Abstract

We analyze the optical gain of tensile-strained, n-type Ge material for Si-compatible laser applications. The band structure of unstrained Ge exhibits indirect conduction band valleys (L) lower than the direct valley (Γ) by 136 meV. Adequate strain and n-type doping engineering can effectively provide population inversion in the direct bandgap of Ge. The tensile strain decreases the difference between the L valleys and the Γ valley, while the extrinsic electrons from n-type doping fill the L valleys to the level of the Γ valley to compensate for the remaining energy difference. Our modeling shows that with a combination of 0.25% tensile strain and an extrinsic electron density of 7.6×1019/cm3 by n-type doping, a net material gain of ~400 cm-1 can be obtained from the direct gap transition of Ge despite of the free carrier absorption loss. The threshold current density for lasing is estimated to be ~6kA cm-2 for a typical edge-emitting double heterojunction structure. These results indicate that tensile strained n-type Ge is a good candidate for Si integrated lasers.

© 2007 Optical Society of America

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  1. D. J. Eaglesham, J. Michel, E. A. Fitzgerald, D. C. Jacobson, J. M. Poate, J. L. Benton, A. Polman, Y.-H. Xie, and L. C. Kimerling, "Microstructure of erbium-implanted Si," Appl. Phys. Lett. 58, 2797 (1991).
    [CrossRef]
  2. N. Koshida and H. Koyama, "Visible electroluminescence from porous silicon," Appl. Phys. Lett. 60, 347-349 (1992).
    [CrossRef]
  3. L. Pavesi. L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
    [CrossRef] [PubMed]
  4. B. Zheng, J. Michel, F. Y. G. Ren, L. C. Kimerling, D. C. Jacobson and J. M. Poate, "Room-temperature sharp line electroluminescence at λ=1.54µm from an erbium-doped, silicon light-emitting diode," Appl. Phys. Lett. 64, 2842-2844 (1994).
    [CrossRef]
  5. A. J. Kenyon, P. F. Trwoga, M. Federighi and C. W. Pitt, "Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions," J. Phys.: Condens. Matter 6, L319-L324 (1994).
    [CrossRef]
  6. C. S. Peng, Q. Huang, W. Q. Cheng, J. M. Zhou, Y. H. Zhang, T. T. Sheng and C. H. Tung, "Optical properties of Ge self-organized quantum dots in Si," Phys. Rev. B 57, 8805-8808 (1998).
    [CrossRef]
  7. G. He and H. A. Atwater, "Interband transitions in SnxGe1-x alloys," 79, 1937-1940 (1997).
  8. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang and and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
    [CrossRef] [PubMed]
  9. M. E. Groenert, C. W. Leitz, A. J. Pitera, V. Yang, H. Lee, R. J. Ram and E. A. Fitzgerald, "Monolithic integration of room-temperature GaAs/AlGaAs lasers on Si substrates via relaxed graded GeSi buffer layers," J. Appl. Phys. 93, 362-367 (2003).
    [CrossRef]
  10. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, "Electrically pumped hybrid AlGaInAs-silicon evanescent laser," Opt. Express 14, 9203-9210 (2006).
    [CrossRef] [PubMed]
  11. C. L. Schow, S. J. Koester, L. Schares, G. Dehlinger and R. A. John, "High-speed, low-voltage optical receivers consisting of Ge-on-SOI photodiodes paired with CMOS ICs," Proc SPIE 6477, 647705-1 (2007).
  12. M. Morse, O. I. Dosunmu, G. Sarid, and Y. Chetrit, "Performance of Ge-on-Si p-i-n photodetectors for standard receiver modules," IEEE. Photon. Technol. Lett. 18, 2442-2444 (2006).
    [CrossRef]
  13. D. Ahn, C. Y. Hong, J. F. Liu, W. Giziewicz, M. Beals, L. C. Kimerling and J. Michel, "High performance, waveguide integrated Ge photodetectors," Opt. Express 15, 3916-3921 (2007).
    [CrossRef] [PubMed]
  14. 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, 1334-1336 (2005).
    [CrossRef] [PubMed]
  15. S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling and J. Michel, "Large electro-optic effect in tensile strained Ge-on-Si films," Appl. Phys. Lett. 89, 161115 (2006).
    [CrossRef]
  16. Physics of Group IV Elements and III-V Compounds, edited by O. Madelung, Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1982), Vol. 17a.
  17. Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan and L. C. Kimerling, "Strain-induced direct bandgap shrinkage in Ge grown on Si substrate," Appl. Phys. Lett. 82, 2044-2046 (2003).
    [CrossRef]
  18. J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, S. Jongthammanurak, D. T. Danielson, J. Michel, and LionelC. Kimerling, "Tensile strained Ge p-i-n photodetectors on Si platform for C and L band optical communications," Appl. Phys. Lett. 87, 011110 (2005).
    [CrossRef]
  19. C. G. Van de Walle, "Band lineups and deformation potentials in model-solid theory," Phys. Rev. B 39, 1871-1883 (1989).
    [CrossRef]
  20. V. V. Zhdanova and T. A. Kontorova, "Thermal expansion of doped Ge," Sov. Phys. Solid State 7, 2685-2689 (1966).
  21. S. L. Chuang, Physics of optoelectronic devices, (Wiley, New York, 1995), Chaps. 9-10.
  22. M. V. Hobalen, "Direct optical transitions from the split-off valence band to the conduction band in germanium," J. Phys. Chem. Solids 23, 821-822 (1962).
    [CrossRef]
  23. W. G. Spitzer, F. A. Trumbore, and R. A. Logan, "Properties of heavily doped n-type germanium," J. Appl. Phys. 32, 1822-1830 (1961).
    [CrossRef]
  24. C. Haas, "Infrared absorption in heavily doped n-type germanium," Phys. Rev. 125, 1965-1971 (1962).
    [CrossRef]
  25. H. S. Sommers, Jr., "Degenerate germanium. II. Bandgap and carrier recombination," Phys. Rev. 124, 1101-1110 (1961).
    [CrossRef]
  26. F. Lukeš and J. Humlièek, "Electroreflectance of heavily doped n-type and p-type germanium near the direct gap," Phys. Rev. B 6, 521-533 (1972).
    [CrossRef]
  27. M. J. Chen, C. S. Tsai, and M. K. Wu, "Optical gain and co-stimulated emissions of photons and phonons in indirect bandgap semiconductors," Jpn. J. Appl. Phys. 45, 6576-6588 (2006).
    [CrossRef]
  28. R. Newman and W. W. Tyler, "Effect of impurities on free-hole infrared absorption in p-type germanium," Phys. Rev. 105, 885-886 (1957).
    [CrossRef]
  29. L. Di Gaspare, G. Capellini, M. Sebastiani, C. Chudoba, F. Evangelisti, "Ge/Si(100) heterostructures: a photoemission and low-energy yield spectroscopy investigation," Appl. Surf. Sci. 106, 94 (1996).
    [CrossRef]
  30. P. T. Lansberg, Recombination in Semiconductors (Cambridge University Press, Cambridge, 1991).
  31. J. R. Haynes and N. G. Nilsson, "The direct radiative transitions in germanium and their use in the analysis of lifetime," in Proceedings of VIIth International Conference on Physics of Semiconductors, Paris 1964 (Paris: Dunod, 1964), p. 21.
  32. R. Conradt and J. Aengenheister, "Minority carrier lifetime in highly doped Ge," Solid. State. Commun. 10, 321-323 (1972).
    [CrossRef]
  33. S. Marchetti, M. Martinelli, R. Simili, M. Giorgi and M. Fantoni, "Measurement of Ge electrical parameters by analyzing its optical dynamics," Phys. Script. 64, 509-511 (2001).
    [CrossRef]

2007

C. L. Schow, S. J. Koester, L. Schares, G. Dehlinger and R. A. John, "High-speed, low-voltage optical receivers consisting of Ge-on-SOI photodiodes paired with CMOS ICs," Proc SPIE 6477, 647705-1 (2007).

D. Ahn, C. Y. Hong, J. F. Liu, W. Giziewicz, M. Beals, L. C. Kimerling and J. Michel, "High performance, waveguide integrated Ge photodetectors," Opt. Express 15, 3916-3921 (2007).
[CrossRef] [PubMed]

2006

M. Morse, O. I. Dosunmu, G. Sarid, and Y. Chetrit, "Performance of Ge-on-Si p-i-n photodetectors for standard receiver modules," IEEE. Photon. Technol. Lett. 18, 2442-2444 (2006).
[CrossRef]

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, "Electrically pumped hybrid AlGaInAs-silicon evanescent laser," Opt. Express 14, 9203-9210 (2006).
[CrossRef] [PubMed]

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling and J. Michel, "Large electro-optic effect in tensile strained Ge-on-Si films," Appl. Phys. Lett. 89, 161115 (2006).
[CrossRef]

M. J. Chen, C. S. Tsai, and M. K. Wu, "Optical gain and co-stimulated emissions of photons and phonons in indirect bandgap semiconductors," Jpn. J. Appl. Phys. 45, 6576-6588 (2006).
[CrossRef]

2005

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, 1334-1336 (2005).
[CrossRef] [PubMed]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, S. Jongthammanurak, D. T. Danielson, J. Michel, and LionelC. Kimerling, "Tensile strained Ge p-i-n photodetectors on Si platform for C and L band optical communications," Appl. Phys. Lett. 87, 011110 (2005).
[CrossRef]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang and and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

2003

M. E. Groenert, C. W. Leitz, A. J. Pitera, V. Yang, H. Lee, R. J. Ram and E. A. Fitzgerald, "Monolithic integration of room-temperature GaAs/AlGaAs lasers on Si substrates via relaxed graded GeSi buffer layers," J. Appl. Phys. 93, 362-367 (2003).
[CrossRef]

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan and L. C. Kimerling, "Strain-induced direct bandgap shrinkage in Ge grown on Si substrate," Appl. Phys. Lett. 82, 2044-2046 (2003).
[CrossRef]

2001

S. Marchetti, M. Martinelli, R. Simili, M. Giorgi and M. Fantoni, "Measurement of Ge electrical parameters by analyzing its optical dynamics," Phys. Script. 64, 509-511 (2001).
[CrossRef]

2000

L. Pavesi. L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

1998

C. S. Peng, Q. Huang, W. Q. Cheng, J. M. Zhou, Y. H. Zhang, T. T. Sheng and C. H. Tung, "Optical properties of Ge self-organized quantum dots in Si," Phys. Rev. B 57, 8805-8808 (1998).
[CrossRef]

1996

L. Di Gaspare, G. Capellini, M. Sebastiani, C. Chudoba, F. Evangelisti, "Ge/Si(100) heterostructures: a photoemission and low-energy yield spectroscopy investigation," Appl. Surf. Sci. 106, 94 (1996).
[CrossRef]

1994

B. Zheng, J. Michel, F. Y. G. Ren, L. C. Kimerling, D. C. Jacobson and J. M. Poate, "Room-temperature sharp line electroluminescence at λ=1.54µm from an erbium-doped, silicon light-emitting diode," Appl. Phys. Lett. 64, 2842-2844 (1994).
[CrossRef]

A. J. Kenyon, P. F. Trwoga, M. Federighi and C. W. Pitt, "Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions," J. Phys.: Condens. Matter 6, L319-L324 (1994).
[CrossRef]

1992

N. Koshida and H. Koyama, "Visible electroluminescence from porous silicon," Appl. Phys. Lett. 60, 347-349 (1992).
[CrossRef]

1991

D. J. Eaglesham, J. Michel, E. A. Fitzgerald, D. C. Jacobson, J. M. Poate, J. L. Benton, A. Polman, Y.-H. Xie, and L. C. Kimerling, "Microstructure of erbium-implanted Si," Appl. Phys. Lett. 58, 2797 (1991).
[CrossRef]

1989

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

1972

R. Conradt and J. Aengenheister, "Minority carrier lifetime in highly doped Ge," Solid. State. Commun. 10, 321-323 (1972).
[CrossRef]

F. Lukeš and J. Humlièek, "Electroreflectance of heavily doped n-type and p-type germanium near the direct gap," Phys. Rev. B 6, 521-533 (1972).
[CrossRef]

1966

V. V. Zhdanova and T. A. Kontorova, "Thermal expansion of doped Ge," Sov. Phys. Solid State 7, 2685-2689 (1966).

1962

M. V. Hobalen, "Direct optical transitions from the split-off valence band to the conduction band in germanium," J. Phys. Chem. Solids 23, 821-822 (1962).
[CrossRef]

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

1961

H. S. Sommers, Jr., "Degenerate germanium. II. Bandgap and carrier recombination," Phys. Rev. 124, 1101-1110 (1961).
[CrossRef]

W. G. Spitzer, F. A. Trumbore, and R. A. Logan, "Properties of heavily doped n-type germanium," J. Appl. Phys. 32, 1822-1830 (1961).
[CrossRef]

1957

R. Newman and W. W. Tyler, "Effect of impurities on free-hole infrared absorption in p-type germanium," Phys. Rev. 105, 885-886 (1957).
[CrossRef]

Appl. Phys. Lett.

Y. Ishikawa, K. Wada, D. D. Cannon, J. F. Liu, H. C. Luan and L. C. Kimerling, "Strain-induced direct bandgap shrinkage in Ge grown on Si substrate," Appl. Phys. Lett. 82, 2044-2046 (2003).
[CrossRef]

J. F. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, S. Jongthammanurak, D. T. Danielson, J. Michel, and LionelC. Kimerling, "Tensile strained Ge p-i-n photodetectors on Si platform for C and L band optical communications," Appl. Phys. Lett. 87, 011110 (2005).
[CrossRef]

S. Jongthanmmanurak, J. F. Liu, K. Wada, D. D. Cannon, D. T. Danielson, D. Pan, L. C. Kimeriling and J. Michel, "Large electro-optic effect in tensile strained Ge-on-Si films," Appl. Phys. Lett. 89, 161115 (2006).
[CrossRef]

D. J. Eaglesham, J. Michel, E. A. Fitzgerald, D. C. Jacobson, J. M. Poate, J. L. Benton, A. Polman, Y.-H. Xie, and L. C. Kimerling, "Microstructure of erbium-implanted Si," Appl. Phys. Lett. 58, 2797 (1991).
[CrossRef]

N. Koshida and H. Koyama, "Visible electroluminescence from porous silicon," Appl. Phys. Lett. 60, 347-349 (1992).
[CrossRef]

B. Zheng, J. Michel, F. Y. G. Ren, L. C. Kimerling, D. C. Jacobson and J. M. Poate, "Room-temperature sharp line electroluminescence at λ=1.54µm from an erbium-doped, silicon light-emitting diode," Appl. Phys. Lett. 64, 2842-2844 (1994).
[CrossRef]

Appl. Surf. Sci.

L. Di Gaspare, G. Capellini, M. Sebastiani, C. Chudoba, F. Evangelisti, "Ge/Si(100) heterostructures: a photoemission and low-energy yield spectroscopy investigation," Appl. Surf. Sci. 106, 94 (1996).
[CrossRef]

IEEE. Photon. Technol. Lett.

M. Morse, O. I. Dosunmu, G. Sarid, and Y. Chetrit, "Performance of Ge-on-Si p-i-n photodetectors for standard receiver modules," IEEE. Photon. Technol. Lett. 18, 2442-2444 (2006).
[CrossRef]

J. Appl. Phys.

M. E. Groenert, C. W. Leitz, A. J. Pitera, V. Yang, H. Lee, R. J. Ram and E. A. Fitzgerald, "Monolithic integration of room-temperature GaAs/AlGaAs lasers on Si substrates via relaxed graded GeSi buffer layers," J. Appl. Phys. 93, 362-367 (2003).
[CrossRef]

W. G. Spitzer, F. A. Trumbore, and R. A. Logan, "Properties of heavily doped n-type germanium," J. Appl. Phys. 32, 1822-1830 (1961).
[CrossRef]

J. Phys. Chem. Solids

M. V. Hobalen, "Direct optical transitions from the split-off valence band to the conduction band in germanium," J. Phys. Chem. Solids 23, 821-822 (1962).
[CrossRef]

J. Phys.: Condens. Matter

A. J. Kenyon, P. F. Trwoga, M. Federighi and C. W. Pitt, "Optical properties of PECVD erbium-doped silicon-rich silica: evidence for energy transfer between silicon microclusters and erbium ions," J. Phys.: Condens. Matter 6, L319-L324 (1994).
[CrossRef]

Jpn. J. Appl. Phys.

M. J. Chen, C. S. Tsai, and M. K. Wu, "Optical gain and co-stimulated emissions of photons and phonons in indirect bandgap semiconductors," Jpn. J. Appl. Phys. 45, 6576-6588 (2006).
[CrossRef]

Nature

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, 1334-1336 (2005).
[CrossRef] [PubMed]

L. Pavesi. L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang and and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev.

R. Newman and W. W. Tyler, "Effect of impurities on free-hole infrared absorption in p-type germanium," Phys. Rev. 105, 885-886 (1957).
[CrossRef]

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

H. S. Sommers, Jr., "Degenerate germanium. II. Bandgap and carrier recombination," Phys. Rev. 124, 1101-1110 (1961).
[CrossRef]

Phys. Rev. B

F. Lukeš and J. Humlièek, "Electroreflectance of heavily doped n-type and p-type germanium near the direct gap," Phys. Rev. B 6, 521-533 (1972).
[CrossRef]

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

C. S. Peng, Q. Huang, W. Q. Cheng, J. M. Zhou, Y. H. Zhang, T. T. Sheng and C. H. Tung, "Optical properties of Ge self-organized quantum dots in Si," Phys. Rev. B 57, 8805-8808 (1998).
[CrossRef]

Phys. Script.

S. Marchetti, M. Martinelli, R. Simili, M. Giorgi and M. Fantoni, "Measurement of Ge electrical parameters by analyzing its optical dynamics," Phys. Script. 64, 509-511 (2001).
[CrossRef]

Proc SPIE

C. L. Schow, S. J. Koester, L. Schares, G. Dehlinger and R. A. John, "High-speed, low-voltage optical receivers consisting of Ge-on-SOI photodiodes paired with CMOS ICs," Proc SPIE 6477, 647705-1 (2007).

Solid. State. Commun.

R. Conradt and J. Aengenheister, "Minority carrier lifetime in highly doped Ge," Solid. State. Commun. 10, 321-323 (1972).
[CrossRef]

Sov. Phys. Solid State

V. V. Zhdanova and T. A. Kontorova, "Thermal expansion of doped Ge," Sov. Phys. Solid State 7, 2685-2689 (1966).

Other

S. L. Chuang, Physics of optoelectronic devices, (Wiley, New York, 1995), Chaps. 9-10.

Physics of Group IV Elements and III-V Compounds, edited by O. Madelung, Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1982), Vol. 17a.

P. T. Lansberg, Recombination in Semiconductors (Cambridge University Press, Cambridge, 1991).

J. R. Haynes and N. G. Nilsson, "The direct radiative transitions in germanium and their use in the analysis of lifetime," in Proceedings of VIIth International Conference on Physics of Semiconductors, Paris 1964 (Paris: Dunod, 1964), p. 21.

G. He and H. A. Atwater, "Interband transitions in SnxGe1-x alloys," 79, 1937-1940 (1997).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Schematic band structure of bulk Ge, showing a 136 meV difference between the direct gap and the indirect gap, (b) the difference between the direct and the indirect gaps can be decreased by tensile strain, and (c) the rest of the difference between direct and indirect gaps in tensile strained Ge can be compensated by filling electrons into the L valleys.

Fig. 2.
Fig. 2.

(a) Band-to-band absorption measurement of the direct transition in unstrained [22] and tensile strained Ge (this work); (b) gain spectra from the direct transition in 0.25% tensile-strained n+ Ge with N=7.6×1019 cm-3 at different injected carrier densities; and gain from the direct transition, free carrier loss and net gain as a function of injected carrier density in (c) 0.25% tensile strained n+ Ge, and (d) n+ bulk Ge

Equations (5)

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

γ Γ ( h ν ) = α Γ ( h ν ) ( f c f ν ) ,
α Γ ( h ν ) = A ( h ν E g Γ ) h ν ,
α Γ ( h ν ) = A ( h ν E g Γ ( lh ) + h ν E g Γ ( hh ) ) h ν ,
α f ( λ ) = AN λ a + BP λ b ,
α f ( λ ) = 3.4 × 10 25 N λ 2.25 3.2 × 10 25 P λ 2.43 ,

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