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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 3209–3218
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Low-voltage, high-extinction-ratio, Mach-Zehnder silicon optical modulator for CMOS-compatible integration

Jianfeng Ding, Hongtao Chen, Lin Yang, Lei Zhang, Ruiqiang Ji, Yonghui Tian, Weiwei Zhu, Yangyang Lu, Ping Zhou, and Rui Min  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 3209-3218 (2012)
http://dx.doi.org/10.1364/OE.20.003209


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Abstract

We demonstrate a carrier-depletion Mach-Zehnder silicon optical modulator, which is compatible with CMOS fabrication process and works well at a low driving voltage. This is achieved by the optimization of the coplanar waveguide electrode to reduce the electrical signal transmission loss. At the same time, the velocity and impedance matching are both considered. The 12.5 Gbit/s data transmission experiment of the fabricated device with a 2-mm-long phase shifter is performed. The driving voltages with the swing amplitudes of 1 V and 2 V and the reverse bias voltages of 0.5 V and 0.8 V are applied to the device, respectively. The corresponding extinction ratios are 7.67 and 12.79 dB.

© 2012 OSA

1. Introduction

2. Device design and fabrication

As a result of the relatively low modulation efficiency, the phase shifter of the carrier-depletion MZI silicon optical modulator is always long. For a high-speed modulator, a simple lumped circuit model cannot be used any more. Supposing the mode refractive index of the coplanar waveguide (CPW) electrode is 4, the wavelength of the electrical wave with the frequency of 20 GHz is 3.75 mm, which is comparable to the length of the phase-shifter. So, we should use a distributed circuit model to analyze the modulator. There are three points to be considered for designing a phase shifter with a CPW electrode. Firstly, the characteristic impedance of the phase shifter should be 50 Ω in order to avoid the reflection of the electrical signal from the probe. At the same time, the termination resistor should have the same value with the characteristic impedance of the phase shifter. Otherwise, the reflection at the termination resistor will deteriorate the modulated optical signal. Secondly, the velocities of the electrical and optical signals should be matched well. Otherwise, the modulation efficiency will decrease and the intersymbol interference will occur. Finally, the transmission loss of the CPW electrode should be as small as possible. Otherwise, dynamic modulation depth will be much less than the static extinction ratio. An equivalent circuit model is used to analyze the electrical properties of the phase shifter and reduce its electrical transmission loss.

Figure 1
Fig. 1 (a) Cross section of the diode and (b) its equivalent circuit model.
illustrates the equivalent circuit model of the diode alone. CD and RS represent the depletion capacitance and series resistance per unit length, respectively. is the angular frequency. To achieve a fast response, inequality (1) should be satisfied. This condition guarantees that most of the voltage can be applied to the capacitor which is the modulation part. In other words, the modulated optical signal will have a short rise time.

|1jωCD|RS.
(1)

Figure 2
Fig. 2 Distributed circuit model of the CPW electrode with a diode embedded below.
is the distributed circuit model of the modulator’s CPW electrode with a diode embedded below. LE, RE and CE represent the inductance, resistance and capacitance of the metal electrode with unit length. ΔZ represents a small distance along the electrode. We can use this model to create a differential equation to describe the electrical properties of the phase shifter.

The distributed circuit model can be further transformed to a model shown in Fig. 3
Fig. 3 Transformed circuit model of the CPW electrode with a diode embedded below.
and the classic transmission line theory of microwave engineering [19

19. D. M. Pozar, Microwave Engineering, 2nd, ed. (John Wiley & Sons, 1998), chap.2.

] can be used. The transformed parallel and are expressed by

RT=RS(1+1ω2C2DR2S),CT=CDω2C2DRS2+1.
(2)

Then we can calculate the complex propagation constant and the characteristic impedance Z as

γ=(RE+jωLE)[1RT+jω(CT+CE)],Z=RE+jωLE1RT+jω(CT+CE).
(3)

In order to demonstrate the mechanism qualitatively and clearly, a first-order approximation is adopted and Eq. (4) is simplified to the follow equations:

γ=jωLE(CT+CE)[1j2(REωLE+1ωRT(CT+CE))],Z=LECT+CE.
(4)

Considering the inequality (1), and can be simplified:

RT1ω2C2DRS,CTCD.
(5)

A commercial software package HFSS based on the finite-element method is used to check the theoretical analysis and get the optimized parameters quantitatively. Because the software cannot simulate the active region, the depletion region is replaced by a passive parallel capacitor. Figure 4(a)
Fig. 4 Simulation results with commercial software package HFSS. (a) Attenuation constant α versus track width and signal and ground metal gap, when series resistance Rs, diode capacitance CDand frequency fare 4.5 Ω·mm, 100 pF/mm and 10 GHz, respectively. (b) Attenuation constant α versus track width and series resistance Rs, when signal and ground metal gap, diode capacitance CDand frequency fare 5.5 mm, 100 pF/mm and 10 GHz, respectively. (c) Propagation constant β versus frequency and diode capacitance CD, when series resistance Rs, track width and signal and ground metal gap are 4.5 Ω·mm, 28 um and 5.5 μm, respectively. (d) Characteristic impedance Ζ versus frequency and diode capacitance CD, when series resistance Rs, track width and signal and ground metal gap are 4.5 Ω·mm, 28 μm and 5.5 μm. (e) Attenuation constant α versus frequency and diode capacitance CD, when series resistance Rs, track width and signal and ground metal gap are 18 Ω·mm, 28 μm and 5.5 μm, respectively. (f) Attenuation constant α versus frequency and diode capacitance CD, when series resistance Rs, track width and signal and ground metal gap are 4.5 Ω·mm, 28 μm and 5.5 μm, respectively.
illustrates that the attenuation constant α decreases linearly with an increase in the signal track width. This means that the electrical loss decreases linearly as the electrode resistance RE decreases, as predicted by Eq. (6). Moreover, the attenuation constant α changes with the signal and ground metal gap, which is consistent with the relationship between the attenuation constant α and the electrode capacitance CE in Eq. (6). Figure 4(b) shows that the attenuation constant α decreases linearly as the series resistance Rs decreases, which also can be predicted by Eq. (6). Figures 4(c), 4(d) and 4(e) show the dependence of the propagation constant β, the characteristic impedance Z and the attenuation constant α on the frequency respectively. Figures 4(e) and 4(f) show the dependence of the attenuation constant α on the frequency for Rs = 18 Ω·mm and Rs = 4.5 Ω·mm. Note that all the other parameters are same for two figures. According to Eq. (6), the attenuation constant increases quadratically with the frequency and diode capacitance, as shown in Fig. 4(f). Note that Eq. (6) is valid on condition that inequality (1) is satisfied. If a large series resistance of 18 Ω·mm is adopted and the frequency is larger than 15 GHz, the quadratic relationship of the attenuation constant with the frequency will not be valid, as shown in Fig. 4(e). Although the theoretical equations cannot accurately predict the characteristics of the device at a high frequency, they can still show us a correct direction to optimize the device. According to the simulation results, the optical and electrical velocities can be matched by changing the geometrical parameters of the phase shifter. Reducing the series resistance is very important. Firstly, larger diode capacitor should be adopted to achieve higher modulation efficiency for the carrier-depletion Mach-Zehnder modulator. In order to keep the device working at the same speed, the series resistor should be lower. Secondly, the device with lower series resistance could have lower electrical transmission loss. Higher doped silicon can reduce the series resistance, but a larger optical loss will be induced at the same time. Although the device with a series resistance of 4.5 Ω·mm has a better electrical performance, it is estimated that the doping concentration should be larger than 5 × 1018/cm3, which will cause a massive optical loss. As a compromise, the series resistance is designed to be 14 Ω·mm. Adopting the material with higher electron and hole mobilities may be a promising method to further improve the device performance.

Actually, it is very hard to make all the three targets perfect simultaneously. A tradeoff has to be done. In the on-chip application environment, the characteristic impedance of the modulator should be matched to the output impedance of the driving circuit, which is not always 50 Ω and can be adjusted by electrical circuit design. So the electrical and optical velocities should be matched first. And then the electrical transmission loss should be reduced as small as possible. Finally the characteristic impedance of the device should be an acceptable value. The characteristic impedance of our device is designed to be 33 Ω.

The optical structure of the device is based on a MZI design. There is a built-in arm length difference of 120 μm. A multimode interference (MMI) structure is adopted as the optical splitter and combiner. The silicon ridge waveguide is 600 nm in width, 220 nm in height and 70 nm in the slab thickness. Both arms of the device are doped to balance the transmission loss. Figure 5(a)
Fig. 5 (a) Schematic of the cross section of the modulation region. (b) Optical microscope image of the modulator with a CPW electrode and termination resistors.
illustrates the schematic cross section of the modulation region. The p-doping concentration is 1×1018/cm3, and the n-doping concentration is 8×1017/cm3. The p-n junction locates 100 nm right of the middle of the ridge, because the hole is more efficient to change the refractive index than the electron [11

11. S. Assefa, F. N. Xia, and Y. A. Vlasov, “Reinventing germanium avalanche photodetector for nanophotonic on-chip optical interconnects,” Nature 464(7285), 80–84 (2010). [CrossRef] [PubMed]

]. The p-type doped region is designed to have an efficient overlap with the strongest optical mode in the middle of the waveguide. The P++ and N++ doped regions are 1 μm away from the side of the ridge. In order to reduce the capacitance of the diode, a 40 nm-wide gap between p-type and n-type doped regions is adopted [20

20. S. J. Spector, M. W. Geis, G. R. Zhou, M. E. Grein, F. Gan, M. A. Popovic, J. U. Yoon, D. M. Lennon, E. P. Ippen, F. Z. Kärtner, and T. M. Lyszczarz, “CMOS-compatible dual-output silicon modulator for analog signal processing,” Opt. Express 16(15), 11027–11031 (2008). [CrossRef] [PubMed]

].

Figure 5(b) is the optical microscope image of the device. A CPW electrode is used as the electrical transmission line. A probe with GSG pattern is used to couple the electrical signal into the device. The metal thickness is 1.5 μm. the signal track width is 28 μm and the signal and ground metal gap is 5.5 μm. A termination resistor made of TiN is integrated in the chip to absorb the electrical wave at the other end of the electrode and avoid the reflection, which can deteriorate the performance of the device. The resistance of the terminator is 33 Ω.

3. Experimental result and discussion

Figure 6
Fig. 6 Response spectra of the device with different driving voltages.
shows the normalized spectra of the device under different applied voltages. Obviously, the spectrum shifts to the longer wavelength with an increase in the driving voltage. The insertion loss is about 19 dB, which includes 6 dB coupling loss between the device and the lensed fibers, 9 dB propagation loss originating from the two MMIs and 4 dB propagation loss induced by the doped regions. The on-off extinction ratio is about 27 dB when the driving voltage increases from 0 V to 2 V. For a device with a 3-mm phase shifter, the spectrum could shift by half a free spectral range under a reverse voltage of 5.5 V, which indicates a modulation efficiency of 1.65 V·cm

The data transmission experiment is performed with the following setup (see Fig. 7
Fig. 7 Experimental setup of the data transmission experiment.
). Monochromatic light with the wavelength of 1551.66 nm from a tunable laser is amplified by an erbium-doped fiber amplifier (EDFA) and then coupled into the input port of the device through a lensed fiber. A signal quality analyzer (Anritsu MP1800A) is used to provide a 12.5 Gbit/s data stream. The electrical signal is directly coupled into the device by a probe without any amplification. The output light is amplified by another EDFA and then passes through a tunable bandpass optical filter. The modulated optical signal is fed into a digital communication analyzer (Agilent 86100A) with a 20 GHz optical head for eye diagram observation. The device is reversely biased at 0.8 V. When the driving voltage swing is 2 V, the device exhibits an extinction ratio of 12.79 dB with a reverse bias of 0.8 V. There is even an extinction ratio of 7.67 dB when the driving voltage swing is 1 V with a reverse bias voltage of 0.5 V. The maximum power consumptions of the modulator are 98 mW and 30 mW when the driving voltage swings are 2 V and 1 V, respectively. The corresponding energy efficiency is 7.8 pJ/bit and 2.4 pJ/bit. The maximum power consumption happens when the modulator is DC biased to transmit a data of continuous “1”. However, they will dramatically decrease to 20 mW and 5 mW, if a DC block termination is adopted and the DC power consumption is eliminated [21

21. 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). [CrossRef] [PubMed]

]. Then the maximum power consumption will happen when the modulator transmits “1” and “0” repeatedly. Finally the energy efficiency could be reduced to 400 fJ/bit. Such a design is in process and the discussion is left for future.

4. Conclusion

We use the equivalent distributed circuit model to analyze the electrical properties of the phase shifter with a CPW electrode and optimize its performance. We have successfully reduced the driving voltage swing of the carrier-depletion Mach-Zehnder silicon optical modulator to an acceptable value for CMOS-compatible integration. As a result of the low electrical transmission loss of a 2-mm-long phase shifter, 2 V driving voltage swing leads to an extinction ratio of about 13 dB even with the deterioration effect of the EDFA. The device can even work with the driving voltage swing of 1 V to achieve an extinction ratio of about 7.67 dB. The energy efficiency is 7.8 pJ/bit and 2.4 pJ/bit for 2 V and 1 V driving voltage. This could be reduced to only 400 fJ/bit with the help of a DC block termination.

Acknowledgment

This work has been supported by the National Natural Science Foundation of China (NSFC) under grants 60977037.

References and links

1.

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). [CrossRef] [PubMed]

2.

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). [CrossRef] [PubMed]

3.

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). [CrossRef] [PubMed]

4.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

5.

M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17(7), 5502–5516 (2009). [CrossRef] [PubMed]

6.

M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kärtner, H. I. Smith, and E. P. Ippen, “Reconfigurable multi-channel second-order silicon microring-resonator filterbanks for on-chip WDM systems,” Opt. Express 19(1), 306–316 (2011). [CrossRef] [PubMed]

7.

R. Q. Ji, L. Yang, L. Zhang, Y. H. Tian, J. F. Ding, H. T. Chen, Y. Y. Lu, P. Zhou, and W. W. Zhu, “Five-port optical router for photonic networks-on-chip,” Opt. Express 19(21), 20258–20268 (2011). [CrossRef] [PubMed]

8.

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). [CrossRef] [PubMed]

9.

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). [CrossRef] [PubMed]

10.

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 (2008). [CrossRef]

11.

S. Assefa, F. N. Xia, and Y. A. Vlasov, “Reinventing germanium avalanche photodetector for nanophotonic on-chip optical interconnects,” Nature 464(7285), 80–84 (2010). [CrossRef] [PubMed]

12.

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

13.

W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15(25), 17106–17113 (2007). [CrossRef] [PubMed]

14.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

15.

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). [CrossRef] [PubMed]

16.

N. N. Feng, S. Liao, D. Z. 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). [CrossRef] [PubMed]

17.

X. G. Tu, T. Y. Liow, J. F. Song, M. B. 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]

18.

F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express 19(12), 11804–11814 (2011). [CrossRef] [PubMed]

19.

D. M. Pozar, Microwave Engineering, 2nd, ed. (John Wiley & Sons, 1998), chap.2.

20.

S. J. Spector, M. W. Geis, G. R. Zhou, M. E. Grein, F. Gan, M. A. Popovic, J. U. Yoon, D. M. Lennon, E. P. Ippen, F. Z. Kärtner, and T. M. Lyszczarz, “CMOS-compatible dual-output silicon modulator for analog signal processing,” Opt. Express 16(15), 11027–11031 (2008). [CrossRef] [PubMed]

21.

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). [CrossRef] [PubMed]

OCIS Codes
(250.3140) Optoelectronics : Integrated optoelectronic circuits
(250.7360) Optoelectronics : Waveguide modulators

ToC Category:
Optoelectronics

History
Original Manuscript: December 5, 2011
Revised Manuscript: January 18, 2012
Manuscript Accepted: January 23, 2012
Published: January 26, 2012

Citation
Jianfeng Ding, Hongtao Chen, Lin Yang, Lei Zhang, Ruiqiang Ji, Yonghui Tian, Weiwei Zhu, Yangyang Lu, Ping Zhou, and Rui Min, "Low-voltage, high-extinction-ratio, Mach-Zehnder silicon optical modulator for CMOS-compatible integration," Opt. Express 20, 3209-3218 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-3209


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References

  1. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005). [CrossRef] [PubMed]
  2. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express14(20), 9203–9210 (2006). [CrossRef] [PubMed]
  3. 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,” Nature427(6975), 615–618 (2004). [CrossRef] [PubMed]
  4. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005). [CrossRef] [PubMed]
  5. M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express17(7), 5502–5516 (2009). [CrossRef] [PubMed]
  6. M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kärtner, H. I. Smith, and E. P. Ippen, “Reconfigurable multi-channel second-order silicon microring-resonator filterbanks for on-chip WDM systems,” Opt. Express19(1), 306–316 (2011). [CrossRef] [PubMed]
  7. R. Q. Ji, L. Yang, L. Zhang, Y. H. Tian, J. F. Ding, H. T. Chen, Y. Y. Lu, P. Zhou, and W. W. Zhu, “Five-port optical router for photonic networks-on-chip,” Opt. Express19(21), 20258–20268 (2011). [CrossRef] [PubMed]
  8. 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. Express16(20), 15915–15922 (2008). [CrossRef] [PubMed]
  9. 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. Express15(7), 3916–3921 (2007). [CrossRef] [PubMed]
  10. 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. Photonics3(1), 59–63 (2008). [CrossRef]
  11. S. Assefa, F. N. Xia, and Y. A. Vlasov, “Reinventing germanium avalanche photodetector for nanophotonic on-chip optical interconnects,” Nature464(7285), 80–84 (2010). [CrossRef] [PubMed]
  12. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4(8), 518–526 (2010). [CrossRef]
  13. W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express15(25), 17106–17113 (2007). [CrossRef] [PubMed]
  14. R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.23(1), 123–129 (1987). [CrossRef]
  15. 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. Express15(2), 660–668 (2007). [CrossRef] [PubMed]
  16. N. N. Feng, S. Liao, D. Z. 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. Express18(8), 7994–7999 (2010). [CrossRef] [PubMed]
  17. X. G. Tu, T. Y. Liow, J. F. Song, M. B. 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]
  18. F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express19(12), 11804–11814 (2011). [CrossRef] [PubMed]
  19. D. M. Pozar, Microwave Engineering, 2nd, ed. (John Wiley & Sons, 1998), chap.2.
  20. S. J. Spector, M. W. Geis, G. R. Zhou, M. E. Grein, F. Gan, M. A. Popovic, J. U. Yoon, D. M. Lennon, E. P. Ippen, F. Z. Kärtner, and T. M. Lyszczarz, “CMOS-compatible dual-output silicon modulator for analog signal processing,” Opt. Express16(15), 11027–11031 (2008). [CrossRef] [PubMed]
  21. 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. Express19(12), 11507–11516 (2011). [CrossRef] [PubMed]

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