Abstract

Barium titanate (BaTiO3 or BTO) is currently one of the most promising ferroelectric materials for enabling Pockels modulation that is compatible with silicon photonic circuits. The relative permittivity of BTO has been characterized in thin films deposited on a silicon-on-insulator (SOI) substrate. High values between 800 and 1600 have been estimated at 20 GHz. Furthermore, no substantial difference has been obtained by using BTO grown by molecular beam epitaxy and sputtering. The obtained permittivity has been used to properly design the RF electrodes for high-speed modulation in hybrid BTO/Si devices. Electrodes have been fabricated and the possibility of achieving modulation bandwidths up to 40 GHz has been demonstrated. The bandwidth is limited by the microwave propagation losses and, in this case, different losses have been measured depending on the BTO growth process.

© 2017 Optical Society of America

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2017 (1)

2016 (4)

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

P. Girouard, Z. Liu, P. Chen, Y. K. Jeong, Y. Tu, S.-T. Ho, and B. W. Wessels, “Enhancement of the pockels effect in photonic crystal modulators through slow light,” Opt. Lett. 41(23), 5531–5534 (2016).
[PubMed]

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

2015 (3)

2014 (2)

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 Films,” IEEE Photonics Technol. Lett. 26, 1344–1347 (2014).

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

2013 (2)

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

P. Rabiei, J. Ma, S. Khan, J. Chiles, and S. Fathpour, “Heterogeneous lithium niobate photonics on silicon substrates,” Opt. Express 21(21), 25573–25581 (2013).
[PubMed]

2010 (1)

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

2008 (1)

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

2005 (1)

2004 (1)

2003 (1)

T. Hamano, D. J. Towner, and B. W. Wessels, “Relative dielectric constant of epitaxial BaTiO3 thin films in the GHz frequency range,” Appl. Phys. Lett. 83, 5274–5276 (2003).

2002 (1)

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002).

1999 (1)

M. D. Janezic and J. a. Jargon, “Complex permittivity determination from propagation constant measurements,” IEEE Microw. Guided Wave Lett. 9, 76–78 (1999).

1997 (2)

L. Sengupta and S. Sengupta, “Novel ferroelectric materials for phased array antennas,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 792–797 (1997).

F. De Flaviis, N. G. Alexopoulos, and O. M. Stafsudd, “Planar microwave integrated phase-shifter design with high purity ferroelectric material,” IEEE Trans. Microw. Theory Tech. 45, 963–969 (1997).

1994 (2)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

T. Hayashi, N. Oji, and H. Maiwa, “Film thickness dependence of dielectric properties of BaTiO3 thin films prepared by sol-gel method,” Jpn. J. Appl. Phys. 33, 5277–5280 (1994).

1991 (2)

H. Chung, W. S. C. Chang, and E. L. Adler, “Modeling and Optimization of Traveling-Wave LiNbO3 Interferometric Modulators,” IEEE J. Quantum Electron. 27, 608–617 (1991).

R. A. McKee, F. J. Walker, J. R. Conner, E. D. Specht, and D. E. Zelmon, “Molecular beam epitaxy growth of epitaxial barium silicide, barium oxide, and barium titanate on silicon,” Appl. Phys. Lett. 59, 782–784 (1991).

1987 (1)

D. Hennings, “Barium titanate based ceramic materials for dielectric use,” Int. J. High Technol. Ceram. 3, 91–111 (1987).

1982 (1)

R. O. D. C. Alferness, “Waveguide Electrooptic Modulators,” IEEE Trans. Microw. Theory Tech. 30, 1121–1137 (1982).

1979 (1)

G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microw. Theory Tech. 27, 987–993 (1979).

1972 (1)

C. A. T. Siciunas and E. Salama, “Characteristics of RF Sputtered Barium Titanate Films on Silicon,” J. Vac. Sci. Technol. 9, 91 (1972).

Abel, S.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Absil, P.

Adler, E. L.

H. Chung, W. S. C. Chang, and E. L. Adler, “Modeling and Optimization of Traveling-Wave LiNbO3 Interferometric Modulators,” IEEE J. Quantum Electron. 27, 608–617 (1991).

Ahn, C. H.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

Alexopoulos, N. G.

F. De Flaviis, N. G. Alexopoulos, and O. M. Stafsudd, “Planar microwave integrated phase-shifter design with high purity ferroelectric material,” IEEE Trans. Microw. Theory Tech. 45, 963–969 (1997).

Alferness, R. O. D. C.

R. O. D. C. Alferness, “Waveguide Electrooptic Modulators,” IEEE Trans. Microw. Theory Tech. 30, 1121–1137 (1982).

Atwater, H. A.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

Bernasconi, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Bhattacharya, K.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

Buchal, C.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002).

Caimi, D.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Castera, P.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

P. Castera, D. Tulli, A. M. Gutierrez, and P. Sanchis, “Influence of BaTiO3 ferroelectric orientation for electro-optic modulation on silicon,” Opt. Express 23(12), 15332–15342 (2015).
[PubMed]

Chang, W. S. C.

H. Chung, W. S. C. Chang, and E. L. Adler, “Modeling and Optimization of Traveling-Wave LiNbO3 Interferometric Modulators,” IEEE J. Quantum Electron. 27, 608–617 (1991).

Chelnokov, A.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Chen, P.

Chiles, J.

Chung, H.

H. Chung, W. S. C. Chang, and E. L. Adler, “Modeling and Optimization of Traveling-Wave LiNbO3 Interferometric Modulators,” IEEE J. Quantum Electron. 27, 608–617 (1991).

Conner, J. R.

R. A. McKee, F. J. Walker, J. R. Conner, E. D. Specht, and D. E. Zelmon, “Molecular beam epitaxy growth of epitaxial barium silicide, barium oxide, and barium titanate on silicon,” Appl. Phys. Lett. 59, 782–784 (1991).

Cueff, S.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

X. Hu, S. Cueff, P. R. Romeo, and R. Orobtchouk, “Modeling the anisotropic electro-optic interaction in hybrid silicon-ferroelectric optical modulator,” Opt. Express 23(2), 1699–1714 (2015).
[PubMed]

Czornomaz, L.

De Flaviis, F.

F. De Flaviis, N. G. Alexopoulos, and O. M. Stafsudd, “Planar microwave integrated phase-shifter design with high purity ferroelectric material,” IEEE Trans. Microw. Theory Tech. 45, 963–969 (1997).

Dicken, M. J.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

Duelli, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Eltes, F.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

Engen, G. F.

G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microw. Theory Tech. 27, 987–993 (1979).

Erni, R.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Fallegger, F.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

Fathpour, S.

Fompeyrine, J.

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Gardes, F. Y.

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

Garrett, M. H.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Girouard, P.

Günter, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Gutierrez, A. M.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

P. Castera, D. Tulli, A. M. Gutierrez, and P. Sanchis, “Influence of BaTiO3 ferroelectric orientation for electro-optic modulation on silicon,” Opt. Express 23(12), 15332–15342 (2015).
[PubMed]

Hamano, T.

P. Tang, D. Towner, T. Hamano, A. Meier, and B. Wessels, “Electrooptic modulation up to 40 GHz in a barium titanate thin film waveguide modulator,” Opt. Express 12(24), 5962–5967 (2004).
[PubMed]

T. Hamano, D. J. Towner, and B. W. Wessels, “Relative dielectric constant of epitaxial BaTiO3 thin films in the GHz frequency range,” Appl. Phys. Lett. 83, 5274–5276 (2003).

Hayashi, T.

T. Hayashi, N. Oji, and H. Maiwa, “Film thickness dependence of dielectric properties of BaTiO3 thin films prepared by sol-gel method,” Jpn. J. Appl. Phys. 33, 5277–5280 (1994).

Heberling, D.

K. Schraml and D. Heberling, “Estimation of the propagation constant in multilayer microwave circuits using a low cost multiline system,” in 2015 Loughborough Antennas and Propagation Conference, LAPC 2015, 1–4 (2015).

Hennings, D.

D. Hennings, “Barium titanate based ceramic materials for dielectric use,” Int. J. High Technol. Ceram. 3, 91–111 (1987).

Ho, S.-T.

Hoer, C. A.

G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microw. Theory Tech. 27, 987–993 (1979).

Hsu, M.-H. M.

Hu, X.

Janezic, M. D.

M. D. Janezic and J. a. Jargon, “Complex permittivity determination from propagation constant measurements,” IEEE Microw. Guided Wave Lett. 9, 76–78 (1999).

Jargon, J. a.

M. D. Janezic and J. a. Jargon, “Complex permittivity determination from propagation constant measurements,” IEEE Microw. Guided Wave Lett. 9, 76–78 (1999).

Jeong, Y. K.

Khan, S.

Kumah, D.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

Lezec, H. J.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

Liu, Z.

Ma, J.

Maiwa, H.

T. Hayashi, N. Oji, and H. Maiwa, “Film thickness dependence of dielectric properties of BaTiO3 thin films prepared by sol-gel method,” Jpn. J. Appl. Phys. 33, 5277–5280 (1994).

Marchiori, C.

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Marinelli, A.

Mashanovich, G.

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

McKee, R. A.

R. A. McKee, F. J. Walker, J. R. Conner, E. D. Specht, and D. E. Zelmon, “Molecular beam epitaxy growth of epitaxial barium silicide, barium oxide, and barium titanate on silicon,” Appl. Phys. Lett. 59, 782–784 (1991).

Meier, A.

Meier, A. L.

Merckling, C.

Ngai, J. H.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

O’Connor, E.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

Offrein, B.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

Offrein, B. J.

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Oji, N.

T. Hayashi, N. Oji, and H. Maiwa, “Film thickness dependence of dielectric properties of BaTiO3 thin films prepared by sol-gel method,” Jpn. J. Appl. Phys. 33, 5277–5280 (1994).

Orobtchouk, R.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

X. Hu, S. Cueff, P. R. Romeo, and R. Orobtchouk, “Modeling the anisotropic electro-optic interaction in hybrid silicon-ferroelectric optical modulator,” Opt. Express 23(2), 1699–1714 (2015).
[PubMed]

Pacifici, D.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

Pantouvaki, M.

Pernice, W. H. P.

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 Films,” IEEE Photonics Technol. Lett. 26, 1344–1347 (2014).

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

Petraru, A.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002).

Rabiei, P.

Reed, G. T.

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

Reiner, J. W.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

Romeo, P. R.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

X. Hu, S. Cueff, P. R. Romeo, and R. Orobtchouk, “Modeling the anisotropic electro-optic interaction in hybrid silicon-ferroelectric optical modulator,” Opt. Express 23(2), 1699–1714 (2015).
[PubMed]

Rossel, C.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Rossell, M. D.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Rytz, D.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Saint-Girons, G.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

Salama, E.

C. A. T. Siciunas and E. Salama, “Characteristics of RF Sputtered Barium Titanate Films on Silicon,” J. Vac. Sci. Technol. 9, 91 (1972).

Sanchis, P.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

P. Castera, D. Tulli, A. M. Gutierrez, and P. Sanchis, “Influence of BaTiO3 ferroelectric orientation for electro-optic modulation on silicon,” Opt. Express 23(12), 15332–15342 (2015).
[PubMed]

Schlesser, R.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Schmid, M.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002).

Schraml, K.

K. Schraml and D. Heberling, “Estimation of the propagation constant in multilayer microwave circuits using a low cost multiline system,” in 2015 Loughborough Antennas and Propagation Conference, LAPC 2015, 1–4 (2015).

Schubert, J.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002).

Sengupta, L.

L. Sengupta and S. Sengupta, “Novel ferroelectric materials for phased array antennas,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 792–797 (1997).

Sengupta, S.

L. Sengupta and S. Sengupta, “Novel ferroelectric materials for phased array antennas,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 792–797 (1997).

Siciunas, C. A. T.

C. A. T. Siciunas and E. Salama, “Characteristics of RF Sputtered Barium Titanate Films on Silicon,” J. Vac. Sci. Technol. 9, 91 (1972).

Sousa, M.

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Specht, E. D.

R. A. McKee, F. J. Walker, J. R. Conner, E. D. Specht, and D. E. Zelmon, “Molecular beam epitaxy growth of epitaxial barium silicide, barium oxide, and barium titanate on silicon,” Appl. Phys. Lett. 59, 782–784 (1991).

Stafsudd, O. M.

F. De Flaviis, N. G. Alexopoulos, and O. M. Stafsudd, “Planar microwave integrated phase-shifter design with high purity ferroelectric material,” IEEE Trans. Microw. Theory Tech. 45, 963–969 (1997).

Stöferle, T.

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, M. Stuckelberger, M. Sousa, B. J. Offrein, and J. Fompeyrine, “A hybrid barium titanate-silicon photonics platform for ultra efficient electro-optic tuning,” J. Lightwave Technol. 34, 1688–1693 (2016).

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Stuckelberger, M.

Sweatlock, L. A.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

Tang, H. X.

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 Films,” IEEE Photonics Technol. Lett. 26, 1344–1347 (2014).

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

Tang, P.

Thomson, D. J.

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

Towner, D.

Towner, D. J.

P. Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, “BaTiO3 thin-film waveguide modulator with a low voltage-length product at near-infrared wavelengths of 0.98 and 1.55 µm,” Opt. Lett. 30(3), 254–256 (2005).
[PubMed]

T. Hamano, D. J. Towner, and B. W. Wessels, “Relative dielectric constant of epitaxial BaTiO3 thin films in the GHz frequency range,” Appl. Phys. Lett. 83, 5274–5276 (2003).

Tu, Y.

Tulli, D.

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

P. Castera, D. Tulli, A. M. Gutierrez, and P. Sanchis, “Influence of BaTiO3 ferroelectric orientation for electro-optic modulation on silicon,” Opt. Express 23(12), 15332–15342 (2015).
[PubMed]

Van Campenhout, J.

Van Thourhout, D.

Walker, F. J.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 Films,” IEEE Photonics Technol. Lett. 26, 1344–1347 (2014).

R. A. McKee, F. J. Walker, J. R. Conner, E. D. Specht, and D. E. Zelmon, “Molecular beam epitaxy growth of epitaxial barium silicide, barium oxide, and barium titanate on silicon,” Appl. Phys. Lett. 59, 782–784 (1991).

Wessels, B.

Wessels, B. W.

Wu, X.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Xiong, C.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 Films,” IEEE Photonics Technol. Lett. 26, 1344–1347 (2014).

Zelmon, D. E.

R. A. McKee, F. J. Walker, J. R. Conner, E. D. Specht, and D. E. Zelmon, “Molecular beam epitaxy growth of epitaxial barium silicide, barium oxide, and barium titanate on silicon,” Appl. Phys. Lett. 59, 782–784 (1991).

Zgonik, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Zhu, Y.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

ACS Photonics (1)

F. Eltes, D. Caimi, F. Fallegger, M. Sousa, E. O’Connor, M. D. Rossell, B. Offrein, J. Fompeyrine, and S. Abel, “Low-Loss BaTiO3-Si Waveguides for Nonlinear Integrated Photonics,” ACS Photonics 3, 1698–1703 (2016).

Appl. Phys. Lett. (3)

T. Hamano, D. J. Towner, and B. W. Wessels, “Relative dielectric constant of epitaxial BaTiO3 thin films in the GHz frequency range,” Appl. Phys. Lett. 83, 5274–5276 (2003).

R. A. McKee, F. J. Walker, J. R. Conner, E. D. Specht, and D. E. Zelmon, “Molecular beam epitaxy growth of epitaxial barium silicide, barium oxide, and barium titanate on silicon,” Appl. Phys. Lett. 59, 782–784 (1991).

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81, 1375–1377 (2002).

IEEE J. Quantum Electron. (1)

H. Chung, W. S. C. Chang, and E. L. Adler, “Modeling and Optimization of Traveling-Wave LiNbO3 Interferometric Modulators,” IEEE J. Quantum Electron. 27, 608–617 (1991).

IEEE Microw. Guided Wave Lett. (1)

M. D. Janezic and J. a. Jargon, “Complex permittivity determination from propagation constant measurements,” IEEE Microw. Guided Wave Lett. 9, 76–78 (1999).

IEEE Photonics Technol. Lett. (2)

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 Films,” IEEE Photonics Technol. Lett. 26, 1344–1347 (2014).

P. Castera, A. M. Gutierrez, D. Tulli, S. Cueff, R. Orobtchouk, P. R. Romeo, G. Saint-Girons, and P. Sanchis, “Electro-Optical Modulation Based on Pockels Effect in BaTiO3 with a Multi-Domain Structure,” IEEE Photonics Technol. Lett. 28, 990–993 (2016).

IEEE Trans. Microw. Theory Tech. (3)

G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microw. Theory Tech. 27, 987–993 (1979).

F. De Flaviis, N. G. Alexopoulos, and O. M. Stafsudd, “Planar microwave integrated phase-shifter design with high purity ferroelectric material,” IEEE Trans. Microw. Theory Tech. 45, 963–969 (1997).

R. O. D. C. Alferness, “Waveguide Electrooptic Modulators,” IEEE Trans. Microw. Theory Tech. 30, 1121–1137 (1982).

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

L. Sengupta and S. Sengupta, “Novel ferroelectric materials for phased array antennas,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 792–797 (1997).

in 2015 Loughborough Antennas and Propagation Conference, LAPC (1)

K. Schraml and D. Heberling, “Estimation of the propagation constant in multilayer microwave circuits using a low cost multiline system,” in 2015 Loughborough Antennas and Propagation Conference, LAPC 2015, 1–4 (2015).

Int. J. High Technol. Ceram. (1)

D. Hennings, “Barium titanate based ceramic materials for dielectric use,” Int. J. High Technol. Ceram. 3, 91–111 (1987).

J. Lightwave Technol. (1)

J. Vac. Sci. Technol. (1)

C. A. T. Siciunas and E. Salama, “Characteristics of RF Sputtered Barium Titanate Films on Silicon,” J. Vac. Sci. Technol. 9, 91 (1972).

Jpn. J. Appl. Phys. (1)

T. Hayashi, N. Oji, and H. Maiwa, “Film thickness dependence of dielectric properties of BaTiO3 thin films prepared by sol-gel method,” Jpn. J. Appl. Phys. 33, 5277–5280 (1994).

Nano Lett. (2)

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[PubMed]

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO3 devices,” Nano Lett. 14(3), 1419–1425 (2014).
[PubMed]

Nat. Commun. (1)

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[PubMed]

Nat. Photonics (1)

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

Opt. Express (4)

Opt. Lett. (2)

Opt. Mater. Express (1)

Phys. Rev. B Condens. Matter (1)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[PubMed]

Other (3)

M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Oxford University Press, 2001).

K. Wu and L. Li, “Numerical calibration and de-embedding techniques for CAD and equivalent circuit models of electromagnetic structures,” Microw. Rev. June, 7–19 (2005).

D. M. Pozar, Microwave engineering (Addison-Wesley Publ. Co., 1993).

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Figures (7)

Fig. 1
Fig. 1

RF coplanar waveguide structure used to characterize the BTO permittivity.

Fig. 2
Fig. 2

Fabricated CPWs with lengths between 1 mm and 3 mm.

Fig. 3
Fig. 3

(a) Schematic of the measurement set-up by using a vector network analyzer (VNA) and photo zoom in the device under test (DUT) area, and (b) measured effective permittivity as a function of the RF frequency for the samples with BTO fabricated by MBE and RF sputtering.

Fig. 4
Fig. 4

(a) Simulated electric field distribution of the quasi-TEM mode at the frequency of 20 GHz. The inset shows with more detail the CPW structure, and (b) simulated effective permittivity of the CPW as a function of the BTO relative permittivity and measured values extracted at 20 GHz from the different delay lines fabricated in the samples with BTO grown by MBE and RF sputtering.

Fig. 5
Fig. 5

(a) Hybrid BTO/Si optical waveguide with coplanar strip-line electrodes and (b) simulated impedance of the CPS electrode and microwave index of the RF mode at 20 GHz as a function of the gap and for an electrodes width of 2 µm, (c) optical mode profile for TE and (d) TM polarizations.

Fig. 6
Fig. 6

Simulated and experimental (a) impedance and (b) microwave propagation losses of the designed CPS electrode as a function of the RF frequency. Only conductor losses are included in the simulations.

Fig. 7
Fig. 7

Simulated electro-optical modulation response for a modulation length of 1.5 mm, TM polarization and taking into account the simulated and measured microwave losses.

Equations (11)

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ε eff = ( γc 2πf ) 2
T= 1 S 21 ( Δ S 11 S 22 1 )
Δ= S 11 S 22 S 12 S 21
T t = T 1 T 2
T d = T 1 T l T 2
T l =( e γΔl 0 0 e γΔl )
( t 11 t 12 t 21 t 22 )= T d T t 1
γ= 1 2Δl ln( t 11 + t 22 ± ( t 11 t 22 ) 2 +4 t 12 t 21 t 11 + t 22 ( t 11 t 22 ) 2 +4 t 12 t 21 )
n m = ε eff
Δf= 2c πL( n m n o )
T EO (f)= e αL 2 sin h 2 ( αL 2 )+ sin 2 ( 2 Δf ) ( αL 2 ) 2 + ( 2 Δf ) 2