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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 15 — Jul. 18, 2011
  • pp: 14182–14187
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Influence of carrier screening and band filling effects on efficiency droop of InGaN light emitting diodes

Lei Wang, Cimang Lu, Jianing Lu, Lei Liu, Ningyang Liu, Yujie Chen, Yanfeng Zhang, Erdan Gu, and Xiaodong Hu  »View Author Affiliations


Optics Express, Vol. 19, Issue 15, pp. 14182-14187 (2011)
http://dx.doi.org/10.1364/OE.19.014182


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Abstract

In this paper, the self-consistent solution of Schrödinger-Poisson equations was realized to estimate the radiative recombination coefficient and the lifetime of a single blue light InGaN/GaN quantum well (QW). The results revealed that the recombination rate was not in proportion to the total injected carriers, and thus the Bnp item was not an accurate method to analyze the recombination process. Carrier screening and band filling effects were also investigated, and an extended Shockley-Read-Hall coefficient A(kt ) with a statistical weight factor due to the carrier distributions in real and phase space of the QW was proposed to estimate the total nonradative current loss including carrier nonradiative recombination, leakage and spillover to explain the efficiency droop behaviors. Without consideration of the Auger recombination, the blue shift of the electroluminescence spectrum, light output power and efficiency droop curves as a function of injected current were all investigated and compared with the experimental data of a high brightness blue light InGaN/GaN multiple QWs light emitting diode to confirm the reliability of our theoretical hypothesis.

© 2011 OSA

1. Introduction

Recently, there has been large progress in the blue and green light InGaN/GaN light-emitting diodes (LEDs), which are attracting great interest as back light unit, automotive headlights, and general illumination, because of their long lifetime, small size, high efficiency and low energy consumption [1

1. S. Nakamura, “Current status of GaN-based solid-state lighting,” MRS Bull. 34(02), 101–107 (2009). [CrossRef]

,2

2. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]

]. In c-plane InGaN/GaN multiple quantum wells (MQWs) LEDs, the light emitting efficiency reaches its peak value at low current density and then rapidly decreases with the injection current. This phenomenon is known as “efficiency droop”, which is a severe problem to achieve high-power and high-efficiency LEDs for applications.

In this paper, an extended carrier Shockley–Read-Hall (SRH) coefficient A(kt) as a function of in-plane wave vector kt due to carrier screening and band filling effects was proposed instead of traditional ABC model as an alternative explanation for the droop behaviors in the framework of the self-consistent solution of Schrödinger-Poisson equations. The light output power and external quantum efficiency were derived and compared with an actual high brightness blue light InGaN/GaN MQWs LED, and we argue that this potential theoretical nonradiative current loss process can also reproduce the experimental observations of our LED chip regardless of Auger recombination.

2. Experiments

3. Theoretical model and simulations

The self-consistent solution of Schrödinger-Poisson equations method was introduced in our simulation [20

20. S. L. Chuang and C. S. Chang, “k•p method for strained wurtzite semiconductors,” Phys. Rev. B 54(4), 2491–2504 (1996). [CrossRef]

,21

21. L. Wang, R. Li, Z. Yang, D. Li, T. Yu, N. Liu, L. Liu, W. Chen, and X. Hu, “High spontaneous emission rate asymmetrically graded 480nm InGaN/GaN quantum well light-emitting diodes,” Appl. Phys. Lett. 95(21), 211104 (2009). [CrossRef]

]. Single InGaN/GaN QW model with the same structure parameters as actual LED mentioned above was proposed to analyze the detailed carrier occupation states in real and phase space because David revealed only the QW nearest the p-type layer emitted light under electrical pumping, regardless of the actual number of QWs [22

22. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN∕GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008). [CrossRef]

]. The spontaneous and piezoelectric polarization fields were all taken into consideration [23

23. F. Bernardini and V. Fiorentini, “Nonlinear behavior of spontaneous and piezoelectric polarization in III–V nitride alloys,” Phys. Status Solidi A 190(1), 65–73 (2002). [CrossRef]

].

Figure 1(a)
Fig. 1 (a) Energy band profiles, subbands and wave functions of the single QW. (b) The occupancy percentages of electron and hole carriers in first conduct and valence subbands as a function of injected carrier densities.
shows the energy band profiles of the lowest conduct band and the uppermost valence band under an injected carrier density of 5 × 1018 cm−3. Spontaneous and piezoelectric polarization fields were set to be −0.0278 C/m2 and 0.0032 C/m2 for blue light emitting. Energy levels and wave functions of two lowest conduct subbands (e1 and e2) and the upmost valence subband (hh1) are showed in this figure. Figure 1(b) shows the occupancy percentages of the electron and hole carriers distributed in e1 and hh1 subbands as a function of total carrier densities, considering that e1 and hh1 are the actual subbands contributed to the EL emission. n1, p1 are electron and hole carrier densities occupied in e1 and hh1 and n, p are the total carrier densities. We can confirm that the electrons almost occupy the e1 energy level even at very high injection case because of the large energy difference between e1 and e2 (about 0.28 eV). However, due to the three adjacent valence bands mixing effect, the percentage of the hole occupied hh1 energy level is just about 81% and decreases sharply when total hole density goes up to 1 × 1017 cm−3. This phenomenon illuminates that the magnitude of hole contributed to the radiative recombination transition (e1-hh1) does not linearly increase with the total injected carriers, so that the expression Bnp in usual ABC model is not an accurate method to calculate the radiative recombination rates. Therefore, a more accurate calculation of the spontaneous emission rate can be achieved in our simulation.

In order to analyze the carrier nonradiative loss mechanisms based on our single QW model, the carrier screening and band filling effects induced by the carrier real and phase space distributions were also analyzed in our simulation. Figure 2(a)
Fig. 2 (a) Normalized electron distribution in the e1 subband with different injected carrier densities. E(kt = 0) represents the ground energy state of e1 subband. (b) Illustration of potential carrier loss channels, such as radiative recombination, nonradiative recombination, leakage and spillover.
shows the normalized electron distribution in phase space as a function of energy state E(kt) of e1 subband. It is clearly to see that most of electrons are collected by the energy band edge of e1 within a small value of wave vector kt at the carrier density blow 1 × 1017 cm−3. As injected carrier density increases, the Brillouin zone center (marked as E(kt = 0) in figure) shifts from 3.044 eV to 3.065 eV due to the carrier screening field estimated by Poisson equation, and much more electrons are collected by higher energy states with a relative larger kt. In detail, the energy value of the most probable electron distribution shifts from 3.057 eV to 3.152 eV when the total injected carrier density increases from 1 × 1016 cm−3 to 5 × 1018 cm−3. In other words, a total shift of 95 meV can be obtained due to the carrier screening and band filling effects.

4. Results and discussion

Based on the carrier distributions in real and phase space of single InGaN/GaN QW model, the variations of radiative recombination lifetime τr and coefficient B as a function of carrier density were investigated and results are shown in Fig. 3(a)
Fig. 3 Simulated variations of (a) the radiative recombination lifetime τr and coefficient B, and (b) total carrier nonradiative loss lifetime τnonr as a function of injected carrier density.
. The lifetime τr is about 100 ns at low carrier density, but goes sharply to less than 20 ns at the carrier density above 1 × 1018 cm−3 owning to the decrease of internal field induced by carrier screening effect. Then the increasing rate of τr becomes lower and reaches a limit value of about 6 ns. On the other hand, the radiative recombination coefficient B increases slowly and reaches its maximum value of 5.12 × 10−11 cm−3s−1 at carrier density of 1.33 × 1018 cm−3. Afterward, the radiative coefficient B begins to decrease with carrier density due to the evident carrier band-filling effect. Overall, through the analysis of these radiative recombination parameters, a more meticulous radiative recombination rate can be obtained than ABC model to reveal the origin of efficiency droop.

To keep consistent with experiment data, 5 × 106 s−1 was fixed as the value of initial SRH coefficient A0, and the relationship between the total nonradiative carrier loss lifetime τnonr and the injected carrier density was simulated and results are shown in Fig. 3(b). The lifetime τnonr keeps almost constant at 100 ns until carrier density reaches 1 × 1018 cm−3. Then τnonr exhibits a superlinear decrease and gets about 7 ns at a high carrier density 5 × 1018 cm−3, which is almost equal to the radiative recombination lifetime, indicating that electrons occupied the high energy states have much larger probability to be captured by nonradiative recombination centers or leak from QW.

At last, the theoretical and experimental light output power and efficiency droop behaviors as a function of injected current were investigated and showed in Figs. 4(b) and 4(c). The theoretical output power also fits very well with experimental data unless at very high injection case. To fit the efficiency droop curve, a presumed light extraction efficiency ηLEE is fixed at 50% in our simulation. For comparison, usual ABC model was also preformed to fit the droop curve with parameters A = 1.3 × 107 s−1 and C = 1 × 1029 cm6s−1, but the values of coefficient B is still dependent on our theoretical calculation. We can see that using 5 × 106 s−1 as A0 in extended SRH coefficient A(kt) and 1.3 × 107 s−1 as A in ABC model both fit very well with the experimental data before the onset of droop at low current densities, once more indicating the reliability of our theoretical model. The little difference between the two SRH coefficients should due to the variation of the carrier filling state with current in our theoretical simulation. After reaching the efficiency maximum, the simulated efficiency began to decrease monotonically and also fit very well with actual data. However, at very high current density (above 200 A/cm2), both theoretical fittings shows a little deviation from the experiment and carrier noncapture mechanism such as electron overflow above active layer should be answerable to it.

5. Summary

Based on the single blue light InGaN/GaN QW model and self-consistent solution of Schrödinger-Poisson equations, the significant carrier distributions in real and phase space of QW should be essential factors for the exploration of radiative and nonradiative process of GaN-based LEDs. The superlinear increase of carrier nonradiative recombination, leakage and spillover loss mechanisms with injected carrier, were considered to be the main reason for the efficiency droop, and the extended SRH coefficient A(kt) was proved to be an alternative method to analyze the nonradiative current loss properties of LEDs. At last, referring to our analysis, we can get the conclusion that, reducing nonradiative recombination centers, threading dislocations or defect states at barriers, as well as using wide thickness QWs or double-heterostructure as active layers to avoid carrier high energy state filling, are effective methods to relieve the severe efficiency droop phenomenon in GaN-based LEDs.

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant Nos. 61076013, 60776042 and 60990313, the National High Technology Program of China under Grant No. 2007AA03Z403.

References and links

1.

S. Nakamura, “Current status of GaN-based solid-state lighting,” MRS Bull. 34(02), 101–107 (2009). [CrossRef]

2.

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]

3.

Y. C. Shen, G. O. Mueller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91(14), 141101 (2007). [CrossRef]

4.

K. T. Delaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94(19), 191109 (2009). [CrossRef]

5.

N. F. Gardner, G. O. Müller, Y. C. Shen, G. Chen, S. Watanabe, W. Götz, and M. R. Krames, “Blue-emitting InGaN–GaN double-heterostructure light-emitting diodes reaching maximum quantum efficiency above 200 A/cm2,” Appl. Phys. Lett. 91(24), 243506 (2007). [CrossRef]

6.

J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the importance of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92(26), 261103 (2008). [CrossRef]

7.

F. Bertazzi, M. Goano, and E. Bellotti, “A numerical study of Auger recombination in bulk InGaN,” Appl. Phys. Lett. 97(23), 231118 (2010). [CrossRef]

8.

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(22), 221106 (2010). [CrossRef]

9.

Q. Dai, M. F. Schubert, M. H. Kim, J. K. Kim, E. F. Schubert, D. D. Koleske, M. H. Crawford, S. R. Lee, A. J. Fischer, G. Thaler, and M. A. Banas, “Internal quantum efficiency and nonradiative recombination coefficient of GaInN/GaN multiple quantum wells with different dislocation densities,” Appl. Phys. Lett. 94(11), 111109 (2009). [CrossRef]

10.

K. Akita, T. Kyono, Y. Yoshizumi, H. Kitabayashi, and K. Katayama, “Improvements of external quantum efficiency of InGaN-based blue light-emitting diodes at high current density using GaN substrates,” J. Appl. Phys. 101(3), 033104 (2007). [CrossRef]

11.

N. I. Bochkareva, V. V. Voronenkov, R. I. Gorbunov, A. S. Zubrilov, Y. S. Lelikov, P. E. Latyshev, Y. T. Rebane, A. I. Tsyuk, and Y. G. Shreter, “Defect-related tunneling mechanism of efficiency droop in III-nitride light-emitting diodes,” Appl. Phys. Lett. 96(13), 133502 (2010). [CrossRef]

12.

Ü. Özgür, H. Liu, X. Li, X. Ni, and H. Morkoç, “GaN-based light emitting diodes: efficiency at high injection levels,” Proc. IEEE 98(7), 1180–1196 (2010). [CrossRef]

13.

Y. Yang, X. A. Cao, and C. H. Yan, “Rapid efficiency roll-off in high-quality green light-emitting diodes on freestanding GaN substrates,” Appl. Phys. Lett. 94(4), 041117 (2009). [CrossRef]

14.

B. Monemar and B. E. Sernelius, “Defect related issues in the ‘current roll-off’ in InGaN based light emitting diodes,” Appl. Phys. Lett. 91(18), 181103 (2007). [CrossRef]

15.

I. A. Pope, P. M. Smowton, P. Blood, J. D. Thomson, M. J. Kappers, and C. J. Humphreys, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480 nm,” Appl. Phys. Lett. 82(17), 2755 (2003). [CrossRef]

16.

A. Hori, D. Yasunaga, A. Satake, and K. Fujiwara, “Temperature dependence of electroluminescence intensity of green and blue InGaN single-quantum-well light-emitting diodes,” Appl. Phys. Lett. 79(22), 3723 (2001). [CrossRef]

17.

K. S. Kim, J. H. Kim, S. J. Jung, Y. J. Park, and S. N. Cho, “Stable temperature characteristics of InGaN blue light emitting diodes using AlGaN/GaN/InGaN superlattices as electron blocking layer,” Appl. Phys. Lett. 96(9), 091104 (2010). [CrossRef]

18.

S.-H. Han, D.-Y. Lee, S.-J. Lee, C.-Y. Cho, M.-K. Kwon, S. P. Lee, D. Y. Noh, D.-J. Kim, Y. C. Kim, and S.-J. Park, “Effect of electron blocking layer on efficiency droop in InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 94(23), 231123 (2009). [CrossRef]

19.

J. H. Son and J.-L. Lee, “Strain engineering for the solution of efficiency droop in InGaN/GaN light-emitting diodes,” Opt. Express 18(6), 5466–5471 (2010). [CrossRef] [PubMed]

20.

S. L. Chuang and C. S. Chang, “k•p method for strained wurtzite semiconductors,” Phys. Rev. B 54(4), 2491–2504 (1996). [CrossRef]

21.

L. Wang, R. Li, Z. Yang, D. Li, T. Yu, N. Liu, L. Liu, W. Chen, and X. Hu, “High spontaneous emission rate asymmetrically graded 480nm InGaN/GaN quantum well light-emitting diodes,” Appl. Phys. Lett. 95(21), 211104 (2009). [CrossRef]

22.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN∕GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008). [CrossRef]

23.

F. Bernardini and V. Fiorentini, “Nonlinear behavior of spontaneous and piezoelectric polarization in III–V nitride alloys,” Phys. Status Solidi A 190(1), 65–73 (2002). [CrossRef]

24.

A. Hangleiter, F. Hitzel, C. Netzel, D. Fuhrmann, U. Rossow, G. Ade, and P. Hinze, “Suppression of nonradiative recombination by V-shaped pits in GaInN/GaN quantum wells produces a large increase in the light emission efficiency,” Phys. Rev. Lett. 95(12), 127402 (2005). [CrossRef] [PubMed]

25.

J. Piprek, “Efficiency droop in nitride-based light-emitting diodes,” Phys. Status Solidi A 207(10), 2217–2225 (2010). [CrossRef]

OCIS Codes
(230.0230) Optical devices : Optical devices
(230.0250) Optical devices : Optoelectronics
(230.3670) Optical devices : Light-emitting diodes

ToC Category:
Optical Devices

History
Original Manuscript: April 26, 2011
Revised Manuscript: June 15, 2011
Manuscript Accepted: June 17, 2011
Published: July 11, 2011

Citation
Lei Wang, Cimang Lu, Jianing Lu, Lei Liu, Ningyang Liu, Yujie Chen, Yanfeng Zhang, Erdan Gu, and Xiaodong Hu, "Influence of carrier screening and band filling effects on efficiency droop of InGaN light emitting diodes," Opt. Express 19, 14182-14187 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14182


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References

  1. S. Nakamura, “Current status of GaN-based solid-state lighting,” MRS Bull. 34(02), 101–107 (2009). [CrossRef]
  2. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]
  3. Y. C. Shen, G. O. Mueller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91(14), 141101 (2007). [CrossRef]
  4. K. T. Delaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94(19), 191109 (2009). [CrossRef]
  5. N. F. Gardner, G. O. Müller, Y. C. Shen, G. Chen, S. Watanabe, W. Götz, and M. R. Krames, “Blue-emitting InGaN–GaN double-heterostructure light-emitting diodes reaching maximum quantum efficiency above 200 A/cm2,” Appl. Phys. Lett. 91(24), 243506 (2007). [CrossRef]
  6. J. Hader, J. V. Moloney, B. Pasenow, S. W. Koch, M. Sabathil, N. Linder, and S. Lutgen, “On the importance of radiative and Auger losses in GaN-based quantum wells,” Appl. Phys. Lett. 92(26), 261103 (2008). [CrossRef]
  7. F. Bertazzi, M. Goano, and E. Bellotti, “A numerical study of Auger recombination in bulk InGaN,” Appl. Phys. Lett. 97(23), 231118 (2010). [CrossRef]
  8. 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(22), 221106 (2010). [CrossRef]
  9. Q. Dai, M. F. Schubert, M. H. Kim, J. K. Kim, E. F. Schubert, D. D. Koleske, M. H. Crawford, S. R. Lee, A. J. Fischer, G. Thaler, and M. A. Banas, “Internal quantum efficiency and nonradiative recombination coefficient of GaInN/GaN multiple quantum wells with different dislocation densities,” Appl. Phys. Lett. 94(11), 111109 (2009). [CrossRef]
  10. K. Akita, T. Kyono, Y. Yoshizumi, H. Kitabayashi, and K. Katayama, “Improvements of external quantum efficiency of InGaN-based blue light-emitting diodes at high current density using GaN substrates,” J. Appl. Phys. 101(3), 033104 (2007). [CrossRef]
  11. N. I. Bochkareva, V. V. Voronenkov, R. I. Gorbunov, A. S. Zubrilov, Y. S. Lelikov, P. E. Latyshev, Y. T. Rebane, A. I. Tsyuk, and Y. G. Shreter, “Defect-related tunneling mechanism of efficiency droop in III-nitride light-emitting diodes,” Appl. Phys. Lett. 96(13), 133502 (2010). [CrossRef]
  12. Ü. Özgür, H. Liu, X. Li, X. Ni, and H. Morkoç, “GaN-based light emitting diodes: efficiency at high injection levels,” Proc. IEEE 98(7), 1180–1196 (2010). [CrossRef]
  13. Y. Yang, X. A. Cao, and C. H. Yan, “Rapid efficiency roll-off in high-quality green light-emitting diodes on freestanding GaN substrates,” Appl. Phys. Lett. 94(4), 041117 (2009). [CrossRef]
  14. B. Monemar and B. E. Sernelius, “Defect related issues in the ‘current roll-off’ in InGaN based light emitting diodes,” Appl. Phys. Lett. 91(18), 181103 (2007). [CrossRef]
  15. I. A. Pope, P. M. Smowton, P. Blood, J. D. Thomson, M. J. Kappers, and C. J. Humphreys, “Carrier leakage in InGaN quantum well light-emitting diodes emitting at 480 nm,” Appl. Phys. Lett. 82(17), 2755 (2003). [CrossRef]
  16. A. Hori, D. Yasunaga, A. Satake, and K. Fujiwara, “Temperature dependence of electroluminescence intensity of green and blue InGaN single-quantum-well light-emitting diodes,” Appl. Phys. Lett. 79(22), 3723 (2001). [CrossRef]
  17. K. S. Kim, J. H. Kim, S. J. Jung, Y. J. Park, and S. N. Cho, “Stable temperature characteristics of InGaN blue light emitting diodes using AlGaN/GaN/InGaN superlattices as electron blocking layer,” Appl. Phys. Lett. 96(9), 091104 (2010). [CrossRef]
  18. S.-H. Han, D.-Y. Lee, S.-J. Lee, C.-Y. Cho, M.-K. Kwon, S. P. Lee, D. Y. Noh, D.-J. Kim, Y. C. Kim, and S.-J. Park, “Effect of electron blocking layer on efficiency droop in InGaN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 94(23), 231123 (2009). [CrossRef]
  19. J. H. Son and J.-L. Lee, “Strain engineering for the solution of efficiency droop in InGaN/GaN light-emitting diodes,” Opt. Express 18(6), 5466–5471 (2010). [CrossRef] [PubMed]
  20. S. L. Chuang and C. S. Chang, “k•p method for strained wurtzite semiconductors,” Phys. Rev. B 54(4), 2491–2504 (1996). [CrossRef]
  21. L. Wang, R. Li, Z. Yang, D. Li, T. Yu, N. Liu, L. Liu, W. Chen, and X. Hu, “High spontaneous emission rate asymmetrically graded 480nm InGaN/GaN quantum well light-emitting diodes,” Appl. Phys. Lett. 95(21), 211104 (2009). [CrossRef]
  22. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, and M. R. Krames, “Carrier distribution in (0001)InGaN∕GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 92(5), 053502 (2008). [CrossRef]
  23. F. Bernardini and V. Fiorentini, “Nonlinear behavior of spontaneous and piezoelectric polarization in III–V nitride alloys,” Phys. Status Solidi A 190(1), 65–73 (2002). [CrossRef]
  24. A. Hangleiter, F. Hitzel, C. Netzel, D. Fuhrmann, U. Rossow, G. Ade, and P. Hinze, “Suppression of nonradiative recombination by V-shaped pits in GaInN/GaN quantum wells produces a large increase in the light emission efficiency,” Phys. Rev. Lett. 95(12), 127402 (2005). [CrossRef] [PubMed]
  25. J. Piprek, “Efficiency droop in nitride-based light-emitting diodes,” Phys. Status Solidi A 207(10), 2217–2225 (2010). [CrossRef]

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