Abstract

The direct gap optical gain of [100] uniaxial tensile strained and n+-doped Ge/GeSi quantum well (QW) is calculated. The theoretical models for strained band structures near the Γ- and L-point, optical gain and free carrier absorption are provided. Simulation results show that the optical gain can be dramatically enhanced with the help of uniaxial tensile strain and n-type doping. Furthermore, to consider the competition between gain and loss and get insight into the effects of strain and doping, the net peak gain and transparency carrier density at various strain value and doping concentration are evaluated. A net peak gain up to 2061 cm−1 for TE-polarized light is predicted at a strain value of 4%, a doping concentration of 1x1019 cm-3and an injected carrier density of 4x1019 cm-3.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Theory for n-type doped, tensile-strained Ge-SixGeySn1-x-y quantum-well lasers at telecom wavelength

Guo-En Chang, Shu-Wei Chang, and Shun Lien Chuang
Opt. Express 17(14) 11246-11258 (2009)

Tensile-strained, n-type Ge as a gain medium for monolithic laser integration on Si

Jifeng Liu, Xiaochen Sun, Dong Pan, Xiaoxin Wang, Lionel C. Kimerling, Thomas L. Koch, and Jurgen Michel
Opt. Express 15(18) 11272-11277 (2007)

Tensile-strained Ge/SiGe multiple quantum well microdisks

Xiaochi Chen, Colleen S. Fenrich, Muyu Xue, Ming-Yen Kao, Kai Zang, Ching-Ying Lu, Edward T. Fei, Yusi Chen, Yijie Huo, Theodore I. Kamins, and James S. Harris
Photon. Res. 5(6) B7-B14 (2017)

References

  • View by:
  • |
  • |
  • |

  1. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
    [Crossref]
  2. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
    [Crossref]
  3. 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(20), 9203–9210 (2006).
    [Crossref] [PubMed]
  4. S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
    [Crossref]
  5. 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(18), 11272–11277 (2007).
    [Crossref] [PubMed]
  6. J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, “Ge-on-Si laser operating at room temperature,” Opt. Lett. 35(5), 679–681 (2010).
    [Crossref] [PubMed]
  7. R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, and J. Michel, “An electrically pumped germanium laser,” Opt. Express 20(10), 11316–11320 (2012).
    [Crossref] [PubMed]
  8. A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
    [Crossref]
  9. M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
    [Crossref]
  10. R. W. Millar, K. Gallacher, J. Frigerio, A. Ballabio, A. Bashir, I. MacLaren, G. Isella, and D. J. Paul, “Analysis of Ge micro-cavities with in-plane tensile strains above 2%,” Opt. Express 24(5), 4365–4374 (2016).
    [Crossref]
  11. D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
    [Crossref]
  12. A. Yariv, “Scaling laws and minimum threshold currents for quantum-confined semiconductor lasers,” Appl. Phys. Lett. 53(12), 1033–1035 (1988).
    [Crossref]
  13. H. K. Choi and C. A. Wang, “InGaAs/AlGaAs strained single quantum well diode lasers with extremely low threshold current density and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
    [Crossref]
  14. Y. Cai, Z. Han, X. Wang, R. Camacho-Aguilera, L. C. Kimerling, J. Michel, and J. Liu, “Analysis of threshold current behavior for bulk and quantum-well germanium laser structures,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1901009 (2013).
    [Crossref]
  15. 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).
  16. 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).
    [Crossref]
  17. T. B. Bahder, “Eight-band k∙p model of strained zinc-blende crystals,” Phys. Rev. B 41(17), 11992–12001 (1990).
    [Crossref]
  18. C. G. Van de Walle and Van de Walle CG, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
    [Crossref] [PubMed]
  19. B. A. Foreman, “Elimination of spurious solutions from eight-band k∙p theory,” Phys. Rev. B 56(20), R12748 (1997).
    [Crossref]
  20. S. Birner, “Modeling of semiconductor nanostructures and semiconductor-electrolyte interfaces”, Ph.D. thesis, (Technical University Muenchen, Germany, 2011).
  21. S.-W. Chang and S. L. Chuang, “Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers,” IEEE J. Quantum Electron. 43(3), 249–256 (2007).
    [Crossref]
  22. S. L. Chuang, Physics of Photonic Devices, 2nd ed., (Wiley, 2009).
  23. G.-E. Chang, S.-W. Chang, and S. L. Chuang, “Theory for n-type doped, tensile-strained Ge-Si(x)Ge(y)Sn1-x-y quantum-well lasers at telecom wavelength,” Opt. Express 17(14), 11246–11258 (2009).
    [Crossref] [PubMed]
  24. C. Hilsum, “Simple empirical relationship between mobility and carrier concentration,” Electron. Lett. 10(13), 259–260 (1974).
    [Crossref]
  25. B. G. Streetman, Solid State Electronic Devices, 4th ed. (Prentice-Hall, 1995).
  26. S. M. Sze and J. C. Irvin, “Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300°K,” Solid-State Electron. 11(6), 599–602 (1968).
    [Crossref]
  27. M. Lundstrom, Fundamentals of Carrier Transport, 2nd ed. (Cambridge University, 2000).
  28. 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).
    [Crossref] [PubMed]
  29. 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).
    [Crossref]
  30. V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
    [Crossref]

2016 (2)

R. W. Millar, K. Gallacher, J. Frigerio, A. Ballabio, A. Bashir, I. MacLaren, G. Isella, and D. J. Paul, “Analysis of Ge micro-cavities with in-plane tensile strains above 2%,” Opt. Express 24(5), 4365–4374 (2016).
[Crossref]

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

2015 (1)

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

2014 (1)

D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
[Crossref]

2013 (3)

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Y. Cai, Z. Han, X. Wang, R. Camacho-Aguilera, L. C. Kimerling, J. Michel, and J. Liu, “Analysis of threshold current behavior for bulk and quantum-well germanium laser structures,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1901009 (2013).
[Crossref]

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 (2)

R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, and J. Michel, “An electrically pumped germanium laser,” Opt. Express 20(10), 11316–11320 (2012).
[Crossref] [PubMed]

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

2010 (2)

2009 (1)

2007 (2)

2006 (2)

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).
[Crossref]

1997 (1)

B. A. Foreman, “Elimination of spurious solutions from eight-band k∙p theory,” Phys. Rev. B 56(20), R12748 (1997).
[Crossref]

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).
[Crossref] [PubMed]

1990 (3)

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).
[Crossref]

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

H. K. Choi and C. A. Wang, “InGaAs/AlGaAs strained single quantum well diode lasers with extremely low threshold current density and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
[Crossref]

1989 (1)

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

1988 (1)

A. Yariv, “Scaling laws and minimum threshold currents for quantum-confined semiconductor lasers,” Appl. Phys. Lett. 53(12), 1033–1035 (1988).
[Crossref]

1974 (1)

C. Hilsum, “Simple empirical relationship between mobility and carrier concentration,” Electron. Lett. 10(13), 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(6), 599–602 (1968).
[Crossref]

Bahder, T. B.

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

Ballabio, A.

Bashir, A.

Beaudoin, G.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Bellet Amalric, E.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Bessette, J. T.

Boucaud, P.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Bowers, J. E.

Brongersma, M. L.

D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
[Crossref]

Buca, D.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

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).
[Crossref]

Cai, Y.

Y. Cai, Z. Han, X. Wang, R. Camacho-Aguilera, L. C. Kimerling, J. Michel, and J. Liu, “Analysis of threshold current behavior for bulk and quantum-well germanium laser structures,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1901009 (2013).
[Crossref]

R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, and J. Michel, “An electrically pumped germanium laser,” Opt. Express 20(10), 11316–11320 (2012).
[Crossref] [PubMed]

Calvo, V.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Camacho-Aguilera, R.

Y. Cai, Z. Han, X. Wang, R. Camacho-Aguilera, L. C. Kimerling, J. Michel, and J. Liu, “Analysis of threshold current behavior for bulk and quantum-well germanium laser structures,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1901009 (2013).
[Crossref]

J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, “Ge-on-Si laser operating at room temperature,” Opt. Lett. 35(5), 679–681 (2010).
[Crossref] [PubMed]

Camacho-Aguilera, R. E.

Chaigneau, M.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Chang, G.-E.

Chang, S.-W.

G.-E. Chang, S.-W. Chang, and S. L. Chuang, “Theory for n-type doped, tensile-strained Ge-Si(x)Ge(y)Sn1-x-y quantum-well lasers at telecom wavelength,” Opt. Express 17(14), 11246–11258 (2009).
[Crossref] [PubMed]

S.-W. Chang and S. L. Chuang, “Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers,” IEEE J. Quantum Electron. 43(3), 249–256 (2007).
[Crossref]

Chelnokov, A.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Chiussi, S.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Choi, H. K.

H. K. Choi and C. A. Wang, “InGaAs/AlGaAs strained single quantum well diode lasers with extremely low threshold current density and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
[Crossref]

Chrastina, D.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Chuang, S. L.

G.-E. Chang, S.-W. Chang, and S. L. Chuang, “Theory for n-type doped, tensile-strained Ge-Si(x)Ge(y)Sn1-x-y quantum-well lasers at telecom wavelength,” Opt. Express 17(14), 11246–11258 (2009).
[Crossref] [PubMed]

S.-W. Chang and S. L. Chuang, “Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers,” IEEE J. Quantum Electron. 43(3), 249–256 (2007).
[Crossref]

Cohen, O.

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).
[Crossref]

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).
[Crossref]

de Kersauson, M.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Duchemin, I.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

El Kurdi, M.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Escalante, J. M.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Faist, J.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

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).

Fang, A. W.

Fathpour, S.

Fishman, G.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Foreman, B. A.

B. A. Foreman, “Elimination of spurious solutions from eight-band k∙p theory,” Phys. Rev. B 56(20), R12748 (1997).
[Crossref]

Fowler, D.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Frigerio, J.

R. W. Millar, K. Gallacher, J. Frigerio, A. Ballabio, A. Bashir, I. MacLaren, G. Isella, and D. J. Paul, “Analysis of Ge micro-cavities with in-plane tensile strains above 2%,” Opt. Express 24(5), 4365–4374 (2016).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Gallacher, K.

Gassenq, A.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Geiger, R.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Ghrib, A.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Gomez, E.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Grützmacher, D.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Guilloy, K.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Han, Z.

Y. Cai, Z. Han, X. Wang, R. Camacho-Aguilera, L. C. Kimerling, J. Michel, and J. Liu, “Analysis of threshold current behavior for bulk and quantum-well germanium laser structures,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1901009 (2013).
[Crossref]

Hartmann, J. M.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Hartmann, J.-M.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Hilsum, C.

C. Hilsum, “Simple empirical relationship between mobility and carrier concentration,” Electron. Lett. 10(13), 259–260 (1974).
[Crossref]

Ikonic, Z.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[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(6), 599–602 (1968).
[Crossref]

Isella, G.

R. W. Millar, K. Gallacher, J. Frigerio, A. Ballabio, A. Bashir, I. MacLaren, G. Isella, and D. J. Paul, “Analysis of Ge micro-cavities with in-plane tensile strains above 2%,” Opt. Express 24(5), 4365–4374 (2016).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Jakomin, R.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Jalali, B.

Jones, R.

Kang, J.-H.

D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
[Crossref]

Kimerling, L. C.

Koch, T. L.

Liu, J.

Luysberg, M.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

MacLaren, I.

Mantl, S.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Marin, E.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Michel, J.

Millar, R. W.

Minamisawa, R. A.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Mussler, G.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Nam, D.

D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
[Crossref]

Ndong, G.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Niquet, Y. M.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Ossikovski, R.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Osvaldo Dias, G.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Pan, D.

Paniccia, M. J.

Park, H.

Patel, N.

Pauc, N.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Paul, D. J.

Reboud, V.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

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).
[Crossref] [PubMed]

Rieutord, F.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Romagnoli, M.

Rouchon, D.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Sagnes, I.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Saraswat, K. C.

D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
[Crossref]

Sauvage, S.

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

Schiefler, G.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Sigg, H.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Soref, R.

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[Crossref]

Spolenak, R.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Stoica, T.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Süess, M. J.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Sukhdeo, D. S.

D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
[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(6), 599–602 (1968).
[Crossref]

Tardif, S.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Van de Walle, C. G.

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

von den Driesch, N.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Wang, C. A.

H. K. Choi and C. A. Wang, “InGaAs/AlGaAs strained single quantum well diode lasers with extremely low threshold current density and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
[Crossref]

Wang, X.

Y. Cai, Z. Han, X. Wang, R. Camacho-Aguilera, L. C. Kimerling, J. Michel, and J. Liu, “Analysis of threshold current behavior for bulk and quantum-well germanium laser structures,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1901009 (2013).
[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(18), 11272–11277 (2007).
[Crossref] [PubMed]

Widiez, J.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Wirths, S.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

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).
[Crossref]

Yariv, A.

A. Yariv, “Scaling laws and minimum threshold currents for quantum-confined semiconductor lasers,” Appl. Phys. Lett. 53(12), 1033–1035 (1988).
[Crossref]

Zabel, T.

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Appl. Phys. Lett. (4)

A. Ghrib, M. de Kersauson, M. El Kurdi, R. Jakomin, G. Beaudoin, S. Sauvage, G. Fishman, G. Ndong, M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud, “Control of tensile strain in germanium waveguides through silicon nitride layers,” Appl. Phys. Lett. 100(20), 201104 (2012).
[Crossref]

A. Yariv, “Scaling laws and minimum threshold currents for quantum-confined semiconductor lasers,” Appl. Phys. Lett. 53(12), 1033–1035 (1988).
[Crossref]

H. K. Choi and C. A. Wang, “InGaAs/AlGaAs strained single quantum well diode lasers with extremely low threshold current density and high efficiency,” Appl. Phys. Lett. 57(4), 321–323 (1990).
[Crossref]

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).
[Crossref]

Electron. Lett. (1)

C. Hilsum, “Simple empirical relationship between mobility and carrier concentration,” Electron. Lett. 10(13), 259–260 (1974).
[Crossref]

IEEE J. Quantum Electron. (1)

S.-W. Chang and S. L. Chuang, “Theory of optical gain of Ge-SixGeySn1−x−y quantum-well lasers,” IEEE J. Quantum Electron. 43(3), 249–256 (2007).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Cai, Z. Han, X. Wang, R. Camacho-Aguilera, L. C. Kimerling, J. Michel, and J. Liu, “Analysis of threshold current behavior for bulk and quantum-well germanium laser structures,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1901009 (2013).
[Crossref]

J. Appl. Phys. (1)

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).

J. Lightwave Technol. (1)

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).
[Crossref]

Nat. Photonics (3)

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[Crossref]

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Photonics Res. (1)

D. S. Sukhdeo, D. Nam, J.-H. Kang, M. L. Brongersma, and K. C. Saraswat, “Direct bandgap germanium-on-silicon inferred from 5.7% <100> uniaxial tensile strain [Invited],” Photonics Res. 2(3), A8–A13 (2014).
[Crossref]

Phys. Rev. B (2)

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

B. A. Foreman, “Elimination of spurious solutions from eight-band k∙p theory,” Phys. Rev. B 56(20), R12748 (1997).
[Crossref]

Phys. Rev. B Condens. Matter (2)

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

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).
[Crossref] [PubMed]

Proc. SPIE (1)

V. Reboud, A. Gassenq, G. Osvaldo Dias, K. Guilloy, J. M. Escalante, S. Tardif, N. Pauc, J.-M. Hartmann, J. Widiez, E. Gomez, E. Bellet Amalric, D. Fowler, D. Rouchon, I. Duchemin, Y. M. Niquet, F. Rieutord, J. Faist, R. Geiger, T. Zabel, E. Marin, H. Sigg, A. Chelnokov, and V. Calvo, “Ultra-high amplified strains in 200-mm optical germanium-on-insulator (GeOI) substrates: towards CMOS-compatible Ge lasers,” Proc. SPIE 9752, 97520F (2016).
[Crossref]

Solid-State Electron. (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(6), 599–602 (1968).
[Crossref]

Other (4)

M. Lundstrom, Fundamentals of Carrier Transport, 2nd ed. (Cambridge University, 2000).

B. G. Streetman, Solid State Electronic Devices, 4th ed. (Prentice-Hall, 1995).

S. Birner, “Modeling of semiconductor nanostructures and semiconductor-electrolyte interfaces”, Ph.D. thesis, (Technical University Muenchen, Germany, 2011).

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Band structure of (a) unstrained and (b) 4% uniaxial tensile strained Ge/Ge0.85Si0.15 QW
Fig. 2
Fig. 2 Band lineups and subband edges of 4% uniaxial tensile strained Ge/Ge0.85Si0.15 QW (a) conduction band (b) valence band
Fig. 3
Fig. 3 The ratio of electron density in Γ-valley to the total electron density versus the injected carrier density at various (a) uniaxial tensile strain with a doping concentration of 1× 10 19 cm -3 and (b) n-type doping concentration with a strain value of 4%.
Fig. 4
Fig. 4 (a) Gain spectra for TE-polarized light and FCA loss of the QW under various tensile strain value. The n-type doping concentration is 1× 10 19 cm 3 . The injected carrier density is 4× 10 19 cm 3 . (b) Gain spectra for TE-polarized light and FCA loss of the QW under various n-type doping concentration. The tensile strain value is 4%. The injected carrier density is 4× 10 19 cm 3 .
Fig. 5
Fig. 5 Neat peak gain for TE-polarized light as a function of (a) tensile strain and doping concentration with an injected carrier density of 4× 10 19 cm 3 , (b) tensile strain and injected carrier density with a doping concentration of 1× 10 19 cm 3 , (c) doping concentration and injected carrier density with a strain value of 4%.

Tables (1)

Tables Icon

Table 1 Material parameters for bulk Ge and Si at 300K in the calculationa

Equations (32)

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

| S ,| X ,| Y ,| Z ,| S ,| X ,| Y ,| Z
ψ m (r, k t )= e i k t ρ A i=1 8 g m (i) (z)| u i
H= H 0 + H so + H st
( H 0 4×4 H 0 4×4 ),( H st 4×4 H st 4×4 )
H 0 4×4 =( E c +S k 2 iP k x iP k y iP k z iP k x E v,av + 2 k 2 /2 m 0 L' k x 2 +M( k y 2 + k z 2 ) N' k x k y N' k x k z iP k y N' k y k x E v,av + 2 k 2 /2 m 0 L' k y 2 +M( k x 2 + k z 2 ) N' k y k z iP k z N' k z k x N' k z k y E v,av + 2 k 2 /2 m 0 L' k z 2 +M( k x 2 + k y 2 ) )
S= 1 m c E p E g +2Δ/3 E g ( E g +Δ) L'=L+ P 2 E g N'=N+ P 2 E g
E p =( 1 m c 1) E g ( E g +Δ) E g +2Δ/3
H st 4×4 =( a c Tr(ε) 0 0 0 0 l ε xx +m( ε yy + ε zz ) n ε xy n ε xz 0 n ε xy l ε yy +m( ε xx + ε zz ) n ε yz 0 n ε xz n ε yz l ε zz +m( ε xx + ε yy ) )
ε yy = ε zz = C 12 C 12 + C 11 ε xx
l=a+2b m=ab n= 3 d
H so 8×8 = Δ 3 ( 0 0 0 0 0 0 0 0 0 0 i 0 0 0 0 1 0 i 0 0 0 0 0 i 0 0 0 0 0 1 i 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 i 0 0 0 0 i 0 i 0 0 0 1 i 0 0 0 0 0 )
j=1 8 H i,j ( k ^ z =i z ) g m (j) (z, k t ) = E m g m (i) (z, k t )
k x N' k z = k x N + k z + k z N k x N + =N'M, N =M
H L [111] χ l, k t (z)= E l, k t χ l, k t (z)
g(ω)= π q 2 n r c ε 0 ω L z m 0 2 n c , n v d k t 4 π 2 | e ^ M n c , n v ( k t ) | 2 ( f n c f n v ) /πτ [ E n c ( k t ) E n v ( k t )ω ] 2 + (/τ) 2
f n c = 1 1+exp[ ( E n c ( k t ) F c )/ k B T ] , f n v = 1 1+exp[ ( E n v ( k t ) F v )/ k B T ]
| x ^ M m,n ( k t ) |= ψ m (r, k t ) | p x | ψ n (r, k t ) = E p m 0 2 dz[ g m (1) * (z) g n (2) (z)+ g m (5) * (z) g n (6) (z) g m (2) * (z) g n (1) (z) g m (6) * (z) g n (5) (z) ]
| y ^ M m,n ( k t ) |= ψ m (r, k t ) | p y | ψ n (r, k t ) = E p m 0 2 dz[ g m (1) * (z) g n (3) (z)+ g m (5) * (z) g n (7) (z) g m (3) * (z) g n (1) (z) g m (7) * (z) g n (5) (z) ]
| z ^ M m,n ( k t ) |= ψ m (r, k t ) | p z | ψ n (r, k t ) = E p m 0 2 dz[ g m (1) * (z) g n (4) (z)+ g m (5) * (z) g n (8) (z) g m (4) * (z) g n (1) (z) g m (8) * (z) g n (5) (z) ]
α FCA = λ 2 q 2 4 π 2 c 3 ε 0 n r [ i n Γ i η Γ × m Γ i + j n h j η h × m h j + k n L k η L × m L k ]
μ L = 3900 1+ N D × 10 17 , μ h = 1900 1+ N A ×2.1× 10 17 m L * = 3 1/ m l,L * +2/ m t,L * , m h * = m hh * 3/2 + m lh * 3/2 m hh * 1/2 + m lh * 1/2
σ υ,ξ = q 2 2 π 2 2 L z τ f 0 k υ E k ξ d k x d k y
n 0 + N A = p 0 + N D +
n 0 N D + N A >> p 0 = n i 2 n 0
n= n 0 +δn= n Γ + n L
p= p 0 +δp
n Γ = n c 1 2 π 2 L z 1 1+exp[ ( E n c Γ ( k t ) F c )/ k B T ] d k x d k y
n L = γ 2 π 2 L z 1 1+exp[ ( E γ L ( k t ) F c )/ k B T ] d k x d k y
p= n v 1 2 π 2 L z 1 1+exp[ ( F v E n v h ( k t ))/ k B T ] d k x d k y
E g Γ,GeSi =0.7985x+4.185(1x)0.14x(1x)
Q(x)=Q(0)+αln(1W x β ) W=1exp{ [Q(1)Q(0)]/α }
α=6.7064,β=1.35 L(0)=6.69,M(0)=4.62,N(0)=8.56 L(1)=21.65,M(1)=5.02,N(1)=23.48

Metrics