Abstract

A compact silicon electro-optic modulator that operates in the breakdown delay based depletion mode is introduced. This operation mode has not previously been utilized for optical modulators, and represents a way to potentially achieve much higher modulation speeds and carrier extraction efficiencies without sacrificing energy efficiency, which is a critical criterion for realizing miniaturized sub-THz modulation components in silicon. Our study shows a speed of at least 238 GHz modulation is achievable along with an ultra-low energy consumption of 26.6 fJ/bit in a simple planar P+PNN+ diode example structure, which is embedded in a 2D hybrid photonic lattice mode gap resonator. The optical resonator itself is only 69 µm2 in footprint and is designed for optimized electro-optic sensitivity and conversion efficiency with reduced carrier scattering. Both the static and dynamic device performance are backed up by fully integrated 3D optical and 3D electrical numerical results. The compact device dimensions and low energy consumption are favorable to high density photonic integration.

© 2011 OSA

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

2009 (8)

B. Jalali, S. Fathpour, and K. Tsia, “Green silicon photonics,” Opt. Photon. News 20(6), 18–23 (2009).
[CrossRef]

P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung, W. Qian, G. Li, X. 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]

F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fedeli, 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]

Q. Xu, “Silicon dual-ring modulator,” Opt. Express 17(23), 20783–20793 (2009).
[CrossRef] [PubMed]

M. Xin, A. J. Danner, C. E. Png, and S. T. Lim, “Theoretical study of a cross waveguide resonator-based silicon electro-optic modulator with low power consumption,” J. Opt. Soc. Am. B 26(11), 2176–2180 (2009).
[CrossRef]

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]

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]

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (5)

2006 (2)

R. A. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[CrossRef]

T. Asano, B.-S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1123–1134 (2006).
[CrossRef]

2005 (3)

D. Englund, I. Fushman, and J. Vucković, “General recipe for designing photonic crystal cavities,” Opt. Express 13(16), 5961–5975 (2005).
[CrossRef] [PubMed]

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

F. Zhang, L. Shi, C. Li, W. Yu, and X. Sun, “A high-power solid-state p+–n–n+ diode for picosecond-range closing switching,” Semicond. Sci. Technol. 20(10), 991–997 (2005).
[CrossRef]

2004 (1)

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

2003 (1)

S. L. Konsek and T. P. Pearsall, “Dynamics of electron tunneling in semiconductor nanostructures,” Phys. Rev. B 67(4), 045306 (2003).
[CrossRef]

Akahane, Y.

T. Asano, B.-S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1123–1134 (2006).
[CrossRef]

Andreani, L. C.

Asakawa, K.

Asano, T.

T. Asano, B.-S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1123–1134 (2006).
[CrossRef]

Asghari, M.

Baba, T.

Baets, R.

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]

Barrios, C. A.

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

Biaggio, I.

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]

Brimont, A.

Brosi, J.-M.

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]

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]

Cassan, E.

Chen, R. T.

L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Chen, X.

L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Chetrit, Y.

Ciftcioglu, B.

Cunningham, J. E.

Danner, A. J.

Diederich, F.

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]

Dong, F.

Dong, P.

Dumon, P.

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]

F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fedeli, 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]

Ebert, U.

P. Rodin, U. Ebert, A. Minarsky, and I. Grekhov, “Theory of superfast fronts of impact ionization in semiconductor structures,” J. Appl. Phys. 102(3), 034508 (2007).
[CrossRef]

Eich, M.

Englund, D.

Fathpour, S.

B. Jalali, S. Fathpour, and K. Tsia, “Green silicon photonics,” Opt. Photon. News 20(6), 18–23 (2009).
[CrossRef]

Fedeli, J. M.

Fédéli, J. M.

Feng, D.

Feng, N.-N.

Frank, B.

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]

Freude, W.

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]

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]

Fushman, I.

Gardes, F. Y.

Grekhov, I.

P. Rodin, U. Ebert, A. Minarsky, and I. Grekhov, “Theory of superfast fronts of impact ionization in semiconductor structures,” J. Appl. Phys. 102(3), 034508 (2007).
[CrossRef]

Gu, L.

L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Hamachi, Y.

Hugonin, J. P.

Ikeda, N.

Izhaky, N.

Jalali, B.

B. Jalali, S. Fathpour, and K. Tsia, “Green silicon photonics,” Opt. Photon. News 20(6), 18–23 (2009).
[CrossRef]

Jiang, W.

L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Kitagawa, Y.

Konsek, S. L.

S. L. Konsek and T. P. Pearsall, “Dynamics of electron tunneling in semiconductor nanostructures,” Phys. Rev. B 67(4), 045306 (2003).
[CrossRef]

Koos, C.

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]

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]

Krauss, T. F.

Krishnamoorthy, A. V.

Kubo, S.

Kung, C.-C.

Lalanne, P.

Laval, S.

Leuthold, J.

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]

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]

Li, C.

F. Zhang, L. Shi, C. Li, W. Yu, and X. Sun, “A high-power solid-state p+–n–n+ diode for picosecond-range closing switching,” Semicond. Sci. Technol. 20(10), 991–997 (2005).
[CrossRef]

Li, G.

Liang, H.

Liao, L.

Liao, S.

Lim, S. T.

Lipson, M.

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

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

Liu, A.

Lyan, P.

Marris-Morini, D.

Martí, J.

Mashanovich, G.

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

Matsuo, S.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

Minarsky, A.

P. Rodin, U. Ebert, A. Minarsky, and I. Grekhov, “Theory of superfast fronts of impact ionization in semiconductor structures,” J. Appl. Phys. 102(3), 034508 (2007).
[CrossRef]

Mizutani, A.

Nguyen, H.

Noda, S.

T. Asano, B.-S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1123–1134 (2006).
[CrossRef]

Notomi, M.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

Nozaki, K.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

O’Faolain, L.

Ozaki, N.

Paniccia, M.

Pearsall, T. P.

S. L. Konsek and T. P. Pearsall, “Dynamics of electron tunneling in semiconductor nanostructures,” Phys. Rev. B 67(4), 045306 (2003).
[CrossRef]

Petrov, A.

Png, C. E.

Pradhan, S.

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

Qian, W.

Rasigade, G.

Reed, G. T.

Rodin, P.

P. Rodin, U. Ebert, A. Minarsky, and I. Grekhov, “Theory of superfast fronts of impact ionization in semiconductor structures,” J. Appl. Phys. 102(3), 034508 (2007).
[CrossRef]

Rubin, D.

Sanchis, P.

Sato, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

Schmidt, B.

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

Scimeca, M. L.

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]

Shafiiha, R.

Shi, L.

F. Zhang, L. Shi, C. Li, W. Yu, and X. Sun, “A high-power solid-state p+–n–n+ diode for picosecond-range closing switching,” Semicond. Sci. Technol. 20(10), 991–997 (2005).
[CrossRef]

Shinya, A.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

Song, B.-S.

T. Asano, B.-S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1123–1134 (2006).
[CrossRef]

Soref, R. A.

R. A. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[CrossRef]

Sugimoto, Y.

Sun, X.

F. Zhang, L. Shi, C. Li, W. Yu, and X. Sun, “A high-power solid-state p+–n–n+ diode for picosecond-range closing switching,” Semicond. Sci. Technol. 20(10), 991–997 (2005).
[CrossRef]

Takata, Y.

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

Thomson, D. J.

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[CrossRef]

Tsia, K.

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[CrossRef]

Vivien, L.

Vuckovic, J.

Waldow, M.

Wang, L.

L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

Watanabe, Y.

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[CrossRef] [PubMed]

Yu, W.

F. Zhang, L. Shi, C. Li, W. Yu, and X. Sun, “A high-power solid-state p+–n–n+ diode for picosecond-range closing switching,” Semicond. Sci. Technol. 20(10), 991–997 (2005).
[CrossRef]

Zhang, F.

F. Zhang, L. Shi, C. Li, W. Yu, and X. Sun, “A high-power solid-state p+–n–n+ diode for picosecond-range closing switching,” Semicond. Sci. Technol. 20(10), 991–997 (2005).
[CrossRef]

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Zheng, X.

Appl. Phys. Lett. (1)

L. Gu, W. Jiang, X. Chen, L. Wang, and R. T. Chen, “High speed silicon photonic crystal waveguide modulator for low voltage operation,” Appl. Phys. Lett. 90(7), 071105 (2007).
[CrossRef]

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T. Asano, B.-S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q Nanocavities in Two-Dimensional Photonic Crystal Slabs,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1123–1134 (2006).
[CrossRef]

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[CrossRef]

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[CrossRef]

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

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Nat. Photonics (2)

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[CrossRef]

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

Nature (1)

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

Opt. Express (10)

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F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fedeli, 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).
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Opt. Lett. (2)

Opt. Photon. News (1)

B. Jalali, S. Fathpour, and K. Tsia, “Green silicon photonics,” Opt. Photon. News 20(6), 18–23 (2009).
[CrossRef]

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[CrossRef]

Semicond. Sci. Technol. (1)

F. Zhang, L. Shi, C. Li, W. Yu, and X. Sun, “A high-power solid-state p+–n–n+ diode for picosecond-range closing switching,” Semicond. Sci. Technol. 20(10), 991–997 (2005).
[CrossRef]

Other (3)

ATLAS user’s manual, SILVACO International, Santa Clara, California.

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (John Wiley & Sons, Inc., 2007).

M. R. Watts, D. C. Trotter, R. W. Young, and A. L. Lentine, “Ultralow power silicon microdisk modulators and switches,” in Proceedings of 5th IEEE International Conference on Group IV Photonics (IEEE 2008), pp. 4 - 6.

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Figures (11)

Fig. 1
Fig. 1

(a) 3D schematic of the device showing the planar HLMG resonator and electrode configuration for external driving signal. (b) The magnified 2D demonstration of the HLMG resonator constructed by hybrid PC lattice transition and additional insertion stages.

Fig. 2
Fig. 2

(a) The defect lattice constant a2 is selected at 400 nm for optimized cavity confinement and EO sensitivity. (b) The projected band diagram shows a wide mode gap between PC1 and PC2, which is the origin of the highly confined optical cavity resonance.

Fig. 3
Fig. 3

(a) Transmission spectrum of the HLMG resonator indicates a highly confined resonance mode in the NIR range. (b) 2D profile of the resonance mode in the xy plane. (c) 2D profile of the resonance mode in the xz plane.

Fig. 4
Fig. 4

Significantly improved insertion efficiency is detected with 6 periods of PC3 when a3 is kept at 450 nm.

Fig. 5
Fig. 5

(a) 2D schematic of the lateral P+PNN+ diode embedded in the HLMG cavity. yz cross section of the embedded diode shows (b) indirect carrier depletion path in a rib waveguide based diode (not recommended) and (c) direct depletion path in the planar diode design that we employ instead.

Fig. 6
Fig. 6

(a) Static carrier level near the center of the waveguide shows different hole contrasts at the same bias voltage for diodes embedded in different lattice patterns. 2D hole profiles at −8 V indicate in the x direction (b) highly uniform carrier distribution for the HLMG cavity and (c) periodically modulated concentration for the DHS cavity.

Fig. 7
Fig. 7

(a) A finite breakdown delay time is found in the post breakdown operation regime where the carrier level can be further depleted with increase of the bias voltage. (b) The leakage current is found to be negligible within the breakdown delay and increases drastically after breakdown takes place.

Fig. 8
Fig. 8

Magnified 2D hole profiles at −15 V indicate the depletion region (a) in the xy plane and (b) in the yz plane.

Fig. 9
Fig. 9

(a) 1D cutline of the hole/electron concentration along the y direction indicates the depletion width movement at −15 V bias. (b) 1D carrier contrast profile between 0 and −15 V within the depletion region.

Fig. 10
Fig. 10

(a) The transient carrier response at different locations of the depletion region at −15 V indicates uniform switching speed of 238 GHz. (b) Equivalent RC circuit of the embedded P+PNN+ diode. (c) Tradeoff relationship between MD and bias voltage among different operation regimes.

Fig. 11
Fig. 11

(a) The applied 238 GHz RZ voltage signal switching between 0 and −15 V. (b) The representative hole response at the center of the waveguide. (c) The 3D FDTD interpreted transmission evolution of the HLMG resonator corresponding to (b). (d) The transient current flow of the device at voltage transitions.

Tables (1)

Tables Icon

Table 1 Comparison of our Device with Recently Proposed Silicon Integrated Modulators

Equations (10)

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1 μ = m * q ( 1 τ m i + 1 τ m o )
E m = 4 × 10 5 1 ( 1 / 3 ) log 10 ( N / 10 16 )
d V over / d t > 2 v s q N B ( V bi V over ) / 2 ε
W D = W D p + W D n = 2 ε ( N p + N n ) q N p N n ( V bi V over 2 k T q )
f U L 1 t r + t f 1 4.4 τ R C = 1 4.4 ( R p + + R p + R n + R n + ) C D W D 4.4 ε ( ρ e f f p L p + ρ e f f n L n )
E bit = 1 / 4 0 1 V over I over d t
P OFF ( ω ) = A e ( ω ω 0 ) 2 / 2 σ 2          Δ ω FWHM = ω 0 Q = 2.35 σ
P ON ( ω 0 ) = A e ( ω 0 ω 0 ' ) 2 / 2 σ 2    MD= 10 log [ P OFF ( ω 0 ) / P ON ( ω 0 ) ] = 5 log e ( ω 0 ω 0 ' ) 2 / σ 2
λ = λ 0 / n eff = 2 L cav / k        Δ n eff Δ n V ol / V mod
η EO ( 3.5 n eff ) 2 ( Q V mod ) 2 V ol 2

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