Abstract

In this work, GaInAs/InP membrane p-i-n photodiodes integrated with a back-end distributed Bragg reflector were numerically investigated for a backreflection of 30dB. The results showed that a 3-dB bandwidth of 17 GHz and reverse bias of 1 V can be obtained for an absorption section length of 12 μm. The 3-dB bandwidth is approximately twice faster and the absorption length is 1/3 times smaller compared to those of a similar photodiode without the back-end DBR.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  19. Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
    [Crossref]
  20. Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
    [Crossref]
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    [Crossref]
  22. S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
    [Crossref]
  23. K. Nozaki, S. Matsuo, K. Takeda, T. Sato, E. Kuramochi, and M. Notomi, “InGaAs nano-photodetectors based on photonic crystal waveguide including ultracompact buried heterostructure,” Opt. Express 21, 19022–19028 (2013).
    [Crossref]
  24. K. Nozaki, S. Matsuo, T. Fujii, K. Takeda, M. Ono, A. Shakoor, E. Kuramochi, and M. Notomi, “Photonic-crystal nano-photodetector with ultrasmall capacitance for on-chip light-to-voltage conversion without an amplifier,” Optica 3, 483–492 (2016).
    [Crossref]
  25. G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010).
  26. S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
    [Crossref]
  27. J. M. T. Pereira, “Modeling the frequency response of p+InP/n–InGaAs/n+InP photodiodes with an arbitrary electric field profile,” COMPEL 26, 1114–1122 (2007).
    [Crossref]

2018 (1)

Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
[Crossref]

2017 (5)

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

2016 (2)

2015 (4)

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

2013 (1)

2011 (1)

S. Arai, N. Nishiyama, T. Maruyama, and T. Okumura, “GaInAsP/InP membrane lasers for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17, 1381–1389 (2011).
[Crossref]

2010 (1)

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

2009 (2)

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
[Crossref]

2008 (1)

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

2007 (1)

J. M. T. Pereira, “Modeling the frequency response of p+InP/n–InGaAs/n+InP photodiodes with an arbitrary electric field profile,” COMPEL 26, 1114–1122 (2007).
[Crossref]

2006 (1)

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

2003 (1)

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Agarwal, D.

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010).

Albonesi, D. H.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Amemiya, T.

Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Low-bias current 10 Gbit/s direct modulation of GaInAsP/InP membrane DFB laser on silicon,” Opt. Express 24, 18571–18579 (2016).
[Crossref]

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

S. Arai and T. Amemiya, “Semiconductor membrane lasers and photodiode on Si,” in Silicon Photonics, Vol. 99 of Semiconductors and Semimetals (Elsevier, 2018), pp. 71–95.

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

Ang, L. P.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Arai, S.

Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Low-bias current 10 Gbit/s direct modulation of GaInAsP/InP membrane DFB laser on silicon,” Opt. Express 24, 18571–18579 (2016).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

S. Arai, N. Nishiyama, T. Maruyama, and T. Okumura, “GaInAsP/InP membrane lasers for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17, 1381–1389 (2011).
[Crossref]

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

S. Arai and T. Amemiya, “Semiconductor membrane lasers and photodiode on Si,” in Silicon Photonics, Vol. 99 of Semiconductors and Semimetals (Elsevier, 2018), pp. 71–95.

Assefa, S.

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

Atsuji, Y.

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

Berger, R.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Berroth, M.

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
[Crossref]

Bhatnagar, A.

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Canegallo, R.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Chen, G.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Chen, H.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Chen, R.

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Ciccarelli, L.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Clark, S.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Debaes, C.

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Doi, K.

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

Fauchet, P. M.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Fazzi, A.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Friedman, E. G.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Fujii, T.

Fukuda, K.

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Low-bias current 10 Gbit/s direct modulation of GaInAsP/InP membrane DFB laser on silicon,” Opt. Express 24, 18571–18579 (2016).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

Futami, M.

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

Green, W. M. J.

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

Gu, Z.

Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
[Crossref]

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

Guerrieri, R.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Hasegawa, A.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Hattori, T.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Haurylau, M.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Helman, N. C.

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Hiratani, T.

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Low-bias current 10 Gbit/s direct modulation of GaInAsP/InP membrane DFB laser on silicon,” Opt. Express 24, 18571–18579 (2016).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

Inoue, D.

Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Low-bias current 10 Gbit/s direct modulation of GaInAsP/InP membrane DFB laser on silicon,” Opt. Express 24, 18571–18579 (2016).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

Irie, N.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Jung, E.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Kada, M.

M. Kada, “Development of functionally innovative 3D-integrated circuit (dream chip) technology/high-density 3D-integration technology for multifunctional devices,” in IEEE International Conference on 3D System Integration (IEEE, 2009), pp. 1–6.

Kaschel, M.

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
[Crossref]

Kasper, E.

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
[Crossref]

Kasuga, K.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Keeler, G. A.

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Klinger, S.

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
[Crossref]

Knecht, J.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Kohama, Y.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Komatsu, S.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Kuramochi, E.

Kuroda, T.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Lee, J.

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

Magagni, L.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Mansoorian, B.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Maruyama, T.

S. Arai, N. Nishiyama, T. Maruyama, and T. Okumura, “GaInAsP/InP membrane lasers for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17, 1381–1389 (2011).
[Crossref]

Matsuo, S.

Messier, A.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Miller, D. A. B.

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Nakamura, N.

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

Natali, F.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Nelson, N. A.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Newcomb, K.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Niitsu, K.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Nishiyama, N.

Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Low-bias current 10 Gbit/s direct modulation of GaInAsP/InP membrane DFB laser on silicon,” Opt. Express 24, 18571–18579 (2016).
[Crossref]

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

S. Arai, N. Nishiyama, T. Maruyama, and T. Okumura, “GaInAsP/InP membrane lasers for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17, 1381–1389 (2011).
[Crossref]

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

Nonomura, I.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Notomi, M.

Nozaki, K.

Oehme, M.

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
[Crossref]

Okumura, T.

S. Arai, N. Nishiyama, T. Maruyama, and T. Okumura, “GaInAsP/InP membrane lasers for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17, 1381–1389 (2011).
[Crossref]

Ono, M.

Osada, K.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Pereira, J. M. T.

J. M. T. Pereira, “Modeling the frequency response of p+InP/n–InGaAs/n+InP photodiodes with an arbitrary electric field profile,” COMPEL 26, 1114–1122 (2007).
[Crossref]

Rathman, D.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Rolandi, P.

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

Rylyakov, A. V.

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

Saen, M.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Sato, T.

Schow, C. L.

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

Shakoor, A.

Shaver, D.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Shimazaki, Y.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Shindo, T.

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

Slattery, R.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Soares, A.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Stevenson, C.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Sugimori, Y.

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

Suntharalingam, V.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Takeda, K.

Thienpont, H.

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

Tomiyasu, T.

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Low-bias current 10 Gbit/s direct modulation of GaInAsP/InP membrane DFB laser on silicon,” Opt. Express 24, 18571–18579 (2016).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “High-modulation efficiency operation of GaInAsP/InP membrane distributed feedback laser on Si substrate,” Opt. Express 23, 29024–29031 (2015).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

Uryu, T.

Z. Gu, T. Uryu, N. Nakamura, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “On-chip membrane-based GaInAs/InP waveguide-type p-i-n photodiode fabricated on silicon substrate,” Appl. Opt. 56, 7841–7848 (2017).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

Vlasov, Y. A.

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

Warner, K.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Xia, F.

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

Young, D.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

Zhang, J.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Express (3)

Z. Gu, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “20-Gbps operation of membrane-based GaInAs/InP waveguide-type p-i-n photodiode bonded on Si substrate,” Appl. Phys. Express 11, 022102 (2018).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, Y. Atsuji, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “Room-temperature continuous-wave operation of membrane distributed-reflector laser,” Appl. Phys. Express 8, 112701 (2015).
[Crossref]

T. Tomiyasu, T. Hiratani, D. Inoue, N. Nakamura, K. Fukuda, T. Uryu, T. Amemiya, N. Nishiyama, and S. Arai, “High-differential quantum efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” Appl. Phys. Express 10, 062702(2017).
[Crossref]

COMPEL (1)

J. M. T. Pereira, “Modeling the frequency response of p+InP/n–InGaAs/n+InP photodiodes with an arbitrary electric field profile,” COMPEL 26, 1114–1122 (2007).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (8)

C. Debaes, A. Bhatnagar, D. Agarwal, R. Chen, G. A. Keeler, N. C. Helman, H. Thienpont, and D. A. B. Miller, “Receiver-less optical clock injection for clock distribution networks,” IEEE J. Sel. Top. Quantum Electron. 9, 400–409 (2003).
[Crossref]

S. Assefa, F. Xia, W. M. J. Green, C. L. Schow, A. V. Rylyakov, and Y. A. Vlasov, “CMOS-integrated optical receivers for on-chip interconnects,” IEEE J. Sel. Top. Quantum Electron. 16, 1376–1385(2010).
[Crossref]

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, T. Amemiya, N. Nishiyama, and S. Arai, “High-efficiency operation of membrane distributed-reflector lasers on silicon substrate,” IEEE J. Sel. Top. Quantum Electron. 23, 3700108 (2017).
[Crossref]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12, 1699–1705 (2006).
[Crossref]

S. Arai, N. Nishiyama, T. Maruyama, and T. Okumura, “GaInAsP/InP membrane lasers for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17, 1381–1389 (2011).
[Crossref]

T. Hiratani, T. Shindo, K. Doi, Y. Atsuji, D. Inoue, T. Amemiya, N. Nishiyama, and S. Arai, “Energy cost analysis of membrane distributed-reflector lasers for on-chip optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 21, 1503410 (2015).
[Crossref]

D. Inoue, T. Hiratani, Y. Atsuji, T. Tomiyasu, T. Amemiya, N. Nishiyama, and S. Arai, “Monolithic integration of membrane-based butt-jointed built-in DFB lasers and p-i-n photodiodes bonded on Si substrate,” IEEE J. Sel. Top. Quantum Electron. 21, 1502907 (2015).
[Crossref]

D. Inoue, T. Hiratani, K. Fukuda, T. Tomiyasu, Z. Gu, T. Amemiya, N. Nishiyama, and S. Arai, “Integrated optical link on Si substrate using membrane distributed-feedback laser and p-i-n photodiode,” IEEE J. Sel. Top. Quantum Electron. 23, 3700208 (2017).
[Crossref]

IEEE J. Solid-State Circuits (1)

A. Fazzi, R. Canegallo, L. Ciccarelli, L. Magagni, F. Natali, E. Jung, P. Rolandi, and R. Guerrieri, “3-D capacitive interconnections with mono- and bi-directional capabilities,” IEEE J. Solid-State Circuits 43, 275–284 (2008).
[Crossref]

IEEE Photonics Technol. Lett. (2)

T. Hiratani, D. Inoue, T. Tomiyasu, K. Fukuda, N. Nakamura, T. Amemiya, N. Nishiyama, and S. Arai, “High efficiency operation of GaInAsP/InP membrane distributed-reflector laser on Si,” IEEE Photonics Technol. Lett. 29, 1832–1835 (2017).
[Crossref]

S. Klinger, M. Berroth, M. Kaschel, M. Oehme, and E. Kasper, “Ge-on-Si p-i-n photodiodes with a 3-dB bandwidth of 49  GHz,” IEEE Photonics Technol. Lett. 21, 920–922 (2009).
[Crossref]

Opt. Express (3)

Optica (1)

Proc. IEEE (1)

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

Other (6)

K. Niitsu, Y. Shimazaki, Y. Sugimori, Y. Kohama, K. Kasuga, I. Nonomura, M. Saen, S. Komatsu, K. Osada, N. Irie, T. Hattori, A. Hasegawa, and T. Kuroda, “An inductive-coupling link for 3D integration of a 90  nm CMOS processor and a 65  nm CMOS SRAM,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 480–481.

M. Kada, “Development of functionally innovative 3D-integrated circuit (dream chip) technology/high-density 3D-integration technology for multifunctional devices,” in IEEE International Conference on 3D System Integration (IEEE, 2009), pp. 1–6.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver, “A 4-side tileable back illuminated 3D-integrated Mpixel CMOS image sensor,” in IEEE International Solid-State Circuits Conference—Digest of Technical Papers (IEEE, 2009), pp. 38–39.

S. Arai and T. Amemiya, “Semiconductor membrane lasers and photodiode on Si,” in Silicon Photonics, Vol. 99 of Semiconductors and Semimetals (Elsevier, 2018), pp. 71–95.

D. Inoue, J. Lee, T. Shindo, M. Futami, K. Doi, T. Amemiya, N. Nishiyama, and S. Arai, “Butt-joint built-in (BJB) structure for membrane photonic integration,” in International Conference on Indium Phosphide and Related Materials (IPRM) (2013), pp. 1–2.

G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010).

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Figures (13)

Fig. 1.
Fig. 1. Conceptual diagram of an MPIC bonded on Si-based CMOS LSI circuit.
Fig. 2.
Fig. 2. (a) Simplified schematic of the membrane interconnection system. (b) Equivalent circuit of the receiverless PD.
Fig. 3.
Fig. 3. (a) Relationship between R L and C j used to determine the required bandwidth. (b) Received power requirement of the membrane PD for a data rate of 10 Gbps (indicated by the red line) and required output power of the laser (indicated by the black line) as a function of the load resistance, R L .
Fig. 4.
Fig. 4. (a) Schematic of the membrane GaInAs p - i - n PD with the back-end DBR. Conceptual diagrams of the membrane GaInAs p - i - n PD with the back-end DBR in the (b) active region and (c) passive region.
Fig. 5.
Fig. 5. Numerical model of the DBR grating structure model used for the TMM simulations.
Fig. 6.
Fig. 6. (a) Reflectivity and (b) transmittivity as a function of the absorption section length and DBR section length for the membrane PD with DBR in the GaInAs absorption region (Type A device).
Fig. 7.
Fig. 7. (a) Reflectivity and (b) transmittivity as a function of the absorption section length and DBR section length for the membrane PD with the back-end DBR in the GaInAsP passive section (Type B device).
Fig. 8.
Fig. 8. Optimum device length as a function of the absorption section length and DBR section length for the (a) Type A and (b) Type B devices.
Fig. 9.
Fig. 9. Required device length as a function of the stripe width.
Fig. 10.
Fig. 10. Junction capacitance as a function of the stripe width for two types of membrane PDs.
Fig. 11.
Fig. 11. Numerical model used for the 3-dB bandwidth estimation.
Fig. 12.
Fig. 12. Theoretical curves of the 3-dB bandwidth for different I pd values: (a) 5 μA, (b) 20 μA, and (c) 80 μA. Red line, PD with the back-end DBR in the GaInAsP passive region (Type B device); blue line, PD with the back-end DBR in the GaInAs absorption region (Type A device); dashed line, PD without the back-end DBR.
Fig. 13.
Fig. 13. Theoretical curves of the 3-dB bandwidth and output voltage V out as a function of the photocurrent I pd for different stripe widths. (a) PD with the back-end DBR in the GaInAs absorption region (Type A device); (b) PD with the back-end DBR in the GaInAsP passive region (Type B device); (c) PD without the back-end DBR.

Equations (19)

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

BER = 1 2 erfc ( SNR 2 2 ) ,
SNR = 4 Q 2 ,
Q = I 1 I 0 σ 1 + σ 0 ,
SNR thermal = R L R esp 2 P in 2 4 k B T emp f 4 Q 2 ,
SNR shot = R esp P in 2 q f Q 2 ,
V out = P in × R esp × R L .
[ E r ( L ) E l ( L ) ] = M ma · ( M sm · M s · M ms · M m ) N · M L [ E r ( 0 ) E l ( 0 ) ] = [ M 11 M 12 M 21 M 22 ] [ E r ( 0 ) E l ( 0 ) ] ,
M m ( s ) = [ e j β m ( s ) L m ( s ) 0 0 e j β m ( s ) L m ( s ) ] ,
M ms ( sm ) = 1 2 n m ( s ) n s ( m ) [ n s ( m ) + n m ( s ) n s ( m ) n m ( s ) n s ( m ) n m ( s ) n s ( m ) + n m ( s ) ] ,
M L = [ e j β abs L abs 0 0 e j β abs L abs ] ,
M ma = 1 1 R [ 1 R R 1 ] { R = ( n s 1 n s + 1 ) 2 } .
R = | E r ( 0 ) E l ( 0 ) | 2 = | M 21 | 2 | M 22 | 2 ,
T = | E r ( L ) E r ( 0 ) | 2 = | M 11 M 22 M 12 M 21 | 2 | M 22 | 2 = 1 | M 22 | 2 .
L = L abs + L DBR .
L = L abs .
1 f 3 dB 2 = 1 f RC 2 + 1 f TT 2 ,
f RC = 1 2 π ( R L + R s ) C j ,
f TT = 2 π υ sat · tanh ( μ h · V i W s · 1 υ sat ) W s ,
V i = V b ( R L + R S ) · I pd .

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