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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25381–25388
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Effects of current crowding on light extraction efficiency of conventional GaN-based light-emitting diodes

Bin Cao, Shuiming Li, Run Hu, Shengjun Zhou, Yi Sun, Zhiying Gan, and Sheng Liu  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 25381-25388 (2013)
http://dx.doi.org/10.1364/OE.21.025381


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Abstract

Current crowding effects (CCEs) on light extraction efficiency (LEE) of conventional GaN-based light-emitting diodes (LEDs) are analyzed through Monte Carlo ray-tracing simulation. The non-uniform radiative power distribution of the active layer of the Monte Carlo model is obtained based on the current spreading theory and rate equation. The simulation results illustrate that CCE around n-pad (n-CCE) has little effect on LEE, while CCE around p-pad (p-CCE) results in a notable LEE droop due to the significant absorption of photons emitted under p-pad. LEE droop is alleviated by a SiO2 current blocking layer (CBL) and reflective p-pad. Compared to the conventional LEDs without CBL, the simulated LEE of LEDs with CBL at 20 A/cm2 and 70 A/cm2 is enhanced by 7.7% and 19.0%, respectively. It is further enhanced by 7.6% and 11.4% after employing a reflective p-pad due to decreased absorption. These enhancements are in accordance with the experimental results. Output power of LEDs with CBL is enhanced by 8.7% and 18.2% at 20 A/cm2 and 70 A/cm2, respectively. And the reflective p-pad results in a further enhancement of 8.9% and 12.7%.

© 2013 OSA

1. Introduction

2 Experimental details

The epitaxial layers of the conventional GaN-based LED chips are grown on c-plane patterned sapphire substrate by a metal-organic chemical vapor deposition (MOCVD) system [13

13. P. Wang, W. Wei, B. Cao, Z. Gan, and S. Liu, “Simulation of current spreading for GaN-based light-emitting diodes,” Opt. Laser Technol. 42(5), 737–740 (2010). [CrossRef]

], as shown in Fig. 1(a). They consists of a 2.5-μm-thick undoped GaN layer, a 3-μm-thick Si-doped n-GaN layer, a six-period In0.2Ga0.8N/GaN multiple quantum well (MQW) active layer, a 20-nm-thick Mg-doped p-Al0.1Ga0.9N electron blocking layer, and a 100-nm-thick Mg-doped p-GaN layer. After the epitaxial growth processes, the wafer is cleaned and an inductively coupled plasma (ICP) etching process is implemented to etch the mesh structure of the LEDs to expose the n-GaN. A 130-nm-thick indium-tin oxide (ITO) layer is deposited on p-GaN as the current spreading layer by thermal evaporator and then the epitaxial wafer is rapidly thermal annealed at 540°C for 5 mins in nitrogen ambient to improve ITO ohmic contact to GaN layer. A Cr/Pt/Au (50/50/1500 nm) layer is then deposited on ITO and n-GaN as n-pad and p-pad, respectively. The epitaxial wafer is then thinned down to about 100 μm. Then, a hybrid reflector combining distributed Bragg reflector (DBR) and a 500-nm-thick Al metal mirror is evaporated on the backside of sapphire to improve the reflectivity [14

14. S. J. Chang, C. F. Shen, M. H. Hsieh, C. T. Kuo, T. K. Ko, W. S. Chen, and S. C. Shei, “Nitride-based LEDs with a hybrid Al mirror+TiO2/SiO2 DBR backside reflector,” J. Lightwave Technol. 26(17), 3131–3136 (2008). [CrossRef]

]. DBR consists of 2-pair TiO2/SiO2 with optical thickness of quarter of 460 nm for each layer. The reflectivity of hybrid reflector is nearly 100%. Finally, the LED wafer is diced into chips with size of 350 × 350 μm2. As comparison, LEDs with the CBL and RCBL are fabricated, respectively. All three kinds of LEDs are equipped with the hybrid reflector structure. For LEDs with CBL, a film of SiO2 layer with thickness of 200 nm is deposited on the p-GaN surface by plasma enhanced chemical vapor deposition (PECVD) before the ITO deposition and then is patterned by photolithography and wet etching to from the CBL. A film of Al layer is inserted underneath the p-pad of LEDs with CBL to form the LEDs with RCBL structure. The reflectivity of Cr/Pt/Au and Al/Cr/Pt/Au are about 30% and 85% at wavelength of 460 nm, respectively, through the measurement of ellipsometry [15

15. S. Zhou, F. Fang, B. Cao, S. Liu, and H. Ding, “Enhancement in light output power of LEDs with reflective current blocking layer and backside hybrid reflector,” Sci. China Technol. Sc. 56(6), 1544–1549 (2013). [CrossRef]

]. The output power-current-voltage (L-I-V) characteristics of the LED chips without silicone are measured in an integrating sphere under pulse current operation at room temperature to eliminate the thermal effect.

3. Non-uniform Radiation Modeling

In order to simulate the LEE of LEDs with CCE by Monte Carlo ray-tracing method, the model with the active layer emitting photons non-uniformly should be built. Thus, we construct the relationship between the radiant power distribution of the active layer and CCE based on the rate equation and current spreading theory, and then the ray-tracing simulation is carried out. The procedure is illustrated in the following:

  • 1) Defining the current density distribution J(x) of the LED chip under injected current density Jinj based on the current spreading theory;
  • 2) Defining the radiant power distribution R(x) based on the rate equation;
  • 3) Defining the top and bottom surface of the active layer as the light source surfaces, and inputting R(x) into the meshed light source surfaces;
  • 4) Defining the material properties of each layer;
  • 5) Ray tracing simulation and collecting the simulation data.

An integral of J(x) with respect to the meshed light source surface S(x) gives injected current I, which is the product of average injected current density Jinj and S

I=JinjS=iJ(xi)S(xi)
(3)

Thus, Ls and J0 are derived from each Jinj based on Eqs. (1)-(3).

Next, the radiant power distribution R(x) is calculated based on the rate equation. When the current density J(x) flows over the active layer, the rate equation for carriers under steady state can be written as [20

20. H. Y. Ryu, H. S. Kim, and J. I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95(8), 081114 (2009). [CrossRef]

, 21

21. P. Kivisaari, L. Riuttanen, J. Oksanen, S. Suihkonen, M. Ali, H. Lipsanen, and J. Tulkki, “Electrical measurement of internal quantum efficiency and extraction efficiency of III-N light-emitting diodes,” Appl. Phys. Lett. 101(2), 021113 (2012). [CrossRef]

]:
J(x)ηinj/(qd)=An(x)+Bn2(x)+Cn3(x)
(4)
where ηinj, d and n are the injection efficiency, thickness of active layer and carrier concentration, respectively. A, B and C are the coefficients of Shockley-Read-Hall (SRH) recombination, radiative recombination and Auger recombination, respectively. According to the definition, internal quantum efficiency ηIQE and radiative recombination efficiency ηrad are expressed as

ηIQE=ηinjηrad
(5)
ηrad=Bn2/(An+Bn2+Cn3)
(6)

Based on Eqs. (4)-(6), we can obtain

Bn2=ηIQEJ(x)/(qd)
(7)

Besides, R(x) of active layer can be expressed as follows [10

10. B. Cao, S. Zhou, and S. Liu, “Effects of ITO pattern on the electrical and optical characteristics of LEDs,” ESC J. Solid State Sci. Technol. 2(1), R24–R28 (2013). [CrossRef]

, 21

21. P. Kivisaari, L. Riuttanen, J. Oksanen, S. Suihkonen, M. Ali, H. Lipsanen, and J. Tulkki, “Electrical measurement of internal quantum efficiency and extraction efficiency of III-N light-emitting diodes,” Appl. Phys. Lett. 101(2), 021113 (2012). [CrossRef]

]:
R(x)=γdBn2
(8)
where γ is the average energy of a photon emitted from active layer, which is approximate to a constant. Therefore, substituting Eq. (7) into Eq. (8), we can obtain:

R(x)=γJ(x)ηIQE/q
(9)

Equation (9) implies that R(x) depends on the current density. The non-uniform current density flowing over the active layer results in non-uniform radiate power distribution. In order to obtain the radiant power distribution R(x) of the active layer, the dependence of ηIQE on J(x) is obtained from theoretical analysis based on the Ref [20

20. H. Y. Ryu, H. S. Kim, and J. I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95(8), 081114 (2009). [CrossRef]

]. The exponential expression of ηIQE versus J(x) is obtained by curve fitting as
ηIQE=a+bexp(J(x)/c)
(10)
where a, b and c are fitting parameters. As demonstrated in Ref [20

20. H. Y. Ryu, H. S. Kim, and J. I. Shim, “Rate equation analysis of efficiency droop in InGaN light-emitting diodes,” Appl. Phys. Lett. 95(8), 081114 (2009). [CrossRef]

], ηIQE versus Jinj is only dependent on the maximum ηIQE and the current density where ηIQE reaches the maximum, therefore, a, b, and c are only dependent on these two parameters. Considering that the maximum ηIQE of above 80% is obtained when the current density is always under 10 A/cm2 for GaN-based LEDs, the fitting parameters of a, b and c with value of 0.50, 0.30 and 145.4 A/cm2, respectively, are employed in the following simulation. In fact, the LEE obtained based on the different fitting parameters shows little variation due to the independence of LEE on ηIQE.

Thus, the radiant power distribution of the active layer is obtained according to Eqs. (1), (9) and (10). The top and bottom surfaces of the active layer are meshed and set as luminescent surfaces with the calculated non-uniform radiant power distribution at each injected current density Jinj. When Monte Carlo ray-tracing simulation is carried out, photons are emitted from the active layer randomly and the power of each photon is dependent on its location. The total power of all the photons escaping into the air is collected by the detector that surrounds the LED chips. The refractive indices and absorption coefficients of sapphire, n-GaN, active layer, p-GaN and ITO are set to be 1.77, 2.45, 2.54, 2.45, and 2.0 and 0, 5 mm−1, 8 mm−1, 5 mm−1, and 0, respectively [7

7. Z. Liu, K. Wang, X. Luo, and S. Liu, “Precise optical modeling of blue light-emitting diodes by Monte Carlo ray-tracing,” Opt. Express 18(9), 9398–9412 (2010). [CrossRef] [PubMed]

]. The reflectivity of bottom surfaces of the three kinds of LEDs is assumed to be 100% considering the reflectivity of the hybrid reflector, that is to say, when the photons transport to backside of sapphire substrate, they will be reflected back without any energy loss. The effect of photon recycling is not considered in this model [22

22. C. C. Sun, T. X. Lee, Y. C. Lo, C. C. Chen, and S. Y. Tsai, “Light extraction enhancement of GaN-based LEDs through passive/active photon recycling,” Opt. Commun. 284(20), 4862–4868 (2011). [CrossRef]

].

4. Results and discussion

The sheet resistances of n-GaN and ITO of our fabricated LEDs are 16.7Ω/□ and 45.1Ω/□ according to the four-point probe measurement, respectively. Current prefers to flow laterally in n-GaN layer rather than the ITO layer due to the smaller sheet resistance of n-GaN. As a result, the current crowds under the p-pad. The current spreading lengths Ls versus injected current density Jinj of LEDs without and with CBL calculated from Eqs. (1)-(3) are shown in Figs. 2(a)
Fig. 2 Current spreading length Ls versus injected current density ηinj of LED (a) without CBL and (b) with CBL.
and 2(b), respectively. In order to compare the effects of different current crowding phenomena on the LEE, the current spreading lengths of LEDs with ITO sheet resistances of 30Ω/□ and 60Ω/□ are also calculated, as shown in Fig. 2. It can be seen that Ls decreases significantly with the increase of injected current density, which implies that CCE becomes serious under high current [9

9. M. V. Bogdanov, K. A. Bulashevich, O. V. Khokhlev, I. Y. Evstratov, M. S. Ramm, and S. Y. Karpov, “Current crowding effect on light extraction efficiency of thin-film LEDs,” Phys. Status Solidi 7(7–8), 2124–2126 (2010) (c).

, 15

15. S. Zhou, F. Fang, B. Cao, S. Liu, and H. Ding, “Enhancement in light output power of LEDs with reflective current blocking layer and backside hybrid reflector,” Sci. China Technol. Sc. 56(6), 1544–1549 (2013). [CrossRef]

]. The decrease of ITO sheet resistance is helpful to alleviating the p-CCE [15

15. S. Zhou, F. Fang, B. Cao, S. Liu, and H. Ding, “Enhancement in light output power of LEDs with reflective current blocking layer and backside hybrid reflector,” Sci. China Technol. Sc. 56(6), 1544–1549 (2013). [CrossRef]

, 16

16. H. Y. Ryu and J. I. Shim, “Effect of current spreading on the efficiency droop of InGaN light-emitting diodes,” Opt. Express 19(4), 2886–2894 (2011). [CrossRef] [PubMed]

, 23

23. S. J. Chang, C. F. Shen, W. S. Chen, T. K. Ko, C. T. Kuo, K. H. Yu, S. C. Shei, and Y. Z. Chiou, “Nitride-based LEDs with an insulating SiO2 layer underneath p-pad electrodes,” Electrochem. Solid-State Lett. 10(6), H175–H177 (2007). [CrossRef]

, 24

24. J. C. Chen, G. J. Shen, F. S. Hwu, H. I. Chen, J. K. Shen, T. X. Lee, and C. C. Sun, “Electrical-optical analysis of a GaN/sapphire LED chip by considering the resistivity of the current-spreading layer,” Opt. Rev. 16(2), 213–215 (2009). [CrossRef]

], as shown in Fig. 2. The difference of sheet resistances between n-GaN and ITO decreases with the decrease of ITO sheet resistance, resulting in a more uniform current distribution and longer Ls [1

1. E. F. Schubert, Light-Emitting Diodes (Cambridge University, 2006).

]. Meanwhile, p-CCE is alleviated by employing the CBL. Compared to the LEDs without CBL, Ls of LEDs with CBL increases by 17.8%, 20.8%, and 18.2% for ITO sheet resistance of 30Ω/□, 45.1Ω/□, and 60Ω/□ at 20 A/cm2, respectively.

Figure 3(a)
Fig. 3 LEE of LEDs with current crowding around (a) p-pad and (b) n-pad.
shows the current crowding effects on LEE of conventional LEDs with different ITO sheet resistances. For comparison, the n-CCE is analyzed with the assumption that the ITO sheet resistance is 16.7Ω/□ and n-GaN sheet resistance varies from 30Ω/□ to 60Ω/□. The LEE of LEDs without CCE (Jinj = 0) is 39.7%. It can be seen that LEE of LEDs with p-CCE drops significantly. When current density increases from 0 to 70 A/cm2, it is decreased by 18.8%, 22.0%, and 24.2% for ITO sheet resistances of 30Ω/□, 45.1Ω/□, and 60Ω/□, respectively, as shown in Fig. 3(a). Lots of photons are emitted under p-pad due to p-CCE, and they are absorbed significantly by the metallic p-pad when they transport upwards for the first time, as illustrated in Fig. 1(a). The number of photon emitted under p-pad increases with degeneration of p-CCE and consequently, the absorption by the p-pad increases. Thus, LEE drops remarkably with degeneration of p-CCE caused by high current density as well as large ITO sheet resistance. However, n-CCE shows little influence on LEE, as show in Fig. 3(b). This is due to the photons crowding around mesh edge are easy to escape into the air without less absorption [4

4. T. X. Lee, C. Y. Lin, S. H. Ma, and C. C. Sun, “Analysis of position-dependent light extraction of GaN-based LEDs,” Opt. Express 13(11), 4175–4179 (2005). [CrossRef] [PubMed]

], as illustrated in Fig. 1(a). As a result, LEDs with n-CCE have a superior LEE.

The radiant power under p-pad decreases due to the reduction of p-CCE achieved by the CBL and improved ITO performance [15

15. S. Zhou, F. Fang, B. Cao, S. Liu, and H. Ding, “Enhancement in light output power of LEDs with reflective current blocking layer and backside hybrid reflector,” Sci. China Technol. Sc. 56(6), 1544–1549 (2013). [CrossRef]

, 16

16. H. Y. Ryu and J. I. Shim, “Effect of current spreading on the efficiency droop of InGaN light-emitting diodes,” Opt. Express 19(4), 2886–2894 (2011). [CrossRef] [PubMed]

, 23

23. S. J. Chang, C. F. Shen, W. S. Chen, T. K. Ko, C. T. Kuo, K. H. Yu, S. C. Shei, and Y. Z. Chiou, “Nitride-based LEDs with an insulating SiO2 layer underneath p-pad electrodes,” Electrochem. Solid-State Lett. 10(6), H175–H177 (2007). [CrossRef]

, 24

24. J. C. Chen, G. J. Shen, F. S. Hwu, H. I. Chen, J. K. Shen, T. X. Lee, and C. C. Sun, “Electrical-optical analysis of a GaN/sapphire LED chip by considering the resistivity of the current-spreading layer,” Opt. Rev. 16(2), 213–215 (2009). [CrossRef]

]. As a result, the absorption of photons transporting upwards for the first time is decreased and subsequently, the LEE of LEDs with p-CCE is increased. Figure 3(a) illustrates that the LEE droop of LEDs with p-CCE is alleviated significantly due to CBL. Compared to LEDs without CBL at 20 A/cm2, LEE of LEDs with CBL is increased by 5.5%, 7.7%, and 8.7% for ITO sheet resistances of 30Ω/□, 45.1Ω/□, and 60Ω/□, respectively. At 70A/cm2, LEE is found to be increased by 15.9%, 19.0%, and 21.5%, respectively.

On the other hand, a reflector underneath the electrode pad is introduced to decrease the absorption to improve LEE of LEDs with p-CCE [15

15. S. Zhou, F. Fang, B. Cao, S. Liu, and H. Ding, “Enhancement in light output power of LEDs with reflective current blocking layer and backside hybrid reflector,” Sci. China Technol. Sc. 56(6), 1544–1549 (2013). [CrossRef]

, 25

25. N. M. Lin, S. C. Shei, S. J. Chang, and X. F. Zeng, “GaN-based LEDs with omnidirectional metal underneath an insulating SiO2 Layer,” IEEE Photon. Technol. Lett. 24(10), 815–817 (2012). [CrossRef]

]. Figure 4
Fig. 4 LEEs of LEDs with ITO sheet resistance of 45.1Ω/□ when reflectivity of p-pad varies.
depicts the effects of reflectivity of p-pad on the LEE of LEDs with ITO sheet resistance of 45.1Ω/□. It can be seen that LEE increases with the increase of reflectivity. With the reflectivity of p-pad increasing from 30% to 85%, the LEE of LEDs without and with CBL increases by 13.4% and 7.6% at 20 A/cm2, and 26.3% and 11.4% at 70 A/cm2. That is to say, the LEEs of LEDs with RCBL are increased by 7.6% and 11.4% compared to these of LEDs with CBL at 20 A/cm2 and 70 A/cm2, respectively. Although the number of photons emitted under p-pad increases with current density, the absorption is decreased by increasing the reflectivity of p-pad.

Figure 5
Fig. 5 L-I-V relationships of LEDs without CBL, with CBL and with RCBL. The inset is TEM image of the deposited SiO2/ITO/Al layers underneath the p-pad of the LED with RCBL.
shows the L-I-V curves of LEDs without CBL, with CBL and with RCBL, respectively. The inset shows the cross-sectional TEM image of the electrode pad of LEDs with RCBL. It can be seen that the SiO2 CBL, ITO layer, and Al metal reflector are subsequently deposited on epitaxial layer. Current density is found to crowd under the p-pad according to the measurement of the sheet resistances of ITO and n-GaN. At injection current density of 20 A/cm2, the forward voltages are 3.20 V, 3.27 V and 3.31 V for LEDs without CBL, with CBL, and with RCBL, respectively. The higher voltages of the LEDs with CBL and RCBL are attributed to larger series resistance caused by the less contact area of ITO and p-GaN [23

23. S. J. Chang, C. F. Shen, W. S. Chen, T. K. Ko, C. T. Kuo, K. H. Yu, S. C. Shei, and Y. Z. Chiou, “Nitride-based LEDs with an insulating SiO2 layer underneath p-pad electrodes,” Electrochem. Solid-State Lett. 10(6), H175–H177 (2007). [CrossRef]

]. Compared to LEDs without CBL, the output power of LEDs with CBL is enhanced by 8.7% and 18.2% at 20 A/cm2 and 70 A/cm2, respectively. The output power of LEDs with RCBL is further enhanced by 8.9% and 12.7% compared to these of LEDs with CBL at 20 A/cm2 and 70 A/cm2, respectively. These results, which are accordance with the simulation results, illustrate that the CBL and RCBL are beneficial to preventing photons being emitted under p-pad and being absorbed, especially under high current density.

5. Conclusions

In this paper, LEEs of the conventional GaN-based LEDs with current crowding around p-pad and n-pad are analyzed respectively by Monte Carlo ray-tracing method to optimize the design of LEDs. The improved LED model with non-uniform distribution of photons emitted from the active layer is constructed based on the rate equation and current spreading theory. The results show that current crowding around n-pad has little effect on the LEE, while current crowding around p-pad has a significant effect on the LEE due to the remarkably absorption of photons emitted under p-pad. Thus, high current density and/or inferior device parameters including low reflectivity of p-pad and large sheet resistance difference between n-GaN and TCL lead to degeneration of LEE droop. In order to increase LEE, we can decrease the emission of photons under p-pad by CBL and/or decrease the absorption by reflective p-pad. The simulated results show that LEE of LEDs with CBL is enhanced by 7.7% and 19.0% and further enhanced by 7.6% and 11.4% with a reflective p-pad at 20 A/cm2 and 70 A/cm2, respectively. The enhancements are in accordance with the experimental results.

Acknowledgments

This work was supported by the State Key Development Program for Basic Research of China under Grant 2011CB013103 and National High Technology Research and Development Program of China under Grant 2011AA03A106.

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S. J. Chang, C. F. Shen, M. H. Hsieh, C. T. Kuo, T. K. Ko, W. S. Chen, and S. C. Shei, “Nitride-based LEDs with a hybrid Al mirror+TiO2/SiO2 DBR backside reflector,” J. Lightwave Technol. 26(17), 3131–3136 (2008). [CrossRef]

15.

S. Zhou, F. Fang, B. Cao, S. Liu, and H. Ding, “Enhancement in light output power of LEDs with reflective current blocking layer and backside hybrid reflector,” Sci. China Technol. Sc. 56(6), 1544–1549 (2013). [CrossRef]

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21.

P. Kivisaari, L. Riuttanen, J. Oksanen, S. Suihkonen, M. Ali, H. Lipsanen, and J. Tulkki, “Electrical measurement of internal quantum efficiency and extraction efficiency of III-N light-emitting diodes,” Appl. Phys. Lett. 101(2), 021113 (2012). [CrossRef]

22.

C. C. Sun, T. X. Lee, Y. C. Lo, C. C. Chen, and S. Y. Tsai, “Light extraction enhancement of GaN-based LEDs through passive/active photon recycling,” Opt. Commun. 284(20), 4862–4868 (2011). [CrossRef]

23.

S. J. Chang, C. F. Shen, W. S. Chen, T. K. Ko, C. T. Kuo, K. H. Yu, S. C. Shei, and Y. Z. Chiou, “Nitride-based LEDs with an insulating SiO2 layer underneath p-pad electrodes,” Electrochem. Solid-State Lett. 10(6), H175–H177 (2007). [CrossRef]

24.

J. C. Chen, G. J. Shen, F. S. Hwu, H. I. Chen, J. K. Shen, T. X. Lee, and C. C. Sun, “Electrical-optical analysis of a GaN/sapphire LED chip by considering the resistivity of the current-spreading layer,” Opt. Rev. 16(2), 213–215 (2009). [CrossRef]

25.

N. M. Lin, S. C. Shei, S. J. Chang, and X. F. Zeng, “GaN-based LEDs with omnidirectional metal underneath an insulating SiO2 Layer,” IEEE Photon. Technol. Lett. 24(10), 815–817 (2012). [CrossRef]

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

ToC Category:
Optical Devices

History
Original Manuscript: May 23, 2013
Revised Manuscript: July 14, 2013
Manuscript Accepted: September 6, 2013
Published: October 17, 2013

Citation
Bin Cao, Shuiming Li, Run Hu, Shengjun Zhou, Yi Sun, Zhiying Gan, and Sheng Liu, "Effects of current crowding on light extraction efficiency of conventional GaN-based light-emitting diodes," Opt. Express 21, 25381-25388 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25381


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References

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