Abstract

We present a vertical Ge quantum well (QW) asymmetric Fabry-Perot modulator design and integration scheme without distributed Bragg reflector (DBR). The field-dependent excitonic absorption and the modulator performance are calculated, showing the wide (20-nm-thick) well design gives a large absorption reduction for the normally-off modulator operation. For a 47 QW modulator, the theoretical contrast ratio exceeds 40 dB at 1 V and increases to 52.3 dB at 4 V bias with a 12.3-dB insertion loss and over-9-nm optical bandwidth (contrast > 3dB). This robust DBR-free design can enable high-contrast-ratio Ge QW modulators.

© 2010 OSA

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  1. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: the quantum-confined Stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984).
    [CrossRef]
  2. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric filed dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
    [CrossRef]
  3. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
    [CrossRef] [PubMed]
  4. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si for optical modulator,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1503–1513 (2006).
    [CrossRef]
  5. S. Tsujino, H. Sigg, G. Mussler, D. Chrastina, and H. von Känel, “Photocurrent and transmission spectroscopy of direct-gap interband transitions in Ge/SiGe quantum wells,” Appl. Phys. Lett. 89(26), 262119 (2006).
    [CrossRef]
  6. R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1082–1089 (2008).
    [CrossRef]
  7. M. Virgilio and G. Grosso, “Quantum-confined Stark effect in Ge/SiGe quantum wells: a tight-binding description,” Phys. Rev. B 77(16), 165315 (2008).
    [CrossRef]
  8. Y.-H. Kuo and Y.-S. Li, “Direct-gap exciton and optical absorption in the Ge/SiGe quantum well system,” Appl. Phys. Lett. 94(12), 121101 (2009).
    [CrossRef]
  9. Y.-H. Kuo and Y.-S. Li, “Variational calculation for the direct-gap exciton in the Ge quantum well systems,” Phys. Rev. B 79(24), 245328 (2009).
    [CrossRef]
  10. M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
    [CrossRef]
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    [CrossRef]
  12. J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
    [CrossRef] [PubMed]
  13. J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44(1), 49 (2008).
    [CrossRef]
  14. Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16(1), 85–92 (2010).
    [CrossRef]
  15. E. H. Edwards, R. M. Audet, S. A. Claussen, R. K. Schaevitz, E. Tasurek, S. Ren, O. I. Dosunmu, M. S. Unlu, and D. A. B. Miller, “Si-Ge surface-normal asymmetric Fabry-Perot electroabsorption modulator,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuA5.
  16. O. Fidaner, A. K. Okyay, J. E. Roth, R. K. Schaevitz, Y.-H. Kuo, K. C. Saraswat, J. S. Harris, and D. A. B. Miller, “Ge-SiGe quantum-well waveguide photodetectors on silicon for the near-infrared,” IEEE Photon. Technol. Lett. 19(20), 1631–1633 (2007).
    [CrossRef]
  17. M. Whitehead and G. Parry, “High-contrast reflection modulation at normal incidence in asymmetric multiple quantum well Fabry-Perot structure,” Electron. Lett. 25(9), 566–568 (1989).
    [CrossRef]
  18. Y.-H. Kuo, Y.-A. Huang, and T.-L. Chen, “A vertical germanium thermooptic modulator for optical interconnects,” IEEE Photon. Technol. Lett. 21(4), 245–247 (2009).
    [CrossRef]
  19. J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
    [CrossRef]
  20. M. Cardona and F. H. Pollak, “Energy-band structure of germanium and silicon: the k.p method,” Phys. Rev. 142(2), 530–543 (1966).
    [CrossRef]
  21. S. Galdin, P. Dollfus, V. Aubry-Fortuna, P. Hesto, and H. J. Osten, “Band offset predictions for strained group IV alloys: Si1-x-yGexCy on Si(001) and Si1-xGex on Si1-zGez (001),” Semicond. Sci. Technol. 15(6), 565–572 (2000).
    [CrossRef]
  22. S.-L. Chuang, Physics of Optoelectronic Devices (Wiley, 1994), Chap. 13.
  23. Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82(13), 2044–2046 (2003).
    [CrossRef]
  24. P. Lefebvre, P. Christol, and H. Mathieu, “Unified formulation of excitonic absorption spectra of semiconductor quantum wells, superlattices, and quantum wires,” Phys. Rev. B Condens. Matter 48(23), 17308–17315 (1993).
    [CrossRef] [PubMed]
  25. X.-F. He, “Excitons in anisotropic solids: The model of fractional-dimensional space,” Phys. Rev. B Condens. Matter 43(3), 2063–2069 (1991).
    [CrossRef] [PubMed]
  26. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  27. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965).
    [CrossRef]
  28. S. Adachi, “Model dielectric constants of Si and Ge,” Phys. Rev. B Condens. Matter 38(18), 12966–12976 (1988).
    [CrossRef] [PubMed]
  29. R. Braunstein, A. R. Moore, and F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109(3), 695–710 (1958).
    [CrossRef]

2010 (2)

P. Moontragoon, N. Vukmirovic, and P. Harrison, “SnGe asymmetric quantum well electroabsorption modulators for long-wavelength silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 16(1), 100–105 (2010).
[CrossRef]

Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16(1), 85–92 (2010).
[CrossRef]

2009 (4)

Y.-H. Kuo, Y.-A. Huang, and T.-L. Chen, “A vertical germanium thermooptic modulator for optical interconnects,” IEEE Photon. Technol. Lett. 21(4), 245–247 (2009).
[CrossRef]

Y.-H. Kuo and Y.-S. Li, “Direct-gap exciton and optical absorption in the Ge/SiGe quantum well system,” Appl. Phys. Lett. 94(12), 121101 (2009).
[CrossRef]

Y.-H. Kuo and Y.-S. Li, “Variational calculation for the direct-gap exciton in the Ge quantum well systems,” Phys. Rev. B 79(24), 245328 (2009).
[CrossRef]

M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
[CrossRef]

2008 (3)

R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1082–1089 (2008).
[CrossRef]

M. Virgilio and G. Grosso, “Quantum-confined Stark effect in Ge/SiGe quantum wells: a tight-binding description,” Phys. Rev. B 77(16), 165315 (2008).
[CrossRef]

J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44(1), 49 (2008).
[CrossRef]

2007 (2)

J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
[CrossRef] [PubMed]

O. Fidaner, A. K. Okyay, J. E. Roth, R. K. Schaevitz, Y.-H. Kuo, K. C. Saraswat, J. S. Harris, and D. A. B. Miller, “Ge-SiGe quantum-well waveguide photodetectors on silicon for the near-infrared,” IEEE Photon. Technol. Lett. 19(20), 1631–1633 (2007).
[CrossRef]

2006 (3)

J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
[CrossRef]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si for optical modulator,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1503–1513 (2006).
[CrossRef]

S. Tsujino, H. Sigg, G. Mussler, D. Chrastina, and H. von Känel, “Photocurrent and transmission spectroscopy of direct-gap interband transitions in Ge/SiGe quantum wells,” Appl. Phys. Lett. 89(26), 262119 (2006).
[CrossRef]

2005 (1)

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[CrossRef] [PubMed]

2003 (1)

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82(13), 2044–2046 (2003).
[CrossRef]

2000 (1)

S. Galdin, P. Dollfus, V. Aubry-Fortuna, P. Hesto, and H. J. Osten, “Band offset predictions for strained group IV alloys: Si1-x-yGexCy on Si(001) and Si1-xGex on Si1-zGez (001),” Semicond. Sci. Technol. 15(6), 565–572 (2000).
[CrossRef]

1993 (1)

P. Lefebvre, P. Christol, and H. Mathieu, “Unified formulation of excitonic absorption spectra of semiconductor quantum wells, superlattices, and quantum wires,” Phys. Rev. B Condens. Matter 48(23), 17308–17315 (1993).
[CrossRef] [PubMed]

1991 (1)

X.-F. He, “Excitons in anisotropic solids: The model of fractional-dimensional space,” Phys. Rev. B Condens. Matter 43(3), 2063–2069 (1991).
[CrossRef] [PubMed]

1989 (1)

M. Whitehead and G. Parry, “High-contrast reflection modulation at normal incidence in asymmetric multiple quantum well Fabry-Perot structure,” Electron. Lett. 25(9), 566–568 (1989).
[CrossRef]

1988 (1)

S. Adachi, “Model dielectric constants of Si and Ge,” Phys. Rev. B Condens. Matter 38(18), 12966–12976 (1988).
[CrossRef] [PubMed]

1985 (1)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric filed dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[CrossRef]

1984 (1)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: the quantum-confined Stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1966 (1)

M. Cardona and F. H. Pollak, “Energy-band structure of germanium and silicon: the k.p method,” Phys. Rev. 142(2), 530–543 (1966).
[CrossRef]

1965 (1)

1958 (1)

R. Braunstein, A. R. Moore, and F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109(3), 695–710 (1958).
[CrossRef]

Adachi, S.

S. Adachi, “Model dielectric constants of Si and Ge,” Phys. Rev. B Condens. Matter 38(18), 12966–12976 (1988).
[CrossRef] [PubMed]

Aubry-Fortuna, V.

S. Galdin, P. Dollfus, V. Aubry-Fortuna, P. Hesto, and H. J. Osten, “Band offset predictions for strained group IV alloys: Si1-x-yGexCy on Si(001) and Si1-xGex on Si1-zGez (001),” Semicond. Sci. Technol. 15(6), 565–572 (2000).
[CrossRef]

Aull, B. F.

J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
[CrossRef]

Bonfanti, M.

M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
[CrossRef]

Braunstein, R.

R. Braunstein, A. R. Moore, and F. Herman, “Intrinsic optical absorption in germanium-silicon alloys,” Phys. Rev. 109(3), 695–710 (1958).
[CrossRef]

Burns, J. A.

J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
[CrossRef]

Burrus, C. A.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric filed dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: the quantum-confined Stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984).
[CrossRef]

Cannon, D. D.

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82(13), 2044–2046 (2003).
[CrossRef]

Cardona, M.

M. Cardona and F. H. Pollak, “Energy-band structure of germanium and silicon: the k.p method,” Phys. Rev. 142(2), 530–543 (1966).
[CrossRef]

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric filed dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: the quantum-confined Stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984).
[CrossRef]

Chen, C. K.

J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
[CrossRef]

Chen, C.-L.

J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
[CrossRef]

Chen, T.-L.

Y.-H. Kuo, Y.-A. Huang, and T.-L. Chen, “A vertical germanium thermooptic modulator for optical interconnects,” IEEE Photon. Technol. Lett. 21(4), 245–247 (2009).
[CrossRef]

Chrastina, D.

M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
[CrossRef]

S. Tsujino, H. Sigg, G. Mussler, D. Chrastina, and H. von Känel, “Photocurrent and transmission spectroscopy of direct-gap interband transitions in Ge/SiGe quantum wells,” Appl. Phys. Lett. 89(26), 262119 (2006).
[CrossRef]

Christol, P.

P. Lefebvre, P. Christol, and H. Mathieu, “Unified formulation of excitonic absorption spectra of semiconductor quantum wells, superlattices, and quantum wires,” Phys. Rev. B Condens. Matter 48(23), 17308–17315 (1993).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Damen, T. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric filed dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: the quantum-confined Stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984).
[CrossRef]

Dollfus, P.

S. Galdin, P. Dollfus, V. Aubry-Fortuna, P. Hesto, and H. J. Osten, “Band offset predictions for strained group IV alloys: Si1-x-yGexCy on Si(001) and Si1-xGex on Si1-zGez (001),” Semicond. Sci. Technol. 15(6), 565–572 (2000).
[CrossRef]

Edwards, E. H.

J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44(1), 49 (2008).
[CrossRef]

Eyatt, P. W.

J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
[CrossRef]

Fidaner, O.

J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44(1), 49 (2008).
[CrossRef]

R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1082–1089 (2008).
[CrossRef]

O. Fidaner, A. K. Okyay, J. E. Roth, R. K. Schaevitz, Y.-H. Kuo, K. C. Saraswat, J. S. Harris, and D. A. B. Miller, “Ge-SiGe quantum-well waveguide photodetectors on silicon for the near-infrared,” IEEE Photon. Technol. Lett. 19(20), 1631–1633 (2007).
[CrossRef]

J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
[CrossRef] [PubMed]

Fiorentino, M.

Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16(1), 85–92 (2010).
[CrossRef]

Galdin, S.

S. Galdin, P. Dollfus, V. Aubry-Fortuna, P. Hesto, and H. J. Osten, “Band offset predictions for strained group IV alloys: Si1-x-yGexCy on Si(001) and Si1-xGex on Si1-zGez (001),” Semicond. Sci. Technol. 15(6), 565–572 (2000).
[CrossRef]

Ge, Y.

Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16(1), 85–92 (2010).
[CrossRef]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si for optical modulator,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1503–1513 (2006).
[CrossRef]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[CrossRef] [PubMed]

Gossard, A. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric filed dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well structures: the quantum-confined Stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984).
[CrossRef]

Grilli, E.

M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
[CrossRef]

Grosso, G.

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J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
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Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
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J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
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Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
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Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
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Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82(13), 2044–2046 (2003).
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Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82(13), 2044–2046 (2003).
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R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1082–1089 (2008).
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J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44(1), 49 (2008).
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J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
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Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
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M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
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Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16(1), 85–92 (2010).
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O. Fidaner, A. K. Okyay, J. E. Roth, R. K. Schaevitz, Y.-H. Kuo, K. C. Saraswat, J. S. Harris, and D. A. B. Miller, “Ge-SiGe quantum-well waveguide photodetectors on silicon for the near-infrared,” IEEE Photon. Technol. Lett. 19(20), 1631–1633 (2007).
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S. Galdin, P. Dollfus, V. Aubry-Fortuna, P. Hesto, and H. J. Osten, “Band offset predictions for strained group IV alloys: Si1-x-yGexCy on Si(001) and Si1-xGex on Si1-zGez (001),” Semicond. Sci. Technol. 15(6), 565–572 (2000).
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R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1082–1089 (2008).
[CrossRef]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si for optical modulator,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1503–1513 (2006).
[CrossRef]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
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Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16(1), 85–92 (2010).
[CrossRef]

Roth, J. E.

J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44(1), 49 (2008).
[CrossRef]

R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1082–1089 (2008).
[CrossRef]

O. Fidaner, A. K. Okyay, J. E. Roth, R. K. Schaevitz, Y.-H. Kuo, K. C. Saraswat, J. S. Harris, and D. A. B. Miller, “Ge-SiGe quantum-well waveguide photodetectors on silicon for the near-infrared,” IEEE Photon. Technol. Lett. 19(20), 1631–1633 (2007).
[CrossRef]

J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
[CrossRef] [PubMed]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si for optical modulator,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1503–1513 (2006).
[CrossRef]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[CrossRef] [PubMed]

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O. Fidaner, A. K. Okyay, J. E. Roth, R. K. Schaevitz, Y.-H. Kuo, K. C. Saraswat, J. S. Harris, and D. A. B. Miller, “Ge-SiGe quantum-well waveguide photodetectors on silicon for the near-infrared,” IEEE Photon. Technol. Lett. 19(20), 1631–1633 (2007).
[CrossRef]

Schaevitz, R. K.

R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, and D. A. B. Miller, “Material properties of Si-Ge/Ge quantum wells,” IEEE J. Sel. Top. Quantum Electron. 14(4), 1082–1089 (2008).
[CrossRef]

J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing,” Electron. Lett. 44(1), 49 (2008).
[CrossRef]

O. Fidaner, A. K. Okyay, J. E. Roth, R. K. Schaevitz, Y.-H. Kuo, K. C. Saraswat, J. S. Harris, and D. A. B. Miller, “Ge-SiGe quantum-well waveguide photodetectors on silicon for the near-infrared,” IEEE Photon. Technol. Lett. 19(20), 1631–1633 (2007).
[CrossRef]

J. E. Roth, O. Fidaner, R. K. Schaevitz, Y.-H. Kuo, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Optical modulator on silicon employing germanium quantum wells,” Opt. Express 15(9), 5851–5859 (2007).
[CrossRef] [PubMed]

Sigg, H.

M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
[CrossRef]

S. Tsujino, H. Sigg, G. Mussler, D. Chrastina, and H. von Känel, “Photocurrent and transmission spectroscopy of direct-gap interband transitions in Ge/SiGe quantum wells,” Appl. Phys. Lett. 89(26), 262119 (2006).
[CrossRef]

Suntharalingam, V.

J. A. Burns, B. F. Aull, C. K. Chen, C.-L. Chen, C. L. Keast, J. M. Knecht, J. M. Knecht, V. Suntharalingam, K. Warner, P. W. Eyatt, and D.-R. W. Yost, “A wafer-scale 3-D circuit integration technology,” IEEE Trans. Electron. Dev. 53(10), 2507–2516 (2006).
[CrossRef]

Tan, M. R. T.

Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris., “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16(1), 85–92 (2010).
[CrossRef]

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S. Tsujino, H. Sigg, G. Mussler, D. Chrastina, and H. von Känel, “Photocurrent and transmission spectroscopy of direct-gap interband transitions in Ge/SiGe quantum wells,” Appl. Phys. Lett. 89(26), 262119 (2006).
[CrossRef]

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M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
[CrossRef]

M. Virgilio and G. Grosso, “Quantum-confined Stark effect in Ge/SiGe quantum wells: a tight-binding description,” Phys. Rev. B 77(16), 165315 (2008).
[CrossRef]

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M. Virgilio, M. Bonfanti, D. Chrastina, A. Neels, G. Isella, E. Grilli, M. Guzzi, G. Grosso, H. Sigg, and H. von Känel, “Polarization-dependent absorption in Ge/SiGe multiple quantum wells: theory and experiment,” Phys. Rev. B 79(7), 075323 (2009).
[CrossRef]

S. Tsujino, H. Sigg, G. Mussler, D. Chrastina, and H. von Känel, “Photocurrent and transmission spectroscopy of direct-gap interband transitions in Ge/SiGe quantum wells,” Appl. Phys. Lett. 89(26), 262119 (2006).
[CrossRef]

Vukmirovic, N.

P. Moontragoon, N. Vukmirovic, and P. Harrison, “SnGe asymmetric quantum well electroabsorption modulators for long-wavelength silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 16(1), 100–105 (2010).
[CrossRef]

Wada, K.

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, and L. C. Kimerling, “Strain-induced band gap shrinkage in Ge grown on Si substrate,” Appl. Phys. Lett. 82(13), 2044–2046 (2003).
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Figures (5)

Fig. 1
Fig. 1

(a) The designed Ge QW structure grown on Si. (b) Flip-chip bonding. (c) The Ge QCSE asymmetric Fabry-Perot modulator with a front SiGe/air interface and a back metal reflector. This device is used in the following modulator simulation and analysis.

Fig. 2
Fig. 2

(a) The simulated direct-gap optical absorption coefficient spectra (at 0 and 3 V/μm) and (b) the contour plot versus wavelength and electric field in the 20-nm-thick Ge QW structure at 100 °C. In this simulation, the coefficient is averaged by the well thickness only.

Fig. 3
Fig. 3

The simulated on-state and off-state reflectivities, Ron and Roff , for the N-period QW modulator at 1531 nm with and without a reverse bias voltage. The reflectivities are calculated using the transfer matrix and ref [17], respectively. The bias voltage increases linearly with N to impose a 3-V/μm field.

Fig. 4
Fig. 4

Modeling of (a) the reflectivity spectra, (b) peak contrast ratio, insertion loss, and optical bandwidth (for contrast ratio > 3 dB) under various bias voltages for the 47 QW modulator without DBR.

Fig. 5
Fig. 5

The simulation of resonance wavelength and the contrast ratios under 4-V bias (at 1531 nm and at the new resonance wavelength) as functions of the total thickness variation (Δtn + Δtp ).

Tables (1)

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Table 1 Effective masses and barrier heights for the Ge/SiGe QW.

Equations (1)

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α 1 s ( ω ) = C o 2 L O n m | e ^ p c v | 2 γ / π ( E h m e n + E B , 1 s ω ) 2 + γ 2

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