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Nitride-based micron-scale hexagonal pyramids array vertical light emitting diodes by N-polar wet etching |
Optics Express, Vol. 21, Issue 3, pp. 3547-3556 (2013)
http://dx.doi.org/10.1364/OE.21.003547
Acrobat PDF (1430 KB)
Abstract
In this work, we reported the fabrication of nitride-based hexagonal pyramids array (HPA) vertical-injection light emitting diodes (V-LEDs) by N-polar wet etching. The performance of HPA V-LEDs devices was significantly improved with 30% higher internal quantum efficiency compared with conventional roughened broad area V-LEDs. The simulated extraction efficiency by finite difference time domain method was 20% higher than typical roughened V-LEDs. The reversed leakage current of HPA V-LEDs was reduced due to better crystal quality, which was confirmed by conductive atomic force microscopy measurement. Furthermore, the efficiency droop for HPA V-LEDs were substantially alleviated.
© 2013 OSA
1. Introduction
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]
F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), R10024–R10027 (1997). [CrossRef]
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]
Y. Yang, X. A. Cao, and C. H. Yan, “Investigation of the nonthermal mechanism of efficiency rolloff in InGaN light-emitting diodes,” IEEE Trans. Electron. Dev. 55(7), 1771–1775 (2008). [CrossRef]
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]
H. P. T. Nguyen, K. Cui, S. Zhang, M. Djavid, A. Korinek, G. A. Botton, and Z. Mi, “Controlling electron overflow in phosphor-free InGaN/GaN nanowire white light-emitting diodes,” Nano Lett. 12(3), 1317–1323 (2012). [CrossRef] [PubMed]
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]
M. Zhang, P. Bhattacharya, J. Singh, and J. Hinckley, “Direct measurement of auger recombination in In0.1Ga0.9N/GaN quantum wells and its impact on the efficiency of In0.1Ga0.9N/GaN multiple quantum well light emitting diodes,” Appl. Phys. Lett. 95(20), 201108 (2009). [CrossRef]
H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483 (2003). [CrossRef]
S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631 (2000). [CrossRef]
H. P. T. Nguyen, K. Cui, S. Zhang, M. Djavid, A. Korinek, G. A. Botton, and Z. Mi, “Controlling electron overflow in phosphor-free InGaN/GaN nanowire white light-emitting diodes,” Nano Lett. 12(3), 1317–1323 (2012). [CrossRef] [PubMed]
H.-M. Kim, Y.-H. Cho, H. Lee, S. I. Kim, S. R. Ryu, D. Y. Kim, T. W. Kang, and K. S. Chung, “High-brightness light emitting diodes using dislocation-free indium gallium nitride/gallium nitride multiquantum-well nanorod arrays,” Nano Lett. 4(6), 1059–1062 (2004). [CrossRef]
O. B. Shchekin, J. E. Epler, T. A. Trottier, T. Margalith, D. A. Steigerwald, M. O. Holcomb, P. S. Martin, and M. R. Krames, “High performance thin-film flip-chip InGaN–GaN light-emitting diodes,” Appl. Phys. Lett. 89(7), 071109 (2006). [CrossRef]
W. Y. Lin, D. S. Wuu, K. F. Pan, S. H. Huang, C. E. Lee, W. K. Wang, S. C. Hsu, Y. Y. Su, S. Y. Huang, and R. H. Horng, “High-power GaN-mirror-Cu light-emitting diodes for vertical current injection using laser liftoff and electroplating techniques,” IEEE Photon. Technol. Lett. 17(9), 1809–1811 (2005). [CrossRef]
C.-F. Chu, C.-C. Yu, H.-C. Cheng, C.-F. Lin, and S.-C. Wang, “Comparison of p-Side Down and p-Side Up GaN Light-Emitting Diodes Fabricated by Laser Lift-Off,” Jpn. J. Appl. Phys. 42(Part 2, No. 2B), L147–L150 (2003). [CrossRef]
J.-T. Chu, H.-W. Huang, C.-C. Kao, W.-D. Liang, F.-I. Lai, C.-F. Chu, H.-C. Kuo, and S.-C. Wang, “Fabrication of large-area GaN-based light-emitting diodes on Cu substrate,” Jpn. J. Appl. Phys. 44(4B), 2509–2511 (2005). [CrossRef]
T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84(6), 855 (2004). [CrossRef]
H. M. Ng, N. G. Weimann, and A. Chowdhury, “GaN nanotip pyramids formed by anisotropic etching,” J. Appl. Phys. 94(1), 650 (2003). [CrossRef]
Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys. 43(No. 5A), L637–L639 (2004). [CrossRef]
T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84(6), 855 (2004). [CrossRef]
J.-H. Kim, C.-S. Oh, Y.-H. Ko, S.-M. Ko, K.-Y. Park, M. Jeong, J. Y. Lee, and Y.-H. Cho, “Dislocation-eliminating chemical control method for high-efficiency GaN-based light emitting nanostructures,” Cryst. Growth Des. 12(3), 1292–1298 (2012). [CrossRef]
2. Experiment
3. Results and discussion
J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273–274, 24–32 (1999). [CrossRef]
Y. B. Tao, T. J. Yu, Z. Y. Yang, D. Ling, Y. Wang, Z. Z. Chen, Z. J. Yang, and G. Y. Zhang, “Evolution and control of dislocations in GaN grown on cone-patterned sapphire substrate by metal organic vapor phase epitaxy,” J. Cryst. Growth 315(1), 183–187 (2011). [CrossRef]
F. E. Williams and H. Eyring, “The mechanism of the luminescence of solids,” J. Chem. Phys. 15(5), 289–304 (1947). [CrossRef]
P. J. Dean, “Absorption and luminescence of excitons at neutral donors in gallium phosphide,” Phys. Rev. 157(3), 655–667 (1967). [CrossRef]
J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J.-L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. (Deerfield Beach Fla.) 24(17), 2259–2262 (2012). [CrossRef] [PubMed]
H. M. Ng, N. G. Weimann, and A. Chowdhury, “GaN nanotip pyramids formed by anisotropic etching,” J. Appl. Phys. 94(1), 650 (2003). [CrossRef]
P. Kozodoy, J. P. Ibbetson, H. Marchand, P. T. Fini, S. Keller, J. S. Speck, S. P. DenBaars, and U. K. Mishra, “Electrical characterization of GaN p-n junctions with and without threading dislocations,” Appl. Phys. Lett. 73(7), 975 (1998). [CrossRef]
4. Conclusion
Acknowledgments
References and links
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] | |
F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), R10024–R10027 (1997). [CrossRef] | |
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] | |
Y. Yang, X. A. Cao, and C. H. Yan, “Investigation of the nonthermal mechanism of efficiency rolloff in InGaN light-emitting diodes,” IEEE Trans. Electron. Dev. 55(7), 1771–1775 (2008). [CrossRef] | |
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] | |
H. P. T. Nguyen, K. Cui, S. Zhang, M. Djavid, A. Korinek, G. A. Botton, and Z. Mi, “Controlling electron overflow in phosphor-free InGaN/GaN nanowire white light-emitting diodes,” Nano Lett. 12(3), 1317–1323 (2012). [CrossRef] [PubMed] | |
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] | |
M. Zhang, P. Bhattacharya, J. Singh, and J. Hinckley, “Direct measurement of auger recombination in In0.1Ga0.9N/GaN quantum wells and its impact on the efficiency of In0.1Ga0.9N/GaN multiple quantum well light emitting diodes,” Appl. Phys. Lett. 95(20), 201108 (2009). [CrossRef] | |
H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett. 83(22), 4483 (2003). [CrossRef] | |
S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett. 76(5), 631 (2000). [CrossRef] | |
H.-M. Kim, Y.-H. Cho, H. Lee, S. I. Kim, S. R. Ryu, D. Y. Kim, T. W. Kang, and K. S. Chung, “High-brightness light emitting diodes using dislocation-free indium gallium nitride/gallium nitride multiquantum-well nanorod arrays,” Nano Lett. 4(6), 1059–1062 (2004). [CrossRef] | |
O. B. Shchekin, J. E. Epler, T. A. Trottier, T. Margalith, D. A. Steigerwald, M. O. Holcomb, P. S. Martin, and M. R. Krames, “High performance thin-film flip-chip InGaN–GaN light-emitting diodes,” Appl. Phys. Lett. 89(7), 071109 (2006). [CrossRef] | |
Ch.-F. Chu, F.-I. Lai, J.-T. Chu, C.-C. Yu, C.-F. Lin, H.-C. Kuo, and S. C. Wang, “Study of GaN light-emitting diodes fabricated by laser lift-off technique,” J. Appl. Phys. 95, 3916 (2004). | |
W. Y. Lin, D. S. Wuu, K. F. Pan, S. H. Huang, C. E. Lee, W. K. Wang, S. C. Hsu, Y. Y. Su, S. Y. Huang, and R. H. Horng, “High-power GaN-mirror-Cu light-emitting diodes for vertical current injection using laser liftoff and electroplating techniques,” IEEE Photon. Technol. Lett. 17(9), 1809–1811 (2005). [CrossRef] | |
C.-F. Chu, C.-C. Yu, H.-C. Cheng, C.-F. Lin, and S.-C. Wang, “Comparison of p-Side Down and p-Side Up GaN Light-Emitting Diodes Fabricated by Laser Lift-Off,” Jpn. J. Appl. Phys. 42(Part 2, No. 2B), L147–L150 (2003). [CrossRef] | |
J.-T. Chu, H.-W. Huang, C.-C. Kao, W.-D. Liang, F.-I. Lai, C.-F. Chu, H.-C. Kuo, and S.-C. Wang, “Fabrication of large-area GaN-based light-emitting diodes on Cu substrate,” Jpn. J. Appl. Phys. 44(4B), 2509–2511 (2005). [CrossRef] | |
T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84(6), 855 (2004). [CrossRef] | |
H. M. Ng, N. G. Weimann, and A. Chowdhury, “GaN nanotip pyramids formed by anisotropic etching,” J. Appl. Phys. 94(1), 650 (2003). [CrossRef] | |
S. L. Qi, Z. Z. Chen, H. Fang, Y. J. Sun, L. W. Sang, X. L. Yang, L. B. Zhao, P. F. Tian, J. J. Deng, Y. B. Tao, T. J. Yu, Z. X. Qin, and G. Y. Zhang, “Study on the formation of dodecagonal pyramid on nitrogen polar GaN surface etched by hot H3PO4,” Appl. Phys. Lett. 95(7), 071114 (2009). [CrossRef] | |
Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys. 43(No. 5A), L637–L639 (2004). [CrossRef] | |
J.-H. Kim, C.-S. Oh, Y.-H. Ko, S.-M. Ko, K.-Y. Park, M. Jeong, J. Y. Lee, and Y.-H. Cho, “Dislocation-eliminating chemical control method for high-efficiency GaN-based light emitting nanostructures,” Cryst. Growth Des. 12(3), 1292–1298 (2012). [CrossRef] | |
P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan, “Electron Microscopy of Thin Crystals” (Krieger, New York, 1977). | |
J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273–274, 24–32 (1999). [CrossRef] | |
T. J. Badcock, R. Hao, M. A. Moram, M. J. Kappers, P. Dawson, and C. J. Humphreys, “The effect of dislocation density and surface morphology on the optical properties of InGaN/GaN quantum wells grown on r-plane sapphire substrates,” Jpn. J. Appl. Phys. 50(8), 080201 (2011). [CrossRef] | |
Y. B. Tao, T. J. Yu, Z. Y. Yang, D. Ling, Y. Wang, Z. Z. Chen, Z. J. Yang, and G. Y. Zhang, “Evolution and control of dislocations in GaN grown on cone-patterned sapphire substrate by metal organic vapor phase epitaxy,” J. Cryst. Growth 315(1), 183–187 (2011). [CrossRef] | |
F. E. Williams and H. Eyring, “The mechanism of the luminescence of solids,” J. Chem. Phys. 15(5), 289–304 (1947). [CrossRef] | |
P. J. Dean, “Absorption and luminescence of excitons at neutral donors in gallium phosphide,” Phys. Rev. 157(3), 655–667 (1967). [CrossRef] | |
J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J.-L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. (Deerfield Beach Fla.) 24(17), 2259–2262 (2012). [CrossRef] [PubMed] | |
P. Kozodoy, J. P. Ibbetson, H. Marchand, P. T. Fini, S. Keller, J. S. Speck, S. P. DenBaars, and U. K. Mishra, “Electrical characterization of GaN p-n junctions with and without threading dislocations,” Appl. Phys. Lett. 73(7), 975 (1998). [CrossRef] |
OCIS Codes
(250.0250) Optoelectronics : Optoelectronics
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices
ToC Category:
Optoelectronics
History
Original Manuscript: October 31, 2012
Revised Manuscript: January 11, 2013
Manuscript Accepted: January 23, 2013
Published: February 5, 2013
Citation
Jun Ma, Liancheng Wang, Zhiqiang Liu, Guodong Yuan, Xiaoli Ji, Ping Ma, Junxi Wang, Xiaoyan Yi, Guohong Wang, and Jinmin Li, "Nitride-based micron-scale hexagonal pyramids array vertical light emitting diodes by N-polar wet etching," Opt. Express 21, 3547-3556 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3547
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References
- 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]
- F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B56(16), R10024–R10027 (1997). [CrossRef]
- 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]
- Y. Yang, X. A. Cao, and C. H. Yan, “Investigation of the nonthermal mechanism of efficiency rolloff in InGaN light-emitting diodes,” IEEE Trans. Electron. Dev.55(7), 1771–1775 (2008). [CrossRef]
- 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]
- H. P. T. Nguyen, K. Cui, S. Zhang, M. Djavid, A. Korinek, G. A. Botton, and Z. Mi, “Controlling electron overflow in phosphor-free InGaN/GaN nanowire white light-emitting diodes,” Nano Lett.12(3), 1317–1323 (2012). [CrossRef] [PubMed]
- 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]
- M. Zhang, P. Bhattacharya, J. Singh, and J. Hinckley, “Direct measurement of auger recombination in In0.1Ga0.9N/GaN quantum wells and its impact on the efficiency of In0.1Ga0.9N/GaN multiple quantum well light emitting diodes,” Appl. Phys. Lett.95(20), 201108 (2009). [CrossRef]
- H. W. Choi, M. D. Dawson, P. R. Edwards, and R. W. Martin, “High extraction efficiency InGaN micro-ring light-emitting diodes,” Appl. Phys. Lett.83(22), 4483 (2003). [CrossRef]
- S. X. Jin, J. Li, J. Z. Li, J. Y. Lin, and H. X. Jiang, “GaN microdisk light emitting diodes,” Appl. Phys. Lett.76(5), 631 (2000). [CrossRef]
- H.-M. Kim, Y.-H. Cho, H. Lee, S. I. Kim, S. R. Ryu, D. Y. Kim, T. W. Kang, and K. S. Chung, “High-brightness light emitting diodes using dislocation-free indium gallium nitride/gallium nitride multiquantum-well nanorod arrays,” Nano Lett.4(6), 1059–1062 (2004). [CrossRef]
- O. B. Shchekin, J. E. Epler, T. A. Trottier, T. Margalith, D. A. Steigerwald, M. O. Holcomb, P. S. Martin, and M. R. Krames, “High performance thin-film flip-chip InGaN–GaN light-emitting diodes,” Appl. Phys. Lett.89(7), 071109 (2006). [CrossRef]
- Ch.-F. Chu, F.-I. Lai, J.-T. Chu, C.-C. Yu, C.-F. Lin, H.-C. Kuo, and S. C. Wang, “Study of GaN light-emitting diodes fabricated by laser lift-off technique,” J. Appl. Phys.95, 3916 (2004).
- W. Y. Lin, D. S. Wuu, K. F. Pan, S. H. Huang, C. E. Lee, W. K. Wang, S. C. Hsu, Y. Y. Su, S. Y. Huang, and R. H. Horng, “High-power GaN-mirror-Cu light-emitting diodes for vertical current injection using laser liftoff and electroplating techniques,” IEEE Photon. Technol. Lett.17(9), 1809–1811 (2005). [CrossRef]
- C.-F. Chu, C.-C. Yu, H.-C. Cheng, C.-F. Lin, and S.-C. Wang, “Comparison of p-Side Down and p-Side Up GaN Light-Emitting Diodes Fabricated by Laser Lift-Off,” Jpn. J. Appl. Phys.42(Part 2, No. 2B), L147–L150 (2003). [CrossRef]
- J.-T. Chu, H.-W. Huang, C.-C. Kao, W.-D. Liang, F.-I. Lai, C.-F. Chu, H.-C. Kuo, and S.-C. Wang, “Fabrication of large-area GaN-based light-emitting diodes on Cu substrate,” Jpn. J. Appl. Phys.44(4B), 2509–2511 (2005). [CrossRef]
- T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett.84(6), 855 (2004). [CrossRef]
- H. M. Ng, N. G. Weimann, and A. Chowdhury, “GaN nanotip pyramids formed by anisotropic etching,” J. Appl. Phys.94(1), 650 (2003). [CrossRef]
- S. L. Qi, Z. Z. Chen, H. Fang, Y. J. Sun, L. W. Sang, X. L. Yang, L. B. Zhao, P. F. Tian, J. J. Deng, Y. B. Tao, T. J. Yu, Z. X. Qin, and G. Y. Zhang, “Study on the formation of dodecagonal pyramid on nitrogen polar GaN surface etched by hot H3PO4,” Appl. Phys. Lett.95(7), 071114 (2009). [CrossRef]
- Y. Gao, T. Fujii, R. Sharma, K. Fujito, S. P. DenBaars, S. Nakamura, and E. L. Hu, “Roughening hexagonal surface morphology on laser lift-off (LLO) N-face GaN with simple photo-enhanced chemical wet etching,” Jpn. J. Appl. Phys.43(No. 5A), L637–L639 (2004). [CrossRef]
- J.-H. Kim, C.-S. Oh, Y.-H. Ko, S.-M. Ko, K.-Y. Park, M. Jeong, J. Y. Lee, and Y.-H. Cho, “Dislocation-eliminating chemical control method for high-efficiency GaN-based light emitting nanostructures,” Cryst. Growth Des.12(3), 1292–1298 (2012). [CrossRef]
- P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan, “Electron Microscopy of Thin Crystals” (Krieger, New York, 1977).
- J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B273–274, 24–32 (1999). [CrossRef]
- T. J. Badcock, R. Hao, M. A. Moram, M. J. Kappers, P. Dawson, and C. J. Humphreys, “The effect of dislocation density and surface morphology on the optical properties of InGaN/GaN quantum wells grown on r-plane sapphire substrates,” Jpn. J. Appl. Phys.50(8), 080201 (2011). [CrossRef]
- Y. B. Tao, T. J. Yu, Z. Y. Yang, D. Ling, Y. Wang, Z. Z. Chen, Z. J. Yang, and G. Y. Zhang, “Evolution and control of dislocations in GaN grown on cone-patterned sapphire substrate by metal organic vapor phase epitaxy,” J. Cryst. Growth315(1), 183–187 (2011). [CrossRef]
- F. E. Williams and H. Eyring, “The mechanism of the luminescence of solids,” J. Chem. Phys.15(5), 289–304 (1947). [CrossRef]
- P. J. Dean, “Absorption and luminescence of excitons at neutral donors in gallium phosphide,” Phys. Rev.157(3), 655–667 (1967). [CrossRef]
- J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J.-L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. (Deerfield Beach Fla.)24(17), 2259–2262 (2012). [CrossRef] [PubMed]
- P. Kozodoy, J. P. Ibbetson, H. Marchand, P. T. Fini, S. Keller, J. S. Speck, S. P. DenBaars, and U. K. Mishra, “Electrical characterization of GaN p-n junctions with and without threading dislocations,” Appl. Phys. Lett.73(7), 975 (1998). [CrossRef]
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