Abstract

Bandstructure properties in wurtzite quantum wells can change appreciably with changing carrier density because of screening of quantum-confined Stark effect. An approach for incorporating these changes in an InGaN light-emitting-diode model is described. Bandstructure is computed for different carrier densities by solving Poisson and k·p equations in the envelop approximation. The information is used as input in a dynamical model for populations in momentum-resolved electron and hole states. Application of the approach is illustrated by modeling device internal quantum efficiency as a function of excitation.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Technol. 3, 160–175 (2007).
    [CrossRef]
  2. M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
    [CrossRef]
  3. Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
    [CrossRef]
  4. A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
    [CrossRef]
  5. S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
    [CrossRef]
  6. I. A. Pope, P. M. Smowton, P. Blood, and J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
    [CrossRef]
  7. H.-Y Ryu, H.-S. Kim, and J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114–081117 (2009).
    [CrossRef]
  8. J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
    [CrossRef]
  9. K. T. Dellaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109–191111 (2009).
    [CrossRef]
  10. A. Bykhovshi, B. Gelmonst, and M. Shur, “The influence of the strain-induced electric field on the charge distribution in GaN-AlN-GaN structure,” J. Appl. Phys. 74, 6734–6739 (1993).
    [CrossRef]
  11. J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
    [CrossRef]
  12. W. W. Chow, M. H. Crawford, J. Y. Tsao, and M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105–121107 (2010).
    [CrossRef]
  13. S. L. Chuang and C. S. Chang, “k · p method for strained wurtzite semiconductors,” Phys. Rev. B 54, 2491–2504 (1996).
    [CrossRef]
  14. E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
    [CrossRef]
  15. W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
    [CrossRef]
  16. I. Waldmueller, W. W. Chow, M. C. Wanke, and E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
    [CrossRef]
  17. W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
    [CrossRef]
  18. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999).
  19. H. Zhao, G. Liu, J. Zhang, J. Poplawsky, V. Dierolf, and N. Tansu, “Approaches for high internal quantum efficiency green InGaN light-emitting diodes with large overlap quantum wells,” Opt. Express 19, A991–A1007 (2011).
    [CrossRef] [PubMed]
  20. W. W. Chow, A. Knorr, and S. W. Koch, “Theory of laser gain in group-III nitrides,” Appl. Phys. Lett. 67, 754–756 (1995).
    [CrossRef]
  21. W. W. Chow, A. F. Wright, and J. S. Nelson, “Theoretical study of room temperate optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
    [CrossRef]
  22. S.-H. Park, D. Ahn, J. Park, and T -T. Lee, “Optical properties of staggered InGaN/InGaN/GaN quantum-well structures with Ga- and N-Faces,” Jpn. J. Appl. Phys. 50, 072101–07214 (2011).
    [CrossRef]
  23. S. J. Jenkins, G. P. Srivastava, and J. C. Inkson, “Simple approach to self-energy corrections in semiconductors and insulators,” Phys. Rev. B 48, 4388–4397 (1993).
    [CrossRef]
  24. A. F. Wright and J. S. Nelson, “Consistent structural properties for AlN, GaN, and InN,” Phys. Rev. B 51, 7866–7869 (1995).
    [CrossRef]
  25. S. H. Wei and A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2711 (1996).
    [CrossRef]
  26. O. Ambacher, “Growth and applications of Group III-nitrides,” J. Phys. D: Appl. Phys. 31, 2653–2710 (1998).
    [CrossRef]
  27. A. Armstrong, Sandia National Laboratories, Albuquerque, NM 87185 (personal communication, 2010).
  28. S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
    [CrossRef]
  29. J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96, 221106–221108 (2010).
    [CrossRef]
  30. Y. Y. Kudryk and A. V. Zinovchuk, “Efficiency droop in InGaN/GaN multiple quantum well light-emitting diodes with nonuniform current spreading,” Semicond. Sci. Technol. 26, 095007–095011 (2011).
    [CrossRef]
  31. C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclassical Opt. 9, 681–691 (1997).
    [CrossRef]
  32. L. V. Keldysh, “Behaviour of non-metallic crystals in strong electric fields,” Sov. Phys. JETP 6, 763–770 (1958).

2011 (3)

S.-H. Park, D. Ahn, J. Park, and T -T. Lee, “Optical properties of staggered InGaN/InGaN/GaN quantum-well structures with Ga- and N-Faces,” Jpn. J. Appl. Phys. 50, 072101–07214 (2011).
[CrossRef]

Y. Y. Kudryk and A. V. Zinovchuk, “Efficiency droop in InGaN/GaN multiple quantum well light-emitting diodes with nonuniform current spreading,” Semicond. Sci. Technol. 26, 095007–095011 (2011).
[CrossRef]

H. Zhao, G. Liu, J. Zhang, J. Poplawsky, V. Dierolf, and N. Tansu, “Approaches for high internal quantum efficiency green InGaN light-emitting diodes with large overlap quantum wells,” Opt. Express 19, A991–A1007 (2011).
[CrossRef] [PubMed]

2010 (3)

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96, 221106–221108 (2010).
[CrossRef]

W. W. Chow, M. H. Crawford, J. Y. Tsao, and M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105–121107 (2010).
[CrossRef]

2009 (2)

H.-Y Ryu, H.-S. Kim, and J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114–081117 (2009).
[CrossRef]

K. T. Dellaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109–191111 (2009).
[CrossRef]

2008 (1)

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

2007 (3)

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Technol. 3, 160–175 (2007).
[CrossRef]

2006 (2)

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

I. Waldmueller, W. W. Chow, M. C. Wanke, and E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

2003 (1)

I. A. Pope, P. M. Smowton, P. Blood, and J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
[CrossRef]

2002 (1)

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

2001 (1)

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

1998 (2)

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

O. Ambacher, “Growth and applications of Group III-nitrides,” J. Phys. D: Appl. Phys. 31, 2653–2710 (1998).
[CrossRef]

1997 (2)

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclassical Opt. 9, 681–691 (1997).
[CrossRef]

W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
[CrossRef]

1996 (3)

W. W. Chow, A. F. Wright, and J. S. Nelson, “Theoretical study of room temperate optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
[CrossRef]

S. L. Chuang and C. S. Chang, “k · p method for strained wurtzite semiconductors,” Phys. Rev. B 54, 2491–2504 (1996).
[CrossRef]

S. H. Wei and A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2711 (1996).
[CrossRef]

1995 (2)

A. F. Wright and J. S. Nelson, “Consistent structural properties for AlN, GaN, and InN,” Phys. Rev. B 51, 7866–7869 (1995).
[CrossRef]

W. W. Chow, A. Knorr, and S. W. Koch, “Theory of laser gain in group-III nitrides,” Appl. Phys. Lett. 67, 754–756 (1995).
[CrossRef]

1993 (2)

A. Bykhovshi, B. Gelmonst, and M. Shur, “The influence of the strain-induced electric field on the charge distribution in GaN-AlN-GaN structure,” J. Appl. Phys. 74, 6734–6739 (1993).
[CrossRef]

S. J. Jenkins, G. P. Srivastava, and J. C. Inkson, “Simple approach to self-energy corrections in semiconductors and insulators,” Phys. Rev. B 48, 4388–4397 (1993).
[CrossRef]

1963 (1)

E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

1958 (1)

L. V. Keldysh, “Behaviour of non-metallic crystals in strong electric fields,” Sov. Phys. JETP 6, 763–770 (1958).

Ahn, D.

S.-H. Park, D. Ahn, J. Park, and T -T. Lee, “Optical properties of staggered InGaN/InGaN/GaN quantum-well structures with Ga- and N-Faces,” Jpn. J. Appl. Phys. 50, 072101–07214 (2011).
[CrossRef]

Ambacher, O.

O. Ambacher, “Growth and applications of Group III-nitrides,” J. Phys. D: Appl. Phys. 31, 2653–2710 (1998).
[CrossRef]

Armstrong, A.

A. Armstrong, Sandia National Laboratories, Albuquerque, NM 87185 (personal communication, 2010).

Azuhata, T.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Blood, P.

I. A. Pope, P. M. Smowton, P. Blood, and J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
[CrossRef]

Bochkareva, N. I.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Bykhovshi, A.

A. Bykhovshi, B. Gelmonst, and M. Shur, “The influence of the strain-induced electric field on the charge distribution in GaN-AlN-GaN structure,” J. Appl. Phys. 74, 6734–6739 (1993).
[CrossRef]

Chang, C. H.

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

Chang, C. S.

S. L. Chuang and C. S. Chang, “k · p method for strained wurtzite semiconductors,” Phys. Rev. B 54, 2491–2504 (1996).
[CrossRef]

Chang-Hasnain, C. J.

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

Chichibu, S. F.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Choi, S.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Chow, W. W.

W. W. Chow, M. H. Crawford, J. Y. Tsao, and M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105–121107 (2010).
[CrossRef]

I. Waldmueller, W. W. Chow, M. C. Wanke, and E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
[CrossRef]

W. W. Chow, A. F. Wright, and J. S. Nelson, “Theoretical study of room temperate optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
[CrossRef]

W. W. Chow, A. Knorr, and S. W. Koch, “Theory of laser gain in group-III nitrides,” Appl. Phys. Lett. 67, 754–756 (1995).
[CrossRef]

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999).

Chrostowski, L.

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

Chuang, S. L.

S. L. Chuang and C. S. Chang, “k · p method for strained wurtzite semiconductors,” Phys. Rev. B 54, 2491–2504 (1996).
[CrossRef]

Craford, M. G.

Crawford, M. H.

W. W. Chow, M. H. Crawford, J. Y. Tsao, and M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105–121107 (2010).
[CrossRef]

Cummings, F.

E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Dai, Q.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Dellaney, K. T.

K. T. Dellaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109–191111 (2009).
[CrossRef]

Dierolf, V.

Dupuis, R. D.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Efremov, A. A.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Egan, A.

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclassical Opt. 9, 681–691 (1997).
[CrossRef]

Fishcer, A. M.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Gardner, N. F.

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

Gelmonst, B.

A. Bykhovshi, B. Gelmonst, and M. Shur, “The influence of the strain-induced electric field on the charge distribution in GaN-AlN-GaN structure,” J. Appl. Phys. 74, 6734–6739 (1993).
[CrossRef]

Girndt, A.

W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
[CrossRef]

Gorbunov, R. I.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Hader, J.

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96, 221106–221108 (2010).
[CrossRef]

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

Hangleiter, A.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

Harbers, G.

Im, J. S.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

Indik, R. A.

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclassical Opt. 9, 681–691 (1997).
[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. B 48, 4388–4397 (1993).
[CrossRef]

Ishida, Y.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Jahnke, F.

W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
[CrossRef]

Jaynes, E.

E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[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. B 48, 4388–4397 (1993).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, “Behaviour of non-metallic crystals in strong electric fields,” Sov. Phys. JETP 6, 763–770 (1958).

Kim, H. J.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Kim, H.-S.

H.-Y Ryu, H.-S. Kim, and J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114–081117 (2009).
[CrossRef]

Kim, J.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Kim, J. K.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Kim, M. H.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Kim, S.-S.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Kitamura, T.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Kneissl, M.

W. W. Chow, M. H. Crawford, J. Y. Tsao, and M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105–121107 (2010).
[CrossRef]

Knorr, A.

W. W. Chow, A. Knorr, and S. W. Koch, “Theory of laser gain in group-III nitrides,” Appl. Phys. Lett. 67, 754–756 (1995).
[CrossRef]

Koch, S. W.

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96, 221106–221108 (2010).
[CrossRef]

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
[CrossRef]

W. W. Chow, A. Knorr, and S. W. Koch, “Theory of laser gain in group-III nitrides,” Appl. Phys. Lett. 67, 754–756 (1995).
[CrossRef]

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999).

Kollmer, H.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

Krames, M. R.

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Technol. 3, 160–175 (2007).
[CrossRef]

Kudryk, Y. Y.

Y. Y. Kudryk and A. V. Zinovchuk, “Efficiency droop in InGaN/GaN multiple quantum well light-emitting diodes with nonuniform current spreading,” Semicond. Sci. Technol. 26, 095007–095011 (2011).
[CrossRef]

Larinvovich, D. A.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Lee, T -T.

S.-H. Park, D. Ahn, J. Park, and T -T. Lee, “Optical properties of staggered InGaN/InGaN/GaN quantum-well structures with Ga- and N-Faces,” Jpn. J. Appl. Phys. 50, 072101–07214 (2011).
[CrossRef]

Linder, N.

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

Liu, G.

Liu, J.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Lutgen, S.

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

Moloney, J. V.

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96, 221106–221108 (2010).
[CrossRef]

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclassical Opt. 9, 681–691 (1997).
[CrossRef]

Mueller, G. O.

Mueller-Mach, R.

Mukai, T.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Müller, G. O.

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

Munkholm, A.

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

Nakanishi, H.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Nelson, J. S.

W. W. Chow, A. F. Wright, and J. S. Nelson, “Theoretical study of room temperate optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
[CrossRef]

A. F. Wright and J. S. Nelson, “Consistent structural properties for AlN, GaN, and InN,” Phys. Rev. B 51, 7866–7869 (1995).
[CrossRef]

Ning, C. Z.

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclassical Opt. 9, 681–691 (1997).
[CrossRef]

Off, J.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

Okumurac, H.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Park, J.

S.-H. Park, D. Ahn, J. Park, and T -T. Lee, “Optical properties of staggered InGaN/InGaN/GaN quantum-well structures with Ga- and N-Faces,” Jpn. J. Appl. Phys. 50, 072101–07214 (2011).
[CrossRef]

Park, S.-H.

S.-H. Park, D. Ahn, J. Park, and T -T. Lee, “Optical properties of staggered InGaN/InGaN/GaN quantum-well structures with Ga- and N-Faces,” Jpn. J. Appl. Phys. 50, 072101–07214 (2011).
[CrossRef]

Park, Y.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Pasenow, B.

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

Piprek, J.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Ponce, F. A.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Pope, I. A.

I. A. Pope, P. M. Smowton, P. Blood, and J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
[CrossRef]

Poplawsky, J.

Rebane, Yu. T.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Rinke, P.

K. T. Dellaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109–191111 (2009).
[CrossRef]

Ryou, J.-H.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

Ryu, H.-Y

H.-Y Ryu, H.-S. Kim, and J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114–081117 (2009).
[CrossRef]

Sabathil, M.

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

Schneider, H. C.

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

Scholz, F.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

Schubert, E. F.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Schubert, M. F.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Shchekin, O. B.

Shen, Y. C.

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

Shim, J.-I.

H.-Y Ryu, H.-S. Kim, and J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114–081117 (2009).
[CrossRef]

Shreter, Yu. G.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Shur, M.

A. Bykhovshi, B. Gelmonst, and M. Shur, “The influence of the strain-induced electric field on the charge distribution in GaN-AlN-GaN structure,” J. Appl. Phys. 74, 6734–6739 (1993).
[CrossRef]

Smowton, P. M.

I. A. Pope, P. M. Smowton, P. Blood, and J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
[CrossRef]

Sohmer, A.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

Sota, T.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[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. B 48, 4388–4397 (1993).
[CrossRef]

Sugiyama, M.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Tansu, N.

Tarkhin, D. V.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Thompson, J. D.

I. A. Pope, P. M. Smowton, P. Blood, and J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
[CrossRef]

Tsao, J. Y.

W. W. Chow, M. H. Crawford, J. Y. Tsao, and M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105–121107 (2010).
[CrossRef]

Van de Walle, C. G.

K. T. Dellaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109–191111 (2009).
[CrossRef]

Waldmueller, I.

I. Waldmueller, W. W. Chow, M. C. Wanke, and E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

Wanke, M. C.

I. Waldmueller, W. W. Chow, M. C. Wanke, and E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

Watanabe, S.

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

Wei, S. H.

S. H. Wei and A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2711 (1996).
[CrossRef]

Wright, A. F.

W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
[CrossRef]

W. W. Chow, A. F. Wright, and J. S. Nelson, “Theoretical study of room temperate optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
[CrossRef]

A. F. Wright and J. S. Nelson, “Consistent structural properties for AlN, GaN, and InN,” Phys. Rev. B 51, 7866–7869 (1995).
[CrossRef]

Young, E. W.

I. Waldmueller, W. W. Chow, M. C. Wanke, and E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

Zhang, J.

Zhao, H.

Zhou, L.

Zinovchuk, A. V.

Y. Y. Kudryk and A. V. Zinovchuk, “Efficiency droop in InGaN/GaN multiple quantum well light-emitting diodes with nonuniform current spreading,” Semicond. Sci. Technol. 26, 095007–095011 (2011).
[CrossRef]

Zunger, A.

S. H. Wei and A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2711 (1996).
[CrossRef]

Appl. Phys. Lett. (13)

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507–183510 (2007).
[CrossRef]

Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101–141101 (2007).
[CrossRef]

I. A. Pope, P. M. Smowton, P. Blood, and J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
[CrossRef]

H.-Y Ryu, H.-S. Kim, and J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114–081117 (2009).
[CrossRef]

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103–261105 (2008).
[CrossRef]

K. T. Dellaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109–191111 (2009).
[CrossRef]

W. W. Chow, M. H. Crawford, J. Y. Tsao, and M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105–121107 (2010).
[CrossRef]

W. W. Chow, A. Knorr, and S. W. Koch, “Theory of laser gain in group-III nitrides,” Appl. Phys. Lett. 67, 754–756 (1995).
[CrossRef]

W. W. Chow, A. F. Wright, and J. S. Nelson, “Theoretical study of room temperate optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
[CrossRef]

W. W. Chow, A. F. Wright, A. Girndt, F. Jahnke, and S. W. Koch, “Microscopic theory of gain for an In-GaN/AlGaN quantum well laser,” Appl. Phys. Lett. 71, 2608–2610 (1997).
[CrossRef]

S. H. Wei and A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2711 (1996).
[CrossRef]

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, and F. A. Ponce, “Improvement of peak quantum efficiency and efficiency droop in III-nitride visible light-emitting diodes with an InAlN electron-blocking layer,” Appl. Phys. Lett. 96, 221105–221107 (2010).
[CrossRef]

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96, 221106–221108 (2010).
[CrossRef]

IEEE J. Quantum Electron. (2)

W. W. Chow, H. C. Schneider, S. W. Koch, C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Nonequilibrium model for semiconductor laser modulation response,” IEEE J. Quantum Electron. 38, 402–409 (2002).
[CrossRef]

I. Waldmueller, W. W. Chow, M. C. Wanke, and E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

J. Appl. Phys. (1)

A. Bykhovshi, B. Gelmonst, and M. Shur, “The influence of the strain-induced electric field on the charge distribution in GaN-AlN-GaN structure,” J. Appl. Phys. 74, 6734–6739 (1993).
[CrossRef]

J. Display Technol. (1)

J. Phys. D: Appl. Phys. (1)

O. Ambacher, “Growth and applications of Group III-nitrides,” J. Phys. D: Appl. Phys. 31, 2653–2710 (1998).
[CrossRef]

J. Vac. Sci. Technol. B (1)

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, and T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Jpn. J. Appl. Phys. (1)

S.-H. Park, D. Ahn, J. Park, and T -T. Lee, “Optical properties of staggered InGaN/InGaN/GaN quantum-well structures with Ga- and N-Faces,” Jpn. J. Appl. Phys. 50, 072101–07214 (2011).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (4)

S. J. Jenkins, G. P. Srivastava, and J. C. Inkson, “Simple approach to self-energy corrections in semiconductors and insulators,” Phys. Rev. B 48, 4388–4397 (1993).
[CrossRef]

A. F. Wright and J. S. Nelson, “Consistent structural properties for AlN, GaN, and InN,” Phys. Rev. B 51, 7866–7869 (1995).
[CrossRef]

S. L. Chuang and C. S. Chang, “k · p method for strained wurtzite semiconductors,” Phys. Rev. B 54, 2491–2504 (1996).
[CrossRef]

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, and A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
[CrossRef]

Proc. IEEE (1)

E. Jaynes and F. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
[CrossRef]

Quantum Semiclassical Opt. (1)

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principles fully space-time resolved model of a semiconductor laser,” Quantum Semiclassical Opt. 9, 681–691 (1997).
[CrossRef]

Semicond. Sci. Technol. (1)

Y. Y. Kudryk and A. V. Zinovchuk, “Efficiency droop in InGaN/GaN multiple quantum well light-emitting diodes with nonuniform current spreading,” Semicond. Sci. Technol. 26, 095007–095011 (2011).
[CrossRef]

Semiconductors (1)

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, and Yu. G. Shreter, “Effect of the joule heating on the quantum efficiency and choice of thermal conditions for high-power blue InGaN/GaN LEDs,” Semiconductors 40, 605–610 (2006).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Keldysh, “Behaviour of non-metallic crystals in strong electric fields,” Sov. Phys. JETP 6, 763–770 (1958).

Other (2)

A. Armstrong, Sandia National Laboratories, Albuquerque, NM 87185 (personal communication, 2010).

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials (Springer, 1999).

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 (6)

Fig. 1
Fig. 1

Internal quantum efficiency versus current density for different A/Ab. The curves are computed using the k–resolved model described by Eqs. (11) and (13) for a LED with a In0.2Ga0.8N/GaN multi-QW active region (see Fig. 4).

Fig. 2
Fig. 2

Average QW confinement energies (left axis) and electron-hole wavefunction overlap (right axis) versus carrier density. The curves are extracted from solving k · p and Poisson equations. A negative average hole confinement energy is possible because of the tilt in QW confinement potential and the presence of states in the outer barrier regions cladding the QWs, as shown in Fig. 4(a).

Fig. 3
Fig. 3

Internal quantum efficiency versus current density computed using Eq. (25) from an extended ABC model, which isolates bandstructure effects. The curves are for different η, a free parameter accounting for difference between QW and barrier bimolecular radiative recombination coefficients (B and Bb, respectively) because of differences in densities of state.

Fig. 4
Fig. 4

Absolute square of envelope functions for electrons and holes for carrier densities, N2d = (a) 2.25×, (b) 3.47× and (c) 6.89 × 1013 cm−2. Figure 4(d) is the flat-band limit. Each curve is displaced according to its bandedge energy for clarity. Envelope functions belonging to QW and barrier states are indicated by red and blue curves, respectively. The black lines plot the confinement potentials. The x-axis is along the growth direction.

Fig. 5
Fig. 5

Average QW and barrier bandedge energies (solid and dashed curves, respectively) versus carrier density. Optical emission should be centered approximately at the lower curve. The upper and lower dotted lines indicate the strained-InGaN and unstrained-GaN bulk bandgap energies.

Fig. 6
Fig. 6

Internal quantum efficiency versus current density showing the influence of Auger carrier loss for different QW SRH coefficients. The Auger coefficients are C = 0, 10−32, 5 ×10−32 and 10−31 cm6s−1 (dotted, dashed, dot-dashed and solid curves, respectively).

Equations (25)

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

H = i ɛ i e a i a i + j ɛ j h b j b j + q h ¯ Ω q c q c q i , j , q i j h ¯ Ω q V ɛ b ( a i b j c q + c q b j a i ) .
d a i a i d t = cos i j , q i j Ω q h ¯ V ɛ b [ c q b j a i a i b j c q ] ,
d b j b j d t = i i , q i j Ω q h ¯ V ɛ b [ c q b j a i a i b j c q ] ,
d a i b j c q d t = i ( Ω q Ω i j ) a i b j c q + i i j Ω q h ¯ V ɛ b ( a i a i + b j b j 1 ) c q c q + a i b j b j + ,
d a i b j c q d t = i ( Ω q Ω i j ) a i b j c q i i j Ω q h ¯ V ɛ b [ ( a i a i + b j b j 1 ) c q c q + a i a i b j b j ] .
d a i a i d t = a i a i j , q 2 Ω q h ¯ ɛ b V γ | i j | 2 b j b j [ 1 + ( Ω i j Ω q γ ) 2 ] 1 ,
d b j b j d t = b j b j i , q 2 Ω q h ¯ ɛ b V γ | i j | 2 a i a i [ 1 + ( Ω i j Ω q γ ) 2 ] 1 .
q 2 V ( 2 π ) 3 0 d q 4 π q 2 ,
d a i a i d t = a i a i j n b h ¯ ɛ 0 π c 3 | i j | 2 Ω i j 3 b j b j ,
d b j b j d t = b j b j i n b h ¯ ɛ 0 π c 3 | i j | 2 Ω i j 3 a i a i .
d n σ , α σ , k d t = n σ , n σ , k α σ b α σ , α σ , k n σ , α σ , k A n σ , n σ , k γ c c [ n σ , n σ , k f ( ɛ σ , k , μ σ , T ) ] γ c p [ n σ , n σ , k f ( ɛ σ , k , μ σ L , T L ) ] ,
b α σ , α σ , k = 1 h ¯ ɛ b π c 3 | α α , α σ , k | 2 Ω α σ , α σ , k 3 ,
d n σ , k b d t = b k n e , k b n h , k b + J e N σ p f ( ɛ σ , k b , μ σ p , T p ) ( 1 n σ , k b ) A b n σ , k γ c c [ n σ , k b f ( ɛ σ , k b , μ σ , T ) ] γ c p [ n σ , k b f ( ɛ σ , k b , μ σ L , T L ) ] ,
b k = 1 h ¯ ɛ b π c 3 | k | 2 Ω k 3 ,
k S ( 2 π ) 2 2 0 d k 2 π k and k h S ( 2 π ) 3 2 0 d k 4 π k 2 ,
r | ϕ σ , α σ , k = e i k r m σ β σ A β σ , α σ , k u m σ , β σ ( z ) r | m σ ,
| α e , α h , k | 2 | ϕ e , α e , k | e x | ϕ h , α h , k | 2 = | bulk | 2 ξ α e , α h , k ,
ξ α e , α h , k = 1 4 | β e β h m e m h A β e , α e , k A β h , α h , k × dz u m e , β e ( z ) u m h , β e ( z ) | 2 ,
| bulk | 2 = h ¯ 2 2 m 0 ɛ g ( m 0 m e 1 ) ( 1 + Δ 1 + Δ 2 ɛ g ) ,
IQE = e JS ( α e , α h , k b α e , α h , k n e , α e , k n h , α h , k + k b k n e , k b n h , k b ) .
d N σ d t = B N e N h A N σ ,
d N σ b d t = B b N e b N h b A b N σ b + J e h b ,
d N 2 d d t = β N 2 d 2 A b N 2 d + J e ,
β = h h b N qw B + B b exp ( Δ e + Δ h k B T ) [ 1 + exp ( Δ e k B T ) ] [ 1 + exp ( Δ h k B T ) ] ,
IQE = β N 2 d 2 J / e = 1 2 J 0 J [ J J 0 + 1 1 ] ,

Metrics