Abstract

We propose and develop a theoretical gain model for an n-doped, tensile-strained Ge-SixGeySn1-x-y quantum-well laser. Tensile strain and n doping in Ge active layers can help achieve population inversion in the direct conduction band and provide optical gain. We show our theoretical model for the bandgap structure, the polarization-dependent optical gain spectrum, and the free-carrier absorption of the n-type doped, tensile-strained Ge quantum-well laser. Despite the free-carrier absorption due to the n-type doping, a significant net gain can be obtained from the direct transition. We also present our waveguide design and calculate the optical confinement factors to estimate the modal gain and predict the threshold carrier density.

© 2009 Optical Society of America

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  1. O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
    [CrossRef] [PubMed]
  2. L. T. Canham, "Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
    [CrossRef]
  3. H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, "1.54-μm luminescence of erbium-implanted III-V semiconductors and silicon," Appl. Phys. Lett. 43, 943-945 (1983).
    [CrossRef]
  4. R. A. Soref and L. Friedman, "Direct-gap Ge/GeSn/Si and GeSn/Ge/Si heterostructure," Superlattices Microstruct. 14, 189-193 (1993).
    [CrossRef]
  5. J. Menéndeza and J. Kouvetakis, "Type-I Ge/Ge1−x−ySixSny strained-layer heterostructures with a direct Ge bandgap," Appl. Phys. Lett. 85, 1175-1177 (2004).
    [CrossRef]
  6. S. W. Chang and S. L. Chuang, "Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers," IEEE J. Quantum Electron. 43, 249-256 (2007).
    [CrossRef]
  7. J. Kouvetakis, J. Tolle, J. Menéndeza, and V. R. D’Costa, "Advances in Si-Ge-Sn materials science and technology," in Proceedings of IEEE 4th International Conference on Group IV Photonics (Institute of Electrical and Electronics Engineers, Tokyo, Japan, 2007), pp. 1-3.
  8. J. Kouvetakis and A. V. G. Chizmeshya, "New classes of Si-based photonic materials and device architectures via designer molecular routes," J. Mater. Chem. 17, 1649-1655 (2007).
    [CrossRef]
  9. J. Liu, X. Sun, D. Pan, X. Wang, L. C. Kimerling, T. L. Koch, and J. Michel, "Tensile-strained, n-type Ge as a gain medium for monolithic laser integration on Si," Opt. Express 15, 11272-11277 (2007).
    [CrossRef] [PubMed]
  10. N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
    [CrossRef]
  11. C. G. Van de Walle, "Band lineups and deformation potentials in the model-solid theory," Phys. Rev. B 39, 1871-1883 (1989).
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  12. S. L. Chuang, Physics of Photonic Devices, 2nd Ed. (Wiley, New York, 2009).
  13. Y. H. Li, X. G. Gong, and S. H. Wei, "Ab initio all-electron calculation of absolute volume deformation potentials of IV-IV, III-V, and II-VI semiconductors: The chemical trends," Phys. Rev. B 73, 245206 (2006).
    [CrossRef]
  14. T. Brudevoll, D. S. Citrin, M. Cardona, and N. E. Christensen, "Electronic structure of 〈-Sn and its dependence on hydrostatic strain," Phys. Rev. B 48, 8629-8635 (1993).
    [CrossRef]
  15. V. R. D’Costa, Y. Y. Fang, J. Tolleb, J. Kouvetakis, and J. Menéndeza, "Direct absorption edge in GeSiSn alloys," International Conference on the Physics of Semiconductors, Rio de Janeiro, Brazil, 2008.
  16. T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
    [CrossRef]
  17. J. Minch, S. H. Park, T. Keating, and S. L. Chuang, "Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers," IEEE J. Quantum Electron. 35, 771-782 (1999).
    [CrossRef]
  18. R. A. Soref and J. P. Lorenzo, "All-silicon active and passive guided-wave components for λ = 1.3 and λ= 1.6μm," IEEE J. Quantum Electron. QE-22, 873-879 (1986).
    [CrossRef]
  19. C. Hilsum, "Simple empirical relationship between mobility and carrier concentration," Electron. Lett. 10, 259-260 (1974).
    [CrossRef]
  20. B. G. Streetman, Solid State Electronic Devices, 4th Ed. (Prentice-Hall, New Jersey, 1995).
  21. S. M. Sze and J. C. Irvin, "Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300◦K," Solid State Electron. 11, 599-602 (1968).
    [CrossRef]
  22. J. I. Pankove, "Optical absorption by degenerate germanium," Phys. Rev. Lett. 4, 454-455 (1960).
    [CrossRef]
  23. J. I. Pankove, "Properties of heavily doped germanium," Prog. Semicond. 9, 48 (1965).
  24. T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
    [CrossRef]
  25. A. V. Maslov, and C. Z. Ning, "Modal gain in a semiconductor nanowire laser with anisotropic bandstructure," IEEE J. Quantum Electron. 40, 1389-1397 (2004).
    [CrossRef]
  26. S. W. Chang and S. L. Chuang, "Fundamental formulation for plasmonic nanolasers," IEEE J. Quantum Electron. (in press).
  27. C. Hass, "Infrared absorption in heavily doped n-type germanium," Phys. Rev. 125, 1965-1971 (1962).
    [CrossRef]
  28. R. E. Lindquist and A. W. Ewald, "Optical constants of single-crystal gray tin in the infrared," Phys. Rev. 135, A191-A194 (1964).
    [CrossRef]
  29. D. F. Edwards, "Silicon (Si)," in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Florida, 1985), pp. 547-569.
  30. R. F. Potter, "Germanium (Ge)," in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Florida, 1985), pp. 465-478.

2007 (3)

S. W. Chang and S. L. Chuang, "Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers," IEEE J. Quantum Electron. 43, 249-256 (2007).
[CrossRef]

J. Kouvetakis and A. V. G. Chizmeshya, "New classes of Si-based photonic materials and device architectures via designer molecular routes," J. Mater. Chem. 17, 1649-1655 (2007).
[CrossRef]

J. Liu, X. Sun, D. Pan, X. Wang, L. C. Kimerling, T. L. Koch, and J. Michel, "Tensile-strained, n-type Ge as a gain medium for monolithic laser integration on Si," Opt. Express 15, 11272-11277 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. H. Li, X. G. Gong, and S. H. Wei, "Ab initio all-electron calculation of absolute volume deformation potentials of IV-IV, III-V, and II-VI semiconductors: The chemical trends," Phys. Rev. B 73, 245206 (2006).
[CrossRef]

2004 (3)

O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
[CrossRef] [PubMed]

J. Menéndeza and J. Kouvetakis, "Type-I Ge/Ge1−x−ySixSny strained-layer heterostructures with a direct Ge bandgap," Appl. Phys. Lett. 85, 1175-1177 (2004).
[CrossRef]

A. V. Maslov, and C. Z. Ning, "Modal gain in a semiconductor nanowire laser with anisotropic bandstructure," IEEE J. Quantum Electron. 40, 1389-1397 (2004).
[CrossRef]

2003 (1)

N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
[CrossRef]

1999 (2)

T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
[CrossRef]

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, "Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers," IEEE J. Quantum Electron. 35, 771-782 (1999).
[CrossRef]

1997 (1)

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

1993 (2)

T. Brudevoll, D. S. Citrin, M. Cardona, and N. E. Christensen, "Electronic structure of 〈-Sn and its dependence on hydrostatic strain," Phys. Rev. B 48, 8629-8635 (1993).
[CrossRef]

R. A. Soref and L. Friedman, "Direct-gap Ge/GeSn/Si and GeSn/Ge/Si heterostructure," Superlattices Microstruct. 14, 189-193 (1993).
[CrossRef]

1990 (1)

L. T. Canham, "Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
[CrossRef]

1989 (1)

C. G. Van de Walle, "Band lineups and deformation potentials in the model-solid theory," Phys. Rev. B 39, 1871-1883 (1989).
[CrossRef]

1986 (1)

R. A. Soref and J. P. Lorenzo, "All-silicon active and passive guided-wave components for λ = 1.3 and λ= 1.6μm," IEEE J. Quantum Electron. QE-22, 873-879 (1986).
[CrossRef]

1983 (1)

H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, "1.54-μm luminescence of erbium-implanted III-V semiconductors and silicon," Appl. Phys. Lett. 43, 943-945 (1983).
[CrossRef]

1974 (1)

C. Hilsum, "Simple empirical relationship between mobility and carrier concentration," Electron. Lett. 10, 259-260 (1974).
[CrossRef]

1968 (1)

S. M. Sze and J. C. Irvin, "Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300◦K," Solid State Electron. 11, 599-602 (1968).
[CrossRef]

1965 (1)

J. I. Pankove, "Properties of heavily doped germanium," Prog. Semicond. 9, 48 (1965).

1964 (1)

R. E. Lindquist and A. W. Ewald, "Optical constants of single-crystal gray tin in the infrared," Phys. Rev. 135, A191-A194 (1964).
[CrossRef]

1962 (1)

C. Hass, "Infrared absorption in heavily doped n-type germanium," Phys. Rev. 125, 1965-1971 (1962).
[CrossRef]

1960 (1)

J. I. Pankove, "Optical absorption by degenerate germanium," Phys. Rev. Lett. 4, 454-455 (1960).
[CrossRef]

Axmann, A.

H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, "1.54-μm luminescence of erbium-implanted III-V semiconductors and silicon," Appl. Phys. Lett. 43, 943-945 (1983).
[CrossRef]

Blok, H.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Boyraz, O.

Brudevoll, T.

T. Brudevoll, D. S. Citrin, M. Cardona, and N. E. Christensen, "Electronic structure of 〈-Sn and its dependence on hydrostatic strain," Phys. Rev. B 48, 8629-8635 (1993).
[CrossRef]

Canham, L. T.

L. T. Canham, "Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
[CrossRef]

Cardona, M.

T. Brudevoll, D. S. Citrin, M. Cardona, and N. E. Christensen, "Electronic structure of 〈-Sn and its dependence on hydrostatic strain," Phys. Rev. B 48, 8629-8635 (1993).
[CrossRef]

Chang, S. W.

S. W. Chang and S. L. Chuang, "Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers," IEEE J. Quantum Electron. 43, 249-256 (2007).
[CrossRef]

S. W. Chang and S. L. Chuang, "Fundamental formulation for plasmonic nanolasers," IEEE J. Quantum Electron. (in press).

Chizmeshya, A. V. G.

J. Kouvetakis and A. V. G. Chizmeshya, "New classes of Si-based photonic materials and device architectures via designer molecular routes," J. Mater. Chem. 17, 1649-1655 (2007).
[CrossRef]

Christensen, N. E.

T. Brudevoll, D. S. Citrin, M. Cardona, and N. E. Christensen, "Electronic structure of 〈-Sn and its dependence on hydrostatic strain," Phys. Rev. B 48, 8629-8635 (1993).
[CrossRef]

Chuang, S. L.

S. W. Chang and S. L. Chuang, "Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers," IEEE J. Quantum Electron. 43, 249-256 (2007).
[CrossRef]

T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
[CrossRef]

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, "Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers," IEEE J. Quantum Electron. 35, 771-782 (1999).
[CrossRef]

S. W. Chang and S. L. Chuang, "Fundamental formulation for plasmonic nanolasers," IEEE J. Quantum Electron. (in press).

Cirlin, G. E.

N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
[CrossRef]

Citrin, D. S.

T. Brudevoll, D. S. Citrin, M. Cardona, and N. E. Christensen, "Electronic structure of 〈-Sn and its dependence on hydrostatic strain," Phys. Rev. B 48, 8629-8635 (1993).
[CrossRef]

Demeulenaere, B.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Ennen, H.

H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, "1.54-μm luminescence of erbium-implanted III-V semiconductors and silicon," Appl. Phys. Lett. 43, 943-945 (1983).
[CrossRef]

Ewald, A. W.

R. E. Lindquist and A. W. Ewald, "Optical constants of single-crystal gray tin in the infrared," Phys. Rev. 135, A191-A194 (1964).
[CrossRef]

Friedman, L.

R. A. Soref and L. Friedman, "Direct-gap Ge/GeSn/Si and GeSn/Ge/Si heterostructure," Superlattices Microstruct. 14, 189-193 (1993).
[CrossRef]

Gong, X. G.

Y. H. Li, X. G. Gong, and S. H. Wei, "Ab initio all-electron calculation of absolute volume deformation potentials of IV-IV, III-V, and II-VI semiconductors: The chemical trends," Phys. Rev. B 73, 245206 (2006).
[CrossRef]

Hass, C.

C. Hass, "Infrared absorption in heavily doped n-type germanium," Phys. Rev. 125, 1965-1971 (1962).
[CrossRef]

Hilsum, C.

C. Hilsum, "Simple empirical relationship between mobility and carrier concentration," Electron. Lett. 10, 259-260 (1974).
[CrossRef]

Irvin, J. C.

S. M. Sze and J. C. Irvin, "Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300◦K," Solid State Electron. 11, 599-602 (1968).
[CrossRef]

Jalali, B.

Jin, X.

T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
[CrossRef]

Keating, T.

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, "Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers," IEEE J. Quantum Electron. 35, 771-782 (1999).
[CrossRef]

T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
[CrossRef]

Kimerling, L. C.

Koch, T. L.

Kouvetakis, J.

J. Kouvetakis and A. V. G. Chizmeshya, "New classes of Si-based photonic materials and device architectures via designer molecular routes," J. Mater. Chem. 17, 1649-1655 (2007).
[CrossRef]

J. Menéndeza and J. Kouvetakis, "Type-I Ge/Ge1−x−ySixSny strained-layer heterostructures with a direct Ge bandgap," Appl. Phys. Lett. 85, 1175-1177 (2004).
[CrossRef]

Lenstra, D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Li, Y. H.

Y. H. Li, X. G. Gong, and S. H. Wei, "Ab initio all-electron calculation of absolute volume deformation potentials of IV-IV, III-V, and II-VI semiconductors: The chemical trends," Phys. Rev. B 73, 245206 (2006).
[CrossRef]

Lindquist, R. E.

R. E. Lindquist and A. W. Ewald, "Optical constants of single-crystal gray tin in the infrared," Phys. Rev. 135, A191-A194 (1964).
[CrossRef]

Liu, J.

Lorenzo, J. P.

R. A. Soref and J. P. Lorenzo, "All-silicon active and passive guided-wave components for λ = 1.3 and λ= 1.6μm," IEEE J. Quantum Electron. QE-22, 873-879 (1986).
[CrossRef]

Maslov, A. V.

A. V. Maslov, and C. Z. Ning, "Modal gain in a semiconductor nanowire laser with anisotropic bandstructure," IEEE J. Quantum Electron. 40, 1389-1397 (2004).
[CrossRef]

Menéndeza, J.

J. Menéndeza and J. Kouvetakis, "Type-I Ge/Ge1−x−ySixSny strained-layer heterostructures with a direct Ge bandgap," Appl. Phys. Lett. 85, 1175-1177 (2004).
[CrossRef]

Michel, J.

Minch, J.

T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
[CrossRef]

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, "Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers," IEEE J. Quantum Electron. 35, 771-782 (1999).
[CrossRef]

Ning, C. Z.

A. V. Maslov, and C. Z. Ning, "Modal gain in a semiconductor nanowire laser with anisotropic bandstructure," IEEE J. Quantum Electron. 40, 1389-1397 (2004).
[CrossRef]

Pan, D.

Pankove, J. I.

J. I. Pankove, "Properties of heavily doped germanium," Prog. Semicond. 9, 48 (1965).

J. I. Pankove, "Optical absorption by degenerate germanium," Phys. Rev. Lett. 4, 454-455 (1960).
[CrossRef]

Park, S. H.

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, "Theory and experiment of In1−xGaxAsyP1−y and In1−x−yGaxAlyAs long-wavelength strained quantum-well lasers," IEEE J. Quantum Electron. 35, 771-782 (1999).
[CrossRef]

T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
[CrossRef]

Pomrenke, G.

H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, "1.54-μm luminescence of erbium-implanted III-V semiconductors and silicon," Appl. Phys. Lett. 43, 943-945 (1983).
[CrossRef]

Schneider, J.

H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, "1.54-μm luminescence of erbium-implanted III-V semiconductors and silicon," Appl. Phys. Lett. 43, 943-945 (1983).
[CrossRef]

Soref, R. A.

R. A. Soref and L. Friedman, "Direct-gap Ge/GeSn/Si and GeSn/Ge/Si heterostructure," Superlattices Microstruct. 14, 189-193 (1993).
[CrossRef]

R. A. Soref and J. P. Lorenzo, "All-silicon active and passive guided-wave components for λ = 1.3 and λ= 1.6μm," IEEE J. Quantum Electron. QE-22, 873-879 (1986).
[CrossRef]

Sun, X.

Sze, S. M.

S. M. Sze and J. C. Irvin, "Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300◦K," Solid State Electron. 11, 599-602 (1968).
[CrossRef]

Talalaev, V. G.

N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
[CrossRef]

Tanbun-Ek, T.

T. Keating, S. H. Park, J. Minch, X. Jin, S. L. Chuang, and T. Tanbun-Ek, "Optical gain measurements based on fundamental properties and comparison with many-body theory," J. Appl. Phys. 86, 2945-2952 (1999).
[CrossRef]

Tonkikh, A. A.

N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
[CrossRef]

Van de Walle, C. G.

C. G. Van de Walle, "Band lineups and deformation potentials in the model-solid theory," Phys. Rev. B 39, 1871-1883 (1989).
[CrossRef]

Visser, T. D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, "Confinement factors and gain in optical amplifiers," IEEE J. Quantum Electron. 33, 1763-1766 (1997).
[CrossRef]

Wang, X.

Wei, S. H.

Y. H. Li, X. G. Gong, and S. H. Wei, "Ab initio all-electron calculation of absolute volume deformation potentials of IV-IV, III-V, and II-VI semiconductors: The chemical trends," Phys. Rev. B 73, 245206 (2006).
[CrossRef]

Werner, P.

N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
[CrossRef]

Zakharov, N. D.

N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
[CrossRef]

Appl. Phys. Lett. (4)

L. T. Canham, "Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
[CrossRef]

H. Ennen, J. Schneider, G. Pomrenke, and A. Axmann, "1.54-μm luminescence of erbium-implanted III-V semiconductors and silicon," Appl. Phys. Lett. 43, 943-945 (1983).
[CrossRef]

J. Menéndeza and J. Kouvetakis, "Type-I Ge/Ge1−x−ySixSny strained-layer heterostructures with a direct Ge bandgap," Appl. Phys. Lett. 85, 1175-1177 (2004).
[CrossRef]

N. D. Zakharov, V. G. Talalaev, P. Werner, A. A. Tonkikh, and G. E. Cirlin, "Room-temperature light emission from a highly strained Si/Ge superlattice," Appl. Phys. Lett. 83, 3084-3086 (2003).
[CrossRef]

Electron. Lett. (1)

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Figures (7)

Fig. 1.
Fig. 1.

Diagram of our proposed n-doped, tensile-strained Ge/Si0.2Ge0.7Sn0.1 MQW structure. The strain-compensated Ge/Si0.2Ge0.7Sn0.1 MQW structure is grown on the silicon substrate via the strain-relaxed Ge0.965Sn0.035 buffer layer.

Fig. 2.
Fig. 2.

(a) Schematic subband structure of an unstrained Ge well. The energy difference between its direct- and indirect-conduction edges is only 134.5 meV. (b) The introduction of a biaxially tensile strain of 0.514% can effectively reduce the energy difference to 91.5 meV. In the valence band, the light-hole (LH) band is the highest valance band due to the tensile strain. (c) Extrinsic electrons from n doping are employed to fill into the L-valley conduction subbands up to the onset of the Γ-valley conduction subband, and make up the remaining energy difference. (d) The injected electrons via bias current can populate the Γ-conduction subband to achieve population inversion and provide significant optical gain.

Fig. 3.
Fig. 3.

(a) Potential profiles of various bands. In the Ge well region, the 0.514% tensile strain reduces the energy difference between the Γ- and L-conduction band edges to 91.5 meV. In the valence band, the LH band edge is lifted and HH band edge is lowered due to the tensile strain. (b) Dispersion relation of the valence subband for the Ge well. Because of the tensile strain, there is only one quantized LH subband in this Ge/Si0.2Ge0.7Sn0.1 QW.

Fig. 4.
Fig. 4.

(a) Injected surface carrier densities of the Γ- and L-conduction valleys in the Ge well as a function of the total injected surface carrier density Ns inj . Because the L-conduction valleys have a larger density of states than that of the Γ-conduction valley, a significant electron occupation is present in the L-conduction valleys. (b) TE and TM normalized squared magnitudes of the momentum matrix elements. Because only one LH subband exists, the TM component is about four times larger than that of the TE component.

Fig. 5.
Fig. 5.

(a) TM and (b) TE material gain spectra under different injected surface carrier densities N s inj. The carrier leakage of the L-conduction subbands is included and it does not contribute to the optical gain. The peak gain is around 0.8 eV, corresponding to an emission wavelength of 1550 nm. Because only one quantized LH subband exists, the TM gain is about four times larger than the TE gain under different surface carrier densities.

Fig. 6.
Fig. 6.

(a) Schematic diagram of our designed silica ridge waveguide structure for index guidance. The silicon-oxide ridge structure has a small refractive index and can provide a proper optical confinement for the active region. (b) Guided power distribution of the quasi-TM fundamental mode. The peak power is located at the active region, leading to a high TM optical confinement factor of 5.9166% in the Ge wells.

Fig. 7.
Fig. 7.

(a) TM material gain, TE material gain, and free-carrier absorption per well as a function of the injected surface carrier density N s inj. The quantum-well structure can provide a high gain, which can overcome the free-carrier absorption. (b) Modal gain, modal loss, and threshold modal gain for the quasi-TM fundamental mode as a function of the injected surface carrier density N s inj. The modal gain can reach the threshold modal gain at a reasonable threshold surface carrier density to make the device lase.

Tables (1)

Tables Icon

Table 1. Doping concentrations, optical confinement factors of the quasi-TM fundamental mode, and absorption losses in various regions

Equations (23)

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Eg,Γ(SixGeySn1xy)=xEg,ΓSi+yEg,ΓGe+(1xy)Eg,ΓSn
bSiGexybGeSny(1xy)bSiSnx(1xy),
p+ND+=n+NA,
n=Ninj+ND+=ΣnkBTmn,th̅2πLQWIn[exp(FcEnkBT)+1]+Σl81(2π)2LQWdktfL,l(kt),
fL,l(kt)=[exp(ElL(kt)FckBT)+1]1,
p=Ninj=Σσ=U,LΣm12πLQWdktkt[1fmσ(kt)],
fmσ(kt)=[exp(Emσ(kt)FvkBT)+1]1,
MnmU,TE(kt)=32dzϕn*(z)Mbgm(1)(kt,z)2+12dzϕn*(z)Mbgm(2)(kt,z)2,
MnmL,TE(kt)=32dzϕn*(z)Mbgm(4)(kt,z)2+12dzϕn*(z)Mbgm(3)(kt,z)2,
Mb2=SpxX23=m06Ep,
MnmU,TM(kt)=2 dzϕn*(z)Mbgm(2)(kt,z)2 ,
MnmL,TM(kt)=2 dzϕn*(z)Mbgm(3)(kt,z)2 .
gwTE(h̅ω)=πn1cε0LQW(em0)2[1exp(h̅ωΔFkBT)]̅Σσ=L,UΣn,m0dkt2πktMnmσ,TE(kt)fn(kt)[1fmσ(kt)]Γ/(2π)[En(kt)Emσ(kt)h̅ω]2+(Γ/2)2,
gwTM(h̅ω)=πn1cε0LQW(em0)2[1exp(h̅ωΔFkBT)]̅Σσ=L,UΣn,m0dkt2πktMnmσ,TM(kt)fn(kt)[1fmσ(kt)]Γ/(2π)[En(kt)Emσ(kt)h̅ω]2+(Γ/2)2,
αf=e3λ24π2c3ε0nr[nΓμΓ(mc*)2+nLμL(mL*)2+pμp(mh*)2],
μL=μL01+nL×1017,
μp=μp01+p×2.1×1017,
Gmod=NwΓwTEgwTE(h̅ω)+NwΓwTMgwTM(h̅ω),
ΓwTE=nw2η0w(Ex2+Ey2)dydz12Re[E×H*]·x̂dydz,
ΓwTM=nw2η0wEz2dydz12Re[E×H*]·x̂dydz,
α(n)=NwΓwαw(n)+Γpαp+Γnαn,
Γi=ni2η0iE2dydz12Re[E×H*].x̂dydz,
Gth=α(n)+12LIn1R1R2,

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