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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 12 — Jun. 6, 2011
  • pp: 11841–11851
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42.7 Gbit/s electro-optic modulator in silicon technology

L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold  »View Author Affiliations


Optics Express, Vol. 19, Issue 12, pp. 11841-11851 (2011)
http://dx.doi.org/10.1364/OE.19.011841


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Abstract

CMOS-compatible optical modulators are key components for future silicon-based photonic transceivers. However, achieving low modulation voltage and high speed operation still remains a challenge. As a possible solution, the silicon-organic hybrid (SOH) platform has been proposed. In the SOH approach the optical signal is guided by a silicon waveguide while the electro-optic effect is provided by an organic cladding with a high χ(2)-nonlinearity. In these modulators the optical nonlinear region needs to be connected to the modulating electrical source. This requires electrodes, which are both optically transparent and electrically highly conductive. To this end we introduce a highly conductive electron accumulation layer which is induced by an external DC “gate” voltage. As opposed to doping, the electron mobility is not impaired by impurity scattering. This way we demonstrate for the first time data encoding with an SOH electro-optic modulator. Using a first-generation device at a data-rate of 42.7 Gbit/s, widely open eye diagrams were recorded. The measured frequency response suggests that significantly larger data rates are feasible.

© 2011 OSA

1. Introduction

One of the most important properties of an optical modulator is its modulation speed or bandwidth, which should be at least as fast as the available electronics. Transistors having transit frequencies well above 100 GHz have already been demonstrated in 90 nm silicon technology, and the speed will further increase as the minimum feature size is reduced [1

1. S. P. Voinigescu, T. O. Dickson, R. Beerkens, I. Khalid, and P. Westergaard, “A comparison of SiCMOS, SiGeBiCMOS, and InPHBT technologies for high-speed and millimeter-wave ICs,” 2004 Topical Meeting on Silicon Monolithic Integrated Circuits inRF Systems, Digest of Papers, 111–114 (2004).

]. However, the bandwidth of present-day silicon-based modulators is limited. Silicon does not possess a χ(2)-nonlinearity due to its centro-symmetric crystalline structure. The use of strained silicon has led to interesting results already [2

2. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006). [CrossRef] [PubMed]

], but the nonlinearities do not yet allow for practical devices. State-of-the art silicon photonic modulators therefore still rely on free-carrier dispersion in pn or pin junctions [3

3. P. Dong, S. R. Liao, D. Z. Feng, H. Liang, D. W. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. L. Li, X. Z. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009). [CrossRef]

5

5. 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]

]. Forward biased junctions have been shown to exhibit a voltage-length product as low as VπL = 0.36 V mm, but the modulation speed is limited by the dynamics of minority carriers. Still, data rates of 10 Gbit/s have been generated with the help of a pre-emphasis of the electrical signal [4

4. 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]

]. Using reverse biased junctions instead, the bandwidth has been increased to about 30 GHz [5

5. 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]

,6

6. 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]

], but the voltage-length product rose to VπL = 40 V mm. Unfortunately, such plasma effect phase modulators produce undesired intensity modulation as well [7

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

], and they respond nonlinearly to the applied voltage. Advanced modulation formats like QAM require, however, a linear response and pure phase modulation, making the exploitation of the electro-optic effect (Pockels effect [8

8. R. W. Boyd, Nonlinear Optics (Academic press, 2008).

]) particularly desirable.

2. SOH approach

Indeed, first implementations of SOH modulators with sub-volt operation [11

11. M. Hochberg, T. Baehr-Jones, G. Wang, J. Huang, P. Sullivan, L. Dalton, and A. Scherer, “Towards a millivolt optical modulator with nano-slot waveguides,” Opt. Express 15(13), 8401–8410 (2007). [CrossRef] [PubMed]

] have been already shown, and sinusoidal modulation up to 40 GHz was demonstrated [15

15. W. Freude, J. Leuthold, L. Alloatti, T. Vallaitis, D. Korn, R. Palmer, C. Koos, J.-M. Brosi, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, B. Breiten, F. Diederich, A. Barklund, R. Dinu, and J. Wieland, “100 Gbit/s electro-optic modulator and 56 Gbit/s wavelength converter for DQPSK data in silicon-organic hybrid (SOH) technology,” Proc. IEEE Conf. on Novel Waveguiding, Structures and Phenomena, Summer Topicals, Paper WB2.1 (2010).

,16

16. J. H. Wülbern, S. Prorok, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, M. Jenett, and A. Jacob, “40 GHz electro-optic modulation in hybrid silicon-organic slotted photonic crystal waveguides,” Opt. Lett. 35(16), 2753–2755 (2010). [CrossRef] [PubMed]

]. However, the challenge in building low-voltage high-speed SOH modulators is to create a highly conductive connecting strip. In an equivalent circuit the slot can be represented by a capacitor C and the conductive strips by resistors R, Fig. 1(b). The corresponding RC time constant determines the bandwidth of the device [10

10. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]

,14

14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

,17

17. T. Baehr-Jones, B. Penkov, J. Q. Huang, P. Sullivan, J. Davies, J. Takayesu, J. D. Luo, T. D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008). [CrossRef]

,18

18. J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon Organic Hybrid Technology-A Platform for Practical Nonlinear Optics,” Proc. IEEE 97(7), 1304–1316 (2009). [CrossRef]

]. In order to decrease the resistance R, it has been suggested to dope the silicon strips [10

10. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]

,14

14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

]. While doping increases the conductivity of the silicon strips (and therefore increases optical losses), one pays an additional loss penalty because the electron mobility is impaired by impurity scattering [10

10. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]

,14

14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

,19

19. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

]. Moreover, the most recent fabrication attempts showed unexpectedly low conductivity [20

20. L. Alloatti, D. Korn, D. Hillerkuss, T. Vallaitis, J. Li, R. Bonk, R. Palmer, T. Schellinger, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “Silicon high-speed electro-optic modulator,” Proc. IEEE Conf. on Group IV Photonics, Paper ThC2 (2010).

,21

21. R. Ding, T. Baehr-Jones, Y. Liu, R. Bojko, J. Witzens, S. Huang, J. Luo, S. Benight, P. Sullivan, J. M. Fedeli, M. Fournier, L. Dalton, A. Jen, and M. Hochberg, “Demonstration of a low V π L modulator with GHz bandwidth based on electro-optic polymer-clad silicon slot waveguides,” Opt. Express 18(15), 15618–15623 (2010). [CrossRef] [PubMed]

].

3. The vision

We present an SOH-based slot-waveguide phase modulator, where the conductivity of the silicon strips connecting the slot region to the modulation electrodes is increased with a novel method which does not create significant optical loss. This enables the first experimental demonstration of data encoding with an SOH modulator. Even though our demonstrator is our very first specimen, which has not at all been optimized, the performance can already compete with that of state-of-the-art plasma-effect modulators [4

4. 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]

,5

5. 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]

,22

22. N. N. Feng, S. R. Liao, D. Z. Feng, P. Dong, D. W. Zheng, H. Liang, R. Shafiiha, G. L. 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]

]. The data rate of 42.7 Gbit/s that we achieved was limited by the available equipment; the modulator performance suggests, however, that significantly higher data rates are possible.

The structure of the modulator we propose is shown in Fig. 1(a). The slot region in the center, where both the optical and the modulating microwave fields interact, is connected to the metal electrodes by thin silicon strips. On top of these strips a slightly conductive layer (“gate”) is deposited, isolated from the strips by a thin silicon oxide film. The structure obtained in this way is similar to the well-known metal-insulator-semiconductor (MIS) [23

23. S. M. Sze, and K. N. G. Kwok, Physics of Semiconductor Devices, Third Edition (Wiley, 2006).

]. When a positive voltage V gate is applied across the oxide (see Fig. 1(a)), the energy bands in the strips are bent (Fig. 1(c)), and a high-mobility electron accumulation layer is formed at the Si/SiO2 interface. Since the strip conductivity is proportional to the mobility and the free-electron density, the limiting frequency fRC = 1/(2πRC) increases with increasing gate voltage. For convenience the structure is referred below as an accumulation-layer electro-optic modulator (ALMod).

The gate of the device depicted in Fig. 1(a) must be optically transparent. This can in principle be achieved by using a thin layer of n-doped polysilicon driven to depletion. The ion concentration is adjusted such that when the desired gate voltage is applied all free carriers in the polysilicon are removed. In this way the net positive charge of the gate is mainly caused by fixed nuclei which cannot cause free-carrier absorption.

4. The fabricated device

In order to validate the ALMod concept we fabricated the technologically simpler structure depicted in Fig. 2
Fig. 2 The SOH modulator used in this work. (a) The slightly conductive silicon substrate is used as a gate. (b) SEM picture of the cross section of the fabricated device. The SiO2 mask was used as a protection layer during fabrication and lies on top of the strips. In the center the silicon optical waveguide is visible. The slot extends for about 1 µm into the SiO2 substrate for fabrication issues. (c) When a positive gate voltage is applied across the 2 µm thick SiO2 substrate a highly conductive electron accumulation layer forms in the strips. The thickness of the strips is 60 nm; for clarity they are not drawn to scale. The gate voltage V gate bends the energy bands in the strips [23]. EF,C,V are Fermi energy, conduction and valence band energy, respectively; q is the elementary charge.
. Here, the gate voltage is applied between the metal electrodes and the silicon substrate. Since the silicon substrate has a conductivity σ = 0.05 Ω−1 cm−1, the gate voltage drops essentially across the 2 µm silicon oxide which separates the optical layer from the silicon substrate, Fig. 2(a). To avoid any damage to the chip, we did not apply gate voltages larger than 270 V. This corresponds to an electric field Egate = 0.135 V/nm in the 2 µm thick SiO2, which is much smaller than the breakdown voltage of 1 V/nm achievable in state-of-the art thin SiO2 films [24

24. J. S. Suehle and P. Chaparala, “Low electric field breakdown of thin SiO2 films under static and dynamic stress,” IEEE Trans. Electron. Dev. 44(5), 801–808 (1997). [CrossRef]

]. The gate voltage of 270 V can be reduced by more than two orders of magnitude when using few-nanometers-thick gate oxides, as in the optimized structure envisaged in Fig. 1. The device was fabricated in a CMOS fab using deep-UV lithography (see Appendix B), and the commercially available [25

25. “GigOptix”, retrieved http://www.gigoptix.com/.

] organic material M1 was subsequently deposited and poled in situ (see Appendix D). The material M1 consists of chromophores dispersed in amorphous polycarbonate (APC), has a nonlinear electro-optic coefficient up to r 33 = 70 pm/V (see Appendix D) and an index of refraction n = 1.67 ± 0.02, both measured at the wavelength of 1550 nm. The RF dielectric constant is εr = 3.3 ± 0.1 (3.1 ± 0.1) at 10 GHz (60 GHz). A thermal study indicates that operation at 85°C over 25 years results in a change of the nonlinear coefficient by less than 20% [26

26. D. Jin, H. Chen, A. Barklund, J. Mallari, G. M. Yu, E. Miller, and R. Dinu, “EO polymer modulators reliability study,” Proc. SPIE 7599, 75990H, 75990H-8 (2010). [CrossRef]

].

The slot waveguide has a “rail” width and a slot width of 240 nm and 120 nm respectively. The light is coupled by means of grating couplers [27

27. “ePIXfab: Vertical fiber couplers”, retrieved http://www.epixfab.eu/design/predefined_masks/imec/fxt_vertical_fiber_couplers.

], whose separation is 2.6 mm. The optical waveguide comprises the 1.7 mm long phase shifting section, two tapers and two 67 µm long strip-to-slot waveguide converters [28

28. J. Blasco, and C. A. Barrios, “Compact slot-waveguide/channel-waveguide mode-converter,” Lasers and Electro-Optics Europe, 2005. CLEO/Europe. 2005 Conference on, 607 (2005).

]. The silicon strips used for connecting electrically the slot waveguide have a thickness of 60 nm (about 10 nm have been oxidized during the high temperature annealing). The ground-signal (GS) metal electrodes have a gap of 4 µm, and their nominal line impedance is 50 Ω. The length of the electrodes is 3.0 mm and comprises two tapered regions for contacting with a length of 0.55 mm each. On the output side, the 50 Ω line is connected to another transmission line which has a length of 3.0 mm and a line impedance of 75 Ω. This transmission line belongs to a second device and is not terminated. It could not be cleaved away since this would lead to an electrical breakdown at the chip edge when applying the gate voltage. The presence of the 75 Ω line is responsible for the local maximum in the S 21 parameter around 10 GHz as shown in Fig. 4(a)
Fig. 4 Response of the DUT vs. frequency and gate field for 1 V modulation amplitude. (a) Phase modulation index η vs. frequency for selected electrical gate fields. The measured modulation frequency range is 1 kHz to 60 GHz. When varying the gate field from −0.025 V/nm to 0.135 V/nm the silicon strips become more conductive, and the modulation index increases accordingly. The gray curve is the S 21 electrical transmission of the metallic electrical waveguide (voltage ratio); the decrease to 0.3 is an undesired effect of the electrical losses of our test device. (b) Modulation index vs. gate field for selected modulation frequencies. Each curve reaches a plateau at high gate fields. For a gate field strength of Egate = −0.025 V/nm the silicon strips become highly insulating, therefore a minimum is observed. At more negative fields the modulation increases again because of the formation of a conductive hole inversion layer in the silicon strips.
; this deviation was not observed in cleaved samples.

5. Device characterization

To demonstrate the high-speed capabilities of the phase modulator we performed a 42.7 Gbit/s data modulation experiment. A 1550 nm laser was used as an optical source, and a pseudorandom bit sequence (PRBS) with a length of 231−1 controlled the modulator. A one-bit delay-interferometer (DI) on the receiver side was used to convert phase modulation to intensity modulation, which was then detected with a photodiode. The DI has the further effect of cutting off the low frequency modulation components. The RF voltage swing was set to V pp = 4.1 V (measured before the probe), and the device was terminated with an external broadband 50 Ω resistor. When the gate field was increased from zero to its maximum value, the optical loss increased by less than 1 dB. The gate leakage current was always below 10 nA, corresponding to a gate power consumption of less than 3 μW. Clear and open eye diagrams at 42.7 Gbit/s were found with the highest gate field, Fig. 3
Fig. 3 Setup of the modulation experiment. A pulse pattern generator (PPG) creates a 42.7 Gbit/s electrical signal. Light from a 1550 nm laser is launched into the slot-waveguide. The device is electrically terminated with an external 50 Ω resistor. A gate voltage is applied between the silicon substrate and the silicon strips. The 50 Ω resistance is responsible of keeping both strips at the same electrical DC potential. On the receiver side a delay-interferometer converts the phase modulation into intensity modulation for detection. By increasing the gate voltage to Vgate = 270 V (gate field Egate = 0.135 V/nm) clear and open eyes are found.
. Bit-error-ratios (BER) smaller than 3 × 10−10 were recorded, demonstrating the usability of our device in real data links.

We further determined the frequency response of the device by applying a sinusoidal voltage with frequencies fmod between 1 kHz and 60 GHz. The chip was contacted as in the data modulation experiment. The RF power at the probe input was kept constant at 10 dBm (1.0 V amplitude). We measured the resulting phase modulation index η, which represents the achieved phase shift in radians. The data are shown in Fig. 4(a) for different gate fields together with the electrical transmission characteristic of the metal electrodes (S 21 voltage ratio). By increasing the gate field from Egate = −0.025 V/nm to Egate = 0.135 V/nm, the modulation index increases by more than a factor of five in the frequency range above 1 GHz. For the highest gate field, a voltage length product of VπL = 9 V mm (58 V mm) was measured in the low frequency limit and at 60 GHz, respectively. For our 1.7 mm long device this corresponds to a π-voltage of Vπ = 5.3 V (34 V). Above 2 GHz, the frequency response is essentially flat (less than 3dB decrease between 2 GHz and 60 GHz) suggesting that data rates could be extended well beyond the 42.7 Gbit/s limit of our equipment.

In order to better investigate the effect of the gate, we recorded the modulation index as a function of the gate field for selected frequencies, Fig. 4(b). For more positive gate fields, an increasing number of electrons accumulate in the silicon strips. The strip resistance decreases accordingly, leading to higher modulation indices. Our simulations indicate that the sheet resistance of the silicon strips becomes smaller than 1500 Ω/sq for gate fields Egate > 0.135 V/nm, which could otherwise be achieved only by doping the silicon strips with an ion-concentration as high as 3 × 1018 cm−3. At the gate field Egate = 0.025 V/nm, a minimum in the modulation index is observed. This indicates that the silicon strips have become highly insulating. Our simulations indicate indeed that for this gate field the slightly n-doped strips are fully depleted of free electrons. At more negative gate fields, the modulation index increases again because of the formation of a conductive hole inversion layer.

Charge density and resistance of the real structure were simulated as a function of the gate voltage by means of the two-dimensional simulation package DESSIS [31

31. “Synopsys, tools for simulating device performance”, retrieved http://www.synopsys.com/Tools/TCAD/DeviceSimulation/Pages/default.aspx.

]. For a qualitative confirmation, both quantities were then compared with the numerical solution of the one-dimensional MIS equations [23

23. S. M. Sze, and K. N. G. Kwok, Physics of Semiconductor Devices, Third Edition (Wiley, 2006).

]. Both methods predicted the three different regimes (accumulation, depletion and inversion), as observed in our experiments.

6. Discussion and conclusion

In this first implementation, the poling of the organic cladding is incomplete. By exploiting the full potential of organic electro-optic materials, the drive voltage can be decreased by a factor of eight (see Appendix D). Moreover, the electrical performance of the current metal electrodes is not optimal, Fig. 4(a). This can be improved in future devices by increasing the thickness of the metallization [14

14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

], or by using a distributed on-chip RF driver [32

32. X. Z. Zheng, J. Lexau, Y. Luo, H. Thacker, T. Pinguet, A. Mekis, G. L. Li, J. Shi, P. Amberg, N. Pinckney, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-low-energy all-CMOS modulator integrated with driver,” Opt. Express 18(3), 3059–3070 (2010). [CrossRef] [PubMed]

].

The ALMod structure proposed in Fig. 1 offers a number of advantages when compared with structures made conductive by ion implant [10

10. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]

,14

14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

]. First, the silicon strips of Fig. 1 can be made notably thinner than the 60 nm used in Fig. 2. In fact, thin strips are good enough since for gate fields of 0.135 V/nm or higher, more than 90% of the free carriers are already concentrated in the first 10 nm from the Si/SiO2 interface. Also, for thin strips the optical field is concentrated more strongly inside the slot leading to a more efficient modulation [14

14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

]. The second advantage is that the strips do not require doping anymore, so that the electron mobility remains unperturbed and high [33

33. S. S. Li and W. R. Thurber, “Dopant density and temperature-dependence of electron-mobility and resistivity in n-type silicon,” Solid-State Electron. 20(7), 609–616 (1977). [CrossRef]

], leading to lower optical losses for a given conductivity (see Appendix A). Third, when using thin gate oxides (in the order of 10 nm), gate fields seven times larger than those used in our work can be applied [24

24. J. S. Suehle and P. Chaparala, “Low electric field breakdown of thin SiO2 films under static and dynamic stress,” IEEE Trans. Electron. Dev. 44(5), 801–808 (1997). [CrossRef]

] decreasing the strip resistances even more. This will become important once narrower slots are fabricated, since then an additional factor ten in the modulation efficiency can be gained [14

14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

], at the price of a larger slot capacitance.

In summary, we demonstrated the first 42.7 Gbit/s operation of an SOH electro-optic modulator. We introduced a method for increasing the conductivity of the thin silicon electrodes by using a novel electron accumulation-layer technique. This way, the modulation increased by a factor of five at 60 GHz while the optical loss increased by less than 1 dB.

Appendix

A. Optical absorption caused by injected carriers

The well-known empirical equations of Soref and Bennett [34

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

] relating the optical absorption in silicon to the free carrier density is based on experimental data where the free carriers come from impurity ionization and not from carrier injection. Soref and Bennett explicitly assumed equivalence between the two cases [34

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

]. Instead, the Drude-Lorenz model predicts that the optical absorption coefficient is proportional to the free carrier density N and to the inverse of the mobility μ. In doped samples the mobility is strongly impaired by scattering at impurities, while this is not the case for injected carriers in pure silicon [33

33. S. S. Li and W. R. Thurber, “Dopant density and temperature-dependence of electron-mobility and resistivity in n-type silicon,” Solid-State Electron. 20(7), 609–616 (1977). [CrossRef]

]. As an example, the electron mobility drops from roughly 1200 cm2/(Vs) to less than 300 cm2/(Vs) passing from an impurity concentration of 1016 cm−3 to 1018 cm−3 [35

35. D. M. Caughey and R. E. Thomas, “Carrier Mobilities In Silicon Empirically Related To Doping and Field,” Proc. IEEE 55(12), 2192–2193 (1967). [CrossRef]

]. As a consequence, for a given free electron concentration Ne, not only the conductivity σ = q Ne μe is lower for doping than for injection, but also the optical loss αDrudeNee is higher. This indicates that injected carriers have an intrinsic advantage over carriers coming from impurity ionization when both, high conductivity and low optical loss, are required [36

36. W. Spitzer and H. Y. Fan, “Infrared absorption in n-type silicon,” Phys. Rev. 108(2), 268–271 (1957). [CrossRef]

].

B. Waveguide fabrication

The waveguides were fabricated within the ePIXfab framework by CEA-LETI according to standard processes of the microelectronic industry [37

37. “ePIXfab: LETI3 March 2009”, retrieved http://www.epixfab.eu/mpw_shuttles/shuttles/leti03.

]. Two silicon-on-insulator (SOI) wafers were used, with layers of 220 nm thick crystalline silicon and 2 µm thick silicon oxide. The wafers were first implanted with arsenic for reaching a uniform ion concentration of 1017/cm−3. To this end, a dose of 5 × 1012/cm2, energy of 150 keV, tilt 0°, and twist 0° was used. Grating couplers [27

27. “ePIXfab: Vertical fiber couplers”, retrieved http://www.epixfab.eu/design/predefined_masks/imec/fxt_vertical_fiber_couplers.

] were then created by means of a 248 nm DUV lithography followed by 70 nm silicon etch performed with HBr. A high temperature oxide (HTO) layer of 130 nm used as a hard mask was grown and subsequently structured by means of 193 nm DUV lithography. A 150 nm silicon etch was used to define the waveguides. Taking advantage of the self-alignment with the pre-existing hard-mask, a 248 nm lithography defined the regions for a full silicon etch inside the slots. A thermal oxidation at 1100°C for 10 minutes was performed for reducing the surface roughness. A 248 nm DUV lithography defined the high-doping regions for the formation of ohmic contacts beneath the metal electrodes. To this end, the wafers were implanted with arsenic using a dose of 2 × 1015/cm2 and an energy of 30 keV. The ions were activated with a 1050°C annealing for 15 minutes. At this point, one wafer was not processed further for future optical loss measurements. Waveguides belonging to this wafer, but also coated with the nonlinear organic material, had an insertion loss of 16 dB (10 dB of which is caused by the grating couplers). A 500 nm thick silica protection layer was deposited on the entire wafer. A 248 nm DUV lithography was followed by a silica etch down to the silicon layer. A Ti/TiN/AlCu metal stack having a total thickness of 600 nm was deposited by physical vapor deposition (PVD) on the entire wafer. A 248 nm DUV lithography and a reactive ion etch (RIE) with chlorine was used to structure the metal electrodes. The wafer was then annealed for 30 minutes at 425°C. Finally, the slots were opened by means of a silica etch. The waveguides were spin-coated with the nonlinear organic material and poled in situ. The insertion loss of the waveguide is 40 dB. This 24 dB increase is mostly due to an error that occurred in the last silica etch step, which considerably increased the surface roughness of the waveguide. We are currently working on improving this process.

C. Method used for determining the modulation index

In the frequency range between 40 MHz and 60 GHz we derived the phase modulation index η by evaluating the ratio J02(η)/J12(η) between the central intensity peak and the first sideband intensity of the phase modulated signal (Jν is the Bessel function of the first kind). The spectra were recorded with an optical spectrum analyser (Apex AP2050). In the frequency range between 1 kHz and 40 MHz we inserted the phase modulator in one arm of a fiber-based Mach-Zehnder interferometer. The interference was recorded by means of a wide-band photodetector (Thorlabs PDA10CF) and a 1 GHz oscilloscope. The achieved phase modulation was derived from the amplitude of the intensity modulation.

D. Poling of the electro-optic material and origin of the phase shift

The commercially available nonlinear material M1 [25

25. “GigOptix”, retrieved http://www.gigoptix.com/.

] was poled by applying 16 V to the metal electrodes while the device was heated from room temperature to 141°C and then rapidly cooled as soon as this temperature was reached. Unpoled samples showed no detectable spectral sidebands (phase modulation smaller than 0.002 rad/V), demonstrating that the measured phase shift is actually due to the cladding nonlinearity and is not caused by free carriers. From the modulation index in the low frequency limit we estimate an actual nonlinearity coefficient of r 33 = 20 ± 2 pm/V. There is large potential for further increasing this value: The same material is used in commercially available polymer modulators where values of r 33 = 70 pm/V are routinely achieved by parallel plate poling. In SOH systems, values as high as r 33 = 40 pm/V have been reported [21

21. R. Ding, T. Baehr-Jones, Y. Liu, R. Bojko, J. Witzens, S. Huang, J. Luo, S. Benight, P. Sullivan, J. M. Fedeli, M. Fournier, L. Dalton, A. Jen, and M. Hochberg, “Demonstration of a low V π L modulator with GHz bandwidth based on electro-optic polymer-clad silicon slot waveguides,” Opt. Express 18(15), 15618–15623 (2010). [CrossRef] [PubMed]

]. The highest r 33 value achieved by in situ poling amounts to 170 pm/V [38

38. Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics 1(3), 180–185 (2007). [CrossRef]

]. This would result in a reduction of the operation voltage by a factor of eight.

Acknowledgments

We acknowledge support by the DFG Center for Functional Nanostructures (CFN), the KIT Initiative of Excellence, the Karlsruhe School of Optics and Photonics (KSOP), the EU-FP7 projects EURO-FOS (grant 224402) and SOFI (grant 248609), and by the BMBF joint project MISTRAL, funded by the German Ministry of Education and Research under grant 01BL0804. We further acknowledge technological support by the Karlsruhe Nano-Micro Facility (KNMF). We are grateful for technological support by the Light Technology Institute (KIT-LTI) and the ePIXfab (silicon photonics platform). W. Bogaerts acknowledges the Flemish Research Foundation (FWO-Vlaanderen) for a postdoctoral fellowship. We thank J. Groß and S. Schneider (KIT-IPQ) for helping with the modulator design. We thank M. Pauli and K. P. Pahl (KIT-IHE), H. Kleinjans, M. Schmidt and M. Karl (AMO), and F. Milesi (CEA-LETI) for valuable discussions, and we are grateful to Prof. D. Gerthsen (KIT-LEM) for support in nano-inspection and analysis.

References and links

1.

S. P. Voinigescu, T. O. Dickson, R. Beerkens, I. Khalid, and P. Westergaard, “A comparison of SiCMOS, SiGeBiCMOS, and InPHBT technologies for high-speed and millimeter-wave ICs,” 2004 Topical Meeting on Silicon Monolithic Integrated Circuits inRF Systems, Digest of Papers, 111–114 (2004).

2.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006). [CrossRef] [PubMed]

3.

P. Dong, S. R. Liao, D. Z. Feng, H. Liang, D. W. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. L. Li, X. Z. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009). [CrossRef]

4.

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]

5.

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]

6.

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]

7.

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

8.

R. W. Boyd, Nonlinear Optics (Academic press, 2008).

9.

T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: A platform for practical nonlinear optics,” J. Phys. Chem. C 112(21), 8085–8090 (2008). [CrossRef]

10.

J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]

11.

M. Hochberg, T. Baehr-Jones, G. Wang, J. Huang, P. Sullivan, L. Dalton, and A. Scherer, “Towards a millivolt optical modulator with nano-slot waveguides,” Opt. Express 15(13), 8401–8410 (2007). [CrossRef] [PubMed]

12.

J. H. Wülbern, A. Petrov, and M. Eich, “Electro-optical modulator in a polymerinfiltrated silicon slotted photonic crystal waveguide heterostructure resonator,” Opt. Express 17(1), 304–313 (2009). [CrossRef] [PubMed]

13.

C. Koos, J. Brosi, M. Waldow, W. Freude, and J. Leuthold, “Silicon-on-insulator modulators for next-generation 100 Gbit/s-Ethernet,” Proc. European Conf. on Optical Communication (ECOC), Paper P056 (2007).

14.

J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]

15.

W. Freude, J. Leuthold, L. Alloatti, T. Vallaitis, D. Korn, R. Palmer, C. Koos, J.-M. Brosi, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, B. Breiten, F. Diederich, A. Barklund, R. Dinu, and J. Wieland, “100 Gbit/s electro-optic modulator and 56 Gbit/s wavelength converter for DQPSK data in silicon-organic hybrid (SOH) technology,” Proc. IEEE Conf. on Novel Waveguiding, Structures and Phenomena, Summer Topicals, Paper WB2.1 (2010).

16.

J. H. Wülbern, S. Prorok, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, M. Jenett, and A. Jacob, “40 GHz electro-optic modulation in hybrid silicon-organic slotted photonic crystal waveguides,” Opt. Lett. 35(16), 2753–2755 (2010). [CrossRef] [PubMed]

17.

T. Baehr-Jones, B. Penkov, J. Q. Huang, P. Sullivan, J. Davies, J. Takayesu, J. D. Luo, T. D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008). [CrossRef]

18.

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon Organic Hybrid Technology-A Platform for Practical Nonlinear Optics,” Proc. IEEE 97(7), 1304–1316 (2009). [CrossRef]

19.

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

20.

L. Alloatti, D. Korn, D. Hillerkuss, T. Vallaitis, J. Li, R. Bonk, R. Palmer, T. Schellinger, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “Silicon high-speed electro-optic modulator,” Proc. IEEE Conf. on Group IV Photonics, Paper ThC2 (2010).

21.

R. Ding, T. Baehr-Jones, Y. Liu, R. Bojko, J. Witzens, S. Huang, J. Luo, S. Benight, P. Sullivan, J. M. Fedeli, M. Fournier, L. Dalton, A. Jen, and M. Hochberg, “Demonstration of a low V π L modulator with GHz bandwidth based on electro-optic polymer-clad silicon slot waveguides,” Opt. Express 18(15), 15618–15623 (2010). [CrossRef] [PubMed]

22.

N. N. Feng, S. R. Liao, D. Z. Feng, P. Dong, D. W. Zheng, H. Liang, R. Shafiiha, G. L. 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]

23.

S. M. Sze, and K. N. G. Kwok, Physics of Semiconductor Devices, Third Edition (Wiley, 2006).

24.

J. S. Suehle and P. Chaparala, “Low electric field breakdown of thin SiO2 films under static and dynamic stress,” IEEE Trans. Electron. Dev. 44(5), 801–808 (1997). [CrossRef]

25.

“GigOptix”, retrieved http://www.gigoptix.com/.

26.

D. Jin, H. Chen, A. Barklund, J. Mallari, G. M. Yu, E. Miller, and R. Dinu, “EO polymer modulators reliability study,” Proc. SPIE 7599, 75990H, 75990H-8 (2010). [CrossRef]

27.

“ePIXfab: Vertical fiber couplers”, retrieved http://www.epixfab.eu/design/predefined_masks/imec/fxt_vertical_fiber_couplers.

28.

J. Blasco, and C. A. Barrios, “Compact slot-waveguide/channel-waveguide mode-converter,” Lasers and Electro-Optics Europe, 2005. CLEO/Europe. 2005 Conference on, 607 (2005).

29.

C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26(2), 58–66 (2006). [CrossRef]

30.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguidesx,” Nat. Photonics 3(4), 216–219 (2009). [CrossRef]

31.

“Synopsys, tools for simulating device performance”, retrieved http://www.synopsys.com/Tools/TCAD/DeviceSimulation/Pages/default.aspx.

32.

X. Z. Zheng, J. Lexau, Y. Luo, H. Thacker, T. Pinguet, A. Mekis, G. L. Li, J. Shi, P. Amberg, N. Pinckney, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-low-energy all-CMOS modulator integrated with driver,” Opt. Express 18(3), 3059–3070 (2010). [CrossRef] [PubMed]

33.

S. S. Li and W. R. Thurber, “Dopant density and temperature-dependence of electron-mobility and resistivity in n-type silicon,” Solid-State Electron. 20(7), 609–616 (1977). [CrossRef]

34.

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

35.

D. M. Caughey and R. E. Thomas, “Carrier Mobilities In Silicon Empirically Related To Doping and Field,” Proc. IEEE 55(12), 2192–2193 (1967). [CrossRef]

36.

W. Spitzer and H. Y. Fan, “Infrared absorption in n-type silicon,” Phys. Rev. 108(2), 268–271 (1957). [CrossRef]

37.

“ePIXfab: LETI3 March 2009”, retrieved http://www.epixfab.eu/mpw_shuttles/shuttles/leti03.

38.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics 1(3), 180–185 (2007). [CrossRef]

OCIS Codes
(060.4080) Fiber optics and optical communications : Modulation
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits
(250.7360) Optoelectronics : Waveguide modulators

ToC Category:
Optoelectronics

History
Original Manuscript: April 14, 2011
Revised Manuscript: May 27, 2011
Manuscript Accepted: May 30, 2011
Published: June 3, 2011

Citation
L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, "42.7 Gbit/s electro-optic modulator in silicon technology," Opt. Express 19, 11841-11851 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11841


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References

  1. S. P. Voinigescu, T. O. Dickson, R. Beerkens, I. Khalid, and P. Westergaard, “A comparison of SiCMOS, SiGeBiCMOS, and InPHBT technologies for high-speed and millimeter-wave ICs,” 2004 Topical Meeting on Silicon Monolithic Integrated Circuits inRF Systems, Digest of Papers, 111–114 (2004).
  2. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006). [CrossRef] [PubMed]
  3. P. Dong, S. R. Liao, D. Z. Feng, H. Liang, D. W. Zheng, R. Shafiiha, C. C. Kung, W. Qian, G. L. Li, X. Z. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009). [CrossRef]
  4. 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]
  5. 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]
  6. 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]
  7. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]
  8. R. W. Boyd, Nonlinear Optics (Academic press, 2008).
  9. T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: A platform for practical nonlinear optics,” J. Phys. Chem. C 112(21), 8085–8090 (2008). [CrossRef]
  10. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008). [CrossRef] [PubMed]
  11. M. Hochberg, T. Baehr-Jones, G. Wang, J. Huang, P. Sullivan, L. Dalton, and A. Scherer, “Towards a millivolt optical modulator with nano-slot waveguides,” Opt. Express 15(13), 8401–8410 (2007). [CrossRef] [PubMed]
  12. J. H. Wülbern, A. Petrov, and M. Eich, “Electro-optical modulator in a polymerinfiltrated silicon slotted photonic crystal waveguide heterostructure resonator,” Opt. Express 17(1), 304–313 (2009). [CrossRef] [PubMed]
  13. C. Koos, J. Brosi, M. Waldow, W. Freude, and J. Leuthold, “Silicon-on-insulator modulators for next-generation 100 Gbit/s-Ethernet,” Proc. European Conf. on Optical Communication (ECOC), Paper P056 (2007).
  14. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010). [CrossRef] [PubMed]
  15. W. Freude, J. Leuthold, L. Alloatti, T. Vallaitis, D. Korn, R. Palmer, C. Koos, J.-M. Brosi, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, B. Breiten, F. Diederich, A. Barklund, R. Dinu, and J. Wieland, “100 Gbit/s electro-optic modulator and 56 Gbit/s wavelength converter for DQPSK data in silicon-organic hybrid (SOH) technology,” Proc. IEEE Conf. on Novel Waveguiding, Structures and Phenomena, Summer Topicals, Paper WB2.1 (2010).
  16. J. H. Wülbern, S. Prorok, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, M. Jenett, and A. Jacob, “40 GHz electro-optic modulation in hybrid silicon-organic slotted photonic crystal waveguides,” Opt. Lett. 35(16), 2753–2755 (2010). [CrossRef] [PubMed]
  17. T. Baehr-Jones, B. Penkov, J. Q. Huang, P. Sullivan, J. Davies, J. Takayesu, J. D. Luo, T. D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008). [CrossRef]
  18. J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon Organic Hybrid Technology-A Platform for Practical Nonlinear Optics,” Proc. IEEE 97(7), 1304–1316 (2009). [CrossRef]
  19. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]
  20. L. Alloatti, D. Korn, D. Hillerkuss, T. Vallaitis, J. Li, R. Bonk, R. Palmer, T. Schellinger, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “Silicon high-speed electro-optic modulator,” Proc. IEEE Conf. on Group IV Photonics, Paper ThC2 (2010).
  21. R. Ding, T. Baehr-Jones, Y. Liu, R. Bojko, J. Witzens, S. Huang, J. Luo, S. Benight, P. Sullivan, J. M. Fedeli, M. Fournier, L. Dalton, A. Jen, and M. Hochberg, “Demonstration of a low V π L modulator with GHz bandwidth based on electro-optic polymer-clad silicon slot waveguides,” Opt. Express 18(15), 15618–15623 (2010). [CrossRef] [PubMed]
  22. N. N. Feng, S. R. Liao, D. Z. Feng, P. Dong, D. W. Zheng, H. Liang, R. Shafiiha, G. L. 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]
  23. S. M. Sze, and K. N. G. Kwok, Physics of Semiconductor Devices, Third Edition (Wiley, 2006).
  24. J. S. Suehle and P. Chaparala, “Low electric field breakdown of thin SiO2 films under static and dynamic stress,” IEEE Trans. Electron. Dev. 44(5), 801–808 (1997). [CrossRef]
  25. “GigOptix”, retrieved http://www.gigoptix.com/ .
  26. D. Jin, H. Chen, A. Barklund, J. Mallari, G. M. Yu, E. Miller, and R. Dinu, “EO polymer modulators reliability study,” Proc. SPIE 7599, 75990H, 75990H-8 (2010). [CrossRef]
  27. “ePIXfab: Vertical fiber couplers”, retrieved http://www.epixfab.eu/design/predefined_masks/imec/fxt_vertical_fiber_couplers .
  28. J. Blasco, and C. A. Barrios, “Compact slot-waveguide/channel-waveguide mode-converter,” Lasers and Electro-Optics Europe, 2005. CLEO/Europe. 2005 Conference on, 607 (2005).
  29. C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26(2), 58–66 (2006). [CrossRef]
  30. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguidesx,” Nat. Photonics 3(4), 216–219 (2009). [CrossRef]
  31. “Synopsys, tools for simulating device performance”, retrieved http://www.synopsys.com/Tools/TCAD/DeviceSimulation/Pages/default.aspx .
  32. X. Z. Zheng, J. Lexau, Y. Luo, H. Thacker, T. Pinguet, A. Mekis, G. L. Li, J. Shi, P. Amberg, N. Pinckney, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-low-energy all-CMOS modulator integrated with driver,” Opt. Express 18(3), 3059–3070 (2010). [CrossRef] [PubMed]
  33. S. S. Li and W. R. Thurber, “Dopant density and temperature-dependence of electron-mobility and resistivity in n-type silicon,” Solid-State Electron. 20(7), 609–616 (1977). [CrossRef]
  34. R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]
  35. D. M. Caughey and R. E. Thomas, “Carrier Mobilities In Silicon Empirically Related To Doping and Field,” Proc. IEEE 55(12), 2192–2193 (1967). [CrossRef]
  36. W. Spitzer and H. Y. Fan, “Infrared absorption in n-type silicon,” Phys. Rev. 108(2), 268–271 (1957). [CrossRef]
  37. “ePIXfab: LETI3 March 2009”, retrieved http://www.epixfab.eu/mpw_shuttles/shuttles/leti03 .
  38. Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics 1(3), 180–185 (2007). [CrossRef]

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