Abstract

We propose and analyze theoretically an asymmetric Ge/SiGe coupled quantum well (CQW) for silicon based optical phase modulator. An 8-band kp model is used to calculate the eigenstates and absorption spectra of the CQWs. The simulation results exhibit unique physical characteristics owing to the coupling between the two wave functions through the thin barriers. We can achieve an electro-refractive index variation as high as 9 × 10−3 at the wavelength of about 1461 nm under the electric field of 30 kV/cm. The product VπLπ of half-wave voltage and length of phase shift region is estimated to be 0.01 V cm. The proposed asymmetric Ge/SiGe CQW scheme provides a promising candidate for high speed, low voltage, low power consumption and compact optical phase modulators in silicon-based integrated optoelectronic devices.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  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).
    [PubMed]
  2. P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
    [PubMed]
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    [PubMed]
  4. P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).
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    [PubMed]
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  12. T. B. Bahder, “Eight-band k·p model of strained zinc-blende crystals,” Phys. Rev. B 41(17), 11992–12001 (1990).
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    [PubMed]
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  18. R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Adv. 1(3), 032164 (2011).
  19. Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).
  20. J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).
  21. M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si1-xGex alloys on Si1-yGey substrates,” Phys. Rev. B Condens. Matter 48(19), 14276–14287 (1993).
    [PubMed]
  22. W. J. Fan, “Tensile-strain and doping enhanced direct bandgap optical transition of n+ doped Ge/GeSi quantum wells,” J. Appl. Phys. 114(18), 183106 (2013).
  23. S. W. Corzine, R. H. Yan, and L. A. Coldren, “Theoretical gain in strained InGaAs/AlGaAs quantum wells including valence-band mixing effects,” Appl. Phys. Lett. 57(26), 2835–2837 (1990).
  24. J. Gao, J. Sun, J. Jiang, H. Zhou, and Y. Zhou, “Design and analysis of electro-absorption modulators with uniaxially stressed Ge/SiGe multiple quantum wells,” Opt. Express 25(10), 10874–10884 (2017).
    [PubMed]
  25. J. Gao, H. Zhou, J. Jiang, Y. Zhou, and J. Sun, “Design of low bias voltage Ge/SiGe multiple quantum wells electro-absorption modulator at 1550 nm,” AIP Adv. 7(3), 035317 (2017).
  26. G. G. Macfarlane and V. Roberts, “Infrared absorption of germanium near the lattice edge,” Phys. Rev. 97(6), 1714 (1955).

2017 (2)

J. Gao, J. Sun, J. Jiang, H. Zhou, and Y. Zhou, “Design and analysis of electro-absorption modulators with uniaxially stressed Ge/SiGe multiple quantum wells,” Opt. Express 25(10), 10874–10884 (2017).
[PubMed]

J. Gao, H. Zhou, J. Jiang, Y. Zhou, and J. Sun, “Design of low bias voltage Ge/SiGe multiple quantum wells electro-absorption modulator at 1550 nm,” AIP Adv. 7(3), 035317 (2017).

2016 (1)

2015 (1)

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

2014 (3)

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

D. C. S. Dumas, K. Gallacher, S. Rhead, M. Myronov, D. R. Leadley, and D. J. Paul, “Ge/SiGe quantum confined Stark effect electro-absorption modulation with low voltage swing at λ = 1550 nm,” Opt. Express 22(16), 19284–19292 (2014).
[PubMed]

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

2013 (3)

E. H. Edwards, L. Lever, E. T. Fei, T. I. Kamins, Z. Ikonic, J. S. Harris, R. W. Kelsall, and D. A. B. Miller, “Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon,” Opt. Express 21(1), 867–876 (2013).
[PubMed]

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

W. J. Fan, “Tensile-strain and doping enhanced direct bandgap optical transition of n+ doped Ge/GeSi quantum wells,” J. Appl. Phys. 114(18), 183106 (2013).

2012 (1)

2011 (2)

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Adv. 1(3), 032164 (2011).

2008 (1)

D. J. Paul, “8-band k.p modeling of the quantum confined Stark effect in Ge quantum wells on Si substrates,” Phys. Rev. B 77(15), 155323 (2008).

2005 (2)

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).
[PubMed]

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

2004 (1)

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

1999 (1)

M. G. Burt, “Fundamentals of envelope function theory for electronic states and photonic modes in nanostructures,” J. Phys. Condens. Matter 11(9), R53–R83 (1999).

1993 (1)

M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si1-xGex alloys on Si1-yGey substrates,” Phys. Rev. B Condens. Matter 48(19), 14276–14287 (1993).
[PubMed]

1990 (2)

T. B. Bahder, “Eight-band k·p model of strained zinc-blende crystals,” Phys. Rev. B 41(17), 11992–12001 (1990).

S. W. Corzine, R. H. Yan, and L. A. Coldren, “Theoretical gain in strained InGaAs/AlGaAs quantum wells including valence-band mixing effects,” Appl. Phys. Lett. 57(26), 2835–2837 (1990).

1989 (1)

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[PubMed]

1987 (1)

J. S. Weiner, D. A. B. Miller, and D. S. Chemla, “Quadratic electro-optic effect due to the quantum-confined Stark effect in quantum wells,” Appl. Phys. Lett. 50(13), 842–844 (1987).

1955 (1)

G. G. Macfarlane and V. Roberts, “Infrared absorption of germanium near the lattice edge,” Phys. Rev. 97(6), 1714 (1955).

Arakawa, T.

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

Bahder, T. B.

T. B. Bahder, “Eight-band k·p model of strained zinc-blende crystals,” Phys. Rev. B 41(17), 11992–12001 (1990).

Burt, M. G.

M. G. Burt, “Fundamentals of envelope function theory for electronic states and photonic modes in nanostructures,” J. Phys. Condens. Matter 11(9), R53–R83 (1999).

Cannon, D. D.

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Cecchi, S.

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

Chaisakul, P.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
[PubMed]

Chemla, D. S.

J. S. Weiner, D. A. B. Miller, and D. S. Chemla, “Quadratic electro-optic effect due to the quantum-confined Stark effect in quantum wells,” Appl. Phys. Lett. 50(13), 842–844 (1987).

Chen, X.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Chen, Y.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Chrastina, D.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
[PubMed]

Coldren, L. A.

S. W. Corzine, R. H. Yan, and L. A. Coldren, “Theoretical gain in strained InGaAs/AlGaAs quantum wells including valence-band mixing effects,” Appl. Phys. Lett. 57(26), 2835–2837 (1990).

Corzine, S. W.

S. W. Corzine, R. H. Yan, and L. A. Coldren, “Theoretical gain in strained InGaAs/AlGaAs quantum wells including valence-band mixing effects,” Appl. Phys. Lett. 57(26), 2835–2837 (1990).

Coudevylle, J.-R.

Crozat, P.

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

Danielson, D. T.

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Dumas, D. C. S.

Edmond, S.

Edwards, E. H.

Fan, W. J.

W. J. Fan, “Tensile-strain and doping enhanced direct bandgap optical transition of n+ doped Ge/GeSi quantum wells,” J. Appl. Phys. 114(18), 183106 (2013).

Fei, E. T.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

E. H. Edwards, L. Lever, E. T. Fei, T. I. Kamins, Z. Ikonic, J. S. Harris, R. W. Kelsall, and D. A. B. Miller, “Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon,” Opt. Express 21(1), 867–876 (2013).
[PubMed]

Ferretto, M.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

Frigerio, J.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
[PubMed]

Gallacher, K.

Gao, J.

J. Gao, J. Sun, J. Jiang, H. Zhou, and Y. Zhou, “Design and analysis of electro-absorption modulators with uniaxially stressed Ge/SiGe multiple quantum wells,” Opt. Express 25(10), 10874–10884 (2017).
[PubMed]

J. Gao, H. Zhou, J. Jiang, Y. Zhou, and J. Sun, “Design of low bias voltage Ge/SiGe multiple quantum wells electro-absorption modulator at 1550 nm,” AIP Adv. 7(3), 035317 (2017).

Ge, Y.

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).
[PubMed]

Goda, Y.

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

Haneji, N.

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

Harris, J. S.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

E. H. Edwards, L. Lever, E. T. Fei, T. I. Kamins, Z. Ikonic, J. S. Harris, R. W. Kelsall, and D. A. B. Miller, “Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon,” Opt. Express 21(1), 867–876 (2013).
[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, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[PubMed]

Huo, Y.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Ikonic, Z.

Isella, G.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
[PubMed]

Iseri, Y.

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

Ishikawa, Y.

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Jia, J.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Jiang, J.

Jongthammanurak, S.

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Kamins, T. I.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

E. H. Edwards, L. Lever, E. T. Fei, T. I. Kamins, Z. Ikonic, J. S. Harris, R. W. Kelsall, and D. A. B. Miller, “Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon,” Opt. Express 21(1), 867–876 (2013).
[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, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[PubMed]

Kang, Y.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Kelsall, R. W.

Kimerling, L. C.

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Kuo, Y. H.

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).
[PubMed]

Le Roux, X.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
[PubMed]

Leadley, D. R.

Lee, Y. K.

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).
[PubMed]

Lever, L.

Liu, J.

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Lu, C.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Luan, H. C.

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

Ly-Gagnon, D. S.

R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Adv. 1(3), 032164 (2011).

Macfarlane, G. G.

G. G. Macfarlane and V. Roberts, “Infrared absorption of germanium near the lattice edge,” Phys. Rev. 97(6), 1714 (1955).

Marris-Morini, D.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
[PubMed]

Michel, J.

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Miller, D. A. B.

E. H. Edwards, L. Lever, E. T. Fei, T. I. Kamins, Z. Ikonic, J. S. Harris, R. W. Kelsall, and D. A. B. Miller, “Low-voltage broad-band electroabsorption from thin Ge/SiGe quantum wells epitaxially grown on silicon,” Opt. Express 21(1), 867–876 (2013).
[PubMed]

R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Adv. 1(3), 032164 (2011).

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).
[PubMed]

J. S. Weiner, D. A. B. Miller, and D. S. Chemla, “Quadratic electro-optic effect due to the quantum-confined Stark effect in quantum wells,” Appl. Phys. Lett. 50(13), 842–844 (1987).

Myronov, M.

Paul, D. J.

Ren, S.

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).
[PubMed]

Rhead, S.

Rieger, M. M.

M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si1-xGex alloys on Si1-yGey substrates,” Phys. Rev. B Condens. Matter 48(19), 14276–14287 (1993).
[PubMed]

Roberts, V.

G. G. Macfarlane and V. Roberts, “Infrared absorption of germanium near the lattice edge,” Phys. Rev. 97(6), 1714 (1955).

Roth, J. E.

R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Adv. 1(3), 032164 (2011).

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).
[PubMed]

Roufied, M. S.

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

Rouifed, M. S.

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

Rouifed, M.-S.

Schaevitz, R. K.

R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Adv. 1(3), 032164 (2011).

Shang, C.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Sun, J.

Tada, K.

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

Vakarin, V.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

Van de Walle, C. G.

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[PubMed]

Vivien, L.

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

P. Chaisakul, D. Marris-Morini, M.-S. Rouifed, G. Isella, D. Chrastina, J. Frigerio, X. Le Roux, S. Edmond, J.-R. Coudevylle, and L. Vivien, “23 GHz Ge/SiGe multiple quantum well electro-absorption modulator,” Opt. Express 20(3), 3219–3224 (2012).
[PubMed]

Vogl, P.

M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si1-xGex alloys on Si1-yGey substrates,” Phys. Rev. B Condens. Matter 48(19), 14276–14287 (1993).
[PubMed]

Wada, K.

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Weiner, J. S.

J. S. Weiner, D. A. B. Miller, and D. S. Chemla, “Quadratic electro-optic effect due to the quantum-confined Stark effect in quantum wells,” Appl. Phys. Lett. 50(13), 842–844 (1987).

Yamada, H.

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

Yan, R. H.

S. W. Corzine, R. H. Yan, and L. A. Coldren, “Theoretical gain in strained InGaAs/AlGaAs quantum wells including valence-band mixing effects,” Appl. Phys. Lett. 57(26), 2835–2837 (1990).

Zang, K.

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Zhou, H.

J. Gao, H. Zhou, J. Jiang, Y. Zhou, and J. Sun, “Design of low bias voltage Ge/SiGe multiple quantum wells electro-absorption modulator at 1550 nm,” AIP Adv. 7(3), 035317 (2017).

J. Gao, J. Sun, J. Jiang, H. Zhou, and Y. Zhou, “Design and analysis of electro-absorption modulators with uniaxially stressed Ge/SiGe multiple quantum wells,” Opt. Express 25(10), 10874–10884 (2017).
[PubMed]

Zhou, Y.

J. Gao, J. Sun, J. Jiang, H. Zhou, and Y. Zhou, “Design and analysis of electro-absorption modulators with uniaxially stressed Ge/SiGe multiple quantum wells,” Opt. Express 25(10), 10874–10884 (2017).
[PubMed]

J. Gao, H. Zhou, J. Jiang, Y. Zhou, and J. Sun, “Design of low bias voltage Ge/SiGe multiple quantum wells electro-absorption modulator at 1550 nm,” AIP Adv. 7(3), 035317 (2017).

AIP Adv. (2)

R. K. Schaevitz, D. S. Ly-Gagnon, J. E. Roth, E. H. Edwards, and D. A. B. Miller, “Indirect absorption in germanium quantum wells,” AIP Adv. 1(3), 032164 (2011).

J. Gao, H. Zhou, J. Jiang, Y. Zhou, and J. Sun, “Design of low bias voltage Ge/SiGe multiple quantum wells electro-absorption modulator at 1550 nm,” AIP Adv. 7(3), 035317 (2017).

Appl. Phys. Lett. (3)

J. S. Weiner, D. A. B. Miller, and D. S. Chemla, “Quadratic electro-optic effect due to the quantum-confined Stark effect in quantum wells,” Appl. Phys. Lett. 50(13), 842–844 (1987).

S. W. Corzine, R. H. Yan, and L. A. Coldren, “Theoretical gain in strained InGaAs/AlGaAs quantum wells including valence-band mixing effects,” Appl. Phys. Lett. 57(26), 2835–2837 (1990).

J. Frigerio, P. Chaisakul, D. Marris-Morini, S. Cecchi, M. S. Roufied, G. Isella, and L. Vivien, “Electro-refractive effect in Ge/SiGe multiple quantum wells,” Appl. Phys. Lett. 102(6), 061102 (2013).

J. Appl. Phys. (2)

W. J. Fan, “Tensile-strain and doping enhanced direct bandgap optical transition of n+ doped Ge/GeSi quantum wells,” J. Appl. Phys. 114(18), 183106 (2013).

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H. C. Luan, J. Michel, and L. C. Kimerling, “Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate,” J. Appl. Phys. 98(1), 013501 (2005).

J. Phys. Condens. Matter (1)

M. G. Burt, “Fundamentals of envelope function theory for electronic states and photonic modes in nanostructures,” J. Phys. Condens. Matter 11(9), R53–R83 (1999).

Nat. Photonics (1)

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M. S. Rouifed, S. Cecchi, P. Crozat, G. Isella, and L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).

Nature (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).
[PubMed]

Opt. Express (5)

Phys. E (1)

Y. Iseri, H. Yamada, Y. Goda, T. Arakawa, K. Tada, and N. Haneji, “Analysis of electrorefractive index change in Ge/SiGe coupled quantum well for low-voltage silicon-based optical modulators,” Phys. E 43(8), 1433–1438 (2011).

Phys. Rev. (1)

G. G. Macfarlane and V. Roberts, “Infrared absorption of germanium near the lattice edge,” Phys. Rev. 97(6), 1714 (1955).

Phys. Rev. B (3)

D. J. Paul, “8-band k.p modeling of the quantum confined Stark effect in Ge quantum wells on Si substrates,” Phys. Rev. B 77(15), 155323 (2008).

T. B. Bahder, “Eight-band k·p model of strained zinc-blende crystals,” Phys. Rev. B 41(17), 11992–12001 (1990).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si (100),” Phys. Rev. B 70(15), 155309 (2004).

Phys. Rev. B Condens. Matter (2)

M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si1-xGex alloys on Si1-yGey substrates,” Phys. Rev. B Condens. Matter 48(19), 14276–14287 (1993).
[PubMed]

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[PubMed]

Proc. SPIE (1)

Y. Chen, X. Chen, Y. Huo, C. Lu, E. T. Fei, K. Zang, C. Shang, Y. Kang, J. Jia, T. I. Kamins, and J. S. Harris, “A new electro-absorption modulator structure based on Ge/SiGe coupled quantum wells for on-chip optical interconnects,” Proc. SPIE 9277, 92770Y (2014).

Sci. Rep. (1)

J. Frigerio, V. Vakarin, P. Chaisakul, M. Ferretto, D. Chrastina, X. Le Roux, L. Vivien, G. Isella, and D. Marris-Morini, “Giant electro-optic effect in Ge/SiGe coupled quantum wells,” Sci. Rep. 5, 15398 (2015).
[PubMed]

Other (2)

S. L. Chuang, Physics of Photonic Devices, 2nd ed. (Wiley, 2009).

F. Seitz and D. Turnbull, Solid State Physics (Academic, 1963).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the asymmetric CQW. (b) Epitaxy design of the CQWs structure.
Fig. 2
Fig. 2 Energy dispersion near the Γ point of the CQW.
Fig. 3
Fig. 3 Energy eigenvalue of electron and hole states at the Γ point of the CQW as a function of electric field.
Fig. 4
Fig. 4 Simulated wave functions at the Γ point of the CQW under the electric field of: (a) 0 kV/cm, (b) 10 kV/cm, (c) 20 kV/cm, (d) 30 kV/cm, (e) 40 kV/cm, (f) 50 kV/cm.
Fig. 5
Fig. 5 Normalized momentum matrix elements (MME) at the Γ point of several optical transitions as a function of electric field for: (a) TE polarization, (b) TM polarization.
Fig. 6
Fig. 6 Absorption spectrum of the CQWs under different electric field for: (a) TE polarization, (b) TM polarization.
Fig. 7
Fig. 7 Electro-refractive index variation of the CQWs under different electric field operation for: (a) TE polarization, (b) TM polarization.

Tables (1)

Tables Icon

Table 1 The parameters at 300 K of Si and Ge used in the proposed scheme.

Equations (8)

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

| S,| X,| Y,| Z,| S,| X,| Y,| Z
H=[ H 4×4 0 0 H 4×4 ]+ H so + H str
a || = a 1 G 1 h 1 + a 2 G 2 h 2 ++ a n G n h n G 1 h 1 + G 2 h 2 ++ G n h n ε || i = a || a i 1
α σ ( ω )= π q 2 n r c m 0 2 ω L w s,t 2d k x d k y ( 2π ) 2 | Ψ s c | p ^ σ | Ψ t v | 2 [ f s c ( k || ) f t v ( k || ) ] × γ/( 2π ) [ E s c ( k || ) E t v ( k || )ω ] 2 + ( γ/2 ) 2
f s c ( k || )= { 1+exp[ E s c ( k || ) F c k B T ] } 1 f t v ( k || )= { 1+exp[ E t v ( k || ) F v k B T ] } 1
α ind =A[ 1 1 e Θ/T ( ω E g,ind k B Θ ω ) 2 + 1 e Θ/T 1 ( ω E g,ind + k B Θ ω ) 2 ]
Δn(v)= c π Δα( v ' ) v '2 v 2 d v '
Eg(S i 1x G e x )=0.7985x+4.185(1x)0.14x(1x)(eV)

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