High extinction ratio 10 Gbit/s silicon optical modulator

doi:10.1364/OE.19.005827

High extinction ratio 10 Gbit/s silicon optical modulator

Gilles Rasigade, Melissa Ziebell, Delphine Marris-Morini, Jean-Marc Fédéli, Frédéric Milesi, Philippe Grosse, David Bouville, Eric Cassan, and Laurent Vivien »View Author Affiliations

Optics Express, Vol. 19, Issue 7, pp. 5827-5832 (2011)
http://dx.doi.org/10.1364/OE.19.005827

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– Abstract
1. Introduction
2. Device design and fabrication
3. Characterization
4. Conclusion
– References and links

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Abstract

High speed and high extinction ratio silicon optical modulator using carrier depletion is experimentally demonstrated. The phase-shifter is a 1.8 mm-long PIPIN diode which is integrated in a Mach Zehnder interferometer. 8.1 dB Extinction Ratio at 10 Gbit/s is obtained simultaneously with optical loss as low as 6 dB.

1. Introduction

Silicon photonics is about to revolutionize telecommunications and data communication in computing. Light emission in silicon is now possible using hybrid or heterogeneous integration [1

B. B. Bakir, N. Olivier, P. Grosse, S. Messaoudène, S. Brision, E. Augendre, P. Philippe, K. Gilbert, D. Bordel, J. Harduin, and J-M Fédéli, “Electrically driven hybrid Si/III-V lasers based on adiabatic mode transformers,” SPIE 7719 (2010).

-2

A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y.-H. Kuo, and J. E. Bowers, “A distributed Bragg Reflector Silicon evanescent laser,” IEEE Photon. Technol. Lett. 20(20), 1667–1669 (2008). [CrossRef]

]. High sensitivity Ge photodetectors showing bandwidths larger than 40 GHz have been demonstrated [3

L. Vivien, J. Osmond, J. M. Fédéli, D. Marris-Morini, P. Crozat, J. F. Damlencourt, E. Cassan, Y. Lecunff, and S. Laval, “42 GHz p.i.n Germanium photodetector integrated in a silicon-on-insulator waveguide,” Opt. Express 17(8), 6252–6257 (2009). [CrossRef] [PubMed]

]. In regards to silicon modulators, extensive work has been done in the recent years. Modulation in silicon is usually obtained by free carrier concentration variation [4

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

]. Carrier depletion is a high speed effect that has been widely used to achieve fast modulators [5

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005). [CrossRef] [PubMed]

–14

G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Quant. Electron. 16(1), 179–184 (2010). [CrossRef]

]. Data rates up to 40 Gbit/s have even been obtained [6

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef]

]. However, to be useful in data communication systems, speed is not the only specification. The modulator should present simultaneously a large extinction ratio at high data rate as well as low optical loss.

This paper reports experimental results on a Mach Zehnder modulator based on carrier depletion in a PIPIN diode, demonstrating large 10 Gbit/s extinction ratio simultaneously with low optical loss. In comparison with previous demonstration [13

D. Marris-Morini, L. Vivien, G. Rasigade, E. Cassan, J. M. Fédéli, X. Le Roux, P. Crozat, S. Maine, A. Lupu, M. Halbwax, and S. Laval, “Recent progress in high speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]

], improvements have been made on the structure design and on the RF electrodes, to achieve better high speed properties.

Device design and fabrication are presented in section 2, while section 3 is dedicated to DC and high speed characterizations.

2. Device design and fabrication

A schematic view of the device cross section is shown in Fig. 1(a) . The silicon rib waveguide width is 420 nm, the rib height is 390 nm and the etching depth is 290 nm, leading to quasi-TE and quasi-TM single mode propagations at a wavelength of 1.55 µm. The waveguide dimensions have been chosen in order to maximize the optical TE-mode confinement in the region that is depleted when the reverse bias is applied (as illustrated in Fig. 1(b)). However, as a 100 nm thick slab is not large enough to achieve a small access resistance between the active region and the metal, the rib is only etched in an 800 nm-wide region on each side of the rib.

Fig. 1 (a) Schematic view of lateral PIPIN phase shifter; (b) Optical mode profile at 1.55 µm ; (c) Optical microscope view of the MZI modulator.

A p-doped slit with a nominal doping concentration of 3.10¹⁷ cm⁻³ is inserted in the intrinsic region of the lateral PIN diode and acts as a source of holes. Doping concentrations in the P and N parts of the diode are 8.10¹⁷ and 10¹⁸ cm⁻³ respectively. The n-doped region slightly overlaps the guided mode, to ensure an efficient depletion of the thin p-doped slit. All the doping concentrations inside the rib waveguide have been kept as moderate as possible in order to obtain low optical propagation loss together with high modulation efficiency. Compared to the first PIPIN design [13

], P⁺ and N⁺ regions with higher doping concentration are added to reduce access resistances. Their doping levels are 10¹⁹ cm⁻³ and they are placed 500 nm away from the rib edges, in order to have a small influence on the total optical loss. Optical loss is then reduced due to the fact that a large part of the waveguide is not intentionally doped, and the metallic contact regions are considerably distant from the light propagation area.

The principle of the modulator is described hereafter: at equilibrium, holes are confined in the p-doped slit centered in the rib. When a reverse bias is applied to the diode, holes are swept out of the active region. The total hole concentration variation is responsible for effective index variation, which creates a phase shift of the guided mode. An asymmetric Mach-Zehnder Interferometer (MZI) is used to convert phase modulation into intensity modulation (Fig. 1(c)). Waveguide splitters are star couplers with a reduced area (10 × 2 µm²) [15

G. Rasigade, X. Le Roux, D. Marris-Morini, E. Cassan, and L. Vivien, “Compact wavelength-insensitive fabrication-tolerant silicon-on-insulator beam splitter,” Opt. Lett. 35(21), 3700–3702 (2010). [CrossRef] [PubMed]

]. The phase shifter is inserted in both arms but only one arm is biased. Coplanar waveguide electrodes have been optimized by electrical simulations, taking into account the RC equivalent scheme of the phase shifter between the electrodes. The width of the signal electrode is 10 µm and the gap between the signal and ground electrode is 25 µm. Speed limitation is mainly due to the RF signal propagation along the travelling wave electrodes. To achieve high data rate, the phase shifter length is reduced to 1.8 mm, in order to avoid RF signal propagation loss and to reduce the influence of the velocity difference between optical and electrical signals.

The optical modulator is fabricated on a 200mm SOI wafer with a 2 µm-thick buried oxide (BOX) layer and a 400 nm-thick crystalline silicon film. Deep-UV optical lithography and ion implantation is used to obtain the highly doped P⁺ and N⁺ regions. For hard mask purpose, SiO₂ is then deposited by LPCVD. The waveguides and the slits are patterned using Deep-UV lithography. After hard mask etching by reactive ion etching, Boron implantation (P in the slit) is performed to obtain the doped layer in the middle of the waveguide. N and P doped regions are then obtained by lithography and ion implantation, followed by thermal annealing. Finally, Ti/TiN/AlCu/Ti/TiN metal stack is deposited onto the wafer, and the electrodes are patterned and etched down to the SiO₂ cap layer. The process used is fully compatible with SOI CMOS technology and could be transferred in high-volume microelectronic manufacturing. Optical microscope view of the fabricated device is shown in Fig. 1(c).

3. Characterization

The experimental set-up uses a tunable laser centered at 1.55 µm. A linearly TE polarized light beam is coupled into the waveguide using a polarization-maintaining lensed-fiber. The output light is collected by an objective and focused on an IR detector. Electrical probes are used to bias the diode. Very low values of reverse current (−2 nA at −4 V) are measured ensuring low electrical power dissipation in DC configurations.

The output transmission of the modulator as a function of the wavelength is plotted in Fig. 2(a) for reverse bias from 0 to 8 V. The measured spectra are normalized with the transmission of straight waveguides without phase shifters nearby to the device. The maximum value of the transmission (i.e. insertion loss) is - 4 dB. This low value is due to the small overlap of the guided mode with doped regions. The increase of the effective index due to hole depletion in the longer arm of the asymmetric MZI leads to a red-shift of the optical transmission spectrum.

Fig. 2 (a) Modulator transmission as a function of the wavelength for different applied bias. (b) Zoom of the transmission for different applied bias voltages: at a wavelength of 1561 nm optical loss of 6 dB and extinction ratio of 8 dB are simultaneously obtained. (c) V_πL_π as a function of the reverse bias deduced from (a) V_πL_π equals to 6 V.cm for reverse bias larger than 4 V, and 4 V.cm at a reverse bias of 2 V.

The product V_πL_π can be deduced from the experimental transmission shift in wavelength and is reported in Fig. 2(c). Its value is 6 V.cm for a reverse bias larger than 4 V, and is reduced at low bias (4 V.cm at 2 V). The theoretical value is 1.7 V.cm. The difference between theoretical and experimental value as well as the experimental reduction of depletion efficiency when the voltage increases are mainly due to the variations of actual dopant concentrations and distributions inside the waveguide. Due to this moderate efficiency, the Mach Zehnder transmission does not go from maximum to minimum value when the reverse bias goes from 0 to 8 V. However, it can be seen that good modulation properties can be obtained in this bias range. A zoom-in of the transmission between 1558 and 1564 nm is reported in Fig. 2(b). It can be seen that both high extinction ratio of 8 dB and low optical loss of 6 dB are simultaneously obtained.

High-speed performance of the modulator is investigated by measuring optical eye diagrams. A Centellax G2P1A pattern generator is used to obtain 10 Gbit/s PRBS signal with a 2⁷-1 pattern length. The PRBS output signal is passed through a driver amplifier, which produced electrical voltage with more than 7 V peak to peak. A bias tee is used to add a −4 V DC bias to the RF signal so that the diode is always reverse-biased. High-speed ground-signal-ground probes are used to apply the RF signal to the device. At the end of the electrical line, a second probe is used, connected to a 50-Ω load through a second bias tee. The load is then applied on the RF signal only. The output light from the modulator is passed through an Erbium Doped Fiber Amplifier (EDFA) and a tunable wavelength filter is used to suppress the noise due to the amplified spontaneous emission of the EDFA. Light is then detected using 86100C Agilent oscilloscope with 86106B optical module.

Measured 10 Gbit/s Extinction Ratios (ERs) as a function of the wavelength are reported in Fig. 3 . ERs larger than 8 dB are measured at 1556 and 1564 nm, respectively. The ER decreases between these values, and is difficult to be measured between 1558 and 1561 nm. However, the largest optical power is seen on the oscilloscope at 1560 nm. In comparison with Fig. 2(a), a maximum power could be expected at 1557 nm. By measuring the optical spectra with and without RF signal applied on the diode, it has been checked that there is a 3 nm red-shift of the spectra with RF signal applied on the diode, corresponds to heating of the structure due to the RF signal dissipation when charging/discharging the active region capacitance. The corresponding effective index variation is 2.10⁻⁴ which correspond to temperature elevation of 1°C [16

G. T. Reed, and A. P. Knights, Silicon Photonics, an Introduction (Wiley, 2004).

]. In addition, it can be clearly seen in Fig. 2(a) that, at the wavelength where the transmission is maximum, no optical modulation between 0 and 8 V can be observed. This is consistent with high speed measurements: when the RF signal is applied to the diode, the maximum power on the oscilloscope is obtained at 1560 nm wavelength, correlated with a low (non-measurable) extinction ratio from eye diagram measurements at this wavelength.

Fig. 3 Extinction ratio at 10 Gbit/s as a function of the wavelength (experimental values are the red dots).

Optical eye diagrams at 1561, 1562, 1563 and 1564 nm are reported in Fig. 4 . At 1561 nm, a saturation of the maximum signal is clearly seen, corresponding to a modulation close to the maximum transmission of the Mach Zehnder interferometer. When the wavelength increases, this saturation decreases and extinction ratio increases from 1.8 dB to 8.1 dB at 1564 nm. At larger wavelengths, the measurements are limited by the sensitivity of the experimental set-up due to a decrease of the transmission level.

Fig. 4 Optical eye diagram and extinction ratio for different wavelengths. (a): ER = 1.8 dB at 1561 nm, (b): ER = 3.6 dB at 1562 nm, (c): ER = 6.2 dB at 1563 nm, (d): ER = 8.1 dB at 1564 nm.

To estimate the optical loss corresponding to each eye diagram measurement of Fig. 4, the red-shift due to heating of the structure due to the RF signal dissipation has to be applied on the static transmission measurement. Taking into account the 3 nm redshift between DC and RF characterization, the RF transmission at 1564 nm is the same as the DC transmission at 1561 nm. Using this method, optical loss of 6 dB, 5 dB and 4 dB are evaluated for extinction ratio of 8.1 dB, 6.2 dB, 3.6 dB, respectively.

Table 1 reports on the comparison of the performances of this PIPIN phase shifter-based modulator with silicon modulators based on Mach Zehnder interferometers, using PN diodes that are widely used in lateral or vertical configurations, and MOS capacitor working in accumulation. For a comparison purposes, we report data rate, measured extinction ratio at this data rate, and on-chip insertion loss at maximum transmission wavelength as optical loss at the same working point as the extinction ratio is hardly ever reported.

Table 1 Performances Comparison with Silicon Mach Zehnder Modulators in the Literature

	Data rate	Extinction ratio at this data rate	On-chip insertion loss (at the wavelength where the transmission is maximum)
MOS capacitor [5 L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005). [CrossRef] [PubMed] ]	10 Gbis/s	3.8 dB	10 dB
Vertical PN diode [6 L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef] ]	40 Gbit/s	1 dB	< 4 dB
Lateral PN diode [8 D. J. Thomson, F. Y. Gardes, G. T. Reed, F. Milesi, and J.-M. Fédéli, “High speed silicon optical modulator with self aligned fabrication process,” Opt. Express 18(18), 19064–19069 (2010). [CrossRef] [PubMed] ]	10 Gbit/s	6 dB	7 dB
Lateral PN diode [9 T.-Y. Liow, K.-W. Ang, Q. Fang, J.-F. Song, Y.-Z. Xiong, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon modulators an germanium photodetectors on SOI: monolithic integration, compatibility and performance optimization,” IEEE J. Sel. Top. Quant. Electron. 16(1), 307–315 (2010) [CrossRef] ]	10 Gbit/s	6.1 dB	-
Vertical PN diode [10 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. Quant. Electron. 16(1), 159–164 (2010). [CrossRef] ]	10 Gbit/s	-	5 dB
Lateral PN diode [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 1.4V-cm V(π)L integrated on 0.25microm silicon-on-insulator waveguides,” Opt. Express 18(8), 7994–7999 (2010). [CrossRef] [PubMed] ]	12.5 Gbit/s	> 7 dB	2.5 dB
Lateral PN diode [12 J. W. Park, J.-B. You, I. G. Kim, and G. Kim, “High-modulation efficiency silicon Mach-Zehnder optical modulator based on carrier depletion in a PN Diode,” Opt. Express 17(18), 15520–15524 (2009). [CrossRef] [PubMed] ]	12.5 Gbit/s	3 dB	7.6 dB
Lateral PIPIN diode [This work]	10 Gbit/s	8.1 dB	4 dB

We can see in this table that the PIPIN diode gives the largest extinction ratio and one of the lowest on-chip insertion loss at 10 Gbit/s. A detailed theoretical comparison between PN and PIPIN diodes has been reported previously [14

4. Conclusion

To summarize, a simultaneously fast, low loss and efficient silicon optical modulator is experimentally demonstrated, using 1.8 mm-long PIPIN phase shifter integrated in a Mach Zehnder interferometer. An extinction ratio of 8.1 dB at a bit rate of 10 Gbit/s is obtained and the optical loss is estimated to be 6 dB at the working wavelength. The maximum transmission leads to insertion loss below 4dB. Further improvements can be considered as larger modulation efficiency is theoretically predicted. In addition, push-pull operation can be used, which will open the possibility to decrease the phase shifter length while keeping a large extinction ratio. This configuration would be favorable to achieve higher data rate. The proposed PIPIN structure offers then great potential in order to keep increasing the performances of integrated high-speed modulators. Data transmissions up to 40 Gbit/s can be forecasted in the near future with such devices.

Acknowledgements

The research leading to these results has received funding from the European Community's under grant agreement n° 224312 HELIOS and from the French ANR under project SILVER.

References and links

1.	B. B. Bakir, N. Olivier, P. Grosse, S. Messaoudène, S. Brision, E. Augendre, P. Philippe, K. Gilbert, D. Bordel, J. Harduin, and J-M Fédéli, “Electrically driven hybrid Si/III-V lasers based on adiabatic mode transformers,” SPIE 7719 (2010).
2.	A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y.-H. Kuo, and J. E. Bowers, “A distributed Bragg Reflector Silicon evanescent laser,” IEEE Photon. Technol. Lett. 20(20), 1667–1669 (2008). [CrossRef]
3.	L. Vivien, J. Osmond, J. M. Fédéli, D. Marris-Morini, P. Crozat, J. F. Damlencourt, E. Cassan, Y. Lecunff, and S. Laval, “42 GHz p.i.n Germanium photodetector integrated in a silicon-on-insulator waveguide,” Opt. Express 17(8), 6252–6257 (2009). [CrossRef] [PubMed]
4.	A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quant. Electron. 23(1), 123–129 (1987). [CrossRef]
5.	L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005). [CrossRef] [PubMed]
6.	L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef]
7.	F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fédéli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009). [CrossRef] [PubMed]
8.	D. J. Thomson, F. Y. Gardes, G. T. Reed, F. Milesi, and J.-M. Fédéli, “High speed silicon optical modulator with self aligned fabrication process,” Opt. Express 18(18), 19064–19069 (2010). [CrossRef] [PubMed]
9.	T.-Y. Liow, K.-W. Ang, Q. Fang, J.-F. Song, Y.-Z. Xiong, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon modulators an germanium photodetectors on SOI: monolithic integration, compatibility and performance optimization,” IEEE J. Sel. Top. Quant. Electron. 16(1), 307–315 (2010) [CrossRef]
10.	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. Quant. Electron. 16(1), 159–164 (2010). [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 1.4V-cm V(π)L integrated on 0.25microm silicon-on-insulator waveguides,” Opt. Express 18(8), 7994–7999 (2010). [CrossRef] [PubMed]
12.	J. W. Park, J.-B. You, I. G. Kim, and G. Kim, “High-modulation efficiency silicon Mach-Zehnder optical modulator based on carrier depletion in a PN Diode,” Opt. Express 17(18), 15520–15524 (2009). [CrossRef] [PubMed]
13.	D. Marris-Morini, L. Vivien, G. Rasigade, E. Cassan, J. M. Fédéli, X. Le Roux, P. Crozat, S. Maine, A. Lupu, M. Halbwax, and S. Laval, “Recent progress in high speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]
14.	G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Quant. Electron. 16(1), 179–184 (2010). [CrossRef]
15.	G. Rasigade, X. Le Roux, D. Marris-Morini, E. Cassan, and L. Vivien, “Compact wavelength-insensitive fabrication-tolerant silicon-on-insulator beam splitter,” Opt. Lett. 35(21), 3700–3702 (2010). [CrossRef] [PubMed]
16.	G. T. Reed, and A. P. Knights, Silicon Photonics, an Introduction (Wiley, 2004).

OCIS Codes
(130.0250) Integrated optics : Optoelectronics
(130.4110) Integrated optics : Modulators

ToC Category:
Integrated Optics

History
Original Manuscript: January 19, 2011
Revised Manuscript: February 22, 2011
Manuscript Accepted: March 2, 2011
Published: March 14, 2011

Citation
Gilles Rasigade, Melissa Ziebell, Delphine Marris-Morini, Jean-Marc Fédéli, Frédéric Milesi, Philippe Grosse, David Bouville, Eric Cassan, and Laurent Vivien, "High extinction ratio 10 Gbit/s silicon optical modulator," Opt. Express 19, 5827-5832 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-5827

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References

B. B. Bakir, N. Olivier, P. Grosse, S. Messaoudène, S. Brision, E. Augendre, P. Philippe, K. Gilbert, D. Bordel, J. Harduin, and J-M Fédéli, “Electrically driven hybrid Si/III-V lasers based on adiabatic mode transformers,” SPIE 7719 (2010).
A. W. Fang, B. R. Koch, R. Jones, E. Lively, D. Liang, Y.-H. Kuo, and J. E. Bowers, “A distributed Bragg Reflector Silicon evanescent laser,” IEEE Photon. Technol. Lett. 20(20), 1667–1669 (2008). [CrossRef]
L. Vivien, J. Osmond, J. M. Fédéli, D. Marris-Morini, P. Crozat, J. F. Damlencourt, E. Cassan, Y. Lecunff, and S. Laval, “42 GHz p.i.n Germanium photodetector integrated in a silicon-on-insulator waveguide,” Opt. Express 17(8), 6252–6257 (2009). [CrossRef] [PubMed]
A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quant. Electron. 23(1), 123–129 (1987). [CrossRef]
L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005). [CrossRef] [PubMed]
L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef]
F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fédéli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009). [CrossRef] [PubMed]
D. J. Thomson, F. Y. Gardes, G. T. Reed, F. Milesi, and J.-M. Fédéli, “High speed silicon optical modulator with self aligned fabrication process,” Opt. Express 18(18), 19064–19069 (2010). [CrossRef] [PubMed]
T.-Y. Liow, K.-W. Ang, Q. Fang, J.-F. Song, Y.-Z. Xiong, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon modulators an germanium photodetectors on SOI: monolithic integration, compatibility and performance optimization,” IEEE J. Sel. Top. Quant. Electron. 16(1), 307–315 (2010) [CrossRef]
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. Quant. Electron. 16(1), 159–164 (2010). [CrossRef]
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). [CrossRef] [PubMed]
J. W. Park, J.-B. You, I. G. Kim, and G. Kim, “High-modulation efficiency silicon Mach-Zehnder optical modulator based on carrier depletion in a PN Diode,” Opt. Express 17(18), 15520–15524 (2009). [CrossRef] [PubMed]
D. Marris-Morini, L. Vivien, G. Rasigade, E. Cassan, J. M. Fédéli, X. Le Roux, P. Crozat, S. Maine, A. Lupu, M. Halbwax, and S. Laval, “Recent progress in high speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]
G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Quant. Electron. 16(1), 179–184 (2010). [CrossRef]
G. Rasigade, X. Le Roux, D. Marris-Morini, E. Cassan, and L. Vivien, “Compact wavelength-insensitive fabrication-tolerant silicon-on-insulator beam splitter,” Opt. Lett. 35(21), 3700–3702 (2010). [CrossRef] [PubMed]
G. T. Reed, and A. P. Knights, Silicon Photonics, an Introduction (Wiley, 2004).

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