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Energy Express

  • Editor: Bernard Kippelen
  • Vol. 20, Iss. S1 — Jan. 2, 2012
  • pp: A133–A140
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Performance enhancement of blue light-emitting diodes without an electron-blocking layer by using special designed p-type doped InGaN barriers

Yun-Yan Zhang, Guang-Han Fan, Yi-An Yin, and Guang-Rui Yao  »View Author Affiliations


Optics Express, Vol. 20, Issue S1, pp. A133-A140 (2012)
http://dx.doi.org/10.1364/OE.20.00A133


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Abstract

In this study, the characteristics of the nitride-based blue light-emitting diode (LED) without an electron-blocking layer (EBL) are analyzed numerically. The emission spectra, carrier concentrations in the quantum wells (QWs), energy band diagrams, electrostatic fields, and internal quantum efficiency (IQE) are investigated. The simulation results indicate that the LED without an EBL has a better hole-injection efficiency and smaller electrostatic fields in its active region over the conventional LED with an AlGaN EBL. The simulation results also show that the LED without an EBL has severe efficiency droop. However, when the special designed p-type doped InGaN QW barriers are used, the efficiency droop is markedly improved and the electroluminescence (EL) emission intensity is greatly enhanced which is due to the improvement of the hole uniformity in the active region and small electron leakage.

© 2012 OSA

1. Introduction

The group III nitride-based light-emitting diode (LED) has attracted much attention due to its high efficiency, energy-saving capacity, small size, and long lifetime. This solid lighting source is expected to be employed in display, general lighting, and other applications, replacing conventional incandescent and fluorescent lamps for general lighting in near future due to its inherent higher energy efficiency and other advantages. In spite of significant improvements in its performance, there still remain many technical challenges for the blue LED to be competitive in terms of its high-brightness and high-power applications [1

1. C.-T. Liao, M.-C. Tsai, B.-T. Liou, S.-H. Yen, and Y.-K. Kuo, “Improvement in output power of a 460 nm InGaN light-emitting diode using staggered quantum well,” J. Appl. Phys. 108(6), 063107 (2010). [CrossRef]

]. A serious challenge to be addressed is a phenomenon commonly referred to as the efficiency droop [2

2. Y.-L. Li, Y.-R. Huang, and Y.-H. Lai, “Efficiency droop behaviors of InGaN/GaN multiple-quantum-well light-emitting diodes with varying quantum well thickness,” Appl. Phys. Lett. 91(18), 181113 (2007). [CrossRef]

5

5. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, M. R. Krames, 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]

], which is observed as a reduction in emission efficiency with increasing injection current under high current density conditions. As a result, the performance improvement under high injection current density becomes an important issue and has aroused widespread interests [6

6. T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum-confined stark effect due to Piezoelectric fields in GaInN strained quantum wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997). [CrossRef]

12

12. V. S. Sizov, V. V. Neploh, A. F. Tsatsulnikov, A. V. Sakharov, W. V. Lundin, E. E. Zavarin, A. E. Nikolaev, A. M. Mintairov, and J. L. Merz, “Study of tunneling transport of carriers in structures with an InGaN/GaN active region,” Semiconductors 44(12), 1567–1575 (2010). [CrossRef]

].

Among the numerous suggestions, it is widely regarded that the electron leakage may play an important role for the issue. As a result, the insertion of an AlGaN layer between the active region and p-type hole-injection layer has been suggested with the hope that this wide-band gap material layer would act as an electron-blocking layer (EBL) to suppress the escape of the electrons out of the active region into the p-type hole-injection layer. However, recently published studies point out that the electron confinement by a typical AlGaN EBL is not sufficiently effective to solve the efficiency droop problem. Furthermore, the use of AlGaN EBL can cause some undesired effects such as prohibiting the injection efficiency of holes into the active region, which degrades the luminescence characteristics of the blue LED [13

13. S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleischer, J. E. Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBaars, and T. Sota, “Effective band gap inhomogeneity and piezoelectric field in InGaN/GaN multiquantum well structures,” Appl. Phys. Lett. 73(14), 2006–2008 (1998). [CrossRef]

, 14

14. E. Kuokstis, J. W. Yang, G. Simin, M. A. Khan, R. Gaska, and M. S. Shur, “Two mechanisms of blueshift of edge emission in InGaN-based epilayers and multiple quantum wells,” Appl. Phys. Lett. 80(6), 977–1000 (2002). [CrossRef]

]. Therefore, some scientists have tried to use an InAlN EBL to suppress the electron leakage [15

15. S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fischer, 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(22), 221105 (2010). [CrossRef]

]. However, the difficulty of high-quality InAlN material growth is a big challenge.

Besides, many other mechanisms, such as dislocation density, are also regarded to have some influence on internal quantum efficiency (IQE) of the InGaN-based LED.

Although numerous researches have been reported, the mechanism of this well-recognized problem is not very clear, and hence, there is no effective way to completely solve this troublesome issue. With the purpose of relieving the efficiency droop problem and achieving higher hole-injection efficiency from p-side layers into the active region, in this study, the characteristics of the nitride-based blue LED without an EBL are analyzed numerically in detail. We have discussed the advantages of the LED without an EBL, when compared with those of the similar LED with an AlGaN EBL. We also investigated the optical and electrical properties of the LEDs with p-type doped InGaN QW barriers when no EBL is used.

2. LED structure and numerical parameters

The optical and electrical properties of the LEDs were investigated numerically with the APSYS (Advance Physical Model of Semiconductor Devices) simulation software, which was developed by the Crosslight Software Inc. APSYS software is capable of dealing with the physical properties of LEDs by solving the Poisson’s equation, current continuity equations, carrier transport equation, quantum mechanical wave equation, and photon rate equation.

The structure of the original LED (denoted as structure A) used in this study as a reference is identical to an already existing actual device which was grown on a c-plane sapphire substrate, followed by a 50-nm-thick undoped nucleation GaN layer and a 4.5-μm-thick n-GaN layer (n-doping = 5 × 1018cm−3). The active region consisted of four 2.2-nm-thick In0.2Ga0.8N QWs, sandwiched by five 10-nm-thick GaN barriers. The first barrier close to the n-type electron-injection layer was partially n-type doped (n-doping = 5 × 1018cm−3) and the last barrier close to the p-type hole-injection layer was partially p-type doped (p-doping = 7 × 1017cm−3). The other three barriers in the middle of the active region were undoped. On top of the active region were a 20-nm-thick p-Al0.15Ga0.85N EBL (p-doping = 5 × 1017cm−3) and a 0.2-μm-thick p-GaN cap layer (p-doping = 7 × 1017cm−3). The device geometry was designed into a rectangular shape of 300μm × 300μm. Another LED epitaxial structure (denoted as structure B) having similar layer structure but without an EBLwas presented for comparison. To relive the severe efficiency droop problem caused by electron spill-over and improve the performance of the LED without an EBL as well as increase the uniformity of the hole distribution in the QWs, we investigated another epitaxial structure (denoted as structure C) which was similar to structure B except for the three u-GaN QW barriers in the middle of the active region, which were replaced by p-In0.05Ga0.95N barriers of gradual changed doping concentration and thickness. The central area of the barriers were p-type doped which means that the doped GaN barriers were sandwiched by two undoped GaN layers to prevent diffusion of acceptor to the well layer during the subsequent high temperature growth of the p-AlGaN EBL, p-GaN, and the rapid thermal annealing of p-GaN. The detail structures of these three LEDs are shown in Fig. 1
Fig. 1 Schematic of original LEDs with an EBL and u-GaN barriers (structure A), non-EBL LEDs with u-GaN barriers (structure B), and non-EBL LEDs with p-type doped InGaN barriers (structure C).
.

The operating temperature was assumed to be 300K. The light extraction efficiency was assumed to be 0.78. Most of the parameters used in this paper are the same as in [27

27. J. Y. Chang, M. C. Tsai, and Y. K. Kuo, “Advantages of blue InGaN light-emitting diodes with AlGaN barriers,” Opt. Lett. 35(9), 1368–1370 (2010). [CrossRef] [PubMed]

]. Other material parameters of the devices used in the simulation can be found in [28

28. I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003). [CrossRef]

].

3. Results and discussion

The electrostatic fields in the active region of the LEDs with and without an EBL are quite different. Figure 2
Fig. 2 The electrostatic fields of LEDs with (structure A) and without (structure B) an AlGaN EBL at 200 A/cm2 when u-GaN barriers are used.(there is a small location shift on horizontal axis for better observation .)
demonstrates that the AlGaN EBL has great influence on the electrostatic fields in the active region. As can be seen in the figure, the electrostatic fields in the LED with an EBL are much stronger than those of the LED without an EBL especially for the last QW which is near the EBL. The stronger electrostatic fields in the active region will lead to the situation of band bending, poor overlap of electron and hole wave function, and hence, reduced radiative recombination rate.

It can be seen in Fig. 2 that the lattice mismatch between the last GaN QW barrier and AlGaN EBL can generate a strong piezoelectric polarization field. As shown in Fig. 3
Fig. 3 The energy band diagrams of u-GaN barrier LEDs (a) with (structure A) and (b) without (structure B) an AlGaN EBL at 200 A/cm2
, this piezoelectric polarization field along with the spontaneous polarization field pulls down the energy band at the GaN/AlGaN interface. As a result, the effective potential barrier height for electrons in the conduction band of the EBL is reduced and the electron leakage cannot be effectively suppressed. On the other hand, because of the band bending effect caused by the polarization field, the EBL acts as a potential barrier also for holes that can hinder the injection of holes into the active region. As shown in the figure, the effective potential height for holes in the valance band near the last QW barrier and the AlGaN EBL of structure A is 564meV and that of structure B is 339 meV which means that holes are much more difficult to move into the active region in the LED with an AlGaN EBL.

As shown in Fig. 4(a)
Fig. 4 (a) Electron and (b) hole concentrations of LEDs with (structure A) and without (structure B) an AlGaN EBL in the active region at 200 A/cm2
the electron leakage of the both structures is severe. And the electron leakage of the LED with an EBL is only slightly smaller than that of the LED without an EBL which indicates that the EBL is not very effective in suppressing the electron spill-over. In most of the cases, electrons in group III nitride-based materials have a relatively small effective mass and therefore a very high mobility. As a result, electrons are very easy to move into and between the QWs. At the same time, electrons with a mobility much greater than that of holes have a greater chance to spill over the active region into the p-type hole-injection layer. Furthermore, the typical AlGaN EBL with an Al composition ranging from 0.15 to 0.2 is not sufficiently effective to suppress the escape of electrons out of the active region. Although the effective potential barrier height of the AlGaN EBL can be augmented with higher Al mole fraction and accordingly wider energy band and larger conduction-band offset relative to GaN, the increase in Al composition in the EBL will degrade the layer crystalline quality with the generation of strain-induced defects, and lead to an even stronger piezoelectric polarization field. Therefore, the pulling down of the energy band will become worse. From the above-mentioned analysis, it can be observed that the traverse transport of the injected electrons over the active region is rather easy no matter whether the LED is with or without an EBL. And the situation of electron leakage will become even worse with the increase in the injection current density.

In order to reduce the effective potential barrier height for holes in the valance band of QW barriers and increase the uniformity of the hole distribution in the active region, the GaN barriers in structure B are replaced by InGaN barriers in structure C. The InGaN barriers can help the holes to transport in the active region more easily because of the lower barrier height in valence band of QW barriers which can be seen in Fig. 5
Fig. 5 The energy band diagrams of non-EBL LEDs w ith (a) GaN (structure B) and (b) InGaN (structure C) barriers at 200 A/cm2
.

In structure C, the thicknesses of the three barriers in the middle of the active region increase gradually from the n-side to p-side layers. The thicker barrier has a greater p-type doping concentration which is to help holes to transport across the thick barrier into the QWs near the n-type layer. It is apparent in Fig. 6 (a)
Fig. 6 (a) Hole concentrations of structure B and C, and (b) Electron concentrations of structure A and C at 200 A/cm2 (the x axis ranges are stretched for better observation)
that the hole distribution is much greater and more uniform in the active region of structure C. The increasing barrier thickness and p-type doping concentration are beneficial for reducing the electron current leakage. Electrons become more and more difficult to transport through barriers with the increasing barrier thickness and p-type doping concentration from n-type to p-type layer. Therefore, more electrons can stay in the active region to recombine with holes. It can be seen in Fig. 6(b) that the electron leakage of structure C is much smaller than that of structure A. As a result, more QWs can contribute to radiative recombination. Therefore, the InGaN barriers with gradual changed thickness and doping concentration can greatly improve the uniformity of hole distribution in the active region and reduce the electron spill-over.

Because of the better lattice match between the InGaN barrier and InGaN well in structure C, the electrostatic field in the LED with InGaN barriers are much smaller which can be seen in Fig. 7
Fig. 7 The electrostatic field diagrams of non-EBL LEDs with GaN (structure B) and InGaN (structure C) barriers at 200 A/cm2
. Thus, the band bending situation is less severe, which in turn results in less quantum conðned Stark effect (QCSE). As a result, the overlap of electron and hole wave function is increased and more carriers can recombine via the radiative recombination process.

4. Conclusion

The injection efficiency of holes into the active region from the p-type layer can be greatly improved and the electrostatic fields in the active region can be significantly relieved in the LED without conventional AlGaN EBL. The use of the p-type doped InGaN barriers with gradually changed thickness and doping concentration can effectively suppress the spill-over of electrons out of the active region as well as increase the hole concentration and uniformity in the QWs. The LED with new designed structure has significantly improved electrical and optical performance such as much higher IQE and stronger EL emission intensity. Furthermore, the efficiency droop of the new structure is markedly improved.

Acknowledgment

This work was supported by the Project of fabrication and characterization of three dimension InP photonic crystal by MOCVD (Grant No. 20060574007), structure investigation of high power white light LED (Grant No. 2009B090300338), LED board lighting system (Grant No. 2010B090400192), investigation of key factors which influence the response time of blue GaN LED (Grant No. 61176043), the project of Nature Science Foundation of Guangdong Province and Hong Kong, China(Grant No. 2007A010501008), investigation and industrialization of crucial LED technologies (Grant No. 2010A081002005), and project of LED lighting panel system (Grant No. 2010B090400192).

References and links

1.

C.-T. Liao, M.-C. Tsai, B.-T. Liou, S.-H. Yen, and Y.-K. Kuo, “Improvement in output power of a 460 nm InGaN light-emitting diode using staggered quantum well,” J. Appl. Phys. 108(6), 063107 (2010). [CrossRef]

2.

Y.-L. Li, Y.-R. Huang, and Y.-H. Lai, “Efficiency droop behaviors of InGaN/GaN multiple-quantum-well light-emitting diodes with varying quantum well thickness,” Appl. Phys. Lett. 91(18), 181113 (2007). [CrossRef]

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(18), 183507 (2007). [CrossRef]

4.

M. F. Schubert, J. Xu, J. K. Kim, E. F. Schubert, M. H. Kim, S. Yoon, S. M. Lee, C. Sone, T. Sakong, and Y. Park, “Polarization-matched GaInN/AlGaInN multi-quantum-well light-emitting diodes with reduced efficiency droop,” Appl. Phys. Lett. 93(4), 041102 (2008). [CrossRef]

5.

A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, M. R. Krames, 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]

6.

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum-confined stark effect due to Piezoelectric fields in GaInN strained quantum wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997). [CrossRef]

7.

N. F. Gardner, G. O. Muller, Y. C. Shen, G. Chen, S. Watanabe, W. Gotz, 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(1), 019903–1 (2007).

8.

H. Zhao, G. Liu, R. A. Arif, and N. Tansu, “Current injection efficiency induced efficiency-droop in InGaN quantum well light-emitting diodes,” Solid-State Electron. 54(10), 1119–1124 (2010). [CrossRef]

9.

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(12), 121105 (2010). [CrossRef]

10.

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

11.

U. Ozgur, 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]

12.

V. S. Sizov, V. V. Neploh, A. F. Tsatsulnikov, A. V. Sakharov, W. V. Lundin, E. E. Zavarin, A. E. Nikolaev, A. M. Mintairov, and J. L. Merz, “Study of tunneling transport of carriers in structures with an InGaN/GaN active region,” Semiconductors 44(12), 1567–1575 (2010). [CrossRef]

13.

S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleischer, J. E. Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBaars, and T. Sota, “Effective band gap inhomogeneity and piezoelectric field in InGaN/GaN multiquantum well structures,” Appl. Phys. Lett. 73(14), 2006–2008 (1998). [CrossRef]

14.

E. Kuokstis, J. W. Yang, G. Simin, M. A. Khan, R. Gaska, and M. S. Shur, “Two mechanisms of blueshift of edge emission in InGaN-based epilayers and multiple quantum wells,” Appl. Phys. Lett. 80(6), 977–1000 (2002). [CrossRef]

15.

S. Choi, H. J. Kim, S.-S. Kim, J. Liu, J. Kim, J.-H. Ryou, R. D. Dupuis, A. M. Fischer, 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(22), 221105 (2010). [CrossRef]

16.

R. M. Farrell, D. F. Feezell, M. C. Schmidt, D. A. Haeger, K. M. Kelchner, K. Iso, H. Yamada, M. Saito, K. Fujito, D. A. Cohen, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Continuous-wave operation of AlGaN-cladding-free nonpolar m-plane InGaN/GaN laser diodes,” Jpn. J. Appl. Phys. 46(32), L761–L763 (2007). [CrossRef]

17.

M. C. Schmidt, K.-C. Kim, R. M. Farrell, D. F. Feezell, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Demonstration of nonpolar m-plane InGaN/GaN laser diodes,” Jpn. J. Appl. Phys. 46(9), L190–L191 (2007). [CrossRef]

18.

S. H. Park, D. Ahn, and S. L. Chuang, “Electronic and optical properties of a- and m-plane Wurtzite InGaN–GaN quantum wells,” IEEE J. Quantum Electron. 43(12), 1175–1182 (2007). [CrossRef]

19.

R. A. Arif, H. P. Zhao, Y. K. Ee, and N. Tansu, “Spontaneous emission and characteristics of staggered InGaN quantum wells light emitting diodes,” IEEE J. Quantum Electron. 44(6), 573–580 (2008). [CrossRef]

20.

H. Zhao, G. Liu, J. Zhang, J. D. 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(S4Suppl 4), A991–A1007 (2011). [CrossRef] [PubMed]

21.

R. A. Arif, Y. K. Ee, and N. Tansu, “Polarization engineering via staggered InGaN quantum wells for radiative efficiency enhancement of light emitting diodes,” Appl. Phys. Lett. 91(9), 091110 (2007). [CrossRef]

22.

H. Zhao, R. A. Arif, and N. Tansu, “Self-consistent gain analysis of type-II ‘W’ InGaN–GaNAs quantum well lasers,” J. Appl. Phys. 104(4), 043104 (2008). [CrossRef]

23.

H. Zhao, R. A. Arif, Y. K. Ee, and N. Tansu, “Self-consistent analysis of strain-compensated InGaN–AlGaN quantum wells for lasers and light-emitting diodes,” IEEE J. Quantum Electron. 45(1), 66–78 (2009). [CrossRef]

24.

A. L. Tsai, G. C. Fan, and Y. S. Lee, “Effects of strain-compensated AlGaN/InGaN superlattice barriers on the optical properties of InGaN light-emitting diodes,” Appl. Phys., A Mater. Sci. Process. 104(1), 319–323 (2011). [CrossRef]

25.

J. Park and Y. Kawakami, “Photoluminescence property of InGaN single quantum well with embedded AlGaN δ layer,” Appl. Phys. Lett. 88(20), 202107 (2006). [CrossRef]

26.

H. Zhao, G. Liu, and N. Tansu, “Analysis of InGaN-delta-InN quantum wells for light-emitting diodes,” Appl. Phys. Lett. 97(13), 131114 (2010). [CrossRef]

27.

J. Y. Chang, M. C. Tsai, and Y. K. Kuo, “Advantages of blue InGaN light-emitting diodes with AlGaN barriers,” Opt. Lett. 35(9), 1368–1370 (2010). [CrossRef] [PubMed]

28.

I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003). [CrossRef]

OCIS Codes
(230.3670) Optical devices : Light-emitting diodes
(150.2945) Machine vision : Illumination design

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: August 15, 2011
Revised Manuscript: November 11, 2011
Manuscript Accepted: November 29, 2011
Published: January 1, 2012

Citation
Yun-Yan Zhang, Guang-Han Fan, Yi-An Yin, and Guang-Rui Yao, "Performance enhancement of blue light-emitting diodes without an electron-blocking layer by using special designed p-type doped InGaN barriers," Opt. Express 20, A133-A140 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S1-A133


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References

  1. C.-T. Liao, M.-C. Tsai, B.-T. Liou, S.-H. Yen, and Y.-K. Kuo, “Improvement in output power of a 460 nm InGaN light-emitting diode using staggered quantum well,” J. Appl. Phys.108(6), 063107 (2010). [CrossRef]
  2. Y.-L. Li, Y.-R. Huang, and Y.-H. Lai, “Efficiency droop behaviors of InGaN/GaN multiple-quantum-well light-emitting diodes with varying quantum well thickness,” Appl. Phys. Lett.91(18), 181113 (2007). [CrossRef]
  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(18), 183507 (2007). [CrossRef]
  4. M. F. Schubert, J. Xu, J. K. Kim, E. F. Schubert, M. H. Kim, S. Yoon, S. M. Lee, C. Sone, T. Sakong, and Y. Park, “Polarization-matched GaInN/AlGaInN multi-quantum-well light-emitting diodes with reduced efficiency droop,” Appl. Phys. Lett.93(4), 041102 (2008). [CrossRef]
  5. A. David, M. J. Grundmann, J. F. Kaeding, N. F. Gardner, T. G. Mihopoulos, M. R. Krames, 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]
  6. T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum-confined stark effect due to Piezoelectric fields in GaInN strained quantum wells,” Jpn. J. Appl. Phys.36(Part 2, No. 4A), L382–L385 (1997). [CrossRef]
  7. N. F. Gardner, G. O. Muller, Y. C. Shen, G. Chen, S. Watanabe, W. Gotz, 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(1), 019903–1 (2007).
  8. H. Zhao, G. Liu, R. A. Arif, and N. Tansu, “Current injection efficiency induced efficiency-droop in InGaN quantum well light-emitting diodes,” Solid-State Electron.54(10), 1119–1124 (2010). [CrossRef]
  9. 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(12), 121105 (2010). [CrossRef]
  10. J. Piprek, “Efficiency droop in nitride-based light-emitting diodes,” Phys. Status Solidi., A Appl. Mater. Sci.207(10), 2217–2225 (2010). [CrossRef]
  11. U. Ozgur, H. Liu, X. Li, X. Ni, and H. Morkoç, “GaN-Based Light-Emitting Diodes: Efficiency at High Injection Levels,” Proc. IEEE98(7), 1180–1196 (2010). [CrossRef]
  12. V. S. Sizov, V. V. Neploh, A. F. Tsatsulnikov, A. V. Sakharov, W. V. Lundin, E. E. Zavarin, A. E. Nikolaev, A. M. Mintairov, and J. L. Merz, “Study of tunneling transport of carriers in structures with an InGaN/GaN active region,” Semiconductors44(12), 1567–1575 (2010). [CrossRef]
  13. S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleischer, J. E. Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBaars, and T. Sota, “Effective band gap inhomogeneity and piezoelectric field in InGaN/GaN multiquantum well structures,” Appl. Phys. Lett.73(14), 2006–2008 (1998). [CrossRef]
  14. E. Kuokstis, J. W. Yang, G. Simin, M. A. Khan, R. Gaska, and M. S. Shur, “Two mechanisms of blueshift of edge emission in InGaN-based epilayers and multiple quantum wells,” Appl. Phys. Lett.80(6), 977–1000 (2002). [CrossRef]
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