Abstract

An ultracompact silicon electro-optic modulator operating at 1550-nm telecom wavelengths is proposed and analyzed theoretically, which consists of a Cu-TiO2-Si hybrid plasmonic donut resonator evanescently coupled with a conventional Si channel waveguide. Owing to a negative thermo-optic coefficient of TiO2 (~-1.8 × 10−4 K−1), the real part of effective modal index of the curved Cu-TiO2-Si hybrid waveguide can be temperature-independent (i.e., athermal) if the TiO2 interlayer and the beneath Si core have a certain thickness ratio. A voltage applied between the ring-shaped Cu cap and a cylinder metal electrode positioned at the center of the donut, − which makes Ohmic contact to Si, induces a ~1-nm-thick free-electron accumulation layer at the TiO2/Si interface. The optical field intensity in this thin accumulation layer is significantly enhanced if the accumulation concentration is sufficiently large (i.e., > ~6 × 1020 cm−3), which in turn modulates both the resonance wavelengths and the extinction ratio of the donut resonator simultaneously. For a modulator with the total footprint inclusive electrodes of ~8.6 μm2, 50-nm-thick TiO2, and 160-nm-thick Si core, FDTD simulation predicts that it has an insertion loss of ~2 dB, a modulation depth of ~8 dB at a voltage swing of ~6 V, a speed-of-response of ~35 GHz, and a switching energy of ~0.45 pJ/bit, and it is athermal around room temperature. The modulator’s performances can be further improved by optimization of the coupling strength between the bus waveguide and the donut resonator.

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2013 (1)

2012 (3)

S. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of vertical Cu/SiO2/Si hybrid plasmonic waveguide components on an SOI platform,” IEEE Photon. Technol. Lett.24(14), 1224–1226 (2012).
[CrossRef]

S. Zhu, G. Q. Lo, and D. L. Kwong, “Performance of ultracompact copper-capped silicon hybrid plasmonic waveguide-ring resonators at telecom wavelengths,” Opt. Express20(14), 15232–15246 (2012).
[CrossRef] [PubMed]

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
[CrossRef]

2011 (4)

2010 (5)

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express18(4), 3487–3493 (2010).
[CrossRef] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

K. F. MacDonald and N. I. Zheludev, “Active plasmonics: current status,” Laser Photon. Rev.4(4), 562–567 (2010).
[CrossRef]

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express18(11), 11728–11736 (2010).
[CrossRef] [PubMed]

2009 (3)

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
[CrossRef]

C. T. Shin, Z. W. Zeng, and S. Chao, “Design and analysis of MOS-capacitor microring optical modulator with SPC poly-silicon gate,” J. Lightwave Technol.27, 3861–3873 (2009).
[CrossRef]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (2)

2005 (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

2004 (1)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
[CrossRef] [PubMed]

2002 (2)

G. Gulsen and M. N. Inci, “Thermal optical properties of TiO2 films,” Opt. Mater.18(4), 373–381 (2002).
[CrossRef]

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
[CrossRef]

1992 (1)

J. Sune, P. Olivo, and B. Ricco, “Quantum-mechanical modeling of accumulation layers in MOS structure,” IEEE Trans. Electron. Dev.39(7), 1732–1739 (1992).
[CrossRef]

1985 (1)

A. Tardella and J. N. Chazalviel, “Highly accumulated electron layer at a semiconductor/electrolyte interface,” Phys. Rev. B Condens. Matter32(4), 2439–2448 (1985).
[CrossRef] [PubMed]

1960 (1)

S. Roberts, “Optical properties of copper,” Phys. Rev.118(6), 1509–1518 (1960).
[CrossRef]

Ahn, H.

Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009).
[CrossRef] [PubMed]

Baets, R.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
[CrossRef]

Balamurugan, A. K.

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
[CrossRef]

Beausoleil, R. G.

Bhattacharya, P.

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
[CrossRef]

Bienstman, P.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
[CrossRef]

Bogaerts, W.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
[CrossRef]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Buchwald, W.

Cassan, E.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
[CrossRef]

Chao, S.

Chazalviel, J. N.

A. Tardella and J. N. Chazalviel, “Highly accumulated electron layer at a semiconductor/electrolyte interface,” Phys. Rev. B Condens. Matter32(4), 2439–2448 (1985).
[CrossRef] [PubMed]

Chetrit, Y.

Ciftcioglu, B.

Claes, T.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
[CrossRef]

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Crozat, P.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
[CrossRef]

Dai, D.

DasGupta, A.

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
[CrossRef]

DasGupta, N.

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
[CrossRef]

Diest, K.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009).
[CrossRef] [PubMed]

Dionne, J. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009).
[CrossRef] [PubMed]

Dumon, P.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
[CrossRef]

Fattal, D.

Fedeli, J. M.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
[CrossRef]

Fujikata, J.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

Furue, K.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

Ganguli, T.

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
[CrossRef]

Gardes, F. Y.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Gomyo, A.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Guha, B.

Gulsen, G.

G. Gulsen and M. N. Inci, “Thermal optical properties of TiO2 films,” Opt. Mater.18(4), 373–381 (2002).
[CrossRef]

Guo, J.

Halbwax, M.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
[CrossRef]

Han, Z.

He, S.

Heyn, P. D.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
[CrossRef]

Inci, M. N.

G. Gulsen and M. N. Inci, “Thermal optical properties of TiO2 films,” Opt. Mater.18(4), 373–381 (2002).
[CrossRef]

Ishi, T.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

Izhaky, N.

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Kim, D. J.

Kim, G.

Kinoshita, M.

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

Kukreja, L. M.

R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
[CrossRef]

Kwong, D. L.

Kyotoku, B. B. C.

Laval, S.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
[CrossRef]

Lee, J. M.

Liao, L.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
[CrossRef] [PubMed]

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Lipson, M.

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express18(4), 3487–3493 (2010).
[CrossRef] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
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A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007).
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A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
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Lupu, A.

D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
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D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
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K. F. MacDonald and N. I. Zheludev, “Active plasmonics: current status,” Laser Photon. Rev.4(4), 562–567 (2010).
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D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
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D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
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R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
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R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
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A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007).
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A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
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Peale, R. E.

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
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Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
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R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
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D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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J. Sune, P. Olivo, and B. Ricco, “Quantum-mechanical modeling of accumulation layers in MOS structure,” IEEE Trans. Electron. Dev.39(7), 1732–1739 (1992).
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D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
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D. Marris-Morini, L. Vivien, G. Rasigade, J. M. Fedeli, E. Cassan, X. L. Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE97(7), 1199–1215 (2009).
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A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
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A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
[CrossRef] [PubMed]

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Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
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W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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Soref, R.

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
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J. Sune, P. Olivo, and B. Ricco, “Quantum-mechanical modeling of accumulation layers in MOS structure,” IEEE Trans. Electron. Dev.39(7), 1732–1739 (1992).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009).
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W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
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W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev.6(1), 47–73 (2012).
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K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

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Zhang, X.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
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R. Paily, A. DasGupta, N. DasGupta, P. Bhattacharya, P. Misra, T. Ganguli, L. M. Kukreja, A. K. Balamurugan, S. Rajagopalan, and A. K. Tyagi, “Pulsed laser deposition of TiO2 for MOS gate dielectric,” Appl. Surf. Sci.187(3-4), 297–304 (2002).
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IEEE Photon. Technol. Lett. (1)

S. Zhu, G. Q. Lo, and D. L. Kwong, “Experimental demonstration of vertical Cu/SiO2/Si hybrid plasmonic waveguide components on an SOI platform,” IEEE Photon. Technol. Lett.24(14), 1224–1226 (2012).
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Nano Lett. (1)

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009).
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Nat. Photonics (3)

K. Ohashi, K. Nishi, T. Shimizu, M. Nakada, J. Fujikata, J. Ushida, S. Torii, K. Nose, M. Mizuno, H. Yukawa, M. Kinoshita, N. Suzuki, A. Gomyo, T. Ishi, D. Okamoto, K. Furue, T. Ueno, T. Tsug, T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4, 518–526 (2010).

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
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Nature (2)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Opt. Express (10)

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express15(2), 660–668 (2007).
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[CrossRef] [PubMed]

Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-μm radius,” Opt. Express16(6), 4309–4315 (2008).
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S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Phase modulation in horizontal metal-insulator-silicon-insulator-metal plasmonic waveguides,” Opt. Express21(7), 8320–8330 (2013).
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S. Zhu, G. Q. Lo, and D. L. Kwong, “Toward athermal plasmonic ring resonators based on Cu-TiO2-Si hybrid plasmonic waveguide,” in Optical Fiber Communication Conf. (OFC 2013) (California USA, 2013), art. OW3F.1.

Supplementary Material (1)

» Media 1: MPG (5017 KB)     

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Figures (12)

Fig. 1
Fig. 1

(a) Top view, and (b) cross-sectional view of the proposed Si plasmonic resonator modulator, the bus waveguide is a conventional single-mode Si channel waveguide and the resonator is a Cu-TiO2-Si hybrid plasmonic donut with two electrodes located at the Cu cap and center-donut, respectively. The structural parameters are also indicated.

Fig. 2
Fig. 2

(a) Electric intensity distribution of the fundamental TM mode at 1550 nm in the curved Cu-TiO2-Si HPW with structural parameters as listed in Table 1; (b) The real part (neff) and imaginary part (keff) of the effective modal index of two curved HPWs as a function of temperature, the TiO2 thicknesses of these two HPWs are 10 and 50 nm, respectively.

Fig. 3
Fig. 3

The dneff/dT value of curved Cu-TiO2-Si HPW as a function of the TiO2 thickness for (a) HPWs with H = 220 nm and WP of 100, 200, and 300 nm respectively, and (b) HPWs with WP = 200 nm and H of 340, 280, 220, and 160 nm respectively. The other structural parameters are as listed in Table 1. The athermal point is defined when dneff/dT = 0.

Fig. 4
Fig. 4

(a) Two-dimensional electron distribution of Cu-TiO2-Si MOS capacitor under 5-V bias. Free electrons are accumulated near the TiO2/Si interface. (b) Electron concentration contour near the TiO2/Si interface, different color represents different concentration. (c) One-dimensional electron distribution along y-axis of Cu-TiO2-Si capacitor as shown schematically in the inset under different biases. The depletion width Wdep and the accumulation layer thickness tAcL are also indicated.

Fig. 5
Fig. 5

(a) The transient response of the electron concentration in the 1-nm-thick AcL of the Cu-TiO2-Si MOS capacitor at the gate voltage variation between 0 and 8 V. Rise and fall time are defined as 10% to 90% time period. The solid curve is for a MOS capacitor with n+-contact just below the electrode as shown in Fig. 4(a) and the dash curve is for a MOS capacitor with the n+-contact extended to the Si rib.

Fig. 6
Fig. 6

(a) The real part (nSi) and imaginary part (kSi) of Si refractive index as a function of free electron concentration in the range of 1 × 1020−10 × 1020 cm−3, calculated based on the Drude model. (b) Modification of the calculated effective modal index of the curved Cu-TiO2-Si HPWs as a function of NAcL in the 1-nm AcL (compared with that in the depletion state).

Fig. 7
Fig. 7

(a) The electric field (|Ey|) distribution of the fundamental TM mode in the curved Cu-TiO2-Si HPW, (2) |Ey| distribution along y-axis at x = 0, as shown by the dash line in Fig. 7(a) in the cases of NAcL = 1 × 1020 cm−3 and 8 × 1020 cm−3, respectively, and (c) Optical intensity ratio in the 1-nm-thick AcL as a function of NAcL for HPWs with WP of 100, 200, and 300 nm, respectively.

Fig. 8
Fig. 8

Transmission spectra of the plasmonic donut modulator at depletion, flat-band, and accumulation states with NAcL ranging from 1 × 1020 cm−3 to 8 × 1020 cm−3, calculated based on Eq. (5). (a) At under-coupling with |t| = 0.8 and (b) At over-coupling with |t| = 0.5.

Fig. 9
Fig. 9

(a) Transmission spectra of the plasmonic modulator under accumulation with NAcL of 1 × 1020 cm−3 and 6 × 1020 cm−3, obtained from FDTD simulation; (b) Media 1 the optical power density in the modulator with 1 × 1020 cm−3 NAcL at λ = 1546 nm, and (c) The optical power distribution in the modulator with NAcL = 6 × 1020 cm−3 at λ = 1546 nm. The output power is modulated from ~-10 dB to ~-2 dB at this wavelength.

Fig. 10
Fig. 10

(a) The effective modal index versus radius of curved Cu-TiO2-Si plasmonic waveguides with different WPs (compared with that of the corresponding straight plasmonic waveguide, namely R = ∞), (b) the thermo-optic coefficient of the real part of effective modal index dneff/dT versus radius.

Fig. 11
Fig. 11

(a) The real part of effective modal index for curved Cu-TiO2-Si HPWs versus width difference between the TiO2/Cu cap and the beneath Si core, ΔWP, as shown schematically in the inset, compared to that with the infinite wide TiO2/Cu cap, namely ΔWP = ∞, (b) The imaginary part of effective modal index versus ΔWP.

Fig. 12
Fig. 12

(a) The real part of effective modal index for curved Cu-TiO2-Si plasmonic waveguides versus the deviation of central line of the TiO2/Cu cap from the beneath Si core, ΔWP’, as shown schematically in the inset, compared to that without the deviation, namely ΔWP’ = 0, (b) The imaginary part of effective modal index versus ΔWP’.

Tables (2)

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Table 1 The initial parameter setting of the plasmonic EO modulator

Tables Icon

Table 2 Optical parameters of Si, SiO2, TiO2, and Cu at 1550-nm and RT

Equations (5)

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N AcL = ε 0 ε d e t ox t AcL (V V FB )= ε 0 ε d e t AcL E d .
E s = 1 2 C dep V dep 2 + 1 2 C accu V accu 2 .
Δn=[ 8.8× 10 22 Δ N e +8.5× 10 18 ( Δ N h ) 0.8 ], Δα=8.5× 10 18 Δ N e +6× 10 18 Δ N h .
ε(ω)= ( n Si + k Si i ) 2 = ε Δ N D e 2 /( ε 0 m * ) ω 2 ( 1+i/(ωτ) ) .
T(λ)= α 2 + t 2 2αtcosθ 1+ α 2 t 2 2αtcosθ .

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