integrated Ge photodetectors, Opt. Express 15(7), 3916 3921 (2007). 16. Y. Kang, H. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y. Kuo, H. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain-bandwidth product, Nat. Photonics 3(1), 59 63 (2009). 17. S. Assefa, F. Xia, and Y. A. Vlasov, Reinventing germanium avalanche photodetector for nanophotonic on-chip optical interconnects, Nature 464(7285), 80 84 (2010). 18. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, Silicon optical modulators, Nat. Photonics 4(8), 518 526 (2010). 19. N. N. Feng, S. Liao, D. Feng, P. Dong, D. Zheng, H. Liang, R. Shafiiha, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, High speed carrier-depletion modulators with 1.4V-cm V(π)L integrated on 0.25microm silicon-on-insulator waveguides, Opt. Express 18(8), 7994 7999 (2010). 20. T. Baehr-Jones, R. Ding, Y. Liu, A. Ayazi, T. Pinguet, N. C. Harris, M. Streshinsky, P. Lee, Y. Zhang, A. E. Lim, T. Y. Liow, S. H. Teo, G. Q. Lo, and M. Hochberg, Ultralow drive voltage silicon traveling-wave modulator, Opt. Express 20(11), 12014 12020 (2012). 21. X. Xiao, H. Xu, X. Li, Z. Li, T. Chu, Y. Yu, and J. Yu, High-speed, low-loss silicon Mach-Zehnder modulators with doping optimization, Opt. Express 21(4), 4116 4125 (2013). 22. J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, and R. Min, Low-voltage, highextinction-ratio, Mach-Zehnder silicon optical modulator for CMOS-compatible integration, Opt. Express 20(3), 3209 3218 (2012). 23. H. Yu, W. Bogaerts, and A. De Keersgieter, Optimization of ion implantation condition for depletion-type silicon optical modulators, IEEE J. Quantum Electron. 46(12), 1763 1768 (2010). 24. L. Chen, C. R. Doerr, P. Dong, and Y. K. Chen, Monolithic silicon chip with 10 modulator channels at 25 Gbps and 100-GHz spacing, Opt. Express 19(26), B946 B951 (2011). 25. P. Dong, L. Chen, and Y. K. Chen, High-speed low-voltage single-drive push-pull silicon Mach-Zehnder modulators, Opt. Express 20(6), 6163 6169 (2012). 26. Y. Yang, Q. Fang, M. Yu, X. Tu, R. Rusli, and G.-Q. Lo, High-efficiency Si optical modulator using Cu travelling-wave electrode, Opt. Express 22(24), 29978 29985 (2014). 27. A. D. Simard, B. Filion, D. Patel, D. Plant, and S. LaRochelle, Segmented silicon MZM for PAM-8 transmissions at 114 Gb/s with binary signaling, Opt. Express 24(17), 19467 19472 (2016). 28. M. Streshinsky, A. Ayazi, Z. Xuan, A. E.-J. Lim, G.-Q. Lo, T. Baehr-Jones, and M. Hochberg, Highly linear silicon traveling wave Mach-Zehnder carrier depletion modulator based on differential drive, Opt. Express 21(3), 3818 3825 (2013). 29. Y. Zhou, L. J. Zhou, F. Su, X. W. Li, and J. P. Chen, Linearity measurement and pulse amplitude modulation in a silicon single-drive push-pull mach-zehnder modulator, J. Lightwave Technol. 34(14), 3323 3329 (2016). 30. T. Li, D. Wang, J. Zhang, Z. Zhou, F. Zhang, X. Wang, and H. Wu, Demonstration of 6.25 Gbaud advanced modulation formats with subcarrier multiplexed technique on silicon Mach-Zehnder modulator, Opt. Express 22(16), 19818 19823 (2014). 31. L. Chen, J. Chen, J. Nagy, and R. M. Reano, Highly linear ring modulator from hybrid silicon and lithium niobate, Opt. Express 23(10), 13255 13264 (2015). 32. C. Zhang, P. A. Morton, J. B. Khurgin, J. D. Peters, and J. E. Bowers, Highly linear heterogeneous-integrated Mach-Zehnder interferometer modulators on Si, Opt. Express 24(17), 19040 19047 (2016). 1. Introduction Silicon photonics has developed rapidly for recent decades and shows a great potential of revolutionizing the current communication systems [1 16]. As a key component to connect the electrical signal to the silicon optical link, silicon optical modulator plays a very important role in silicon photonics. Silicon optical modulators for the digital optical communication system have been extensively and intensively explored [17 27]. Actually, it can also be employed for analog optical communication, which has been only investigated by several groups around the world [28 32]. As the fifth-generation wireless communication and other advanced communication systems are on the horizon, the applications such as radio-overfiber, antenna remoting, and phase array control are becoming hotspots in these fields. In such analog communication systems, broad bandwidth and high linearity are two basic requirements for the constituent devices. With respect to bandwidth and linearity, silicon carrier-depletion Mach-Zehnder (M-Z) optical modulator has the better performance combination than those based on the carrier injection effect, carrier accumulation effect and the ring structure. In this paper, we analyze the linearity of silicon carrier-depletion M-Z optical modulators and find that the doping concentration plays an important role in the linearity performance. As the doping concentration gets higher, the depletion width of the PN

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24643 junction will become smaller under the same driving voltage. Because the optical field distribution in the depletion region is not uniform, a shorter depletion region will weaken the distortion caused by the nonuniformity of the optical field overlapping with the depletion region. This leads to a higher linearity of the modulator. Our experimental results indicate that spurious free dynamic range (SFDR) for third-order intermodulation distortion (TID) increases from 109.2 db.hz 2/3 to 113.7 db.hz 2/3 and the SFDR for second harmonic distortion (SHD) increases from 87.6 db.hz 1/2 to 97.5 db.hz 1/2 at a driving frequency of 2 GHz by adopting a ten times doping concentration. 2. Device design y x Fig. 1. Illustration of (a) the optical field distribution in a silicon ridge waveguide. (b) the carrier concentration distribution of a PN junction without any depletion region. (c) the carrier concentration distribution of a PN junction with a depletion region. The refractive index change Δn eff of the phase shifter in a silicon M-Z optical modulator based on the carrier depletion effect is determined by the overlap integration of the carrier concentration distribution change and the optical field distribution. Figure 1(a) illustrates the optical field distribution of a silicon ridge waveguide. Figures 1(b) and 1(c) are the carrier concentration distributions of a PN junction without and with a depletion region respectively. Normally the depletion region and the optical field distribution should overlap in the middle of the optical field as the optical field is strongest in this region. This design can offer maximum modulation efficiency. Δ is expressed by Δ n = eff 1 n eff ( 0) ( 0) nxy (, ) n ( xy, ) E ( xy, ) dxdy (0) 2 n ( 0) eff E ( x, y) dxdy In Eq. (1), Δ nxy (, ) is the material refractive index change of silicon caused by the plasma dispersion effect. And n (0) eff is the original effective refractive index of the doped silicon waveguide without any carrier distribution change. E (0) ( x, y ) is the distribution of electricfield component of the optical mode in the waveguide. The integration area dxdy is the optical field distribution region. For an abrupt PN junction, the depletion region is considered to have a rectangular distribution and Δ nxy (, ) can be assumed to be constant in this area. 2 (1)

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24644 Fig. 2. (a) Normalized power of the two-dimensional optical field distribution in an x range of 1.2 μm and a y range of 1 μm. (b) Normalized power of the one-dimensional optical field distribution in an x range of 1.2 μm after the integration along y axis. Figure 2(a) shows the optical power distribution of a silicon ridge waveguide, which is 400 nm in width, 220 nm in height and 70 nm in slab thickness. When the driving voltage is applied on the PN junction, the depletion region will stretch or shrink along the x axis and remain unchanged along the y axis. Therefore we can do the integration along the y axis first to simplify the calculation and for better visualization. Figure 2(b) shows the normalized onedimensional optical power distribution after the integration along the y axis. The depletion region usually locates in the core region of the silicon waveguide as indicated by the red lines in Fig. 2(b). In this area, the one-dimensional optical power has a Gaussian-like distribution. Figure 3 shows that the fitted Gaussian curve matches the calculated line quite well. Then we can use a Gaussian function to analyze the linearity of the devices with different doping concentrations. The fitted optical power distribution can be expressed as 2x 2 2 ( ) (0) 231 E ( x) = Ae. (2) where A is a normalized coefficient. If the MZI modulator is optically biased at the quadrature point, the output signal will be proportional to the phase change. So the final output signal O s can be expressed as Eq. (3). In Eq. (3), erf means the error function, and x L, C d, V bias, V s, f and 1 f 2 represent the location of the PN junction, a coefficient related to the doping concentrations, the revers bias voltage, the amplitude of the signal, the frequency of one signal and the frequency of the other signal, respectively. B is a normalized coefficient including the photoelectric conversion. 2 2 O = B ( ( )) ( ( ( (sin(2 ) sin(2 ))) )). s erf x C V erf x C V + V π f t + π f t L d bias L d bias s 1 2 231 231 O contains the distortion component. By the overlap integration with the fundamental s signals sin(2 π ft 1 ) and sin(2 π ft 2 ), we can get the fundamental signals. Therefore, after the overlap integration with the distortion signals, we can get the distortion components such as sin(2π 2 f1 t) and sin(2 π (2 f1 f2) t). Finally, we can calculate the SFDRs and show the result in Fig. 4. The noise floor is chosen as 165 dbm/hz, which is consistent with that in the following experiment. When the doping concentration is higher, the depletion region will be smaller. As illustrated in Fig. 3, the width of depletion region in a high-doped PN junction varies smaller than that of a low-doped PN junction under the same driving voltage. Therefore, the high- (3)

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24645 doped PN junction experiences less nonlinear region of the Gaussian curve of the optical field distribution than the low-doped PN junction. In other words, the depletion region of highdoped PN junction sees a more uniform optical field distribution. Thus the modulated signal, as a result of the overlap of the depletion region and the optical field distribution, can have a higher linearity for the device with a high-doped PN junction. Figure 4 shows the simulated SFDR results of a 2-mm-long device for SHD and TID when the doping concentration increases from 2 10 17 cm 3 to 2 10 18 cm 3. The simulation only calculates the SFDR at a low speed and does not considered the EO bandwidth limitation. This result indicates that the SFDR increases as the doping concentration increases. When the doping concentration increases on and on, the depletion region will become narrower and narrower. Then the linearity enhancement caused by reducing the depletion width will become saturated. This is the reason why the slopes of the curves in Fig. 4 decrease as the doping concentration increases. Fig. 3. The fitted Gaussian curve and the calculated curve of the optical field distribution in the core of the silicon ridge waveguide. Fig. 4. The simulated SFDRs for SHD and TID when the doping concentration increases from 2 10 17 cm 3 to 2 10 18 cm 3. 3. Experimental result and discussion We fabricated three devices with different doping concentrations. The details on the fabrication process can be found in [22]. The low doping concentrations are 2 10 17 cm 3 for

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24646 the p-type doping region and 1.6 10 17 cm 3 for the n-type doping region. The medium doping concentrations are 1 10 18 cm 3 for the p-type doping region and 8 10 17 cm 3 for the n-type doping region. The high doping concentrations are 2 10 18 cm 3 for the p-type doping region and 1.6 10 18 cm 3 for the n-type doping region. The other design parameters such as the length, the electrode and the doping location are identical. Figure 5 is the experimental setup for the SFDR test. The light beam from a tunable laser source is coupled into and out of the fabricated device with two lensed fibers. The output optical power of the tunable laser source is 14 dbm. The polarization of the light is transformed to be parallel to the x direction by a polarization controller. Two microwave signals at two near frequencies f 1 and f 2 are combined firstly by an electrical combiner and then used to drive the device. The silicon optical modulator is optically biased at the quadrature point to have a best linearity performance. The average optical power in the output lensed fiber is around 2.2 dbm. An erbium-doped fiber amplifier (EDFA) is used to amplify the optical signal to meet the power requirement of the photodiode with an opto-electrical bandwidth of 40 GHz. Normally a higher received optical power will give a higher SFDR. When the doping concentration increases, the insertion loss will increase at the same time. The insertion loss is 2.2 db/mm for the high-doped device while it is only 1.2 db/mm for the medium-doped device. In order to eliminate the disturbance from the optical loss variation, the optical power fed into the photodiode is around 11 dbm, which is kept constant for different devices. An electrical spectral analyzer is used to measure the distortion components. Fig. 5. Experimental setup of the SFDR test (LD: laser diode; PC: polarization controller; DUT: device under test; PD: photodiode; ESA: electrical spectral analyzer; E.Combiner: electrical combiner; MS: microwave source.)

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24647 Fig. 6. Experimental SFDR results of (a) the high-doped device, (b) the medium-doped device and (c) the low-doped device at a frequency of 2 GHz. The SFDRs for TID are 113.7 db.hz 2/3, 111.3 db.hz 2/3 and 109.2 db.hz 2/3, respectively. The SFDRs for SHD are 97.5 db.hz 1/2, 94.8 db.hz 1/2 and 87.6 db.hz 1/2, respectively. We do the measurements at frequencies of 2 GHz, 5 GHz, 10 GHz, 15 GHz and 20 GHz. The interval between f 1 and f 2 is kept to be 0.2 GHz in all cases. Figure 6 shows the results at the frequency of 2 GHz for the high-doped, medium-doped and low-doped devices. As the input power varies, the fundamental signal of 2 GHz, TID of 1.8 GHz and SHD of 4 GHz are recorded respectively. Then the dots of TID and SHD are fitted to calculate the SFDRs according to a system noise floor of 165 dbm/hz. The electrical signal loss of the fundamental component is 22 db. For the high-doped device, the SFDRs for TID and SHD are 113.7 db.hz 2/3 and 97.5 db.hz 1/2, respectively. These results are very close to those of the commercial lithium niobate optical modulator. Figure 7 shows the SFDR results for TID and SHD in a frequency range from 2 GHz to 20 GHz when the devices are doped by different doping concentrations. At the frequency of 2 GHz, the SFDRs for TID and SHD increase from 109.2 db.hz 2/3 to 113.7 db.hz 2/3 and from 87.6 db.hz 1/2 to 97.5 db.hz 1/2, when the doping concentration increases by ten times. At any frequency, the SFDR enhancement induced by heavy doping can be clearly observed. This is consistent with the above analysis. The SFDR for TID decreases monotonously as the frequency increases. However, the SFDR for SHD increases when the frequency is larger than 15 GHz. This result is caused by the bandwidth limitation of the testing system. The frequency of the SHD component is larger than 30 GHz as the fundamental frequency is larger than 15 GHz. This distortion component exceeds the bandwidth of the testing system. Then the distortion component is suppressed by the testing system and measured to be smaller than that generated by the device. For TID measurements, the frequency of the TID component is very close to that of the fundamental signal. Therefore the bandwidth limitation of the testing system can be neglected. This is the

Vol. 24, No. 21 17 Oct 2016 OPTICS EXPRESS 24648 reason why the tendencies of the TID and SHD SFDRs seem to be different in Fig. 7. Actually we think the tendency of the SFDR for SHD will be the same with that of the SFDR for TID if the bandwidth of the testing system is larger than 40 GHz. 4. Conclusion Fig. 7. (a) Experimental SFDRs for TID of the devces with different doping concentrations in a frequency range from 2 GHz to 20GHz. (b) Experimental SFDRs for SHD of the devces with different doping concentrations in a frequency range from 2 GHz to 20GHz. We have optimized the linearity of the silicon optical modulator based on the depletion of a PN junction. As the doping concentration of the PN junction increases, the linearity of the modulated optical signal will increase. When a p-type concentration of 2 10 18 cm 3 and a n- type concentration of 1.6 10 18 cm 3 are adopted, the SFDRs for TID and SHD are 113.7 db.hz 2/3 and 97.5 db.hz 1/2 at a frequency of 2 GHz. These results indicate that silicon optical modulators are competitive with the commercial lithium niobate modulators for analog optical communication. Funding This work has been supported by the National High Technology Research and Development Program of China (2015AA015503, 2015AA017001), and the National Natural Science Foundation of China (NSFC) (61505198, 61535002).