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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 15093–15099
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High speed silicon Mach-Zehnder modulator based on interleaved PN junctions

Hao Xu, Xi Xiao, Xianyao Li, Yingtao Hu, Zhiyong Li, Tao Chu, Yude Yu, and Jinzhong Yu  »View Author Affiliations


Optics Express, Vol. 20, Issue 14, pp. 15093-15099 (2012)
http://dx.doi.org/10.1364/OE.20.015093


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Abstract

A high speed silicon Mach-Zehnder modulator is proposed based on interleaved PN junctions. This doping profile enabled both high modulation efficiency of VπLπ = 1.5~2.0 V·cm and low doping-induced loss of ~10 dB/cm by applying a relatively low doping concentration of 2 × 1017 cm−3. High speed operation up to 40 Gbit/s with 7.01 dB extinction ratio was experimentally demonstrated with a short phase shifter of only 750 μm.

© 2012 OSA

1. Introduction

2. Device structure and fabrication

Figure 1(a)
Fig. 1 (a) Microscope image of the MZM. (b)Schematic view of the phase shifter with periodically interleaved PN junctions.
shows the microscope image of the MZM, the device was fabricated in an asymmetrical Mach-Zehnder interferometer (MZI) with 170 μm arm length difference. Multi-mode interferences (MMI) and grating couplers were utilized for light splitting, combining and coupling in and out. On the SOI wafer with a 340 nm thick top silicon layer and a 2 μm thick buried oxide layer, the rib waveguide was optimized to be 450 nm wide with an 80nm high slab. To balance the carrier induced optical loss, 750 μm long phase shifters were formed in both arms. The geometry of periodically interleaved PN junctions embedded in the phase shifter is shown in Fig. 1(b). The lengths of both P and N region were 300 nm making a 600 nm long period length.

Interleaved PN junctions were realized by p-type doping and n-type compensation. The waveguide was firstly P-type doped with a background doping concentration of 2 × 1017 cm−3. Regional N-type compensation with higher density of 4 × 1017 cm−3 was employed to form the abrupt interleaved junctions. Highly doped P + and N + regions were respectively defined 1 μm away from the edge of the rib waveguide to ensure low carrier absorption loss. A 1 μm thick aluminum coplanar waveguide (CPW) electrode was designed for drive signal transmission. The device was fabricated by commercial 0.18 μm CMOS process in the Semiconductor Manufacturing International Corporation using the similar processes as Ref. [8

8. X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012). [CrossRef] [PubMed]

].

3. Measurement results and discussion

3.1 DC performance

The transmission spectra of the MZM at different reverse bias voltages is shown in Fig. 2(a)
Fig. 2 (a) Normalized transmission spectra of the MZM and MZI. (b) Comparison of the VπLπ of the MZM based on interleaved PN junctions and lateral PN junctions with offset.
, while a MZI composed of same optical structures without ion implantation was measured for comparison. The recorded spectra in Fig. 2(a) were normalized to a waveguide of the same length. It can be calculated from the spectral curves that the device insertion loss is ~2 dB and carrier induced loss of the phase shifter is ~10 dB/cm by the cut back method. The modulation efficiency VπLπ is 1.5~2.0 V·cm under the bias voltages varying from 0 V to −8 V. These measured results show good agreement with the simulation results of the similar structures proposed in Refs [7

7. Z. Y. Li, D. X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J. Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express 17(18), 15947–15958 (2009). [CrossRef] [PubMed]

] and [8

8. X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012). [CrossRef] [PubMed]

]. In order to evaluated the performance of a phase shifter, a figure-of-merit (FOM) Loss· Efficiency, the product of carrier-induced loss and VπLπ, was defined in Ref [5

5. 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). [CrossRef] [PubMed]

]. For the phased shifter shown in Fig. 1(b), This FOM is not over 20 dB·V which is comparable with the result optimized by doping compensation method proposed in Ref [5

5. 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). [CrossRef] [PubMed]

]. Figure 2(b) presents the comparison of the measured VπLπ of the MZM based on the proposed structure and those based on the lateral PN junction. The lateral PN junctions were designed to be with 50 nm and 100 nm offset in the rib waveguide respectively as described in Ref [11

11. 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 1.4 V-cm VπL integrated on 0.25microm silicon-on-insulator waveguides,” Opt. Express 18(8), 7994–7999 (2010). [CrossRef] [PubMed]

]. It is observed that interleaved PN junctions provided higher modulation efficiency with the same doping concentration and optical structures. Moreover, as the interleaved PN junctions are oriented cross the rib waveguide, the overlap of the depletion regions and the optical mode is insensitive to the location of the PN junctions in the rib waveguide, which enables much higher misalignment tolerance for the fabrication process.

3.2 Dynamic performance

This doping profile is predicted to have ~35 GHz intrinsic bandwidth based on our simulation [7

7. Z. Y. Li, D. X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J. Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express 17(18), 15947–15958 (2009). [CrossRef] [PubMed]

]. However, the high-speed performance of MZM depends on not only the intrinsic device speed governed by motion of carries, but also the issues associated with the relative large parasitic effects of PN junction and electrode [1

1. A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008). [CrossRef]

]. Since the depletion-mode MZM can be considered as a capacitive-load CPW transmission line [12

12. D.Feng, D. Zheng, and T. Smith, “Traveling-wave high-speed silicon modulator,” Integrated Photon. Res. Appl. (IPRA), ITUB4 (2006).

], an equivalent circuit model based on the device’s structure dimensions and material parameters is proposed to characterize the high speed performance of the MZM.

Figure 3(a)
Fig. 3 (a) Equivalent circuit model of the depletion-mode MZM. (b)–(c) Curve-fitting of the measured transmission-line parameters of the MZM based on the lateral PN junction at −3V bias.
shows the distributed circuit model proposed to account for the propagation effects of the depletion-mode MZM. The circuit includes elements from the model in Refs [13

13. Y. R. Kwon, V. M. Hietala, and K. S. Champlin, “Quasi-TEM analysis of‘slow-wave’ mode propagation on coplanar microstructure MIS transmission lines,” IEEE Trans. Microw. Theory Tech. 35(6), 545–551 (1987). [CrossRef]

] and [14

14. V. Milanovic, M. Ozgur, D. C. DeGroot, J. A. Jargon, M. Gaitan, and M. E. Zaghloul, “Characterization of broad-band transmission for coplanar waveguides on CMOS silicon substrates,” IEEE Trans. Microw. Theory Tech. 46(5), 632–640 (1998). [CrossRef]

], which was extracted to characterize CPW on loss silicon substrate and experimental validated over a broad bandwidth. In Fig. 3(a), these parameters were defined as follow: RS and L were the series resistance and inductance of the aluminum conductors of the CPW electrode. RL represented longitudinal current loss in the silicon substrate, CSS and CSG were the signal line to ground line and signal line to silicon substrate capacitance, CSi and GSi were used to describe the relaxation between slow–wave at lower frequency and quasi-TEM modes at higher frequency. Approximate expressions of these parameters can be extracted by using the conformal mapping method and partial capacitance approach. All these parameters above were taken per unit length and described in detail in Refs [13

13. Y. R. Kwon, V. M. Hietala, and K. S. Champlin, “Quasi-TEM analysis of‘slow-wave’ mode propagation on coplanar microstructure MIS transmission lines,” IEEE Trans. Microw. Theory Tech. 35(6), 545–551 (1987). [CrossRef]

] and [14

14. V. Milanovic, M. Ozgur, D. C. DeGroot, J. A. Jargon, M. Gaitan, and M. E. Zaghloul, “Characterization of broad-band transmission for coplanar waveguides on CMOS silicon substrates,” IEEE Trans. Microw. Theory Tech. 46(5), 632–640 (1998). [CrossRef]

]. For a depletion-mode MZM working under reverse bias, the depletion capacitance is significant for the PN junction [15

15. L. Reinhold and B. Pavel, RF Circuit Design: Theory and Applications(PrenticeHall, 2000).

], therefore, the junction capacitance CJ(F/m)can be expressed by
CJ(v)=ALεrε0qNAND2(NA+ND)(VTv)
(1)
where A is the total cross-section area of the PN junctions, L is the length of the phase shifter, ε0 and εr are the permittivity of free space and dielectric constant of silicon, q is the elementary charge, NA and ND are the doping concentration of P-type and N-type, VT and v are the built-in potential and reverse bias voltage. RJ (Ω·m) is the resistance in series with the junction capacitance which represents the contact resistance of the doping regions and the annealed alloy at the interface between metal and semiconductor. It can be extracted by curve-fitting the measured characteristic parameters, namely, the characteristic impedance, attenuation constant and the effective index of the microwave. For a depletion-mode MZM working at a certain reverse bias, the complex characteristic impedance Z0and complex propagation coefficient γ can be evaluated as function of frequency f from [13

13. Y. R. Kwon, V. M. Hietala, and K. S. Champlin, “Quasi-TEM analysis of‘slow-wave’ mode propagation on coplanar microstructure MIS transmission lines,” IEEE Trans. Microw. Theory Tech. 35(6), 545–551 (1987). [CrossRef]

]
Z0=ZRe+jZIm=Z/Y
(2)
γ=α+jβ=ZY
(3)
where
Z=11RL+1RS+jωL
(4)
Y=11jωCSG(1jωCSS+1jωCSi+GSi)(RJ+1jωCJ)
(5)
In Eq. (4), α is the attenuation constant, β is the phase constant, and the effective index of the microwave can be expressed as ne = (c·β), where c is the light speed in free space and ω = 2πf is the angular frequency. Figure 3(b)3(d) illustrate the measured characteristic parameters of the MZM based on the lateral PN junction using the on wafer de-embedding techniques described in [16

16. A. M. Mangan, S. P. Voinigescu, M. T. Yang, and M. Tazlauanu, “De-embedding transmission line measurements for accurate modeling of IC designs,” IEEE Trans. Electron. Dev. 53(2), 235–241 (2006). [CrossRef]

]. The S parameter of the MZMs with different phase shifter length of 1000 μm, 750 μm and 500 μm from DC to 20 GHz were measured by a signal integrity network analyzer (SPARQ) from Lecroy at −3V bias. The testing system, including network analyzer, cables, probes, the bias-Tee and the DC block, was calibrated using short-open-load-through calibration on Impedance Standard Substrate. As shown in Fig. 3(b)3(d), excellent curve fitting was achieved by setting RJ = 0.035Ω·m and CJ = 200 fF/mm which was ~30 fF/mm higher than that calculated from Eq. (1). It is believed this discrepancy results from the simplified method to extract Eq. (1) without considering doping process conditions. More accurately CJ could be calculated by the commercial semiconductor device-modeling package such as Silvaco [17]. As the capacitance is proportional to the total cross-section area of the PN junctions, the junction capacitance CJ of the phase shifter shown in Fig. 1(b) can be approximated by CJ = 615/(0.9-v)1/2 fF/mm and it decreases to be 290 fF/mm at −3.5 V bias accordingly. The CPW electrode induced capacitance is calculated as 156 fF/mm based on the proposed circuited model.

Figure 4(a)
Fig. 4 (a) Transmission parameters S21 of the MZM at different bias voltages. (b) Junction capacitance CJ of the MZM at different bias voltage.
shows the measured transmission data (S21) of this MZM. Since the depletion capacitance of the PN junction decreased with the increasing reverse bias voltage, the electrical 6 dB roll off frequency raised from 11 GHz at 0 V bias to be over 20 GHz at −3 V bias. However, with the increasing bias voltage, the decreasing slope of junction capacitance declined rapidly as shown in Fig. 4(b), so that the transmission line property of the MZM changed slightly when the bias voltage was further raised from −3 V to −5 V.

Optical eye diagrams were measured to demonstrate the high speed performance of this device by applying the non-return-zero pseudorandom binary sequence (PRBS) signal with 231-1 pattern length. The PRBS signal of 30 Gbit/s, 40 Gbit/s and 44 Gbit/s were amplified to be of 7 V peak-to-peak (Vpp) amplitude and biased at −3.5 V to drive the MZM. A standard 50Ω SMA terminal resistance and a DC block were used to terminate the MZM. Continuous-wave laser beam at ~1550 nm was coupled into the MZM through a grating coupler. The output light from the grating coupler on the other side was amplified by Erbium-doped fiber amplifier and transmitted through a band pass filter. Finally, the modulated optical signal was detected by an optical module of a Tektronix digital scope DSA8300. Figure 5(a)
Fig. 5 Eye diagrams measured at (a) 30 Gbit/s, (b) 40 Gbit/s and (c) 44 Gbit/s.
5(c) shows the output eye diagrams measured at −3.5 V bias. It is observed that over 7 dB extinction radio was measured at the modulation speed of 30 Gbit/s and 40 Gbit/s. At the modulation speed of 44 Gbit/s, which is the maximum bit rate of the pattern generator can supply, an open optical eye diagram was achieved with 5.68 dB extinction radio. Without considering the terminal resistance and the optical energy, the power consummation of this device working at 40 Gbit/s and −3.5 V bias is estimated as 4.1 pJ/bit using the equation ofEbit=(1/4)CVPP2 [18

18. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express 20(S2Suppl 2), A293–A308 (2012). [CrossRef] [PubMed]

], where the C is the modulator capacitance and equals to the sum of the junction capacitance and electrode induced capacitance.

4. Conclusion

Benefited from the enhanced overlap between the depletion region and the optical mode by the interleaved PN junctions’ structure, a high speed of 40Gbit/s and low doping-induced loss of ~10 dB/cm silicon MZM was experimentally demonstrated. It was fabricated in a commercial 0.18 μm CMOS process with a relatively low doping concentration of 2 × 1017 cm−3and a short phase-shifter of 750 μm. Further optimization should be carried out to realize optimal trade-off among various FOMs of the MZM, including modulation speed and efficiency, insertion loss, power consumption and area efficiency. The interleaved PN junctions presented can offer flexible designs for the improvement in future.

Acknowledgments

The authors thank Tektronix for the instrument support to our devices measurement and Semiconductor Manufacturing International Corporation (SMIC) for the fabrication support to our Silicon photonics research. This work is supported by the National Basic Research Program of China (Grant No. 2011CB301701, No. 2012CB933502 and No. 2012CB933504), the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KGCX2-EW-102), and the National Natural Science Foundation of China (Grant No. 61107048 and No. 60877036).

References and links

1.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008). [CrossRef]

2.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]

3.

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). [CrossRef] [PubMed]

4.

G. Kim, J. W. Park, I. G. Kim, S. Kim, S. Kim, J. M. Lee, G. S. Park, J. Joo, K. S. Jang, J. H. Oh, S. A. Kim, J. H. Kim, J. Y. Lee, J. M. Park, D. W. Kim, D. K. Jeong, M. S. Hwang, J. K. Kim, K. S. Park, H. K. Chi, H. C. Kim, D. W. Kim, and M. H. Cho, “Low-voltage high-performance silicon photonic devices and photonic integrated circuits operating up to 30 Gb/s,” Opt. Express 19(27), 26936–26947 (2011). [CrossRef] [PubMed]

5.

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). [CrossRef] [PubMed]

6.

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-voltage, compact, depletion-mode, silicon Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 159–164 (2010). [CrossRef]

7.

Z. Y. Li, D. X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J. Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express 17(18), 15947–15958 (2009). [CrossRef] [PubMed]

8.

X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express 20(3), 2507–2515 (2012). [CrossRef] [PubMed]

9.

M. Ziebell, D. Marris-Morini, G. Rasigade, P. Crozat, J.-M. Fédéli, P. Grosse, E. Cassan, and L. Vivien, “Ten Gbit/s ring resonator silicon modulator based on interdigitated PN junctions,” Opt. Express 19(15), 14690–14695 (2011). [CrossRef] [PubMed]

10.

H. Yu, M. Pantouvaki, J. Van Campenhout, D. Korn, K. Komorowska, P. Dumon, Y. Li, P. Verheyen, P. Absil, L. Alloatti, D. Hillerkuss, J. Leuthold, R. Baets, and W. Bogaerts, “Performance tradeoff between lateral and interdigitated doping patterns for high speed carrier-depletion based silicon modulators,” Opt. Express 20(12), 12926–12938 (2012). [CrossRef]

11.

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 1.4 V-cm VπL integrated on 0.25microm silicon-on-insulator waveguides,” Opt. Express 18(8), 7994–7999 (2010). [CrossRef] [PubMed]

12.

D.Feng, D. Zheng, and T. Smith, “Traveling-wave high-speed silicon modulator,” Integrated Photon. Res. Appl. (IPRA), ITUB4 (2006).

13.

Y. R. Kwon, V. M. Hietala, and K. S. Champlin, “Quasi-TEM analysis of‘slow-wave’ mode propagation on coplanar microstructure MIS transmission lines,” IEEE Trans. Microw. Theory Tech. 35(6), 545–551 (1987). [CrossRef]

14.

V. Milanovic, M. Ozgur, D. C. DeGroot, J. A. Jargon, M. Gaitan, and M. E. Zaghloul, “Characterization of broad-band transmission for coplanar waveguides on CMOS silicon substrates,” IEEE Trans. Microw. Theory Tech. 46(5), 632–640 (1998). [CrossRef]

15.

L. Reinhold and B. Pavel, RF Circuit Design: Theory and Applications(PrenticeHall, 2000).

16.

A. M. Mangan, S. P. Voinigescu, M. T. Yang, and M. Tazlauanu, “De-embedding transmission line measurements for accurate modeling of IC designs,” IEEE Trans. Electron. Dev. 53(2), 235–241 (2006). [CrossRef]

17.

http://www.silvaco.com/

18.

D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express 20(S2Suppl 2), A293–A308 (2012). [CrossRef] [PubMed]

OCIS Codes
(130.0250) Integrated optics : Optoelectronics
(250.5300) Optoelectronics : Photonic integrated circuits
(250.7360) Optoelectronics : Waveguide modulators

ToC Category:
Optoelectronics

History
Original Manuscript: May 8, 2012
Revised Manuscript: June 8, 2012
Manuscript Accepted: June 10, 2012
Published: June 20, 2012

Citation
Hao Xu, Xi Xiao, Xianyao Li, Yingtao Hu, Zhiyong Li, Tao Chu, Yude Yu, and Jinzhong Yu, "High speed silicon Mach-Zehnder modulator based on interleaved PN junctions," Opt. Express 20, 15093-15099 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15093


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References

  1. A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol.23(6), 064001 (2008). [CrossRef]
  2. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4(8), 518–526 (2010). [CrossRef]
  3. 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. Express19(26), B946–B951 (2011). [CrossRef] [PubMed]
  4. G. Kim, J. W. Park, I. G. Kim, S. Kim, S. Kim, J. M. Lee, G. S. Park, J. Joo, K. S. Jang, J. H. Oh, S. A. Kim, J. H. Kim, J. Y. Lee, J. M. Park, D. W. Kim, D. K. Jeong, M. S. Hwang, J. K. Kim, K. S. Park, H. K. Chi, H. C. Kim, D. W. Kim, and M. H. Cho, “Low-voltage high-performance silicon photonic devices and photonic integrated circuits operating up to 30 Gb/s,” Opt. Express19(27), 26936–26947 (2011). [CrossRef] [PubMed]
  5. 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. Express19(19), 18029–18035 (2011). [CrossRef] [PubMed]
  6. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-voltage, compact, depletion-mode, silicon Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron.16(1), 159–164 (2010). [CrossRef]
  7. Z. Y. Li, D. X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J. Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express17(18), 15947–15958 (2009). [CrossRef] [PubMed]
  8. X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s silicon microring modulator based on misalignment-tolerant interleaved PN junctions,” Opt. Express20(3), 2507–2515 (2012). [CrossRef] [PubMed]
  9. M. Ziebell, D. Marris-Morini, G. Rasigade, P. Crozat, J.-M. Fédéli, P. Grosse, E. Cassan, and L. Vivien, “Ten Gbit/s ring resonator silicon modulator based on interdigitated PN junctions,” Opt. Express19(15), 14690–14695 (2011). [CrossRef] [PubMed]
  10. H. Yu, M. Pantouvaki, J. Van Campenhout, D. Korn, K. Komorowska, P. Dumon, Y. Li, P. Verheyen, P. Absil, L. Alloatti, D. Hillerkuss, J. Leuthold, R. Baets, and W. Bogaerts, “Performance tradeoff between lateral and interdigitated doping patterns for high speed carrier-depletion based silicon modulators,” Opt. Express20(12), 12926–12938 (2012). [CrossRef]
  11. 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 1.4 V-cm VπL integrated on 0.25microm silicon-on-insulator waveguides,” Opt. Express18(8), 7994–7999 (2010). [CrossRef] [PubMed]
  12. D.Feng, D. Zheng, and T. Smith, “Traveling-wave high-speed silicon modulator,” Integrated Photon. Res. Appl.(IPRA), ITUB4 (2006).
  13. Y. R. Kwon, V. M. Hietala, and K. S. Champlin, “Quasi-TEM analysis of‘slow-wave’ mode propagation on coplanar microstructure MIS transmission lines,” IEEE Trans. Microw. Theory Tech.35(6), 545–551 (1987). [CrossRef]
  14. V. Milanovic, M. Ozgur, D. C. DeGroot, J. A. Jargon, M. Gaitan, and M. E. Zaghloul, “Characterization of broad-band transmission for coplanar waveguides on CMOS silicon substrates,” IEEE Trans. Microw. Theory Tech.46(5), 632–640 (1998). [CrossRef]
  15. L. Reinhold and B. Pavel, RF Circuit Design: Theory and Applications(PrenticeHall, 2000).
  16. A. M. Mangan, S. P. Voinigescu, M. T. Yang, and M. Tazlauanu, “De-embedding transmission line measurements for accurate modeling of IC designs,” IEEE Trans. Electron. Dev.53(2), 235–241 (2006). [CrossRef]
  17. http://www.silvaco.com/
  18. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express20(S2Suppl 2), A293–A308 (2012). [CrossRef] [PubMed]

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