Abstract

The changes in excitation dependence of efficiency with temperature are modeled for a wurtzite InGaN light-emitting diode. The model incorporates bandstructure changes with carrier density because of screening of quantum-confined Stark effect. Bandstructure is computed by solving Poisson and k·p equations in the envelope approximation. The information is used in a dynamical model for populations in momentum-resolved electron and hole states. Application of the approach shows the interplay of quantum-well and barrier emissions giving rise to shape changes in efficiency versus current density with changing temperature, as observed in some experiments.

© 2014 Optical Society of America

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  1. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
    [CrossRef]
  2. D. F. Feezell, J. S. Speck, S. P. DenBaars, S. Nakamura, “Semipolar (2021¯) InGaN/GaN light-emitting diodes for high-efficiency solid-state lighting, ” J. Disp. Technol. 9, 190–198 (2013).
    [CrossRef]
  3. G. Y. Liu, J. Zhang, C. K. Tan, N. Tansu, “Efficiency-droop suppression by using large-bandgap AlGaN thin barrier layers in InGaN quantum-well light-emitting diodes,” IEEE Photonics J. 5, 2201011 (2013).
    [CrossRef]
  4. M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507 (2007).
    [CrossRef]
  5. Y. C. Shen, G. O. Müller, S. Watanabe, N. F. Gardner, A. Munkholm, M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101 (2007).
    [CrossRef]
  6. A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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]
  7. S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
    [CrossRef]
  8. I. A. Pope, P. M. Smowton, P. Blood, J. D. Thompson, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480nm,” Appl. Phys. Lett. 82, 2755–2757 (2003).
    [CrossRef]
  9. J. Hader, J. V. Moloney, S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96, 221106 (2010).
    [CrossRef]
  10. J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103 (2008).
    [CrossRef]
  11. K. T. Dellaney, P. Rinke, C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109 (2009).
    [CrossRef]
  12. W. W. Chow, M. H. Crawford, J. Y. Tsao, M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: Beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105 (2010).
    [CrossRef]
  13. W. W. Chow, “Modeling excitation-dependent bandstructure effects on InGaN light-emitting diode efficiency,” Opt. Express 19, 21818–218312011.
    [CrossRef] [PubMed]
  14. A. Bykhovshi, B. Gelmonst, 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]
  15. J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, A. Hangleiter, “Reduction of oscillator strength due to piezoelectric fields in GaN/AlGaN quantum wells,” Phys. Rev. B 57, R9435–R9438 (1998).
    [CrossRef]
  16. W. Chow, M. Kira, S. W. Koch, “Microscopic theory of optical nonlinearities and spontaneous emission in group-III nitride quantum wells,” Phys. Rev. B. 60, 1947–1952 (1999).
    [CrossRef]
  17. H.-Y Ryu, H.-S. Kim, J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114 (2009).
    [CrossRef]
  18. J. Hader, J. V. Moloney, S. W. Koch, “Temperature-dependence of the internal efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 99, 181127 (2011).
    [CrossRef]
  19. E. Jaynes, F. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89–109 (1963).
    [CrossRef]
  20. I. Waldmueller, W. W. Chow, M. C. Wanke, E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
    [CrossRef]
  21. S. L. Chuang, C. S. Chang, “k· p method for strained wurtzite semiconductors,” Phys. Rev. B 54, 2491–2504 (1996).
    [CrossRef]
  22. S. J. Jenkins, G. P. Srivastava, J. C. Inkson, “Simple approach to self-energy corrections in semiconductors and insulators,” Phys. Rev. B 48, 4388–4397 (1993).
    [CrossRef]
  23. A. F. Wright, J. S. Nelson, “Consistent structural properties for AlN, GaN, and InN,” Phys. Rev. B 51, 7866–7869 (1995).
    [CrossRef]
  24. S. H. Wei, A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2721 (1996).
    [CrossRef]
  25. O. Ambacher, “Growth and applications of Group III-nitrides,” J. Phys. D: Appl. Phys. 31, 2653–2710 (1998).
    [CrossRef]
  26. A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
    [CrossRef]
  27. K. Fujiwara, H. Jimi, K. Kaneda, “Temperature-dependent droop of electroluminescence efficiency in blue (In,Ga)N quantum-well diodes,” Phys. Status Solidi C 6, S814–S817 (2009).
    [CrossRef]
  28. S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, 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 (2010).
    [CrossRef]
  29. N. A. Modine, A. M. Armstrong, M. H. Crawford, W. W. Chow, “Highly nonlinear defect-induced carrier recombination rates in semiconductors,” J. Appl. Phys. 114, 144502 (2013).
    [CrossRef]
  30. W. W. Chow, A. F. Wright, J. S. Nelson, “Theoretical study of room temperature optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
    [CrossRef]

2013

D. F. Feezell, J. S. Speck, S. P. DenBaars, S. Nakamura, “Semipolar (2021¯) InGaN/GaN light-emitting diodes for high-efficiency solid-state lighting, ” J. Disp. Technol. 9, 190–198 (2013).
[CrossRef]

G. Y. Liu, J. Zhang, C. K. Tan, N. Tansu, “Efficiency-droop suppression by using large-bandgap AlGaN thin barrier layers in InGaN quantum-well light-emitting diodes,” IEEE Photonics J. 5, 2201011 (2013).
[CrossRef]

N. A. Modine, A. M. Armstrong, M. H. Crawford, W. W. Chow, “Highly nonlinear defect-induced carrier recombination rates in semiconductors,” J. Appl. Phys. 114, 144502 (2013).
[CrossRef]

2011

W. W. Chow, “Modeling excitation-dependent bandstructure effects on InGaN light-emitting diode efficiency,” Opt. Express 19, 21818–218312011.
[CrossRef] [PubMed]

J. Hader, J. V. Moloney, S. W. Koch, “Temperature-dependence of the internal efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 99, 181127 (2011).
[CrossRef]

2010

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

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

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, 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 (2010).
[CrossRef]

2009

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

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

K. Fujiwara, H. Jimi, K. Kaneda, “Temperature-dependent droop of electroluminescence efficiency in blue (In,Ga)N quantum-well diodes,” Phys. Status Solidi C 6, S814–S817 (2009).
[CrossRef]

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

2008

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

2007

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

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

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

2006

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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, E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

2003

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

2001

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

1999

W. Chow, M. Kira, S. W. Koch, “Microscopic theory of optical nonlinearities and spontaneous emission in group-III nitride quantum wells,” Phys. Rev. B. 60, 1947–1952 (1999).
[CrossRef]

1998

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, 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]

1996

S. H. Wei, A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2721 (1996).
[CrossRef]

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

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

1995

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

1993

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

A. Bykhovshi, B. Gelmonst, 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]

1963

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

Ambacher, O.

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

Armstrong, A. M.

N. A. Modine, A. M. Armstrong, M. H. Crawford, W. W. Chow, “Highly nonlinear defect-induced carrier recombination rates in semiconductors,” J. Appl. Phys. 114, 144502 (2013).
[CrossRef]

Azuhata, T.

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

Bergbauer, W.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

Blood, P.

I. A. Pope, P. M. Smowton, P. Blood, 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, 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, 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. S.

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

Chichibu, S. F.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, 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, 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 (2010).
[CrossRef]

Chow, W.

W. Chow, M. Kira, S. W. Koch, “Microscopic theory of optical nonlinearities and spontaneous emission in group-III nitride quantum wells,” Phys. Rev. B. 60, 1947–1952 (1999).
[CrossRef]

Chow, W. W.

N. A. Modine, A. M. Armstrong, M. H. Crawford, W. W. Chow, “Highly nonlinear defect-induced carrier recombination rates in semiconductors,” J. Appl. Phys. 114, 144502 (2013).
[CrossRef]

W. W. Chow, “Modeling excitation-dependent bandstructure effects on InGaN light-emitting diode efficiency,” Opt. Express 19, 21818–218312011.
[CrossRef] [PubMed]

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

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

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

Chuang, S. L.

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

Craford, M. G.

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

Crawford, M. H.

N. A. Modine, A. M. Armstrong, M. H. Crawford, W. W. Chow, “Highly nonlinear defect-induced carrier recombination rates in semiconductors,” J. Appl. Phys. 114, 144502 (2013).
[CrossRef]

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

Cummings, F.

E. Jaynes, 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, Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507 (2007).
[CrossRef]

Dellaney, K. T.

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

DenBaars, S. P.

D. F. Feezell, J. S. Speck, S. P. DenBaars, S. Nakamura, “Semipolar (2021¯) InGaN/GaN light-emitting diodes for high-efficiency solid-state lighting, ” J. Disp. Technol. 9, 190–198 (2013).
[CrossRef]

Dupuis, R. D.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, 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 (2010).
[CrossRef]

Efremov, A. A.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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]

Feezell, D. F.

D. F. Feezell, J. S. Speck, S. P. DenBaars, S. Nakamura, “Semipolar (2021¯) InGaN/GaN light-emitting diodes for high-efficiency solid-state lighting, ” J. Disp. Technol. 9, 190–198 (2013).
[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, 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 (2010).
[CrossRef]

Fujiwara, K.

K. Fujiwara, H. Jimi, K. Kaneda, “Temperature-dependent droop of electroluminescence efficiency in blue (In,Ga)N quantum-well diodes,” Phys. Status Solidi C 6, S814–S817 (2009).
[CrossRef]

Gardner, N. F.

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

Gelmonst, B.

A. Bykhovshi, B. Gelmonst, 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]

Gorbunov, R. I.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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, S. W. Koch, “Temperature-dependence of the internal efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 99, 181127 (2011).
[CrossRef]

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

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

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

Hangleiter, A.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, 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.

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

Im, J. S.

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

Inkson, J. C.

S. J. Jenkins, G. P. Srivastava, 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, T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Jaynes, E.

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

Jimi, H.

K. Fujiwara, H. Jimi, K. Kaneda, “Temperature-dependent droop of electroluminescence efficiency in blue (In,Ga)N quantum-well diodes,” Phys. Status Solidi C 6, S814–S817 (2009).
[CrossRef]

Kaneda, K.

K. Fujiwara, H. Jimi, K. Kaneda, “Temperature-dependent droop of electroluminescence efficiency in blue (In,Ga)N quantum-well diodes,” Phys. Status Solidi C 6, S814–S817 (2009).
[CrossRef]

Kim, H. J.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, 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 (2010).
[CrossRef]

Kim, H.-S.

H.-Y Ryu, H.-S. Kim, J.-I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95, 081114 (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, 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 (2010).
[CrossRef]

Kim, J. K.

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

Kim, M. H.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507 (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, 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 (2010).
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W. Chow, M. Kira, S. W. Koch, “Microscopic theory of optical nonlinearities and spontaneous emission in group-III nitride quantum wells,” Phys. Rev. B. 60, 1947–1952 (1999).
[CrossRef]

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S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, 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, M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: Beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105 (2010).
[CrossRef]

Koch, S. W.

J. Hader, J. V. Moloney, S. W. Koch, “Temperature-dependence of the internal efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 99, 181127 (2011).
[CrossRef]

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

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

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

W. Chow, M. Kira, S. W. Koch, “Microscopic theory of optical nonlinearities and spontaneous emission in group-III nitride quantum wells,” Phys. Rev. B. 60, 1947–1952 (1999).
[CrossRef]

Kollmer, H.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, 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.

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

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

Larinvovich, D. A.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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]

Laubsch, A.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

Linder, N.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

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

Liu, G. Y.

G. Y. Liu, J. Zhang, C. K. Tan, N. Tansu, “Efficiency-droop suppression by using large-bandgap AlGaN thin barrier layers in InGaN quantum-well light-emitting diodes,” IEEE Photonics J. 5, 2201011 (2013).
[CrossRef]

Liu, J.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fishcer, 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 (2010).
[CrossRef]

Lugauer, H.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

Lutgen, S.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

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

Modine, N. A.

N. A. Modine, A. M. Armstrong, M. H. Crawford, W. W. Chow, “Highly nonlinear defect-induced carrier recombination rates in semiconductors,” J. Appl. Phys. 114, 144502 (2013).
[CrossRef]

Moloney, J. V.

J. Hader, J. V. Moloney, S. W. Koch, “Temperature-dependence of the internal efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 99, 181127 (2011).
[CrossRef]

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

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

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

Mueller, G. O.

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

Mueller-Mach, R.

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

Mukai, T.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, 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, M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101 (2007).
[CrossRef]

Munkholm, A.

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

Nakamura, S.

D. F. Feezell, J. S. Speck, S. P. DenBaars, S. Nakamura, “Semipolar (2021¯) InGaN/GaN light-emitting diodes for high-efficiency solid-state lighting, ” J. Disp. Technol. 9, 190–198 (2013).
[CrossRef]

Nakanishi, H.

S. F. Chichibu, T. Azuhata, M. Sugiyama, T. Kitamura, Y. Ishida, H. Okumurac, H. Nakanishi, T. Sota, 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, J. S. Nelson, “Theoretical study of room temperature optical gain in GaN strained quantum wells,” Appl. Phys. Lett. 68, 296–298 (1996).
[CrossRef]

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

Off, J.

J. S. Im, H. Kollmer, J. Off, A. Sohmer, F. Scholz, 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, T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Park, Y.

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

Pasenow, B.

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

Peter, M.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

Piprek, J.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507 (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, 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 (2010).
[CrossRef]

Pope, I. A.

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

Rebane, Yu. T.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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]

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K. T. Dellaney, P. Rinke, C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94, 191109 (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, 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 (2010).
[CrossRef]

Ryu, H.-Y

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

Sabathil, M.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

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

Scholz, F.

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

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

Schubert, M. F.

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

Shchekin, O. B.

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

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

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

Shreter, Yu. G.

A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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).
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A. Bykhovshi, B. Gelmonst, 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).
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I. A. Pope, P. M. Smowton, P. Blood, 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, 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, T. Mukai, “Optical and structural studies in InGaN quantum well structure laser diodes,” J. Vac. Sci. Technol. B 19, 2177–2183 (2001).
[CrossRef]

Speck, J. S.

D. F. Feezell, J. S. Speck, S. P. DenBaars, S. Nakamura, “Semipolar (2021¯) InGaN/GaN light-emitting diodes for high-efficiency solid-state lighting, ” J. Disp. Technol. 9, 190–198 (2013).
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S. J. Jenkins, G. P. Srivastava, J. C. Inkson, “Simple approach to self-energy corrections in semiconductors and insulators,” Phys. Rev. B 48, 4388–4397 (1993).
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A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

Strebubel, K.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
[CrossRef]

Sugiyama, M.

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

Tan, C. K.

G. Y. Liu, J. Zhang, C. K. Tan, N. Tansu, “Efficiency-droop suppression by using large-bandgap AlGaN thin barrier layers in InGaN quantum-well light-emitting diodes,” IEEE Photonics J. 5, 2201011 (2013).
[CrossRef]

Tansu, N.

G. Y. Liu, J. Zhang, C. K. Tan, N. Tansu, “Efficiency-droop suppression by using large-bandgap AlGaN thin barrier layers in InGaN quantum-well light-emitting diodes,” IEEE Photonics J. 5, 2201011 (2013).
[CrossRef]

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A. A. Efremov, N. I. Bochkareva, R. I. Gorbunov, D. A. Larinvovich, Yu. T. Rebane, D. V. Tarkhin, 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, 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, M. Kneissl, “Internal efficiency of InGaN light-emitting diodes: Beyond a quasiequilibrium model,” Appl. Phys. Lett. 97, 121105 (2010).
[CrossRef]

Van de Walle, C. G.

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

Wagner, J.

A. Laubsch, M. Sabathil, W. Bergbauer, M. Strassburg, H. Lugauer, M. Peter, S. Lutgen, N. Linder, K. Strebubel, J. Wagner, J. Hader, J. V. Moloney, S. W. Koch, “On the origin of IQE-’droop’ in InGaN LEDs,” Phys. Status Solidi C 6, S913–S916 (2009).
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I. Waldmueller, W. W. Chow, M. C. Wanke, E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
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I. Waldmueller, W. W. Chow, M. C. Wanke, 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, M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101 (2007).
[CrossRef]

Wei, S. H.

S. H. Wei, A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2721 (1996).
[CrossRef]

Wright, A. F.

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

A. F. Wright, 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, E. W. Young, “Non-equilibrium many-body theory of intersub-band lasers,” IEEE J. Quantum Electron. 42, 292–301 (2006).
[CrossRef]

Zhang, J.

G. Y. Liu, J. Zhang, C. K. Tan, N. Tansu, “Efficiency-droop suppression by using large-bandgap AlGaN thin barrier layers in InGaN quantum-well light-emitting diodes,” IEEE Photonics J. 5, 2201011 (2013).
[CrossRef]

Zhou, L.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, M. G. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Disp. Technol. 3, 160–175 (2007).
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S. H. Wei, A. Zunger, “Valence band splittings and band offsets of AlN, GaN, and InN,” Appl. Phys. Lett. 69, 2719–2721 (1996).
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Appl. Phys. Lett.

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

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

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

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

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, S. Lutgen, “On the important of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92, 261103 (2008).
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Figures (9)

Fig. 1
Fig. 1

IQE versus current density for LED with single In0.37Ga0.63N quantum well and temperatures TL = 100 to 400K at 50K intervals. The arrows for the TL = 200K IQE curve indicate the current densities for Figs. 3(b) and 3(c).

Fig. 2
Fig. 2

Values of (a) SRH coefficient, (b) Auger coefficient and (c) carrier-phonon scattering rate used in producing the curves in Fig. 1.

Fig. 3
Fig. 3

The solid IQE curves are from Fig. 1, for TL = 200K and 300K. In Fig. 3(a), the dashed and dotted curves are for TL = 200K and C = 3 × 10−31 and 3.7 × 10−31cm6s−1, respectively. In Fig. 3(b), the dashed and dotted curves are for TL = 200K and γcp = 7 × 1011 and 1011s−1, respectively. All other parameters are same as given in Fig. 2.

Fig. 4
Fig. 4

(a) Spontaneous emission contributions from QW and barrier states (solid and dashed curves, respectively) versus current density for T = 200K curve in Fig. 1. Solid curves in (b) and (c) are absolute square of envelope functions at zone center (k = k = 0) for electrons and holes at current densities indicated by arrows in Fig. 4 (a). The x-axis is along the growth direction. Each curve is displaced according to its energy for clarity. Envelope functions belonging to QW and barrier states are indicated by black and grey curves, respectively. Owing to the closeness in hole energies, only every other heavy hole state is plotted. The black dashed lines plot the confinement potentials.

Fig. 5
Fig. 5

Contributions to TL = 200K IQE curve in Fig. 1.

Fig. 6
Fig. 6

(a) IQE and (b) plasma temperature versus current density. In both plots, the lattice temperature is TL = 200K and Auger coefficients are C = 2.3 × 10−31 and 10−34cm6s−1 (solid and dashed curves, respectively).

Fig. 7
Fig. 7

IQE versus current density for LED with single 3nm In0.20Ga0.80N QW and temperatures T = 100K to 400K at 50K intervals. The SRH and Auger coefficients, as well as the carrier-phonon scattering rates are same as those in Fig. 1 for the In0.37Ga0.63N structure.

Fig. 8
Fig. 8

IQE versus current density for LED with (a) 3nm In0.20Ga0.80N QW and (b) 2nm In0.37Ga0.63N QW. The lattice temperatures are T = 100K to 300K at 50K intervals. The SRH and Auger coefficients, as well as the carrier-phonon scattering rates are plotted in Fig. 9.

Fig. 9
Fig. 9

Values of (a) SRH coefficient, (b) Auger coefficient and (c) carrier-phonon scattering rate used in producing the IQE curves in Fig. 8.

Equations (6)

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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 ( ε σ , k , μ σ , T ) ] γ c p [ n σ , n σ , k f ( ε σ , k , μ σ L , T L ) ] γ a g [ n σ , n σ , k f ( ε σ , k , μ a g , T a g ) ]
d n σ , k b d t = b k n e , k b n h , k b + J e N σ p f ( ε 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 ( ε σ , k b , μ σ , T ) ] γ c p [ n σ , k b f ( ε σ , k b , μ σ L , T L ) ] γ a g [ n σ , k b f ( ε σ , k b , μ a g , T a g ) ]
b α σ , α σ , k = 1 h ¯ ε b π c 3 | α σ , α σ , k | 2 Ω α σ , α σ , k 3
b k = 1 h ¯ ε 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
I Q E = e J S ( 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 )

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