Abstract

Design, fabrication, and characterization of an asymmetric metal-semiconductor-metal photodetector, based on internal photoemission effect and integrated into a silicon-on-insulator waveguide, are reported. For this photodetector, a responsivity of 4.5 mA/W has been measured at 1550 nm, making it suitable for power monitoring applications. Because the absorbing metal is deposited strictly around the vertical output facet of the waveguide, a very small contact area of about 3 µm2 is obtained and a transit-time-limited bandwidth of about 1 GHz is demonstrated. Taking advantage of this small area and electrode asymmetry, a significant reduction in the dark current (2.2 nA at −21 V) is achieved. Interestingly, applying reverse voltage, the photodetector is able to tune its cut-off wavelength, extending its range of application into the MID infrared regime.

© 2013 Optical Society of America

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  4. S. Zhu, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications,” Appl. Phys. Lett. 92(8), 081103 (2008).
    [Crossref]
  5. S. Zhu, G. Q. Lo, and D. L. Kwong, “Low-cost and high-speed SOI waveguide-based silicide Schottky-barrier MSM photodetectors for broadband optical communications,” IEEE Photon. Technol. Lett. 20(16), 1396–1398 (2008).
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  6. I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Waveguide based compact silicon Schottky photodetector with enhanced responsivity in the telecom spectral band,” Opt. Express 20(27), 28594–28602 (2012).
    [Crossref] [PubMed]
  7. P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23(44), 444011 (2012).
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  13. S. Averine, O. Bondarenko, and R. Sachot, “High-speed limitations of the metal-semiconductor-metal photodiode structures with submicron gap between the interdigitated contacts,” Solid-State Electron. 46(12), 2045–2051 (2002).
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  14. J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
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    [Crossref]
  28. V. Raghunathan, R. Shori, O. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” J. Phys. Status Solidi 203(5), R38–R40 (2006).
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    [Crossref] [PubMed]
  31. M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
    [Crossref]
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    [Crossref]

2013 (2)

A. Akbari, A. Olivieri, and P. Berini, “Subbandgap Asymmetric Surface Plasmon Waveguide Schottky Detectors on Silicon,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4600209 (2013).
[Crossref]

S. Rao, G. Coppola, M. A. Gioffrè, and F. G. Della Corte, “Hydrogenated amorphous silicon multi-SOI waveguide modulator with low voltage-length product,” Opt. Laser Technol. 45, 204–208 (2013).
[Crossref]

2012 (6)

S. Rao, C. D'Addio, and F. G. Della Corte, “All-optical modulation in a CMOS-compatible amorphous silicon-based device,” J. European Opt. Soc. 7, 12023 (2012).
[Crossref]

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Critically coupled silicon Fabry-Perot photodetectors based on the internal photoemission effect at 1550 nm,” Opt. Express 20(11), 12599–12609 (2012).
[Crossref] [PubMed]

S. Zhu, H. S. Chu, G. Q. Lo, P. Bai, and D. L. Kwong, “Waveguide-integrated near-infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction,” Appl. Phys. Lett. 100(6), 061109 (2012).
[Crossref]

M. Casalino, “Near-Infrared All-Silicon Photodetectors,” Int. J. Opt. Appl. 2, 1–16 (2012).
[Crossref]

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Waveguide based compact silicon Schottky photodetector with enhanced responsivity in the telecom spectral band,” Opt. Express 20(27), 28594–28602 (2012).
[Crossref] [PubMed]

P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23(44), 444011 (2012).
[Crossref] [PubMed]

2011 (2)

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Locally oxidized silicon surface-plasmon Schottky detector for telecom regime,” Nano Lett. 11(6), 2219–2224 (2011).
[Crossref] [PubMed]

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

2010 (4)

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Near-Infrared Sub-Bandgap All-Silicon Photodetectors:State of the Art and Perspectives,” Sensors (Basel) 10(12), 10571–10600 (2010).
[Crossref] [PubMed]

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

C. Scales and P. Berini, “Thin-film Schottky barrier Photodetector Models,” IEEE J. Quantum Electron. 46(5), 633–643 (2010).
[Crossref]

2008 (2)

S. Zhu, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications,” Appl. Phys. Lett. 92(8), 081103 (2008).
[Crossref]

S. Zhu, G. Q. Lo, and D. L. Kwong, “Low-cost and high-speed SOI waveguide-based silicide Schottky-barrier MSM photodetectors for broadband optical communications,” IEEE Photon. Technol. Lett. 20(16), 1396–1398 (2008).
[Crossref]

2007 (1)

2006 (4)

M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
[Crossref]

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A. 8(10), 840–848 (2006).
[Crossref]

V. Raghunathan, R. Shori, O. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” J. Phys. Status Solidi 203(5), R38–R40 (2006).
[Crossref]

A. K. Okyay, C. O. Chui, and K. C. Saraswat, “Leakage suppression by asymmetric area electrodes in metal-semiconductor-metal photodetectors,” Appl. Phys. Lett. 88(6), 063506 (2006).
[Crossref]

2002 (2)

S. Averine, O. Bondarenko, and R. Sachot, “High-speed limitations of the metal-semiconductor-metal photodiode structures with submicron gap between the interdigitated contacts,” Solid-State Electron. 46(12), 2045–2051 (2002).
[Crossref]

B. Aslan and R. Turan, “On the internal photoemission spectrum of PtSi/p-Si infrared detectors,” Infrared Phys. Technol. 43(2), 85–90 (2002).
[Crossref]

2001 (1)

J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
[Crossref]

1996 (1)

W. A. Wohlmuth, M. Arafa, A. Mahajan, P. Fay, and I. Adesida, “InGaAs metal-semiconductor-metal photodetectors with engineered Schottky barrier heights,” Appl. Phys. Lett. 69(23), 3578–3580 (1996).
[Crossref]

1995 (1)

M. Y. Liu and S. Y. Chou, “Internal emission metal‐semiconductor‐metal photodetectors on Si and GaAs for 1.3 μm detection,” Appl. Phys. Lett. 66(20), 2673–2675 (1995).
[Crossref]

1991 (1)

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[Crossref]

1988 (1)

B. Tsaur, M. M. Weeks, R. Trubiano, P. W. Pellegrini, and T. R. Yew, “IrSi Schottky-Barrier Infrared Detectors with 10 pm Cutoff Wavelength,” IEEE Electron Device Lett. 9(12), 650–653 (1988).
[Crossref]

1971 (1)

S. M. Sze, D. J. Coleman, and A. Loya, “Current transport in metal-semiconductor-metal (MSM) structures,” Solid-State Electron. 14(12), 1209–1218 (1971).
[Crossref]

1931 (1)

R. H. Fowler, “The analysis of photoelectric sensitivity curves for clean metals at various temperatures,” Phys. Rev. 38(1), 45–56 (1931).
[Crossref]

Adesida, I.

W. A. Wohlmuth, M. Arafa, A. Mahajan, P. Fay, and I. Adesida, “InGaAs metal-semiconductor-metal photodetectors with engineered Schottky barrier heights,” Appl. Phys. Lett. 69(23), 3578–3580 (1996).
[Crossref]

Akbari, A.

A. Akbari, A. Olivieri, and P. Berini, “Subbandgap Asymmetric Surface Plasmon Waveguide Schottky Detectors on Silicon,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4600209 (2013).
[Crossref]

Arafa, M.

W. A. Wohlmuth, M. Arafa, A. Mahajan, P. Fay, and I. Adesida, “InGaAs metal-semiconductor-metal photodetectors with engineered Schottky barrier heights,” Appl. Phys. Lett. 69(23), 3578–3580 (1996).
[Crossref]

Aslan, B.

B. Aslan and R. Turan, “On the internal photoemission spectrum of PtSi/p-Si infrared detectors,” Infrared Phys. Technol. 43(2), 85–90 (2002).
[Crossref]

Averine, S.

S. Averine, O. Bondarenko, and R. Sachot, “High-speed limitations of the metal-semiconductor-metal photodiode structures with submicron gap between the interdigitated contacts,” Solid-State Electron. 46(12), 2045–2051 (2002).
[Crossref]

Bai, P.

S. Zhu, H. S. Chu, G. Q. Lo, P. Bai, and D. L. Kwong, “Waveguide-integrated near-infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction,” Appl. Phys. Lett. 100(6), 061109 (2012).
[Crossref]

Berini, P.

A. Akbari, A. Olivieri, and P. Berini, “Subbandgap Asymmetric Surface Plasmon Waveguide Schottky Detectors on Silicon,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4600209 (2013).
[Crossref]

P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23(44), 444011 (2012).
[Crossref] [PubMed]

C. Scales and P. Berini, “Thin-film Schottky barrier Photodetector Models,” IEEE J. Quantum Electron. 46(5), 633–643 (2010).
[Crossref]

Bondarenko, O.

S. Averine, O. Bondarenko, and R. Sachot, “High-speed limitations of the metal-semiconductor-metal photodiode structures with submicron gap between the interdigitated contacts,” Solid-State Electron. 46(12), 2045–2051 (2002).
[Crossref]

Borlaug, D.

Buchwald, W. R.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A. 8(10), 840–848 (2006).
[Crossref]

Casalino, M.

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Critically coupled silicon Fabry-Perot photodetectors based on the internal photoemission effect at 1550 nm,” Opt. Express 20(11), 12599–12609 (2012).
[Crossref] [PubMed]

M. Casalino, “Near-Infrared All-Silicon Photodetectors,” Int. J. Opt. Appl. 2, 1–16 (2012).
[Crossref]

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Near-Infrared Sub-Bandgap All-Silicon Photodetectors:State of the Art and Perspectives,” Sensors (Basel) 10(12), 10571–10600 (2010).
[Crossref] [PubMed]

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
[Crossref]

Chen, C.

P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23(44), 444011 (2012).
[Crossref] [PubMed]

Chen, Y.

J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
[Crossref]

Chiu, Y.

J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
[Crossref]

Chou, S. Y.

M. Y. Liu and S. Y. Chou, “Internal emission metal‐semiconductor‐metal photodetectors on Si and GaAs for 1.3 μm detection,” Appl. Phys. Lett. 66(20), 2673–2675 (1995).
[Crossref]

Chu, H. S.

S. Zhu, H. S. Chu, G. Q. Lo, P. Bai, and D. L. Kwong, “Waveguide-integrated near-infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction,” Appl. Phys. Lett. 100(6), 061109 (2012).
[Crossref]

Chui, C. O.

A. K. Okyay, C. O. Chui, and K. C. Saraswat, “Leakage suppression by asymmetric area electrodes in metal-semiconductor-metal photodetectors,” Appl. Phys. Lett. 88(6), 063506 (2006).
[Crossref]

Coleman, D. J.

S. M. Sze, D. J. Coleman, and A. Loya, “Current transport in metal-semiconductor-metal (MSM) structures,” Solid-State Electron. 14(12), 1209–1218 (1971).
[Crossref]

Coppola, G.

S. Rao, G. Coppola, M. A. Gioffrè, and F. G. Della Corte, “Hydrogenated amorphous silicon multi-SOI waveguide modulator with low voltage-length product,” Opt. Laser Technol. 45, 204–208 (2013).
[Crossref]

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Critically coupled silicon Fabry-Perot photodetectors based on the internal photoemission effect at 1550 nm,” Opt. Express 20(11), 12599–12609 (2012).
[Crossref] [PubMed]

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Near-Infrared Sub-Bandgap All-Silicon Photodetectors:State of the Art and Perspectives,” Sensors (Basel) 10(12), 10571–10600 (2010).
[Crossref] [PubMed]

D'Addio, C.

S. Rao, C. D'Addio, and F. G. Della Corte, “All-optical modulation in a CMOS-compatible amorphous silicon-based device,” J. European Opt. Soc. 7, 12023 (2012).
[Crossref]

Della Corte, F.

M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
[Crossref]

Della Corte, F. G.

S. Rao, G. Coppola, M. A. Gioffrè, and F. G. Della Corte, “Hydrogenated amorphous silicon multi-SOI waveguide modulator with low voltage-length product,” Opt. Laser Technol. 45, 204–208 (2013).
[Crossref]

S. Rao, C. D'Addio, and F. G. Della Corte, “All-optical modulation in a CMOS-compatible amorphous silicon-based device,” J. European Opt. Soc. 7, 12023 (2012).
[Crossref]

Desiatov, B.

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Waveguide based compact silicon Schottky photodetector with enhanced responsivity in the telecom spectral band,” Opt. Express 20(27), 28594–28602 (2012).
[Crossref] [PubMed]

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Locally oxidized silicon surface-plasmon Schottky detector for telecom regime,” Nano Lett. 11(6), 2219–2224 (2011).
[Crossref] [PubMed]

Emelett, S. J.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A. 8(10), 840–848 (2006).
[Crossref]

Fay, P.

W. A. Wohlmuth, M. Arafa, A. Mahajan, P. Fay, and I. Adesida, “InGaAs metal-semiconductor-metal photodetectors with engineered Schottky barrier heights,” Appl. Phys. Lett. 69(23), 3578–3580 (1996).
[Crossref]

Fowler, R. H.

R. H. Fowler, “The analysis of photoelectric sensitivity curves for clean metals at various temperatures,” Phys. Rev. 38(1), 45–56 (1931).
[Crossref]

Gan, K.

J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
[Crossref]

Gioffrè, M.

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

Gioffrè, M. A.

S. Rao, G. Coppola, M. A. Gioffrè, and F. G. Della Corte, “Hydrogenated amorphous silicon multi-SOI waveguide modulator with low voltage-length product,” Opt. Laser Technol. 45, 204–208 (2013).
[Crossref]

Goykhman, I.

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Waveguide based compact silicon Schottky photodetector with enhanced responsivity in the telecom spectral band,” Opt. Express 20(27), 28594–28602 (2012).
[Crossref] [PubMed]

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Locally oxidized silicon surface-plasmon Schottky detector for telecom regime,” Nano Lett. 11(6), 2219–2224 (2011).
[Crossref] [PubMed]

Halas, N. J.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Iodice, M.

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Critically coupled silicon Fabry-Perot photodetectors based on the internal photoemission effect at 1550 nm,” Opt. Express 20(11), 12599–12609 (2012).
[Crossref] [PubMed]

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Near-Infrared Sub-Bandgap All-Silicon Photodetectors:State of the Art and Perspectives,” Sensors (Basel) 10(12), 10571–10600 (2010).
[Crossref] [PubMed]

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

Jalali, B.

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express 15(22), 14355–14362 (2007).
[Crossref] [PubMed]

V. Raghunathan, R. Shori, O. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” J. Phys. Status Solidi 203(5), R38–R40 (2006).
[Crossref]

Khurgin, J.

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Waveguide based compact silicon Schottky photodetector with enhanced responsivity in the telecom spectral band,” Opt. Express 20(27), 28594–28602 (2012).
[Crossref] [PubMed]

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Locally oxidized silicon surface-plasmon Schottky detector for telecom regime,” Nano Lett. 11(6), 2219–2224 (2011).
[Crossref] [PubMed]

Knight, M. W.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Kwong, D. L.

S. Zhu, H. S. Chu, G. Q. Lo, P. Bai, and D. L. Kwong, “Waveguide-integrated near-infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction,” Appl. Phys. Lett. 100(6), 061109 (2012).
[Crossref]

S. Zhu, G. Q. Lo, and D. L. Kwong, “Low-cost and high-speed SOI waveguide-based silicide Schottky-barrier MSM photodetectors for broadband optical communications,” IEEE Photon. Technol. Lett. 20(16), 1396–1398 (2008).
[Crossref]

S. Zhu, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications,” Appl. Phys. Lett. 92(8), 081103 (2008).
[Crossref]

Levy, U.

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Waveguide based compact silicon Schottky photodetector with enhanced responsivity in the telecom spectral band,” Opt. Express 20(27), 28594–28602 (2012).
[Crossref] [PubMed]

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Locally oxidized silicon surface-plasmon Schottky detector for telecom regime,” Nano Lett. 11(6), 2219–2224 (2011).
[Crossref] [PubMed]

Liu, M. Y.

M. Y. Liu and S. Y. Chou, “Internal emission metal‐semiconductor‐metal photodetectors on Si and GaAs for 1.3 μm detection,” Appl. Phys. Lett. 66(20), 2673–2675 (1995).
[Crossref]

Lo, G. Q.

S. Zhu, H. S. Chu, G. Q. Lo, P. Bai, and D. L. Kwong, “Waveguide-integrated near-infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction,” Appl. Phys. Lett. 100(6), 061109 (2012).
[Crossref]

S. Zhu, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications,” Appl. Phys. Lett. 92(8), 081103 (2008).
[Crossref]

S. Zhu, G. Q. Lo, and D. L. Kwong, “Low-cost and high-speed SOI waveguide-based silicide Schottky-barrier MSM photodetectors for broadband optical communications,” IEEE Photon. Technol. Lett. 20(16), 1396–1398 (2008).
[Crossref]

Loya, A.

S. M. Sze, D. J. Coleman, and A. Loya, “Current transport in metal-semiconductor-metal (MSM) structures,” Solid-State Electron. 14(12), 1209–1218 (1971).
[Crossref]

Mahajan, A.

W. A. Wohlmuth, M. Arafa, A. Mahajan, P. Fay, and I. Adesida, “InGaAs metal-semiconductor-metal photodetectors with engineered Schottky barrier heights,” Appl. Phys. Lett. 69(23), 3578–3580 (1996).
[Crossref]

Moretti, L.

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
[Crossref]

Nordlander, P.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Okyay, A. K.

A. K. Okyay, C. O. Chui, and K. C. Saraswat, “Leakage suppression by asymmetric area electrodes in metal-semiconductor-metal photodetectors,” Appl. Phys. Lett. 88(6), 063506 (2006).
[Crossref]

Olivieri, A.

A. Akbari, A. Olivieri, and P. Berini, “Subbandgap Asymmetric Surface Plasmon Waveguide Schottky Detectors on Silicon,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4600209 (2013).
[Crossref]

P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23(44), 444011 (2012).
[Crossref] [PubMed]

Pellegrini, P. W.

B. Tsaur, M. M. Weeks, R. Trubiano, P. W. Pellegrini, and T. R. Yew, “IrSi Schottky-Barrier Infrared Detectors with 10 pm Cutoff Wavelength,” IEEE Electron Device Lett. 9(12), 650–653 (1988).
[Crossref]

Petermann, K.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[Crossref]

Raghunathan, V.

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express 15(22), 14355–14362 (2007).
[Crossref] [PubMed]

V. Raghunathan, R. Shori, O. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” J. Phys. Status Solidi 203(5), R38–R40 (2006).
[Crossref]

Rao, S.

S. Rao, G. Coppola, M. A. Gioffrè, and F. G. Della Corte, “Hydrogenated amorphous silicon multi-SOI waveguide modulator with low voltage-length product,” Opt. Laser Technol. 45, 204–208 (2013).
[Crossref]

S. Rao, C. D'Addio, and F. G. Della Corte, “All-optical modulation in a CMOS-compatible amorphous silicon-based device,” J. European Opt. Soc. 7, 12023 (2012).
[Crossref]

Rendina, I.

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Critically coupled silicon Fabry-Perot photodetectors based on the internal photoemission effect at 1550 nm,” Opt. Express 20(11), 12599–12609 (2012).
[Crossref] [PubMed]

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Near-Infrared Sub-Bandgap All-Silicon Photodetectors:State of the Art and Perspectives,” Sensors (Basel) 10(12), 10571–10600 (2010).
[Crossref] [PubMed]

M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
[Crossref]

Rice, R. R.

Sachot, R.

S. Averine, O. Bondarenko, and R. Sachot, “High-speed limitations of the metal-semiconductor-metal photodiode structures with submicron gap between the interdigitated contacts,” Solid-State Electron. 46(12), 2045–2051 (2002).
[Crossref]

Saffioti, N.

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

Saraswat, K. C.

A. K. Okyay, C. O. Chui, and K. C. Saraswat, “Leakage suppression by asymmetric area electrodes in metal-semiconductor-metal photodetectors,” Appl. Phys. Lett. 88(6), 063506 (2006).
[Crossref]

Scales, C.

C. Scales and P. Berini, “Thin-film Schottky barrier Photodetector Models,” IEEE J. Quantum Electron. 46(5), 633–643 (2010).
[Crossref]

Schmidtchen, J.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[Crossref]

Shappir, J.

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Waveguide based compact silicon Schottky photodetector with enhanced responsivity in the telecom spectral band,” Opt. Express 20(27), 28594–28602 (2012).
[Crossref] [PubMed]

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Locally oxidized silicon surface-plasmon Schottky detector for telecom regime,” Nano Lett. 11(6), 2219–2224 (2011).
[Crossref] [PubMed]

Shi, J.

J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
[Crossref]

Shori, R.

V. Raghunathan, R. Shori, O. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” J. Phys. Status Solidi 203(5), R38–R40 (2006).
[Crossref]

Sirleto, L.

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Critically coupled silicon Fabry-Perot photodetectors based on the internal photoemission effect at 1550 nm,” Opt. Express 20(11), 12599–12609 (2012).
[Crossref] [PubMed]

M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, “Cavity enhanced internal photoemission effect in silicon photodiode for sub-bandgap detection,” J. Lightwave Technol. 28, 3266–3272 (2010).

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Near-Infrared Sub-Bandgap All-Silicon Photodetectors:State of the Art and Perspectives,” Sensors (Basel) 10(12), 10571–10600 (2010).
[Crossref] [PubMed]

M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
[Crossref]

Sobhani, H.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Soref, R. A.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A. 8(10), 840–848 (2006).
[Crossref]

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[Crossref]

Stafsudd, O.

V. Raghunathan, R. Shori, O. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” J. Phys. Status Solidi 203(5), R38–R40 (2006).
[Crossref]

Sun, C.

J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
[Crossref]

Sze, S. M.

S. M. Sze, D. J. Coleman, and A. Loya, “Current transport in metal-semiconductor-metal (MSM) structures,” Solid-State Electron. 14(12), 1209–1218 (1971).
[Crossref]

Trubiano, R.

B. Tsaur, M. M. Weeks, R. Trubiano, P. W. Pellegrini, and T. R. Yew, “IrSi Schottky-Barrier Infrared Detectors with 10 pm Cutoff Wavelength,” IEEE Electron Device Lett. 9(12), 650–653 (1988).
[Crossref]

Tsaur, B.

B. Tsaur, M. M. Weeks, R. Trubiano, P. W. Pellegrini, and T. R. Yew, “IrSi Schottky-Barrier Infrared Detectors with 10 pm Cutoff Wavelength,” IEEE Electron Device Lett. 9(12), 650–653 (1988).
[Crossref]

Turan, R.

B. Aslan and R. Turan, “On the internal photoemission spectrum of PtSi/p-Si infrared detectors,” Infrared Phys. Technol. 43(2), 85–90 (2002).
[Crossref]

Weeks, M. M.

B. Tsaur, M. M. Weeks, R. Trubiano, P. W. Pellegrini, and T. R. Yew, “IrSi Schottky-Barrier Infrared Detectors with 10 pm Cutoff Wavelength,” IEEE Electron Device Lett. 9(12), 650–653 (1988).
[Crossref]

Wohlmuth, W. A.

W. A. Wohlmuth, M. Arafa, A. Mahajan, P. Fay, and I. Adesida, “InGaAs metal-semiconductor-metal photodetectors with engineered Schottky barrier heights,” Appl. Phys. Lett. 69(23), 3578–3580 (1996).
[Crossref]

Yew, T. R.

B. Tsaur, M. M. Weeks, R. Trubiano, P. W. Pellegrini, and T. R. Yew, “IrSi Schottky-Barrier Infrared Detectors with 10 pm Cutoff Wavelength,” IEEE Electron Device Lett. 9(12), 650–653 (1988).
[Crossref]

Yu, M. B.

S. Zhu, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications,” Appl. Phys. Lett. 92(8), 081103 (2008).
[Crossref]

Zhu, S.

S. Zhu, H. S. Chu, G. Q. Lo, P. Bai, and D. L. Kwong, “Waveguide-integrated near-infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction,” Appl. Phys. Lett. 100(6), 061109 (2012).
[Crossref]

S. Zhu, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications,” Appl. Phys. Lett. 92(8), 081103 (2008).
[Crossref]

S. Zhu, G. Q. Lo, and D. L. Kwong, “Low-cost and high-speed SOI waveguide-based silicide Schottky-barrier MSM photodetectors for broadband optical communications,” IEEE Photon. Technol. Lett. 20(16), 1396–1398 (2008).
[Crossref]

Appl. Phys. Lett. (6)

S. Zhu, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications,” Appl. Phys. Lett. 92(8), 081103 (2008).
[Crossref]

S. Zhu, H. S. Chu, G. Q. Lo, P. Bai, and D. L. Kwong, “Waveguide-integrated near-infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction,” Appl. Phys. Lett. 100(6), 061109 (2012).
[Crossref]

M. Y. Liu and S. Y. Chou, “Internal emission metal‐semiconductor‐metal photodetectors on Si and GaAs for 1.3 μm detection,” Appl. Phys. Lett. 66(20), 2673–2675 (1995).
[Crossref]

W. A. Wohlmuth, M. Arafa, A. Mahajan, P. Fay, and I. Adesida, “InGaAs metal-semiconductor-metal photodetectors with engineered Schottky barrier heights,” Appl. Phys. Lett. 69(23), 3578–3580 (1996).
[Crossref]

A. K. Okyay, C. O. Chui, and K. C. Saraswat, “Leakage suppression by asymmetric area electrodes in metal-semiconductor-metal photodetectors,” Appl. Phys. Lett. 88(6), 063506 (2006).
[Crossref]

M. Casalino, L. Sirleto, M. Iodice, N. Saffioti, M. Gioffrè, I. Rendina, and G. Coppola, “Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide,” Appl. Phys. Lett. 96(24), 241112 (2010).
[Crossref]

IEEE Electron Device Lett. (1)

B. Tsaur, M. M. Weeks, R. Trubiano, P. W. Pellegrini, and T. R. Yew, “IrSi Schottky-Barrier Infrared Detectors with 10 pm Cutoff Wavelength,” IEEE Electron Device Lett. 9(12), 650–653 (1988).
[Crossref]

IEEE J. Quantum Electron. (2)

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[Crossref]

C. Scales and P. Berini, “Thin-film Schottky barrier Photodetector Models,” IEEE J. Quantum Electron. 46(5), 633–643 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Akbari, A. Olivieri, and P. Berini, “Subbandgap Asymmetric Surface Plasmon Waveguide Schottky Detectors on Silicon,” IEEE J. Sel. Top. Quantum Electron. 19(3), 4600209 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (2)

J. Shi, K. Gan, Y. Chiu, Y. Chen, and C. Sun, “Metal-semiconductor-metal traveling-wave photodetectors,” IEEE Photon. Technol. Lett. 13(6), 623–625 (2001).
[Crossref]

S. Zhu, G. Q. Lo, and D. L. Kwong, “Low-cost and high-speed SOI waveguide-based silicide Schottky-barrier MSM photodetectors for broadband optical communications,” IEEE Photon. Technol. Lett. 20(16), 1396–1398 (2008).
[Crossref]

Infrared Phys. Technol. (1)

B. Aslan and R. Turan, “On the internal photoemission spectrum of PtSi/p-Si infrared detectors,” Infrared Phys. Technol. 43(2), 85–90 (2002).
[Crossref]

Int. J. Opt. Appl. (1)

M. Casalino, “Near-Infrared All-Silicon Photodetectors,” Int. J. Opt. Appl. 2, 1–16 (2012).
[Crossref]

J. European Opt. Soc. (1)

S. Rao, C. D'Addio, and F. G. Della Corte, “All-optical modulation in a CMOS-compatible amorphous silicon-based device,” J. European Opt. Soc. 7, 12023 (2012).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

M. Casalino, L. Sirleto, L. Moretti, F. Della Corte, and I. Rendina, “Design of a silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 μm,” J. Opt. A, Pure Appl. Opt. 8(10), 909–913 (2006).
[Crossref]

J. Opt. A. (1)

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A. 8(10), 840–848 (2006).
[Crossref]

J. Phys. Status Solidi (1)

V. Raghunathan, R. Shori, O. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” J. Phys. Status Solidi 203(5), R38–R40 (2006).
[Crossref]

Nano Lett. (1)

I. Goykhman, B. Desiatov, J. Khurgin, J. Shappir, and U. Levy, “Locally oxidized silicon surface-plasmon Schottky detector for telecom regime,” Nano Lett. 11(6), 2219–2224 (2011).
[Crossref] [PubMed]

Nanotechnology (1)

P. Berini, A. Olivieri, and C. Chen, “Thin Au surface plasmon waveguide Schottky detectors on p-Si,” Nanotechnology 23(44), 444011 (2012).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Laser Technol. (1)

S. Rao, G. Coppola, M. A. Gioffrè, and F. G. Della Corte, “Hydrogenated amorphous silicon multi-SOI waveguide modulator with low voltage-length product,” Opt. Laser Technol. 45, 204–208 (2013).
[Crossref]

Phys. Rev. (1)

R. H. Fowler, “The analysis of photoelectric sensitivity curves for clean metals at various temperatures,” Phys. Rev. 38(1), 45–56 (1931).
[Crossref]

Science (1)

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Sensors (Basel) (1)

M. Casalino, G. Coppola, M. Iodice, I. Rendina, and L. Sirleto, “Near-Infrared Sub-Bandgap All-Silicon Photodetectors:State of the Art and Perspectives,” Sensors (Basel) 10(12), 10571–10600 (2010).
[Crossref] [PubMed]

Solid-State Electron. (2)

S. Averine, O. Bondarenko, and R. Sachot, “High-speed limitations of the metal-semiconductor-metal photodiode structures with submicron gap between the interdigitated contacts,” Solid-State Electron. 46(12), 2045–2051 (2002).
[Crossref]

S. M. Sze, D. J. Coleman, and A. Loya, “Current transport in metal-semiconductor-metal (MSM) structures,” Solid-State Electron. 14(12), 1209–1218 (1971).
[Crossref]

Other (2)

Physics of Semiconductor Devices, S. M. Sze, New York: John Wiley & Sons, (1981).

VLSI Technology, S. M. Sze, New York: McGraw-Hill, (1988).

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Figures (8)

Fig. 1
Fig. 1

Corresponding energy band diagram at applied bias greater than VFB: (a) when Al is positively biased with respect to Cu and (b) when Cu is positively biased with respect to Al.

Fig. 2
Fig. 2

Schematic of the proposed photodetector integrated with SOI waveguide.

Fig. 3
Fig. 3

Top view of the fabricated MSM photodetector acquired by optical microscope; the inset details the patterned copper element deposited on the Si/SiO2 edge (natural colors).

Fig. 4
Fig. 4

I-V characteristic of the Cu/p-Si Schottky diode (forward current is obtained biasing Cu positively with respect to Al). The inset gives the rescaled device dark current (biasing Al positively with respect to Cu).

Fig. 5
Fig. 5

Photogenerated current at 1550 nm as a function of the estimated optical power under various reverse voltages ranging from 0−21 V in steps of 1 V.

Fig. 6
Fig. 6

Responsivity vs reverse voltage applied at 1550 nm. The data has been fitted by a curve using equation reported in the inset.

Fig. 7
Fig. 7

Cu/Si Schottky barrier vs the applied reverse bias. The inset plots the device cut-off wavelength vs reverse voltage.

Fig. 8
Fig. 8

Experimental device bandwidth and its curve fitting.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

V FB = q N 2 ε S L 2 ,
ϕ N Cu + ϕ P Cu = E g ,
ϕ N Al + ϕ P Al = E g ,
J dark AlCu = J N Cu + J P Al = A n * T 2 e ( ϕ N Cu Δ ϕ N Cu ) V T + A p * T 2 e ( ϕ P Al Δ ϕ P Al ) V T
J dark CuAl = J N Al + J P Cu = A n * T 2 e ( ϕ N Al Δ ϕ N Al ) V T + A p * T 2 e ( ϕ P Cu Δ ϕ P Cu ) V T
R= I Ph P OPT =C ( E Ph ϕ N Cu (V) ) 2 E Ph 2 ,
ϕ N Cu (V)= ϕ N Cu Δ ϕ N Cu (V).
Δ ϕ N Cu (V)= q 4π ε S L (V V FB ) .
λ cutoff (V)= 1.24 ϕ N Cu (V) .
f 3dB = 2.4 2π τ tr = 0.45 L v sat .

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