J. Semicond. > 2016, Volume 37 > Issue 6 > 064015
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SEMICONDUCTOR DEVICES

Evaluation of light extraction efficiency for the light-emitting diodes based on the transfer matrix formalism and ray-tracing method

Pingbo An, Li Wang, Hongxi Lu, Zhiguo Yu, Lei Liu, Xin Xi, Lixia Zhao, Junxi Wang and Jinmin Li

+ Author Affiliations

 Corresponding author: Lixia Zhao, lxzhao@semi.ac.cn

DOI: 10.1088/1674-4926/37/6/064015

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Abstract: The internal quantum efficiency (IQE) of the light-emitting diodes can be calculated by the ratio of the external quantum efficiency (EQE) and the light extraction efficiency (LEE). The EQE can be measured experimentally, but the LEE is difficult to calculate due to the complicated LED structures. In this work, a model was established to calculate the LEE by combining the transfer matrix formalism and an in-plane ray tracing method. With the calculated LEE, the IQE was determined and made a good agreement with that obtained by the ABC model and temperature-dependent photoluminescence method. The proposed method makes the determination of the IQE more practical and conventional.

Key words: light extraction efficiency, light-emitting diodes, transfer matrix, ray-tracing



[1]
Hangleiter A, Hitzel F, Netzel C, et al. 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, 2005, 95(12):127402
[2]
Hader J, Moloney J V, Koch S W. Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes. Appl Phys Lett, 2010, 96(22):221106
[3]
Ganesh P, Kent P R C, Mochalin V. Efficiency droop behaviors of the blue LEDs on patterned sapphire substrate. J Appl Phys, 2011, 110(7):073506
[4]
Hader J, Moloney J V, Pasenow B, et al. On the importance of radiative and Auger losses in GaN-based quantum wells. Appl Phys Lett, 2008, 92(26):261103
[5]
Piprek, Joachim. Efficiency droop in nitride-based light-emitting diodes. Phys Status Solidi A, 2010, 207(10):2217
[6]
Kim M H, Schubert M F, Dai Q, et al. Origin of efficiency droop in GaN-based light-emitting diodes. Appl Phys Lett, 2007, 91(18):183507
[7]
Kohno T, Sudo Y, Yamauchi M, et al. Internal quantum efficiency and nonradiative recombination rate in InGaN-based near-ultraviolet light-emitting diodes. Jpn J Appl Phys, 2012, 51:072102
[8]
Fuhrmann D, Retzlaff T, Rossow U, et al. Large internal quantum efficiency of In-free UV-emitting GaN/AlGaN quantum-well structures. Appl Phys Lett, 2006, 88(19):191108
[9]
Hangleiter A, Fuhrmann D, Grewe M, et al. Towards understanding the emission efficiency of nitride quantum wells. Phys Status Solidi A, 2004, 201(12):2808
[10]
Lin E Y, Chen C Y, Lay T S, et al. Internal quantum efficiency and optical polarization analysis of InGaN/GaN multiple quantum wells on a-plane GaN. Physica Status Solidi C, 2008, 5(6):2111
[11]
Titkov I E, Karpov S Y, Yadav A, et al. Temperature-dependent internal quantum efficiency of blue high-brightness light-emitting diodes. IEEE J Quantum Electron, 2014, 50(11):911
[12]
Lee Y J, Chiu C H, Ke C C, et al. Study of the excitation power dependent internal quantum efficiency in InGaN GaN LEDs grown on patterned sapphire substrate. IEEE J Quantum Electron, 2009, 15(4):1137
[13]
Lee J, Ni X, Wu M, et al. Internal quantum efficiency of m-plane InGaN on Si and GaN. Proc SPIE, 2013, 7602:76021N
[14]
Kivisaari P, Riuttanen L, Oksanen J, et al. Electrical measurement of internal quantum efficiency and extraction efficiency of Ⅲ-N light-emitting diodes. Appl Phys Lett, 2012, 101(2):021113
[15]
Ryu H Y, Ryu G H, Lee S H, et al. Evaluation of the internal quantum efficiency in blue and green light-emitting diodes using the rate equation model. Journal of the Korean Physical Society, 2013, 63(2):180
[16]
Getty A, Matioli E, Iza M, et al. Electroluminescent measurement of the internal quantum efficiency of light emitting diodes. Appl Phys Lett, 2009, 94(18):181102
[17]
Matioli E, Weisbuch C. Direct measurement of internal quantum efficiency in light emitting diodes under electrical injection. J Appl Phys, 2011, 109(7):073114
[18]
Nami M, Rishinaramangalam A, Feezell D. Analysis of light extraction efficiency for gallium nitride-based coaxial microwall light-emitting diodes. Phys Status Solidi C, 2014, 11(3/4):766
[19]
Zhmakin A I. Enhancement of light extraction from light emitting diodes. Physics Reports, 2011, 498(4/5):189
[20]
Xia Changsheng, Li Zhifeng, Wang Chong, et al. Ray tracing simulation of InGaN/GaN light-emitting diodes with parabolic substrates. Chinese Journal of Semiconductors, 2006, 27(1):100
[21]
Guo Jinxia, Ma Long, Yi Xiaoyan, et al. Light extraction efficiency of high-power GaN-based light-emitting diodes. Chinese Journal of Semiconductors, 2005, 26(Suppl):170
[22]
Zhu Jihong, Wang Liangji, Zhang Shuming, et al. Simulation of the light extraction efficiency of nanostructure light-emitting diodes. Chin Phys B, 2011, 20(7):077804
[23]
Ryu H Y. Numerical study on the wavelength-dependence of light extraction efficiency in AlGaN-based ultraviolet light-emitting diodes. Opt Quantum Electron, 2014, 46(10):1329
[24]
Kim J W, Jang J H, Oh M C, et al. FDTD analysis of the light extraction efficiency of OLEDs with a random scattering layer. Opt Express, 2014, 22(1):498
[25]
Cui H, Park S H. Numerical simulations of the light-extraction efficiency of LEDs on sapphire substrates patterned with various polygonal pyramids. Journal of the Optical Society of Korea, 2014, 18(6):772
[26]
Lin Z, Yang H, Zhou S, et al. Pattern design of and epitaxial growth on patterned sapphire substrates for highly efficient GaN-based LEDs. Crystal Growth & Design, 2012, 12(6):2836
[27]
Benisty H, Stanley R, Mayer M. Method of source terms for dipole emission modification in modes of arbitrary planar structures. J Opt Soc Am A, 1998, 15(5):1192
[28]
Chew W C. Waves and fields in inhomogeneous media. New York:IEEE Press, 1994
[29]
Xu C, Yu T, Yan J, et al. Analyses of light extraction efficiency in GaN-based LEDs grown on patterned sapphire substrates. Phys Status Solidi C, 2012, 9(3/4):757
[30]
Kong J A. Electromagnetic wave theory. New York:John Wiley & Sons Inc, 1990
Fig. 1.  (Color online) Schematics of the LED structure for the calculation of the top and bottom LEE.

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Fig. 2.  (Color online) Schematics of the LED structure for the calculation of LEE from the substrate side surface. The LEE from the sides of the other layers (epilayer, ITO-layer) can be calculated using the same method.

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Fig. 3.  The calculated LEE from the top surface with consideration of a Gaussian spectra and a monochromatic emission at wavelength 455 nm.

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Fig. 4.  (Color online) The LEE from the top surface varied with wavelength and thickness of the p-GaN layer. The thickness of the ITO layer was 280 nm.

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Fig. 5.  (Color online) The side extraction coefficients averaged over the starting points of emission (see Equation (9)) for TE polarization (solid lines) and TM polarization (dashed lines).

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Fig. 6.  (Color online) The comparison of the IQE by the ratio of the EQE and LEE calculated by using the proposed model (red curve) with the ABC model (blue dash-dot curve). The inset shows emitted photons measured as a function of current density with the ABC fit.

DownLoad: Full-Size Img PowerPoint
Fig. 7.  (Color online) Schematics of the electric fields propagating in a multilayer structure. The discontinuity of the source term is applied to the propagation of the external electric fields from the two sides. In every two adjacent layers, the two electric fields can be related by a transfer matrix Ml.(l-1)/.

DownLoad: Full-Size Img PowerPoint

Table 1.   Optical parameters of each layer in the simulation at wavelength 455 nm.

Layer Refractive index (n+ik) Thickness (nm) Size (mil×mil)
Substrate (Al2O3) 1.7791js-37-06-123
Epilayer 2.4756300
p-GaN 2.4520045 × 45
ITO 1.962 C i 0.0056 280
DownLoad: CSV
[1]
Hangleiter A, Hitzel F, Netzel C, et al. 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, 2005, 95(12):127402
[2]
Hader J, Moloney J V, Koch S W. Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes. Appl Phys Lett, 2010, 96(22):221106
[3]
Ganesh P, Kent P R C, Mochalin V. Efficiency droop behaviors of the blue LEDs on patterned sapphire substrate. J Appl Phys, 2011, 110(7):073506
[4]
Hader J, Moloney J V, Pasenow B, et al. On the importance of radiative and Auger losses in GaN-based quantum wells. Appl Phys Lett, 2008, 92(26):261103
[5]
Piprek, Joachim. Efficiency droop in nitride-based light-emitting diodes. Phys Status Solidi A, 2010, 207(10):2217
[6]
Kim M H, Schubert M F, Dai Q, et al. Origin of efficiency droop in GaN-based light-emitting diodes. Appl Phys Lett, 2007, 91(18):183507
[7]
Kohno T, Sudo Y, Yamauchi M, et al. Internal quantum efficiency and nonradiative recombination rate in InGaN-based near-ultraviolet light-emitting diodes. Jpn J Appl Phys, 2012, 51:072102
[8]
Fuhrmann D, Retzlaff T, Rossow U, et al. Large internal quantum efficiency of In-free UV-emitting GaN/AlGaN quantum-well structures. Appl Phys Lett, 2006, 88(19):191108
[9]
Hangleiter A, Fuhrmann D, Grewe M, et al. Towards understanding the emission efficiency of nitride quantum wells. Phys Status Solidi A, 2004, 201(12):2808
[10]
Lin E Y, Chen C Y, Lay T S, et al. Internal quantum efficiency and optical polarization analysis of InGaN/GaN multiple quantum wells on a-plane GaN. Physica Status Solidi C, 2008, 5(6):2111
[11]
Titkov I E, Karpov S Y, Yadav A, et al. Temperature-dependent internal quantum efficiency of blue high-brightness light-emitting diodes. IEEE J Quantum Electron, 2014, 50(11):911
[12]
Lee Y J, Chiu C H, Ke C C, et al. Study of the excitation power dependent internal quantum efficiency in InGaN GaN LEDs grown on patterned sapphire substrate. IEEE J Quantum Electron, 2009, 15(4):1137
[13]
Lee J, Ni X, Wu M, et al. Internal quantum efficiency of m-plane InGaN on Si and GaN. Proc SPIE, 2013, 7602:76021N
[14]
Kivisaari P, Riuttanen L, Oksanen J, et al. Electrical measurement of internal quantum efficiency and extraction efficiency of Ⅲ-N light-emitting diodes. Appl Phys Lett, 2012, 101(2):021113
[15]
Ryu H Y, Ryu G H, Lee S H, et al. Evaluation of the internal quantum efficiency in blue and green light-emitting diodes using the rate equation model. Journal of the Korean Physical Society, 2013, 63(2):180
[16]
Getty A, Matioli E, Iza M, et al. Electroluminescent measurement of the internal quantum efficiency of light emitting diodes. Appl Phys Lett, 2009, 94(18):181102
[17]
Matioli E, Weisbuch C. Direct measurement of internal quantum efficiency in light emitting diodes under electrical injection. J Appl Phys, 2011, 109(7):073114
[18]
Nami M, Rishinaramangalam A, Feezell D. Analysis of light extraction efficiency for gallium nitride-based coaxial microwall light-emitting diodes. Phys Status Solidi C, 2014, 11(3/4):766
[19]
Zhmakin A I. Enhancement of light extraction from light emitting diodes. Physics Reports, 2011, 498(4/5):189
[20]
Xia Changsheng, Li Zhifeng, Wang Chong, et al. Ray tracing simulation of InGaN/GaN light-emitting diodes with parabolic substrates. Chinese Journal of Semiconductors, 2006, 27(1):100
[21]
Guo Jinxia, Ma Long, Yi Xiaoyan, et al. Light extraction efficiency of high-power GaN-based light-emitting diodes. Chinese Journal of Semiconductors, 2005, 26(Suppl):170
[22]
Zhu Jihong, Wang Liangji, Zhang Shuming, et al. Simulation of the light extraction efficiency of nanostructure light-emitting diodes. Chin Phys B, 2011, 20(7):077804
[23]
Ryu H Y. Numerical study on the wavelength-dependence of light extraction efficiency in AlGaN-based ultraviolet light-emitting diodes. Opt Quantum Electron, 2014, 46(10):1329
[24]
Kim J W, Jang J H, Oh M C, et al. FDTD analysis of the light extraction efficiency of OLEDs with a random scattering layer. Opt Express, 2014, 22(1):498
[25]
Cui H, Park S H. Numerical simulations of the light-extraction efficiency of LEDs on sapphire substrates patterned with various polygonal pyramids. Journal of the Optical Society of Korea, 2014, 18(6):772
[26]
Lin Z, Yang H, Zhou S, et al. Pattern design of and epitaxial growth on patterned sapphire substrates for highly efficient GaN-based LEDs. Crystal Growth & Design, 2012, 12(6):2836
[27]
Benisty H, Stanley R, Mayer M. Method of source terms for dipole emission modification in modes of arbitrary planar structures. J Opt Soc Am A, 1998, 15(5):1192
[28]
Chew W C. Waves and fields in inhomogeneous media. New York:IEEE Press, 1994
[29]
Xu C, Yu T, Yan J, et al. Analyses of light extraction efficiency in GaN-based LEDs grown on patterned sapphire substrates. Phys Status Solidi C, 2012, 9(3/4):757
[30]
Kong J A. Electromagnetic wave theory. New York:John Wiley & Sons Inc, 1990

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    Received: 09 November 2015 Revised: 14 December 2015 Online: Published: 01 June 2016

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      Article Navigation >  Journal of Semiconductors  > 2016  >  37(6): 064015
      Pingbo An, Li Wang, Hongxi Lu, Zhiguo Yu, Lei Liu, Xin Xi, Lixia Zhao, Junxi Wang, Jinmin Li. Evaluation of light extraction efficiency for the light-emitting diodes based on the transfer matrix formalism and ray-tracing method[J]. Journal of Semiconductors, 2016, 37(6): 064015. doi: 10.1088/1674-4926/37/6/064015 ****P B An, L Wang, H X Lu, Z G Yu, L Liu, X Xi, L X Zhao, J X Wang, J M Li. Evaluation of light extraction efficiency for the light-emitting diodes based on the transfer matrix formalism and ray-tracing method[J]. J. Semicond., 2016, 37(6): 064015. doi: 10.1088/1674-4926/37/6/064015.
      Citation:
      Pingbo An, Li Wang, Hongxi Lu, Zhiguo Yu, Lei Liu, Xin Xi, Lixia Zhao, Junxi Wang, Jinmin Li. Evaluation of light extraction efficiency for the light-emitting diodes based on the transfer matrix formalism and ray-tracing method[J]. Journal of Semiconductors, 2016, 37(6): 064015. doi: 10.1088/1674-4926/37/6/064015 ****
      P B An, L Wang, H X Lu, Z G Yu, L Liu, X Xi, L X Zhao, J X Wang, J M Li. Evaluation of light extraction efficiency for the light-emitting diodes based on the transfer matrix formalism and ray-tracing method[J]. J. Semicond., 2016, 37(6): 064015. doi: 10.1088/1674-4926/37/6/064015.
      shu

      Evaluation of light extraction efficiency for the light-emitting diodes based on the transfer matrix formalism and ray-tracing method

      DOI: 10.1088/1674-4926/37/6/064015

      • Semiconductor Lighting Research & Development Center, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

      Funds:

      Project supported by the National Natural Science Foundation of China (Nos.11574306, 61334009), the China International Science and Technology Cooperation Program (No. 2014DFG62280), and the National High Technology Program of China (No. 2015AA03A101)

      China International Science and Technology Cooperation Program No. 2014DFG62280

      Project supported by the National Natural Science Foundation of China Nos.11574306, 61334009

      National High Technology Program of China No. 2015AA03A101

      More Information
      • Corresponding author: lxzhao@semi.ac.cn
      • Received Date: 2015-11-09
      • Revised Date: 2015-12-14
      • Published Date: 2016-06-01

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