Abstract

This paper describes a method for calculating gain spectra of quantum well laser structures. The approach is based on the Semiconductor Bloch equations, with Coulomb correlation effects treated at the level of quantum kinetic theory in the Markovian limit. Results obtained from applying this method to an InGaN quantum well laser are presented.

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References

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  1. B. Zee, "Broadening mechanism in semiconductor (GaAs) lasers: limitations to single mode power emission," IEEE J. Quantum Electron. QE-14, 727 (1978).
    [CrossRef]
  2. M. Yamada and Y. Suematsu, "Analysis of gain suppression in undoped injection lasers," J. Appl. Phys. 52, 2653 (1981).
    [CrossRef]
  3. W.W. Chow, P. M. Smowton, P. Blood, A. Girndt, F. Jahnke and S.W.Koch, "Comparison of experimental and theoretical GaInP quantum well gain spectra," Appl. Phys. Lett. 71, 157 (1997).
    [CrossRef]
  4. M. Lindberg and S. W. Koch, "Effective Bloch equations for semiconductors," Phys. Rev. B38, 3342 (1988).
  5. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, Singapore, 1994).
  6. W. W. Chow, S. W. Koch and M. Sargent III, Semiconductor-Laser Physics (Springer Verlag, Berlin, 1994).
    [CrossRef]
  7. T. Rappen, U-G Peter, M. Wegener and W. Schafer, "Polarization dependence of dephasing processes: A probe for many-body effects," Phys. Rev. B49, 10774 (1994).
  8. F. Rossi, S. Hass and T. Kuhn, "Ultrafast relaxation of photoexcited carriers: The role of coherence in the generation process," Phys. Rev. Lett. 72, 152 (1994).
    [CrossRef] [PubMed]
  9. A. Knorr, S. Hughes, S. W. Koch, R. Indik, M. Mlejnek, R. Binder, J. V. Moloney, "The influence of electron-hole Scattering on linear gain spectra," Solid.State Commun. 100, 555 (1996).
    [CrossRef]
  10. W. W. Chow, A. Knorr, S. Hughes, A. Girndt and S. W. Koch, "Carrier correlation effects in a quantum-well semiconductor laser medium," IEEE J. Sel. Top. Quantum Electron. 3, 136 (1997).
    [CrossRef]
  11. H. Amano, M. Kito, K. Hiramatsu and I. Akasaki, "P-type conduction in Mg-doped GaN treated with low-energy electron beam irradiation (LEEBI)," Jpn. J. Appl. Phys. 28, L2112 (1989).
    [CrossRef]
  12. S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimota and H, Kiyoku, "Room-termperature continuous-wave operation of InGaN multi-quantum-well structure laser diodes," Appl. Phys. Letts. 69, 4056 (1996).
    [CrossRef]
  13. S. L. Chuang and C. S. Chang, " ~ k ~ p method for strained wurzite semiconductors," Phys. Rev. B54, 2491 (1996).
  14. A. F. Wright and J. S. Nelson, "Consistent structural properties for AlN, GaN and InN," Phys. Rev. B51, 7866 (1995) and references.
  15. S. J. Jenkins, G. P. Srivastava and J. C. Inkson, "Simple approach to self-energy corrections in semiconductors and insulators," Phys. Rev. B48, 4388 (1993).
  16. S. H. Wei and A. Zunger, "Valence-band splittings and band offsetsof AlN, GaN and InN," Appl. Phys. Letts. 69, 2719 (1996).
    [CrossRef]
  17. F. Jain and W. Huang, "Modeling of optical gain in In/gaN-AlGaN and InxGa1 quantum well lasers," IEEE J. Quantum Electron. 32, 859, (1996).
    [CrossRef]

Other

B. Zee, "Broadening mechanism in semiconductor (GaAs) lasers: limitations to single mode power emission," IEEE J. Quantum Electron. QE-14, 727 (1978).
[CrossRef]

M. Yamada and Y. Suematsu, "Analysis of gain suppression in undoped injection lasers," J. Appl. Phys. 52, 2653 (1981).
[CrossRef]

W.W. Chow, P. M. Smowton, P. Blood, A. Girndt, F. Jahnke and S.W.Koch, "Comparison of experimental and theoretical GaInP quantum well gain spectra," Appl. Phys. Lett. 71, 157 (1997).
[CrossRef]

M. Lindberg and S. W. Koch, "Effective Bloch equations for semiconductors," Phys. Rev. B38, 3342 (1988).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, Singapore, 1994).

W. W. Chow, S. W. Koch and M. Sargent III, Semiconductor-Laser Physics (Springer Verlag, Berlin, 1994).
[CrossRef]

T. Rappen, U-G Peter, M. Wegener and W. Schafer, "Polarization dependence of dephasing processes: A probe for many-body effects," Phys. Rev. B49, 10774 (1994).

F. Rossi, S. Hass and T. Kuhn, "Ultrafast relaxation of photoexcited carriers: The role of coherence in the generation process," Phys. Rev. Lett. 72, 152 (1994).
[CrossRef] [PubMed]

A. Knorr, S. Hughes, S. W. Koch, R. Indik, M. Mlejnek, R. Binder, J. V. Moloney, "The influence of electron-hole Scattering on linear gain spectra," Solid.State Commun. 100, 555 (1996).
[CrossRef]

W. W. Chow, A. Knorr, S. Hughes, A. Girndt and S. W. Koch, "Carrier correlation effects in a quantum-well semiconductor laser medium," IEEE J. Sel. Top. Quantum Electron. 3, 136 (1997).
[CrossRef]

H. Amano, M. Kito, K. Hiramatsu and I. Akasaki, "P-type conduction in Mg-doped GaN treated with low-energy electron beam irradiation (LEEBI)," Jpn. J. Appl. Phys. 28, L2112 (1989).
[CrossRef]

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimota and H, Kiyoku, "Room-termperature continuous-wave operation of InGaN multi-quantum-well structure laser diodes," Appl. Phys. Letts. 69, 4056 (1996).
[CrossRef]

S. L. Chuang and C. S. Chang, " ~ k ~ p method for strained wurzite semiconductors," Phys. Rev. B54, 2491 (1996).

A. F. Wright and J. S. Nelson, "Consistent structural properties for AlN, GaN and InN," Phys. Rev. B51, 7866 (1995) and references.

S. J. Jenkins, G. P. Srivastava and J. C. Inkson, "Simple approach to self-energy corrections in semiconductors and insulators," Phys. Rev. B48, 4388 (1993).

S. H. Wei and A. Zunger, "Valence-band splittings and band offsetsof AlN, GaN and InN," Appl. Phys. Letts. 69, 2719 (1996).
[CrossRef]

F. Jain and W. Huang, "Modeling of optical gain in In/gaN-AlGaN and InxGa1 quantum well lasers," IEEE J. Quantum Electron. 32, 859, (1996).
[CrossRef]

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Figures (2)

Figure 1.
Figure 1.

Calculated TE gain spectra for a 2nm wurtzite In0.2Ga0.8N/GaN quantum well at T = 300K and densities N = 1012 to 8 × 1012cm-2, in increments of 1012cm-2.

Figure 2.
Figure 2.

Expanded view of the gain portion of the spectra shown in Fig. 1.

Equations (12)

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d dt p k ν e , ν h = i ω k ν e , ν h p k ν e , ν h i Ω k ν e , ν h ( n k ν e + n k ν h 1 )
( Γ k ν e + Γ k ν h ) p k ν e , ν h + q ( Γ k , q ν e + Γ k , q ν h ) p k + q ν e , ν h .
ω k ν e , ν h ( N ) = ħ 1 [ ε e , k ν e + ε h , k ν h + E g , 0 + Δ ε x ν e , ν h ( N ) ] ,
Δ ε x ν e , ν h = q ( V q ν e , ν e , ν e , ν e n k ν e + V q ν h , ν h , ν h , ν h n k ν h ) ,
Ω k ν e , ν h ( N ) = 1 ħ ( μ k ν e , ν h E + q V q ν e , ν h , ν h , ν e p k + q ν e , ν h ( N ) ) ,
V q ν , ν , ν , ν = f q ν , ν , ν , ν e 2 2 ε b A q ,
f q ν , ν , ν , ν = dz dz ' u ν ( z ) u ν ( z ) e q z z u ν ( z ) u ν ( z )
Γ k ν = ν q , k 2 π ħ ( W q ν , ν , ν , ν ) 2 D ( ε k ν + ε k ν ε k + q ν ε k q ν )
× [ n k + q ν ( 1 n k ν ) n k q ν + ( 1 n k + q ν ) n k ν ( 1 n k q ν ) ] ,
Γ k , q ν = ν k 2 π ħ ( W q ν , ν , ν , ν ) 2 D ( ε k + q ν + ε k q ν ε k ν ε k ν )
× [ ( 1 n k ν ) ( 1 n k ν ) n k q ν + n k ν n k ν ( 1 n k q ν ) ] .
G = 2 ω ε 0 ncVε Im ( ν e , , ν h , k ( μ k ν e , ν h ) * p k ν e , ν h e iωt ) ,

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