Abstract

In this paper we report on an electro-refractive modulator based on single or double-layer graphene on top of silicon waveguides. The graphene layers are biased to the transparency condition in order to achieve phase modulation with negligible amplitude modulation. By means of a detailed study of both the electrical and optical properties of graphene and silicon, as well as through optimization of the geometrical parameters, we show that the proposed devices may theoretically outperform existing modulators both in terms of VπL and of insertion losses. The overall figures of merit of the proposed devices are as low as 8.5 and 2dB∙V for the single and double layer cases, respectively.

© 2015 Optical Society of America

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2014 (4)

Y.-C. Chang, C.-H. Liu, C.-H. Liu, Z. Zhong, and T. B. Norris, “Extracting the complex optical conductivity of mono- and bilayer Graphene by ellipsometry,” Appl. Phys. Lett. 104(26), 261909 (2014).
[Crossref]

W. S. Leong, H. Gong, and J. T. L. Thong, “Low-contact-resistance Graphene devices with Nickel-etched-Graphene contacts,” ACS Nano 8(1), 994–1001 (2014).
[Crossref] [PubMed]

F. A. Chaves, D. Jimenez, A. W. Cummings, and S. Roche, “Physical model of the contact resistivity of metal-Graphene junctions,” J. Appl. Phys. 115(16), 164513 (2014).
[Crossref]

M. Midrio, P. Galli, M. Romagnoli, L. C. Kimerling, and J. Michel, “Graphene-based optical phase modulation of waveguide transverse electric modes,” Photon. Res. 2(3), A34–A40 (2014).
[Crossref]

2013 (3)

2012 (6)

P. Dong, L. Chen, and Y.-K. Chen, “High-speed low-voltage single-drive push-pull Silicon Mach-Zehnder modulators,” Opt. Express 20(6), 6163–6169 (2012).
[Crossref] [PubMed]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012).
[Crossref] [PubMed]

S. J. Koester and M. Li, “High-speed waveguide-coupled Graphene-on-Graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
[Crossref]

M. Liu, X. Yin, and X. Zhang, “Double-layer Graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

S. M. Song, J. K. Park, O. J. Sul, and B. J. Cho, “Determination of work function of Graphene under a metal electrode and its role in contact resistance,” Nano Lett. 12(8), 3887–3892 (2012).
[Crossref] [PubMed]

R. Yan, Q. Zhang, W. Li, I. Calizo, T. Shen, C. A. Richter, A. R. Hight-Walker, X. Liang, A. Seabaugh, D. Jena, H. G. Xing, D. J. Gundlach, and N. V. Nguyen, “Determination of Graphene work function and Graphene-insulator-semiconductor band alignment by internal photoemission spectroscopy,” Appl. Phys. Lett. 101(2), 022105 (2012).
[Crossref]

2011 (4)

M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-carrier electrorefraction and electroabsorption modulation predictions for Silicon over 1-14 micron infrared wavelength range,” IEEE Photon. J. 3(6), 1171–1180 (2011).
[Crossref]

S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two-dimensional Graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

K. Kim, J.-Y. Choi, T. Kim, S.-H. Cho, and H.-J. Chung, “A role for Graphene in Silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A Graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

2010 (6)

A. Venugopal, L. Colombo, and E. M. Vogel, “Contact resistance in few and multilayer Graphene devices,” Appl. Phys. Lett. 96(1), 013512 (2010).
[Crossref]

K. Nagashio, T. Nishimura, K. Kita, and A. Toriumi, “Contact resistivity and current flow path at metal/Graphene contact,” Appl. Phys. Lett. 97(14), 143514 (2010).
[Crossref]

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in Graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref] [PubMed]

A. Pachoud, M. Jaiswal, P. K. Ang, K. P. Loh, and B. Ozyilman, “Graphene transport at high carrier densities using polymer electrolyte gate,” EPL 92(2), 27001 (2010).
[Crossref]

W. Zhu, D. Neumayer, V. Perebeinos, and P. Avouris, “Silicon Nitride gate dielectrics and band gap engineering in Graphene layers,” Nano Lett. 10(9), 3572–3576 (2010).
[Crossref] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nature 4, 611–622 (2010).

2008 (5)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in Graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial Graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

L. A. Falkovski, “Optical properties of Graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

G. W. Hanson, “Dyadic Green’s function and guided surface waves for a surface conductivity model of Graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of Graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[Crossref]

2007 (4)

Y. W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007).
[Crossref] [PubMed]

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of Graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
[Crossref]

J. Yan, Y. Zhang, P. Kim, and A. Pinczuk, “Electric field effect tuning of electron-phonon coupling in Graphene,” Phys. Rev. Lett. 98(16), 166802 (2007).
[Crossref] [PubMed]

L. A. Falkovsky and S. S. Pershoguba, “Optical far infrared properties of a Graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

2006 (1)

Y. Hunag, J. Wu, and K. C. Hwang, “Thickness of Graphene and single-wall Carbon nanotubes,” Phys. Rev. B 74(24), 245413 (2006).
[Crossref]

2000 (1)

J. Kolodzey, E. A. Chowdhury, T. N. Adam, G. Qui, I. Rau, J. O. Olowolafe, J. S. Suehle, and Y. Chen, “Electrical conduction and dielectric breakdown in Aluminum oxide insulators on Silicon,” IEEE Trans. Electron. Dev. 47(1), 121–128 (2000).
[Crossref]

1987 (1)

R. Soref and B. Bennet, “Electro-optical effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Adam, S.

S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two-dimensional Graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

Y. W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007).
[Crossref] [PubMed]

Adam, T. N.

J. Kolodzey, E. A. Chowdhury, T. N. Adam, G. Qui, I. Rau, J. O. Olowolafe, J. S. Suehle, and Y. Chen, “Electrical conduction and dielectric breakdown in Aluminum oxide insulators on Silicon,” IEEE Trans. Electron. Dev. 47(1), 121–128 (2000).
[Crossref]

Ang, P. K.

A. Pachoud, M. Jaiswal, P. K. Ang, K. P. Loh, and B. Ozyilman, “Graphene transport at high carrier densities using polymer electrolyte gate,” EPL 92(2), 27001 (2010).
[Crossref]

Avouris, P.

W. Zhu, D. Neumayer, V. Perebeinos, and P. Avouris, “Silicon Nitride gate dielectrics and band gap engineering in Graphene layers,” Nano Lett. 10(9), 3572–3576 (2010).
[Crossref] [PubMed]

Baehr-Jones, T.

Bennet, B.

R. Soref and B. Bennet, “Electro-optical effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Bolotin, K.

Y. W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007).
[Crossref] [PubMed]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nature 4, 611–622 (2010).

Calizo, I.

R. Yan, Q. Zhang, W. Li, I. Calizo, T. Shen, C. A. Richter, A. R. Hight-Walker, X. Liang, A. Seabaugh, D. Jena, H. G. Xing, D. J. Gundlach, and N. V. Nguyen, “Determination of Graphene work function and Graphene-insulator-semiconductor band alignment by internal photoemission spectroscopy,” Appl. Phys. Lett. 101(2), 022105 (2012).
[Crossref]

Chandrashekhar, M.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial Graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

Chang, Y.-C.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, Z. Zhong, and T. B. Norris, “Extracting the complex optical conductivity of mono- and bilayer Graphene by ellipsometry,” Appl. Phys. Lett. 104(26), 261909 (2014).
[Crossref]

Chaves, F. A.

F. A. Chaves, D. Jimenez, A. W. Cummings, and S. Roche, “Physical model of the contact resistivity of metal-Graphene junctions,” J. Appl. Phys. 115(16), 164513 (2014).
[Crossref]

Chee, E. K. S.

Chen, L.

Chen, Y.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial Graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

J. Kolodzey, E. A. Chowdhury, T. N. Adam, G. Qui, I. Rau, J. O. Olowolafe, J. S. Suehle, and Y. Chen, “Electrical conduction and dielectric breakdown in Aluminum oxide insulators on Silicon,” IEEE Trans. Electron. Dev. 47(1), 121–128 (2000).
[Crossref]

Chen, Y.-K.

Cho, B. J.

S. M. Song, J. K. Park, O. J. Sul, and B. J. Cho, “Determination of work function of Graphene under a metal electrode and its role in contact resistance,” Nano Lett. 12(8), 3887–3892 (2012).
[Crossref] [PubMed]

Cho, S.-H.

K. Kim, J.-Y. Choi, T. Kim, S.-H. Cho, and H.-J. Chung, “A role for Graphene in Silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011).
[Crossref] [PubMed]

Choi, J.-Y.

K. Kim, J.-Y. Choi, T. Kim, S.-H. Cho, and H.-J. Chung, “A role for Graphene in Silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011).
[Crossref] [PubMed]

Chowdhury, E. A.

J. Kolodzey, E. A. Chowdhury, T. N. Adam, G. Qui, I. Rau, J. O. Olowolafe, J. S. Suehle, and Y. Chen, “Electrical conduction and dielectric breakdown in Aluminum oxide insulators on Silicon,” IEEE Trans. Electron. Dev. 47(1), 121–128 (2000).
[Crossref]

Chu, T.

Chung, H.-J.

K. Kim, J.-Y. Choi, T. Kim, S.-H. Cho, and H.-J. Chung, “A role for Graphene in Silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011).
[Crossref] [PubMed]

Colombo, L.

A. Venugopal, L. Colombo, and E. M. Vogel, “Contact resistance in few and multilayer Graphene devices,” Appl. Phys. Lett. 96(1), 013512 (2010).
[Crossref]

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in Graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Cummings, A. W.

F. A. Chaves, D. Jimenez, A. W. Cummings, and S. Roche, “Physical model of the contact resistivity of metal-Graphene junctions,” J. Appl. Phys. 115(16), 164513 (2014).
[Crossref]

Das Sarma, S.

S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two-dimensional Graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011).
[Crossref]

Y. W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. Das Sarma, H. L. Stormer, and P. Kim, “Measurement of scattering rate and minimum conductivity in Graphene,” Phys. Rev. Lett. 99(24), 246803 (2007).
[Crossref] [PubMed]

Dawlaty, J. M.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial Graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

Ding, R.

Dong, P.

Efetov, D. K.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in Graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref] [PubMed]

Falkovski, L. A.

L. A. Falkovski, “Optical properties of Graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

Falkovsky, L. A.

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of Graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far infrared properties of a Graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nature 4, 611–622 (2010).

Galli, P.

Geim, A. K.

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Figures (9)

Fig. 1
Fig. 1 Schematic cross-section views of the single (a) and double (b) graphene layer modulators.
Fig. 2
Fig. 2 Graphene optical surface conductivity normalized to the universal conductivity σ0 ≈6.09 Ω−1 (a) and dielectric constant (b) versus Fermi level at T = 300K for an optical field with free-space wavelength λ = 1550nm (ηω = 0.8eV). In both the figures, the real part of the displayed quantities is on the left y-axis, and the imaginary part on the right y-axis.
Fig. 3
Fig. 3 Hole distribution at the middle of the Silicon-Si3N4 interface at different gate voltage applied to the graphene-Si3N4-Silicon capacitor. Inset: simulated device cross-section.
Fig. 4
Fig. 4 Equivalent electric circuits for the single (panel a, upper row) and double (panel b, lower row) graphene layer modulators. RcG, RsG, RsSi, CoxSiN, CpSiO2 are the graphene contact resistance, graphene series resistance, Si series resistance, Silicon Nitride capacitance and Silicon Oxide parasitic capacitance, respectively.
Fig. 5
Fig. 5 Small signal parameters per unit length at low frequency (1kHz) versus applied voltage. a) Capacitance: red curve overall capacitance including lateral parasitic capacitors, blue curve minimum capacitance due to the only Silicon Nitride gate. b) Series resistance: red curve overall resistance with graphene sheet resistance RG = 500Ω/□ and RcG = 1000 Ωμm, blue curve Si series resistance.
Fig. 6
Fig. 6 a) TE fundamental mode optical losses of the single layer configuration of Fig. 1(a) at λ = 1550nm and T = 300K versus applied voltage at different graphene relaxation time: 12fs, 100fs, infinite. In the inset the single contributions due to Si and graphene. b) TE fundamental effective index change of the single layer configuration of Fig. 1(a) at λ = 1550nm and T = 300K versus applied voltage and single contributions due to Si and graphene (relaxation time does not affect the effective index).
Fig. 7
Fig. 7 Single layer modulator phase shift versus applied voltage when biased at V-VDIRAC = −6,5V, λ = 1550nm and T = 300K. Blue curve: Si free carrier phase shift. Black curve: graphene phase shift. Red curve: modulator overall phase shift.
Fig. 8
Fig. 8 a) TE fundamental mode optical losses of the double layer configuration of Fig. 1(b) at λ = 1550nm and T = 300K versus applied voltage at different graphene relaxation time: 12fs, 100fs, infinite. b) Red curve: TE fundamental effective index variation of the double layer configuration of Fig. 1(b) at λ = 1550nm and T = 300K versus applied voltage. Blue curve: Single layer graphene contribution to phase modulation as extracted from Fig. 6(b).
Fig. 9
Fig. 9 Double layer modulator phase shift versus applied voltage when biased at V-VDIRAC = −7,8V, λ = 1550nm and T = 300K

Tables (1)

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Table 1 Comparison of state of the art Si and proposed graphene on Si modulators

Equations (6)

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σ(ω)= σ 0 2 ( tanh( ω+2μ 4 k B T )+tanh( ω2μ 4 k B T ) ) i σ 0 2π log[ (ω+2μ) 2 (ω2μ) 2 + (2 k B T) 2 ] +i 4 σ 0 π μ ω+iγ
ε G (ω)=1+ iσ(ω) ω ε 0 h G
μ( n s )=sgn( n s ) v F π| n s |
| V V Dirac |= q n s C ox + | μ | q = q s C ox μ 2 π ( v F ) 2 + | μ | q
Δn(1550nm)=5.4 10 22 Δ N 1.011 1.53 10 18 Δ P 0.838 Δα(1550nm)=8.88 10 21 Δ N 1.167 +5.84 10 20 Δ P 1.109
E 0.5eV = q n s ε ox ε 0 3.6 10 7 ε ox [ V cm ]

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