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.

© 1998 Optical Society of America

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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. Schäfer, “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, and 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, “k⃗·p⃗ 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-xN quantum-well lasers,” IEEE J. Quantum Electron. 32, 859, (1996).
    [Crossref]

1997 (2)

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]

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]

1996 (5)

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, “k⃗·p⃗ method for strained wurzite semiconductors,” Phys. Rev. B54, 2491 (1996).

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-xN quantum-well lasers,” IEEE J. Quantum Electron. 32, 859, (1996).
[Crossref]

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

1995 (1)

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

1994 (2)

T. Rappen, U-G Peter, M. Wegener, and W. Schäfer, “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]

1993 (1)

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).

1989 (1)

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]

1988 (1)

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

1981 (1)

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

1978 (1)

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

Akasaki, I.

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]

Amano, H.

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]

Binder, R.

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

Blood, P.

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]

Chang, C. S.

S. L. Chuang and C. S. Chang, “k⃗·p⃗ method for strained wurzite semiconductors,” Phys. Rev. B54, 2491 (1996).

Chow, W. W.

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]

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]

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

Chuang, S. L.

S. L. Chuang and C. S. Chang, “k⃗·p⃗ method for strained wurzite semiconductors,” Phys. Rev. B54, 2491 (1996).

Girndt, A.

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]

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]

Hass, S.

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]

Haug, H.

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

Hiramatsu, K.

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]

Huang, W.

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

Hughes, S.

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]

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

Indik, R.

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

Inkson, J. C.

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).

Iwasa, N.

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]

Jahnke, F.

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]

Jain, F.

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

Jenkins, S. J.

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).

Kito, M.

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]

Kiyoku, H,

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]

Knorr, A.

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]

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

Koch, S. W.

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]

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]

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

Kuhn, T.

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]

Lindberg, M.

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

Matsushita, T.

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]

Mlejnek, M.

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

Moloney, J. V.

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

Nagahama, S.

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]

Nakamura, S.

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]

Nelson, J. S

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

Peter, U-G

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

Rappen, T.

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

Rossi, F.

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]

Sargent III, M.

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

Schäfer, W.

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

Senoh, M.

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]

Smowton, P. M.

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]

Srivastava, G. P.

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).

Suematsu, Y.

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

Sugimota, Y.

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]

Wegener, M.

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

Wei, S. H.

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

Wright, A. F.

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

Yamada, M.

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

Yamada, T.

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]

Zee, B.

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

Zunger, A.

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

Appl. Phys. Lett. (1)

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]

Appl. Phys. Letts. (2)

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

IEEE J. Quantum Electron. (2)

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

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

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

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]

J. Appl. Phys. (1)

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

Jpn. J. Appl. Phys. (1)

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]

Phys. Rev. (5)

S. L. Chuang and C. S. Chang, “k⃗·p⃗ 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).

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

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

Phys. Rev. Lett. (1)

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]

Solid.State Commun. (1)

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

Other (2)

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]

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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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