Abstract

Accumulating electrons in transparent conductive oxides such as indium tin oxide (ITO) can induce an ”epsilon-near-zero” (ENZ) in the spectral region near the important telecommunications wavelength of λ = 1.55μm. Here we theoretically demonstrate highly effective optical electro-absorptive modulation in a silicon waveguide overcoated with ITO. This modulator leverages the combination of a local electric field enhancement and increased absorption in the ITO when this material is locally brought into an ENZ state via electrical gating. This leads to large changes in modal absorption upon gating. We find that a 3 dB modulation depth can be achieved in a non-resonant structure with a length under 30 μm for the fundamental waveguide modes of either linear polarization, with absorption contrast values as high as 37. We also show a potential for 100 fJ/bit modulation, with a sacrifice in performance.

© 2013 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2012 (6)

E. H. Edwards, R. M. Audet, E. T. Fei, S. A. Claussen, R. K. Schaevitz, E. Tasyurek, Y. Rong, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Ge/SiGe assymetric Fabry-Perot quantum well electroabsorption modulators,” Opt. Express20, 29164–29173 (2012).
[CrossRef]

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photon. J.4, 735–740 (2012).

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” J. Nanophotonics1, 17–22 (2012).

A. V. Krasavin and A. V. Zayats, “Photonic signal processing on electronic scales: electro-optical field-effect nanoplasmonic modulator,” Phys. Rev. Lett.109, 053901 (2012).
[CrossRef] [PubMed]

D. Feng, S. Liao, H. Liang, J. Fong, B. Bijlani, R. Shafiiha, B. Luff, Y. Luo, J. Cunningham, A. Krishnamoorthy, and M. Asghari, “High speed GeSi electro-absorption modulator at 1550 nm wavelength on SOI waveguide,” Opt. Express20, 22224–22232 (2012).
[CrossRef] [PubMed]

D. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express20, A293–A308 (2012).
[CrossRef] [PubMed]

2010 (3)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett.10, 2111–2116 (2010).
[CrossRef]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).
[CrossRef]

2009 (2)

2008 (1)

2004 (3)

J. Robertson, “High dielectric constant oxides,” Eur. Phys. J. Appl. Phys.28, 265–291 (2004).
[CrossRef]

P. P. Edwards, A. Porch, M. O. Jones, D. V. Morgan, and R. M. Perks, “Basic materials physics of transparent conducting oxides,” Dalton Trans.19, 2995–3002 (2004).
[CrossRef] [PubMed]

Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express12,8, 1622 (2004).
[CrossRef] [PubMed]

1991 (1)

G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 μ m based on free-carrier absorption,” IEEE Electron Dev. Lett., 12, 276–278 (1991).
[CrossRef]

1987 (1)

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

Asghari, M.

Atwater, H. A.

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett.10, 2111–2116 (2010).
[CrossRef]

Audet, R. M.

Bennett, B.

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

Bijlani, B.

Boltasseva, A.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

Claussen, S. A.

Cunningham, J.

Danz, N.

Descrovi, E.

Diest, K.

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett.10, 2111–2116 (2010).
[CrossRef]

Dominici, L.

Edwards, E. H.

Edwards, P. P.

P. P. Edwards, A. Porch, M. O. Jones, D. V. Morgan, and R. M. Perks, “Basic materials physics of transparent conducting oxides,” Dalton Trans.19, 2995–3002 (2004).
[CrossRef] [PubMed]

Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

Fei, E. T.

Feigenbaum, E.

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett.10, 2111–2116 (2010).
[CrossRef]

Feng, D.

Fong, J.

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).
[CrossRef]

Halbout, J. M.

G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 μ m based on free-carrier absorption,” IEEE Electron Dev. Lett., 12, 276–278 (1991).
[CrossRef]

Harris, J. S.

Ishii, S.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

Jones, M. O.

P. P. Edwards, A. Porch, M. O. Jones, D. V. Morgan, and R. M. Perks, “Basic materials physics of transparent conducting oxides,” Dalton Trans.19, 2995–3002 (2004).
[CrossRef] [PubMed]

Kamins, T. I.

Knights, Andrew P.

Graham T. Reed and Andrew P. Knights, Silicon photonics. Wiley (2008).
[CrossRef]

Krasavin, A. V.

A. V. Krasavin and A. V. Zayats, “Photonic signal processing on electronic scales: electro-optical field-effect nanoplasmonic modulator,” Phys. Rev. Lett.109, 053901 (2012).
[CrossRef] [PubMed]

Krishnamoorthy, A.

Lanzillotti-Kimura, N. D.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” J. Nanophotonics1, 17–22 (2012).

Liang, H.

Liao, S.

Lipson, M.

Lu, Z.

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photon. J.4, 735–740 (2012).

Luff, B.

Luo, Y.

Ma, R.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” J. Nanophotonics1, 17–22 (2012).

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).
[CrossRef]

May, P. G.

G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 μ m based on free-carrier absorption,” IEEE Electron Dev. Lett., 12, 276–278 (1991).
[CrossRef]

McNab, S.

Menchini, F.

Michelotti, F.

Miller, D.

Miller, D. A. B.

Morgan, D. V.

P. P. Edwards, A. Porch, M. O. Jones, D. V. Morgan, and R. M. Perks, “Basic materials physics of transparent conducting oxides,” Dalton Trans.19, 2995–3002 (2004).
[CrossRef] [PubMed]

Naik, G. V.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

Painter, O.

Perks, R. M.

P. P. Edwards, A. Porch, M. O. Jones, D. V. Morgan, and R. M. Perks, “Basic materials physics of transparent conducting oxides,” Dalton Trans.19, 2995–3002 (2004).
[CrossRef] [PubMed]

Porch, A.

P. P. Edwards, A. Porch, M. O. Jones, D. V. Morgan, and R. M. Perks, “Basic materials physics of transparent conducting oxides,” Dalton Trans.19, 2995–3002 (2004).
[CrossRef] [PubMed]

Preston, K.

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).
[CrossRef]

Reed, Graham T.

Graham T. Reed and Andrew P. Knights, Silicon photonics. Wiley (2008).
[CrossRef]

Robertson, J.

J. Robertson, “High dielectric constant oxides,” Eur. Phys. J. Appl. Phys.28, 265–291 (2004).
[CrossRef]

Robinson, J.

Rong, Y.

Schaevitz, R. K.

Shafiiha, R.

Shalaev, V. M.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

Shi, K.

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photon. J.4, 735–740 (2012).

Soref, R.

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

Sorger, V. J.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” J. Nanophotonics1, 17–22 (2012).

Tasyurek, E.

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).
[CrossRef]

Treyz, G. V.

G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 μ m based on free-carrier absorption,” IEEE Electron Dev. Lett., 12, 276–278 (1991).
[CrossRef]

Vlasov, Y.

West, P. R.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

Zayats, A. V.

A. V. Krasavin and A. V. Zayats, “Photonic signal processing on electronic scales: electro-optical field-effect nanoplasmonic modulator,” Phys. Rev. Lett.109, 053901 (2012).
[CrossRef] [PubMed]

Zhang, X.

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” J. Nanophotonics1, 17–22 (2012).

Zhao, W.

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photon. J.4, 735–740 (2012).

Dalton Trans. (1)

P. P. Edwards, A. Porch, M. O. Jones, D. V. Morgan, and R. M. Perks, “Basic materials physics of transparent conducting oxides,” Dalton Trans.19, 2995–3002 (2004).
[CrossRef] [PubMed]

Eur. Phys. J. Appl. Phys. (1)

J. Robertson, “High dielectric constant oxides,” Eur. Phys. J. Appl. Phys.28, 265–291 (2004).
[CrossRef]

IEEE Electron Dev. Lett. (1)

G. V. Treyz, P. G. May, and J. M. Halbout, “Silicon optical modulators at 1.3 μ m based on free-carrier absorption,” IEEE Electron Dev. Lett., 12, 276–278 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE Photon. J. (1)

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photon. J.4, 735–740 (2012).

J. Nanophotonics (1)

V. J. Sorger, N. D. Lanzillotti-Kimura, R. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” J. Nanophotonics1, 17–22 (2012).

Laser & Photon. Rev. (1)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev.4, 795–808 (2010).
[CrossRef]

Nano Lett. (1)

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett.10, 2111–2116 (2010).
[CrossRef]

Nat. Photonics (1)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. V. Krasavin and A. V. Zayats, “Photonic signal processing on electronic scales: electro-optical field-effect nanoplasmonic modulator,” Phys. Rev. Lett.109, 053901 (2012).
[CrossRef] [PubMed]

Proc. IEEE (1)

D. A. B. Miller, “Device Requirements for optical interconnects to silicon chips,” Proc. IEEE97, 1166–1185 (2009).
[CrossRef]

Other (1)

Graham T. Reed and Andrew P. Knights, Silicon photonics. Wiley (2008).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

The proposed modulator consists of a silicon-on-insulator (400 × 220nm2) waveguide coated with layers of HfO2 (5 nm) and ITO (10 nm), forming a MOS capacitor (a). Without an applied bias, the ITO absorbs little light leading to a highly tranmissive ON state (upper inset). With a negative bias between the ITO and the Si, an electron accumulation layer is induced at the ITO-HfO2 interface. This accumulation layer modifies ITO’s local optical permittivity, creating an epsilon-near-zero (ENZ) region that perturbs the waveguide mode into a highly absorptive OFF state (lower inset). This electro-absorption modulation occurs for both TE-like and TM-like modes supported by the waveguide structure (b), (c). The TE (TM) mode exhibits discontinuities in |Ex|(|Ey|) at interfaces due to dielectric constant mismatches.

Fig. 2
Fig. 2

Accumulating electrons in ITO via electrical gating tunes its local permittivity for λ0 = 1.55μm light. Increasing the concentration of accumulated electrons by increasing the applied bias leads to a decreasing ε1 and an increasing ε2, as per the Drude model. At an applied voltage of −2.3 Vnacc = 6.33 × 1020cm−3), ε1 approaches zero; this indicates the formation of an ENZ region at the ITO-HfO2 interface.

Fig. 3
Fig. 3

As the gate bias is increased, the modal loss exhibits a local maximum at −2.3 V, precisely the voltage required to induce an ENZ region in ITO (inset), for both TE and TM modes (a). We can express the modal loss as the product between the bulk material loss (b) and the confinement factor (c). Maximal modal loss occurs when a combination of appreciable bulk material loss and modal confinement. At higher voltages where the bulk material loss is higher, but the mode is not as confined within the highly absorptive region does not lead to optimal modal loss. Lower voltages with lower bulk material loss but higher modal confinement are also not optimal.

Fig. 4
Fig. 4

In the ON state, without applied bias, the highest electric field magnitude resides inside the silicon waveguide (a, left). In the OFF state, with a bias that induces an ENZ region, we find two large spikes in the electric field at each ITO-HfO2 interface due to the ENZ regions’ presence and their imposed continuity condition (a, right). A closer look at the region of interest (b) shows that the high electric fields are confined to the electron accumulation layer at the ITO-HfO2 interface, precisely where the permittivity drops near zero (c). This also coincides with the region that most effectively contributes to the modal absorption.

Fig. 5
Fig. 5

(a) The absorption contrast peaks for both TE and TM modes at an applied voltage of 2.3 V, corresponding to the generation of an ENZ region at the ITO/HfO2 interface. We find peak absorption contrasts of 37.3 (5.6) for the TM (TE) mode. (b) Making the waveguide modulator longer increases its modulation depth. We find that a device length of 27 μm yields a modulation depth of 0.5 (3 dB modulation) for both TM and TE operation.

Fig. 6
Fig. 6

There is a trade-off between modulator performance and energy consumption. By increasing the bulk electron concentration in the ITO, we can reduce the voltage needed to reach the ENZ point. This comes at a cost of sacrificing absorption contrast since the ON state absorption would increase with increased bulk electron concentration. We do find that 100 fJ operation is achievable with an absorption contrast of 2.47 (1.78) for the TE (TM) mode. Even lower energy consumption is possible provided that a lower absorption contrast is acceptable.

Equations (7)

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ε = ε ω p 2 ω 2 i γ ω ,
ω p = [ n e 2 ε 0 m * ] 1 / 2 ,
| E ENZ | = | ε d E 0 | | ε ENZ | ,
α m = Γ α b ,
α b = 2 k 0 Im { n ˜ ENZ } ,
Γ = n g ENZ ε ˜ | E | 2 d x d y n ˜ ENZ ε ˜ | E | 2 d x d y ,
M = 1 exp [ Δ α × l ] ,

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