Abstract

We investigate the dependence of various efficiencies in GaN-based vertical blue light-emitting diode (LED) structures on the thickness and doping concentration of the n-GaN layer by using numerical simulations. The electrical efficiency (EE) and the internal quantum efficiency (IQE) are found to increase as the thickness or doping concentration increases due to the improvement of current spreading. On the contrary, the light extraction efficiency (LEE) decreases with increasing doping concentration or n-GaN thickness by the free-carrier absorption. By combining the results of EE, IQE, and LEE, wall-plug efficiency (WPE) of the vertical LED is calculated, and the optimum thickness and doping concentration of the n-GaN layer is found for obtaining the maximum WPE.

©2013 Optical Society of America

1. Introduction

Recently, white light sources based on light-emitting diodes (LEDs) have attracted great attention as high energy-efficiency and environment-friendly lighting technologies [16]. Over the last decade, there has been considerable progress in the development of high-power and high-efficiency LEDs. However, the application of LEDs toward general lighting requires even higher brightness and efficiency. In the development of LEDs, there has been increasing demand on the high internal quantum efficiency (IQE) and light extraction efficiency (LEE), low operation voltage, and thermally stable operation. Recently, thin-film vertical LED structures have been introduced for high-power and high-efficiency lighting applications [610]. In the vertical LED structure, epitaxial layers are placed on a receptor substrate with high thermal conductivity. This LED structure is expected to be a prominent solution to overcome the limitations of current LED structures due to low thermal resistance, uniform current spreading, and high LEE.

The vertical LED structure is typically manufactured by bonding a conventional LED chip on a receptor substrate and subsequently removing the sapphire substrate of the LED chip by the laser lift-off process [7]. It has several advantages over the conventional planar LED structure with lateral current injection geometry. High thermal conductivity of the metal receptor substrate improves thermally-stable operation. Current is injected vertically between top and bottom contacts, which enables more uniform current distribution and reduced operation voltage. It has been reported that the uniform current spreading is also advantageous for reducing efficiency droop at high current density [11, 12]. Thus, relatively high IQE can be achieved at large current density by improving current spreading. In addition, the vertical LED is expected to show high LEE by combining the high-reflectance p-type electrode mirror and light extracting structures in the n-GaN surface such as surface roughening [13] and photonic crystals [14, 15].

Therefore, the vertical LED is expected to show high power-conversion efficiency or wall-plug efficiency (WPE) through the improvement in the electrical efficiency, IQE, and LEE. WPE (ηWPE) of LEDs is defined as

ηWPE=PoutIV,
where Pout is optical output power emitted out of the LED. I and V are applied current and voltage, respectively.

The electrical efficiency (ηelec), IQE (ηint), and LEE (ηextract) are respectively defined as

ηelec=hν¯eV,ηint=Pint/hν¯I/e,ηextraction=PoutPint,
where ν¯is the average frequency of emitted light and e is the elementary charge. Pint is the optical power emitted from active region. By combining Eqs. (1) and (2), WPE is written as

ηWPE=ηelecηintηextraction.

In the vertical LED, the electrical efficiency (EE) and IQE can be increased by improving current spreading. Current can flow more uniformly as the thickness or doping concentration of the n-GaN layer increases. However, increasing the thickness or doping concentration may result in increased optical loss by the increasing contribution of the free carrier absorption, which leads to the decrease in LEE. Thus, in vertical LED structures, it is important to optimize the thickness and doping concentration of the n-GaN layer for obtaining the highest WPE. Although the thickness and doping concentration of the n-GaN layer may have significant influence on the various efficiencies of vertical LED structures, there have been few reports to study the effect of these parameters on LED efficiencies.

In this work, we systematically investigate the dependence of the efficiencies of InGaN/GaN vertical blue LED structures on the thickness and doping concentration of the n-GaN layer by using numerical simulations. For the simulation of EE and IQE, an advanced device simulation software, APSYS is employed [16]. The APSYS program self-consistently solves QW band structures, radiative and nonradiative carrier recombination, and the drift and diffusion equation of carriers. It has been widely used for the simulation of device characteristics of GaN-based LEDs. For the simulation of LEE, the finite-difference time-domain (FDTD) method is employed. The FDTD method is advantageous for simulating photonic structures with micro- or nano-scale patterns. Thus, it has been applied to the LEE simulation of LEDs with photonic crystal patterns or textured surface [1720]. Finally, WPE in Eq. (3) is obtained by combining the results of EE, IQE, and LEE. Then, the dependence of WPE on the thickness and doping concentration of the n-GaN layer will be discussed.

2. Methods of simulation

2.1 Simulation of I-V and IQE curves

A cross section of the vertical LED structure for the APSYS simulation is schematically drawn in Fig. 1 . LED layer structures are basically composed of an n-GaN layer, multiple-quantum-well (MQW) active layers, a p-AlGaN electron-blocking layer (EBL), and a p-GaN layer. MQW layers consist of five 25-Å-thick In0.16Ga0.84N QWs separated by 80-Å-thick GaN barriers. All QW and barrier layers are undoped. The thickness and In composition at the QWs corresponds to the peak emission wavelength of ~0.45 μm. The thickness of EBL and the p-GaN layer is 20 and 150 nm, respectively. The Al composition of EBL is 15%. The hole concentration at both EBL and the p-GaN layer is set at 5 × 1017 cm−3. The dimension of the simulated vertical LED chip is 1 mm × 1mm, which is the typical dimension of high-power vertical LEDs operating with 1-W input power. The entire surface of the p-GaN is covered with a p-type electrode, which also acts as a high-reflectance mirror. N-type electrodes are formed on the surface of the n-GaN layer. Each n-type electrode has a stripe-shape with the dimension of 50 μm × 1mm, and the electrodes are equally spaced on the n-GaN surface.

 

Fig. 1 Schematic diagram of the simulated vertical LED structure.

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In the carrier recombination model of APSYS, the Schockley-Read-Hall (SRH) recombination lifetime (τSRH) is set at 50 ns. The radiative recombination rate is calculated by integrating the spontaneous emission spectrum with a Lorentzian line-shape function. The Auger recombination in InGaN QWs has been one of the central issues in the debate of efficiency droop in InGaN LEDs [2124]. The efficiency droop can be conveniently modeled by using the Auger recombination in the ABC carrier recombination model [2528]. Theoretically calculated Auger recombination coefficients (C coefficients) by indirect Auger processes have been ~10−31 cm−3 [29, 30]. The C coefficient can be obtained by the fit of a measured efficiency curve, and the C coefficient of the order of 10−31 ~10−29 cm6/s has been reported experimentally [21, 23, 31]. However, no consensus has been reached yet regarding the Auger recombination coefficient. Here, we choose a recently reported value of 3.5 × 10−31 cm6/s as the C coefficient of the simulation [31].

IQE is defined as the ratio of radiative recombination current to total injection current. We also include built-in electric fields induced by spontaneous and piezo-electric polarizations at the hetero-interfaces of InGaN/GaN and AlGaN/GaN [32]. The strength of built-in electric fields at the interfaces of the InGaN QW and the GaN barrier is set at approximately 1 MeV/cm. Using these material parameters, the voltage versus current (I-V curve) and the IQE versus current (IQE curve) relations will be calculated when doping concentration of the n-GaN layer is varied from 5 × 1017 to 1 × 1019 cm−3 for three n-GaN thicknesses of 2, 3, and 4 μm. The electron concentration at the n-GaN layer is assumed to be the same as the doping concentration. In the simulation, electron current leakage from active layers to the p-GaN layer was not observed in all cases. Therefore, a possibility of IQE droop by the carrier overflow is excluded in this work.

2.2 Simulation of LEE

In the simulation of LEE, the three-dimensional (3-D) FDTD method based on the Yee’s algorithm with a perfectly-matched layer (PML) boundary condition is employed [33]. The cross sectional view of the FDTD computational domain is schematically drawn in Fig. 2 . LED layer structures are basically the same as those shown in Fig. 1. In vertical LEDs, textured patterns on the n-GaN surface are formed by wet chemical etching and typically show a cone-like shape. Thus, we introduce cone patterns on the surface of the n-GaN layer in the FDTD simulation. It is assumed that the bottom of each cone pattern is in contact with adjacent cones and the height of cones is the same as the bottom diameter of cones, and the cone patterns are formed as a periodic array of square lattice in the simulation. Here, the height and the bottom diameter of cones are fixed at 1.2 μm. In this dimension of cone patterns, LEE of vertical LEDs was found to be nearly the highest by separate simulations.

 

Fig. 2 Computational domain of the vertical LED structure for finite-difference time-domain (FDTD) simulations.

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In the FDTD simulation, a single dipole source is positioned at the center of x-y plane of the computational domain and also in the middle of the MQW active region in the vertical direction. The dipole source is polarized in the in-plane direction for the excitation of transverse-electric (TE) polarized light that is primarily emitted radiation at InGaN QWs. In the spectrum of emitted light, the center wavelength and the full-width at half maximum of the spectrum are set to be 450 nm and 20 nm, respectively. LEE is defined as the fraction of emitted power out of the LED surface to the total emitted power, which is determined by the ratio of Poynting vectors integrated over the extraction surface to total integrated Poynting vectors. Owing to the limitation of computational capacity, the FDTD simulation domain is much smaller than the size of actual LEDs. Lateral dimension of the computational domain is only ~8 μm. In order to truncate the virtually infinite lateral dimension of actual vertical LED structures, perfect mirrors with 100%-reflectance have been placed along the four lateral boundaries of the simulated LED structure as shown in Fig. 2. This perfect-mirror configuration has been frequently employed for the LEE simulation of LED structures [1820, 34, 35].

In vertical LEDs, a high-reflectance p-type electrode reflector exists below the p-GaN layer. In the simulation, the electrode reflector is assumed to be composed of a thin dielectric absorbing layer and a perfect mirror with 100% reflectance because using metal materials in the FDTD simulation increases computational burden considerably. By varying the absorption coefficient of the absorbing layer above the perfect mirror, reflectance of the electrode reflector can be adjusted. Here, the absorption coefficient of the absorbing layer is chosen so that the reflectance of the p-type electrode can be 95% for normal incidence. The refractive index of GaN, InGaN, and AlGaN layers is set at 2.52, 2.58, and 2.48, respectively. The LED chip is assumed to be encapsulated by an epoxy material with the refractive index of 1.5.

LEE in the vertical LED is strongly dependent on the absorption coefficient of materials. Many groups have investigated the absorption coefficient in the GaN-based materials. However, there have been large variations of reported values and it is difficult to know the actual values of the absorption coefficients. Liu et al. well summarized the absorption coefficients in GaN, InGaN, and AlGaN materials [36]. Here, the absorption coefficient of InGaN QW layers is chosen to be 1000 cm−1 according to Ref [36]. Total thickness of InGaN QW layers is 10 nm. Light absorption for sub-bandgap energy is mainly affected by defects, dopants, and the Urbach tail [3638]. In early studies, the absorption coefficient of GaN was reported to be higher than 50 cm−1 [3941], which is attributed to poor material quality. More recent studies reported lower absorption coefficient values of 1~20 cm−1 [4244]. In highly-doped GaN, free-carrier absorption can be significant because it increases with increasing doping concentration. The absorption coefficient by the free-carrier absorption was reported to be 10~20 cm−1 depending on the doping concentration [38, 45].

In this work, we model the absorption coefficient of GaN and AlGaN layers as below.

α=αb+αf,
where αb is the background absorption coefficient independent of doping concentration and αf is the concentration-dependent absorption coefficient by the free-carrier absorption. In the LEE simulation, we consider two cases of αb: high material quality (αb = 5 cm−1) and relatively low material quality (αb = 20 cm−1). In order to find αf in Eq. (4) as a function of the doping concentration, an empirical formula for the free-carrier absorption in GaN materials is used [38]. In Ref [38], a relation between the electron concentration, ne and the absorption coefficient at 0.6 eV, αf (0.6 eV) is expressed as
ne=7.2×1013cm-1[αf(0.6eV)]2+2.2×1015cm-2αf(0.6eV)
By solving Eq. (5), the absorption coefficient at 0.6 eV is obtained as a function of electron concentration. The absorption coefficient at 2.75 eV, which corresponds to the photon energy of blue light, can be known from αf (0.6 eV) by using the fact that the absorption coefficient by the free-carrier absorption is proportional to the square of light wavelength [37, 38]. In Fig. 3 , the absorption coefficient at 2.75 eV is plotted as a function of electron concentration. Figure 3 shows that αf increases from 3.4 to 17.7 cm−1 as electron concentration increases from 5 × 1017 to 1019 cm−3. This value of the absorption coefficient in the GaN layer is much lower than that in InGaN QW layers. However, since the n-GaN layer is much thicker than other epitaxial layers, the thickness and doping concentration of the n-GaN layer play an important role in optical absorption and hence LEE of the vertical LED. Using the model in Eqs. (4) and (5), LEE of the vertical LED will be calculated as the thickness and doping concentration of the n-GaN layer varies.

 

Fig. 3 Absorption coefficient of blue light by the free-carrier absorption as a function of electron concentration.

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3. Simulation results

3.1 EE and IQE

First, we numerically investigate the effects of the thickness and doping concentration of the n-GaN layer on carrier distribution in QW plane. As the thickness or doping concentration of the n-GaN layer increases, improvement in the current spreading is expected, which should result in more homogeneous distribution of carriers in the plane of QWs. Figure 4 shows the distribution of electron carrier concentration in the horizontal direction of the central QW in the MQW active region. In Fig. 4(a), electron concentration in the plane of the QW from 0 to 250 μm is shown for several doping concentration from 1018 to 1019 cm−3 when the thickness of the n-GaN layer is 3 μm. Electron concentration in the region below the n-electrode is flat and it decreases as the region becomes more distant from the electrode, showing nonuniform carrier distribution in the plane of QWs. The electron concentration in the QW plane becomes more uniform as the doping concentration increases from 1018 to 1019 cm−3. In Fig. 4(b), the electron concentration in the plane of the QW is shown for the n-GaN thickness of 2, 3, and 4 μm when doping concentration at n-GaN is 5 × 1018 cm−3. The electron concentration in the QW plane becomes uniform as the n-GaN thickness increases.

 

Fig. 4 (a) Electron concentration in the horizontal direction of the QW plane for several doping concentration from 1018 to 1019 cm−3 when the thickness of the n-GaN is 3 μm. (b) Electron concentration in the horizontal direction of the QW plane for the n-GaN thickness of 2, 3, and 4 μm when doping concentration at the n-GaN is 5 × 1018 cm−3.

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The current spreading and the electron distribution in the plane of QWs may be dependent on the electron mobility of the n-GaN. In the simulation, the mobility model of Ref [46, 47]. was used, where the electron mobility of the n-GaN is ~500 cm2/Vs. We tested the effect of the electron mobility on the electron distribution in the horizontal direction in separate simulations, and found that the electron distribution curves in Fig. 4 were not affected appreciably unless the electron mobility was lower than 100 cm2/Vs. Therefore, it is expected that the uncertainty in the electron mobility does not have significant influence on the electron distribution, and hence the I-V and the IQE characteristics that will be shown below.

As the current spreading improves, series resistance in the n-GaN layer will decrease, which results in the decrease of the forward voltage. In Fig. 5(a) , I-V curves are shown for several doping concentration from 1018 to 1019 cm−3. Here, the n-GaN thickness is fixed at 3.0 μm. At sufficiently large injection current, forward voltage becomes to decrease as the doping concentration of the n-GaN increases due to the improvement in the current spreading. In Fig. 5(b), using the simulated data of I-V curves, EE at 350 mA is plotted as the doping concentration at the n-GaN increases from 5 × 1017 to 1019 cm−3 for three n-GaN thicknesses of 2, 3, and 4 μm. EE is observed to increase as the thickness or doping concentration of the n-GaN layer increases. EE at 350 mA is increased by ~1% as the doping concentration increases from 1018 to 1019 cm−3 for the three n-GaN thicknesses.

 

Fig. 5 (a) Voltage versus current relations (I-V curves) for several doping concentration from 1018 to 1019 cm−3 when the n-GaN thickness is 3 μm. (b) Electrical efficiency (EE) at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three n-GaN thicknesses of 2, 3, and 4 μm.

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Uniform carrier distribution in the QW plane can also be advantageous for reducing the efficiency droop in InGaN LEDs [11, 12]. It has been well known that inhomogeneous carrier distribution in MQW active region could lead to significant efficiency droop because of increased carrier loss at the region of high carrier density [4850]. The concept of a uniform carrier distribution to reduce the efficiency droop effects can also be applied to the carrier distribution in the horizontal direction of QWs. In this sense, carriers should be uniformly distributed in the plane of QWs in order to reduce efficiency droop and hence to increase IQE at high current density [12].

Figure 6(a) shows IQE curves for several doping concentration from 1018 to 1019 cm−3 when the n-GaN thickness is 3.0 μm. The IQE curves exhibit typical efficiency droop behaviors: IQE begins to decrease substantially when injection current is larger than 150 mA. IQE droop becomes less significant as doping concentration of the n-GaN layer increases. Although the peak IQE value is almost the same for different level of doping concentration, the difference of IQE between the high and the low doping concentration becomes large as current increases. The reduction in the IQE droop for high doping concentration is attributed to the improvement in the uniformity of carrier distribution in the plane of QWs. In Fig. 6(b), IQE at 350 mA is plotted as doping concentration of n-GaN increases from 5 × 1017 to 1019 cm−3 for three n-GaN thicknesses of 2, 3, and 4 μm. IQE at 350 mA increases as the thickness or doping concentration of the n-GaN layer increases due to the reduction in the efficiency droop. IQE at 350 mA is increased by 1~2% as doping concentration increases from 1018 to 1019 cm−3 for the three n-GaN thicknesses. By further improving the current spreading and uniformity in carrier distribution in QWs through the optimization of LED structures, efficiency droop will be reduced and IQE at high injection current will be increased even more.

 

Fig. 6 (a) Internal quantum efficiency (IQE) versus current relations for several doping concentration from 1018 to 1019 cm−3 when the n-GaN thickness is 3 μm. (b) IQE at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three n-GaN thicknesses of 2, 3, and 4 μm.

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3.2 LEE and WPE

Then, 3-D FDTD simulation is performed to calculate LEE of vertical LEDs for different doping concentration at the n-GaN layer. Here, Eq. (3) and the data of free carrier absorption in Fig. 3 are used for obtaining the absorption coefficient of the n-GaN layer for the background absorption coefficient αb of 5 and 20 cm−1. In Fig. 7 , LEE is plotted as a function of doping concentration from 5 × 1017 to 1019 cm−3 for three n-GaN thicknesses of 2, 3, and 4 μm. Figures 7(a) and 7(b) show the results when αb is 5 and 20 cm−1, respectively. As the thickness or doping concentration of the n-GaN layer increases, LEE decreases significantly owing to the increased contribution of free-carrier absorption. The simulated LEE lies in 73~80% for αb of 5 cm−1 and in 68~75% for αb of 20 cm−1, respectively. This range of LEE well corresponds to the LEE of current vertical LEDs. When the material quality of GaN is low (αb = 20 cm−1), LEE is lower by ~5% compared with the case of high material quality (αb = 5 cm−1). When αb is 5 cm−1 and doping concentration is low, the difference in LEE between the n-GaN thickness of 2 and 4 μm is only ~2%. However, it is increased to 3~4% when αb is 20 cm−1 and doping concentration is high. This implies that LEDs with a thick n-GaN layer may undergo significant reduction in LEE when the background absorption and the doping concentration at the n-GaN layer is high.

 

Fig. 7 Light extraction efficiency (LEE) at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three n-GaN thicknesses of 2, 3, and 4 μm when αb is (a) 5 and (b) 20 cm−1.

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Finally, WPE in Eq. (3) is calculated by combining the results of EE, IQE, and LEE. As one can see from Figs. 5, 6, and 7, the dependence of EE, IQE, and LEE on the thickness and doping concentration was monotonic: both EE and IQE increases, and LEE decreases with increasing thickness or doping concentration. However, the dependence of WPE on structural parameters is not simple when these results are combined. In Fig. 8 , WPE at 350 mA is plotted as a function of doping concentration from 5 × 1017 to 1019 cm−3 for three n-GaN thicknesses of 2, 3, and 4 μm. Figures 8(a) and 8(b) show the results when αb is 5 and 20 cm−1, respectively. The range of WPE in the simulated range is 43 ~48.5%, which is similar to the WPE of high-performance vertical LEDs [3, 5].

 

Fig. 8 Wall-plug efficiency (WPE) at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three thicknesses of 2, 3, and 4 μm when αb is (a) 5 and (b) 20 cm−1.

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In Fig. 8, there exists the maximum value of WPE at specific doping concentration. The optimum doping concentration for obtaining the maximum WPE exists around 1~3 × 1018 cm−3. At low doping concentration of <1 × 1018 cm−3, WPE increases with doping concentration due to the rapid increase of EE and IQE with doping concentration as shown in Figs. 5 and 6. At high doping concentration of >3 × 1018 cm−3, WPE decreases with doping concentration because the influence of the decreasing LEE becomes more significant than that of the increasing EE and IQE as doping concentration increases. For αb of 5 cm−1, the maximum WPE for three n-GaN thicknesses is almost the same when the doping concentration is 1~2 cm−3. For αb of 20 cm−1, however, the WPE decreases as the n-GaN thickness increases, indicating the significant influence of the LEE on the WPE when the optical absorption at the n-GaN is large.

The results in Fig. 8 show that the maximum WPE exists when the n-GaN thickness is 2~3 μm and the doping concentration is 2~3 × 1018 cm−3. In addition, it does not seem to be desirable to increase the n-GaN thickness too thick or doping concentration too high at the n-GaN layer. In this way, the optimum values of the thickness and doping concentration of the n-GaN layer are found by combining the simulation results of EE, IQE, and LEE. However, these optimum values will change when different material and structural parameters are used in the simulations.

4. Conclusion

We theoretically investigated the dependence of various efficiencies in InGaN/GaN vertical blue LED structures on the thickness and doping concentration of the n-GaN layer. The electrical efficiency (EE) and the internal quantum efficiency (IQE) were calculated by the APSYS program and the light extraction efficiency (LEE) was calculated by 3-D FDTD simulations. As the thickness or doping concentration of the n-GaN layer increased, EE and IQE were found to increase due to the improvement of current spreading. However, LEE was decreased with increasing thickness or doping concentration as a result of increasing contribution of the optical absorption in the n-GaN layer. The wall-plug efficiency (WPE) of the vertical LED was calculated from the simulated results of EE, IQE, and LEE. In the simulated LED structure, the optimum thickness and doping concentration of the n-GaN layer for achieving the maximum WPE was found to be 2~3 μm and 1~3 × 1018 cm−3, respectively.

Acknowledgments

This work was supported by National Research Foundation of Korea Grant funded by the Korean Government (2011-0003376) and by the Ministry of Knowledge Economy (MKE), Korea, under the Information Technology Research Center (ITRC) support program supervised by the National IT Industry Promotion Agency (NIPA) (NIPA-2012-H0301-12-1010)

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24. 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]  

25. J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010). [CrossRef]  

26. A. David and M. J. Grundmann, “Droop in InGaN light-emitting diodes: A differential carrier lifetime analysis,” Appl. Phys. Lett. 96(10), 103504 (2010). [CrossRef]  

27. H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011). [CrossRef]  

28. H. Y. Ryu, D. S. Shin, and J. I. Shim, “Analysis of efficiency droop in nitride light-emitting diodes by the reduced effective volume of InGaN active material,” Appl. Phys. Lett. 100(13), 131109 (2012). [CrossRef]  

29. E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011). [CrossRef]  

30. F. Bertazzi, M. Goano, and E. Bellotti, “Numerical analysis of indirect Auger transitions in InGaN,” Appl. Phys. Lett. 101(1), 011111 (2012). [CrossRef]  

31. B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012). [CrossRef]  

32. V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002). [CrossRef]  

33. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Inc., 1995).

34. S. K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H. G. Park, and Y. H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008). [CrossRef]  

35. D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1257–1263 (2009). [CrossRef]  

36. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9398. [CrossRef]   [PubMed]  

37. E. F. Schubert, Light-Emitting Diodes, 2nd ed. (Cambridge University Press, 2006), chap. 9.

38. O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996). [CrossRef]  

39. G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997). [CrossRef]  

40. D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997). [CrossRef]  

41. G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997). [CrossRef]  

42. Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005). [CrossRef]  

43. H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007). [CrossRef]  

44. Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008). [CrossRef]  

45. H. Ye, G. W. Wicks, and P. M. Fauchet, “Hot electron relaxation time in GaN,” Appl. Phys. Lett. 74(5), 711–713 (1999). [CrossRef]  

46. M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001). [CrossRef]  

47. J. Piprek, Semiconductor Optoelectronic Devices (Academic Press, 2003), chap. 9.

48. X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008). [CrossRef]  

49. J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008). [CrossRef]  

50. D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011). [CrossRef]  

References

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    [Crossref]
  6. A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
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    [Crossref]
  11. V. K. Malyutenko, S. S. Bolgov, and A. D. Podoltsev, “Current crowding effect on the ideality factor and efficiency droop in blue lateral InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 97(25), 251110 (2010).
    [Crossref]
  12. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-2886 .
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  13. 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), 855–857 (2004).
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  14. T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004).
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  15. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
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  16. APSYS by Crosslight Software, Inc., Burnaby, Canada, http://www.crosslight.com
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  19. H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46(5), 714–720 (2010).
    [Crossref]
  20. P. Zhao and H. Zhao, “Analysis of light extraction efficiency enhancement for thin-film-flip-chip InGaN quantum wells light-emitting diodes with GaN micro-domes,” Opt. Express 20(S5Suppl 5), A765–A776 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-105-A765 .
    [Crossref] [PubMed]
  21. 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]
  22. 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]
  23. J. Piprek, “Efficiency droop in nitride-based light-emitting diodes,” Phys. Status Solidi A 207(10), 2217–2225 (2010).
    [Crossref]
  24. 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]
  25. J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
    [Crossref]
  26. A. David and M. J. Grundmann, “Droop in InGaN light-emitting diodes: A differential carrier lifetime analysis,” Appl. Phys. Lett. 96(10), 103504 (2010).
    [Crossref]
  27. H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
    [Crossref]
  28. H. Y. Ryu, D. S. Shin, and J. I. Shim, “Analysis of efficiency droop in nitride light-emitting diodes by the reduced effective volume of InGaN active material,” Appl. Phys. Lett. 100(13), 131109 (2012).
    [Crossref]
  29. E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011).
    [Crossref]
  30. F. Bertazzi, M. Goano, and E. Bellotti, “Numerical analysis of indirect Auger transitions in InGaN,” Appl. Phys. Lett. 101(1), 011111 (2012).
    [Crossref]
  31. B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
    [Crossref]
  32. V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
    [Crossref]
  33. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Inc., 1995).
  34. S. K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H. G. Park, and Y. H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
    [Crossref]
  35. D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1257–1263 (2009).
    [Crossref]
  36. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9398 .
    [Crossref] [PubMed]
  37. E. F. Schubert, Light-Emitting Diodes, 2nd ed. (Cambridge University Press, 2006), chap. 9.
  38. O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
    [Crossref]
  39. G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997).
    [Crossref]
  40. D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
    [Crossref]
  41. G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
    [Crossref]
  42. Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
    [Crossref]
  43. H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007).
    [Crossref]
  44. Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
    [Crossref]
  45. H. Ye, G. W. Wicks, and P. M. Fauchet, “Hot electron relaxation time in GaN,” Appl. Phys. Lett. 74(5), 711–713 (1999).
    [Crossref]
  46. M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
    [Crossref]
  47. J. Piprek, Semiconductor Optoelectronic Devices (Academic Press, 2003), chap. 9.
  48. X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
    [Crossref]
  49. J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
    [Crossref]
  50. D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
    [Crossref]

2012 (6)

J. H. Son, B. J. Kim, C. J. Ryu, Y. H. Song, H. K. Lee, J. W. Choi, and J. L. Lee, “Enhancement of wall-plug efficiency in vertical InGaN/GaN LEDs by improved current spreading,” Opt. Express 20(S2Suppl 2), A287–A292 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-102-A287 .
[Crossref] [PubMed]

T. Jeong, J. H. Baek, J. S. Ha, and H. Y. Ryu, “High-power single-chip InGaN light-emitting diode with 3.3 W output power,” Electron. Lett. 48(21), 1358–1360 (2012).
[Crossref]

P. Zhao and H. Zhao, “Analysis of light extraction efficiency enhancement for thin-film-flip-chip InGaN quantum wells light-emitting diodes with GaN micro-domes,” Opt. Express 20(S5Suppl 5), A765–A776 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-105-A765 .
[Crossref] [PubMed]

H. Y. Ryu, D. S. Shin, and J. I. Shim, “Analysis of efficiency droop in nitride light-emitting diodes by the reduced effective volume of InGaN active material,” Appl. Phys. Lett. 100(13), 131109 (2012).
[Crossref]

F. Bertazzi, M. Goano, and E. Bellotti, “Numerical analysis of indirect Auger transitions in InGaN,” Appl. Phys. Lett. 101(1), 011111 (2012).
[Crossref]

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

2011 (4)

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011).
[Crossref]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-2886 .
[Crossref] [PubMed]

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

2010 (8)

V. K. Malyutenko, S. S. Bolgov, and A. D. Podoltsev, “Current crowding effect on the ideality factor and efficiency droop in blue lateral InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 97(25), 251110 (2010).
[Crossref]

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
[Crossref]

H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46(5), 714–720 (2010).
[Crossref]

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

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]

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

A. David and M. J. Grundmann, “Droop in InGaN light-emitting diodes: A differential carrier lifetime analysis,” Appl. Phys. Lett. 96(10), 103504 (2010).
[Crossref]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9398 .
[Crossref] [PubMed]

2009 (5)

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]

M. H. Crawford, “LEDs for solid-state lighting: Performance challenges and recent advances,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1028–1040 (2009).
[Crossref]

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[Crossref]

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs – designing light extraction,” Laser Photon. Rev. 3(3), 262–286 (2009).
[Crossref]

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1257–1263 (2009).
[Crossref]

2008 (6)

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
[Crossref]

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

J. K. Kim and E. F. Schubert, “Transcending the replacement paradigm of solid-state lighting,” Opt. Express 16(26), 21835–21842 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21835 .
[Crossref] [PubMed]

S. K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H. G. Park, and Y. H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[Crossref]

2007 (4)

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. O. Mueller, L. Zhou, G. Harbers, and M. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Technol. 3(2), 160–175 (2007).
[Crossref]

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

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]

H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007).
[Crossref]

2006 (1)

2005 (2)

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

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

2004 (2)

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), 855–857 (2004).
[Crossref]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004).
[Crossref]

2002 (1)

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

2001 (1)

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

1999 (2)

H. Ye, G. W. Wicks, and P. M. Fauchet, “Hot electron relaxation time in GaN,” Appl. Phys. Lett. 74(5), 711–713 (1999).
[Crossref]

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

1997 (3)

G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997).
[Crossref]

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

1996 (1)

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Albrecht, J. D.

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Ambacher, O.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Angerer, H.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Ansmann, P.

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Bae, D. K.

S. K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H. G. Park, and Y. H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[Crossref]

Baek, J. H.

T. Jeong, J. H. Baek, J. S. Ha, and H. Y. Ryu, “High-power single-chip InGaN light-emitting diode with 3.3 W output power,” Electron. Lett. 48(21), 1358–1360 (2012).
[Crossref]

Baik, K. H.

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Baur, J.

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
[Crossref]

Beaumont, B.

G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997).
[Crossref]

Bellotti, E.

F. Bertazzi, M. Goano, and E. Bellotti, “Numerical analysis of indirect Auger transitions in InGaN,” Appl. Phys. Lett. 101(1), 011111 (2012).
[Crossref]

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Bentoumi, G.

G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997).
[Crossref]

Bergbauer, W.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Bergenek, K.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs – designing light extraction,” Laser Photon. Rev. 3(3), 262–286 (2009).
[Crossref]

Bernardini, F.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

Bertazzi, F.

F. Bertazzi, M. Goano, and E. Bellotti, “Numerical analysis of indirect Auger transitions in InGaN,” Appl. Phys. Lett. 101(1), 011111 (2012).
[Crossref]

Binder, M.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Bochkareva, N.

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

Bolgov, S. S.

V. K. Malyutenko, S. S. Bolgov, and A. D. Podoltsev, “Current crowding effect on the ideality factor and efficiency droop in blue lateral InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 97(25), 251110 (2010).
[Crossref]

Bour, D. P.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Brennan, K. F.

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Brunner, D.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

Bustarret, E.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

Camras, M.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

Chen, G.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

Chen, J. R.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Cheung, N. W.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Cho, H. K.

Cho, J.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Choe, Y. H.

Choi, J.

Choi, J. H.

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

H. K. Cho, J. Jang, J. H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K. D. Lee, S. H. Kim, K. Lee, S. K. Kim, and Y. H. Lee, “Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes,” Opt. Express 14(19), 8654–8660 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-19-8654 .
[Crossref] [PubMed]

Choi, J. W.

Choi, K. K.

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Craford, M.

Craven, M.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

Crawford, M. H.

M. H. Crawford, “LEDs for solid-state lighting: Performance challenges and recent advances,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1028–1040 (2009).
[Crossref]

David, A.

A. David and M. J. Grundmann, “Droop in InGaN light-emitting diodes: A differential carrier lifetime analysis,” Appl. Phys. Lett. 96(10), 103504 (2010).
[Crossref]

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[Crossref]

Delaney, K. T.

E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011).
[Crossref]

DenBaars, S. P.

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), 855–857 (2004).
[Crossref]

Deneuville, A.

G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997).
[Crossref]

Dimitrov, R.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

Drechsel, P.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Edagawa, K.

H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007).
[Crossref]

Egawa, T.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

Eri, T.

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

Fan, Q.

X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
[Crossref]

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

Farahmand, M.

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Fauchet, P. M.

H. Ye, G. W. Wicks, and P. M. Fauchet, “Hot electron relaxation time in GaN,” Appl. Phys. Lett. 74(5), 711–713 (1999).
[Crossref]

Fiorentini, V.

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

Freudenberg, F.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

Froehlich, S.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Fujii, T.

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), 855–857 (2004).
[Crossref]

Galler, B.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Gao, Y.

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), 855–857 (2004).
[Crossref]

Gardner, N. F.

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]

Garetto, C.

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Ghillino, E.

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Ghione, G.

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Gibart, P.

G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997).
[Crossref]

Goano, M.

F. Bertazzi, M. Goano, and E. Bellotti, “Numerical analysis of indirect Auger transitions in InGaN,” Appl. Phys. Lett. 101(1), 011111 (2012).
[Crossref]

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Gorbunov, R.

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

Gotz, W.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

Grundmann, M. J.

A. David and M. J. Grundmann, “Droop in InGaN light-emitting diodes: A differential carrier lifetime analysis,” Appl. Phys. Lett. 96(10), 103504 (2010).
[Crossref]

Ha, J. S.

T. Jeong, J. H. Baek, J. S. Ha, and H. Y. Ryu, “High-power single-chip InGaN light-emitting diode with 3.3 W output power,” Electron. Lett. 48(21), 1358–1360 (2012).
[Crossref]

Hahn, B.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
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Harbers, G.

Hasegawa, H.

H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007).
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Hopler, R.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
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Hu, E. L.

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), 855–857 (2004).
[Crossref]

Hwang, I. K.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1257–1263 (2009).
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Ishikawa, H.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
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Jang, J.

Jeong, T.

T. Jeong, J. H. Baek, J. S. Ha, and H. Y. Ryu, “High-power single-chip InGaN light-emitting diode with 3.3 W output power,” Electron. Lett. 48(21), 1358–1360 (2012).
[Crossref]

Jiang, H. X.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004).
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Jimbo, T.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
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Johnson, N. M.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Jung, H. M.

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

Kamimura, Y.

H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007).
[Crossref]

Kawaguchi, Y.

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
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Kim, A.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

Kim, B. J.

Kim, C. H.

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

Kim, H.

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Kim, H. S.

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]

Kim, J.

Kim, J. K.

Kim, K. H.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004).
[Crossref]

Kim, K. K.

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Kim, M. H.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

Kim, S. H.

Kim, S. K.

Kioupakis, E.

E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011).
[Crossref]

Kneissl, M.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Ko, T. S.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Krames, M. R.

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).
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M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. O. Mueller, L. Zhou, G. Harbers, and M. Craford, “Status and future of high-power light-emitting diodes for solid-state lighting,” J. Display Technol. 3(2), 160–175 (2007).
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Kuo, H. C.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Kuo, Y. K.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Laubsch, A.

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
[Crossref]

Lee, B.

Lee, H. K.

Lee, J. L.

Lee, J. M.

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

Lee, J. S.

Lee, K.

Lee, K. D.

Lee, Y. H.

Lelikov, Y.

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

Li, X.

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]

Lin, G. B.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

Lin, J. Y.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004).
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Linder, N.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs – designing light extraction,” Laser Photon. Rev. 3(3), 262–286 (2009).
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Ling, S. C.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Liu, H.

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]

Liu, S.

Liu, Z.

Long, D. H.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1257–1263 (2009).
[Crossref]

Lu, T. C.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Luo, X.

Malyutenko, V. K.

V. K. Malyutenko, S. S. Bolgov, and A. D. Podoltsev, “Current crowding effect on the ideality factor and efficiency droop in blue lateral InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 97(25), 251110 (2010).
[Crossref]

Martynov, I.

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
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Megens, M. M.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
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Mei, P.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Meyaard, D. S.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

Mishima, T.

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

Monnard, R.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Morkoc, H.

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

Morkoç, H.

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]

X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
[Crossref]

Moustakas, T. D.

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Mueller, G. O.

Mueller-Mach, R.

Munkholm, A.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

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]

Nakamura, S.

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), 855–857 (2004).
[Crossref]

Nam, E. S.

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

Ni, X.

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]

X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
[Crossref]

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

Noh, M. S.

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

Oder, T. N.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004).
[Crossref]

Oshima, Y.

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

Ozgur, U.

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

Özgür, Ü.

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]

X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
[Crossref]

Park, H. G.

S. K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H. G. Park, and Y. H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
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Park, Y.

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Peter, M.

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
[Crossref]

Piprek, J.

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

Podoltsev, A. D.

V. K. Malyutenko, S. S. Bolgov, and A. D. Podoltsev, “Current crowding effect on the ideality factor and efficiency droop in blue lateral InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 97(25), 251110 (2010).
[Crossref]

Rebane, Y.

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

Rieger, W.

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Rinke, P.

E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011).
[Crossref]

Rode, P.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Romano, L. T.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Ruden, P.

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

Ryu, C. J.

Ryu, H. Y.

T. Jeong, J. H. Baek, J. S. Ha, and H. Y. Ryu, “High-power single-chip InGaN light-emitting diode with 3.3 W output power,” Electron. Lett. 48(21), 1358–1360 (2012).
[Crossref]

H. Y. Ryu, D. S. Shin, and J. I. Shim, “Analysis of efficiency droop in nitride light-emitting diodes by the reduced effective volume of InGaN active material,” Appl. Phys. Lett. 100(13), 131109 (2012).
[Crossref]

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-2886 .
[Crossref] [PubMed]

H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46(5), 714–720 (2010).
[Crossref]

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]

Ryu, S. W.

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1257–1263 (2009).
[Crossref]

Sabathil, M.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
[Crossref]

Sands, T.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Schubert, E. F.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

J. K. Kim and E. F. Schubert, “Transcending the replacement paradigm of solid-state lighting,” Opt. Express 16(26), 21835–21842 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21835 .
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E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005).
[Crossref] [PubMed]

Schwarz, U. T.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs – designing light extraction,” Laser Photon. Rev. 3(3), 262–286 (2009).
[Crossref]

Seong, T.-Y.

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Shan, Q.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

Sharma, R.

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), 855–857 (2004).
[Crossref]

Shchekin, O. B.

Shen, Y. C.

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]

Shibata, M.

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

Shim, H.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

Shim, J. I.

H. Y. Ryu, D. S. Shin, and J. I. Shim, “Analysis of efficiency droop in nitride light-emitting diodes by the reduced effective volume of InGaN active material,” Appl. Phys. Lett. 100(13), 131109 (2012).
[Crossref]

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-2886 .
[Crossref] [PubMed]

H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46(5), 714–720 (2010).
[Crossref]

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]

Shimada, R.

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
[Crossref]

Shin, D. S.

H. Y. Ryu, D. S. Shin, and J. I. Shim, “Analysis of efficiency droop in nitride light-emitting diodes by the reduced effective volume of InGaN active material,” Appl. Phys. Lett. 100(13), 131109 (2012).
[Crossref]

Shreter, Y.

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

Soga, T.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

Son, J. H.

Sone, C.

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Song, J. O.

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[Crossref]

Song, Y. H.

Stauss, P.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Steranka, F.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

Stutzmann, M.

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Suzuki, T.

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

Tarkin, D.

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

Umeno, M.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

Van de Walle, C. G.

E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011).
[Crossref]

Wagner, J.

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

Wang, G.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

Wang, K.

Wang, S. C.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Watanabe, J.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

Watanabe, K.

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

Watanabe, S.

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

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]

Wicks, G. W.

H. Ye, G. W. Wicks, and P. M. Fauchet, “Hot electron relaxation time in GaN,” Appl. Phys. Lett. 74(5), 711–713 (1999).
[Crossref]

Wierer, J. J.

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[Crossref]

Wiesmann, C.

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs – designing light extraction,” Laser Photon. Rev. 3(3), 262–286 (2009).
[Crossref]

Wong, W. S.

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

Wu, Y. C.

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Xie, J.

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

Ye, H.

H. Ye, G. W. Wicks, and P. M. Fauchet, “Hot electron relaxation time in GaN,” Appl. Phys. Lett. 74(5), 711–713 (1999).
[Crossref]

Yonenaga, I.

H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007).
[Crossref]

Yu, G.

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

Zhao, H.

Zhao, P.

Zhou, L.

Appl. Phys. B (1)

J. R. Chen, Y. C. Wu, S. C. Ling, T. S. Ko, T. C. Lu, H. C. Kuo, Y. K. Kuo, and S. C. Wang, “Investigation of wavelength-dependent efficiency droop in InGaN light-emitting diodes,” Appl. Phys. B 98(4), 779–789 (2010).
[Crossref]

Appl. Phys. Lett. (19)

A. David and M. J. Grundmann, “Droop in InGaN light-emitting diodes: A differential carrier lifetime analysis,” Appl. Phys. Lett. 96(10), 103504 (2010).
[Crossref]

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]

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]

H. Y. Ryu, D. S. Shin, and J. I. Shim, “Analysis of efficiency droop in nitride light-emitting diodes by the reduced effective volume of InGaN active material,” Appl. Phys. Lett. 100(13), 131109 (2012).
[Crossref]

E. Kioupakis, P. Rinke, K. T. Delaney, and C. G. Van de Walle, “Indirect Auger recombination as a cause of efficiency droop in nitride light-emitting diodes,” Appl. Phys. Lett. 98(16), 161107 (2011).
[Crossref]

F. Bertazzi, M. Goano, and E. Bellotti, “Numerical analysis of indirect Auger transitions in InGaN,” Appl. Phys. Lett. 101(1), 011111 (2012).
[Crossref]

B. Galler, P. Drechsel, R. Monnard, P. Rode, P. Stauss, S. Froehlich, W. Bergbauer, M. Binder, M. Sabathil, B. Hahn, and J. Wagner, “Influence of indium content and temperature on Auger-like recombination in InGaN quantum wells grown on (111) silicon substrates,” Appl. Phys. Lett. 101(13), 131111 (2012).
[Crossref]

V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures,” Appl. Phys. Lett. 80(7), 1204–1206 (2002).
[Crossref]

S. K. Kim, H. K. Cho, D. K. Bae, J. S. Lee, H. G. Park, and Y. H. Lee, “Efficient GaN slab vertical light-emitting diode covered with a patterned high-index layer,” Appl. Phys. Lett. 92(24), 241118 (2008).
[Crossref]

W. S. Wong, T. Sands, N. W. Cheung, M. Kneissl, D. P. Bour, P. Mei, L. T. Romano, and N. M. Johnson, “Fabrication of thin-film InGaN light-emitting diode membranes by laser lift-off,” Appl. Phys. Lett. 75(10), 1360–1362 (1999).
[Crossref]

H. Kim, K. K. Kim, K. K. Choi, H. Kim, J. O. Song, J. Cho, K. H. Baik, C. Sone, Y. Park, and T.-Y. Seong, “Design of high-efficiency GaN-based light emitting diodes with vertical injection geometry,” Appl. Phys. Lett. 91(2), 023510 (2007).
[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), 855–857 (2004).
[Crossref]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, “III-nitride blue and ultraviolet photonic crystal light emitting diodes,” Appl. Phys. Lett. 84(4), 466–468 (2004).
[Crossref]

V. K. Malyutenko, S. S. Bolgov, and A. D. Podoltsev, “Current crowding effect on the ideality factor and efficiency droop in blue lateral InGaN/GaN light emitting diodes,” Appl. Phys. Lett. 97(25), 251110 (2010).
[Crossref]

G. Yu, G. Wang, H. Ishikawa, M. Umeno, T. Soga, T. Egawa, J. Watanabe, and T. Jimbo, “Optical properties of wurtzite structure GaN on sapphire around fundamental absorption edge (0.78–4.77 eV) by spectroscopic ellipsometry and the optical transmission method,” Appl. Phys. Lett. 70(24), 3209–3211 (1997).
[Crossref]

H. Ye, G. W. Wicks, and P. M. Fauchet, “Hot electron relaxation time in GaN,” Appl. Phys. Lett. 74(5), 711–713 (1999).
[Crossref]

X. Ni, Q. Fan, R. Shimada, Ü. Özgür, and H. Morkoç, “Reduction of efficiency droop in InGaN light emitting diodes by coupled quantum wells,” Appl. Phys. Lett. 93(17), 171113 (2008).
[Crossref]

J. Xie, X. Ni, Q. Fan, R. Shimada, U. Ozgur, and H. Morkoc, “On the efficiency droop in InGaN multiple quantum well blue light emitting diodes and its reduction with p-doped quantum well barriers,” Appl. Phys. Lett. 93(12), 121107 (2008).
[Crossref]

D. S. Meyaard, G. B. Lin, Q. Shan, J. Cho, E. F. Schubert, H. Shim, M. H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99(25), 251115 (2011).
[Crossref]

Electron. Lett. (1)

T. Jeong, J. H. Baek, J. S. Ha, and H. Y. Ryu, “High-power single-chip InGaN light-emitting diode with 3.3 W output power,” Electron. Lett. 48(21), 1358–1360 (2012).
[Crossref]

IEEE J. Quantum Electron. (1)

H. Y. Ryu and J. I. Shim, “Structural parameter dependence of light extraction efficiency in photonic crystal InGaN vertical light-emitting diode structures,” IEEE J. Quantum Electron. 46(5), 714–720 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

D. H. Long, I. K. Hwang, and S. W. Ryu, “Design optimization of photonic crystal structure for improved light extraction of GaN LED,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1257–1263 (2009).
[Crossref]

M. H. Crawford, “LEDs for solid-state lighting: Performance challenges and recent advances,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1028–1040 (2009).
[Crossref]

IEEE Photon. Technol. Lett. (1)

H. Y. Ryu, J. I. Shim, C. H. Kim, J. H. Choi, H. M. Jung, M. S. Noh, J. M. Lee, and E. S. Nam, “Efficiency and electron leakage characteristics in GaN-based light-emitting diodes without AlGaN electron-blocking-layer structures,” IEEE Photon. Technol. Lett. 23(24), 1866–1868 (2011).
[Crossref]

IEEE Trans. Electron. Dev. (2)

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-power and high-efficiency InGaN-based light emitters,” IEEE Trans. Electron. Dev. 57(1), 79–87 (2010).
[Crossref]

M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. Ruden, “Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries,” IEEE Trans. Electron. Dev. 48(3), 535–542 (2001).
[Crossref]

J. Appl. Phys. (3)

D. Brunner, H. Angerer, E. Bustarret, F. Freudenberg, R. Hopler, R. Dimitrov, O. Ambacher, and M. Stutzmann, “Optical constants of epitaxial AlGaN films and their temperature dependence,” J. Appl. Phys. 82(10), 5090–5096 (1997).
[Crossref]

Y. Oshima, T. Suzuki, T. Eri, Y. Kawaguchi, K. Watanabe, M. Shibata, and T. Mishima, “Thermal and optical properties of bulk GaN crystals fabricated through hydride vapor phase epitaxy with void-assisted separation,” J. Appl. Phys. 98(10), 103509 (2005).
[Crossref]

H. Hasegawa, Y. Kamimura, K. Edagawa, and I. Yonenaga, “Dislocation-related optical absorption in plastically deformed GaN,” J. Appl. Phys. 102(2), 026103 (2007).
[Crossref]

J. Display Technol. (1)

Laser Photon. Rev. (1)

C. Wiesmann, K. Bergenek, N. Linder, and U. T. Schwarz, “Photonic crystal LEDs – designing light extraction,” Laser Photon. Rev. 3(3), 262–286 (2009).
[Crossref]

Mater. Sci. Eng. B (1)

G. Bentoumi, A. Deneuville, B. Beaumont, and P. Gibart, “Influence of Si doping level on the Raman and IR reflectivity spectra and optical absorption spectrum of GaN,” Mater. Sci. Eng. B 50(1-3), 142–147 (1997).
[Crossref]

Nat. Photonics (1)

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[Crossref]

Opt. Express (6)

H. K. Cho, J. Jang, J. H. Choi, J. Choi, J. Kim, J. S. Lee, B. Lee, Y. H. Choe, K. D. Lee, S. H. Kim, K. Lee, S. K. Kim, and Y. H. Lee, “Light extraction enhancement from nano-imprinted photonic crystal GaN-based blue light-emitting diodes,” Opt. Express 14(19), 8654–8660 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-19-8654 .
[Crossref] [PubMed]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-2886 .
[Crossref] [PubMed]

J. K. Kim and E. F. Schubert, “Transcending the replacement paradigm of solid-state lighting,” Opt. Express 16(26), 21835–21842 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-26-21835 .
[Crossref] [PubMed]

J. H. Son, B. J. Kim, C. J. Ryu, Y. H. Song, H. K. Lee, J. W. Choi, and J. L. Lee, “Enhancement of wall-plug efficiency in vertical InGaN/GaN LEDs by improved current spreading,” Opt. Express 20(S2Suppl 2), A287–A292 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-102-A287 .
[Crossref] [PubMed]

P. Zhao and H. Zhao, “Analysis of light extraction efficiency enhancement for thin-film-flip-chip InGaN quantum wells light-emitting diodes with GaN micro-domes,” Opt. Express 20(S5Suppl 5), A765–A776 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-105-A765 .
[Crossref] [PubMed]

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9398 .
[Crossref] [PubMed]

Phys. Status Solidi A (2)

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

G. Chen, M. Craven, A. Kim, A. Munkholm, S. Watanabe, M. Camras, W. Gotz, and F. Steranka, “Performance of high-power III-nitride light emitting diodes,” Phys. Status Solidi A 205(5), 1086–1092 (2008).
[Crossref]

Proc. IEEE (1)

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]

Science (1)

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

Semiconductors (1)

Y. Lelikov, N. Bochkareva, R. Gorbunov, I. Martynov, Y. Rebane, D. Tarkin, and Y. Shreter, “Measurement of the absorption coefficient for light laterally propagating in light-emitting diode structures with In0.2Ga0.8N/GaN quantum wells,” Semiconductors 42(11), 1342–1345 (2008).
[Crossref]

Solid State Commun. (1)

O. Ambacher, W. Rieger, P. Ansmann, H. Angerer, T. D. Moustakas, and M. Stutzmann, “Sub-bandgap absorption of gallium nitride determined by photothermal deflection spectroscopy,” Solid State Commun. 97(5), 365–370 (1996).
[Crossref]

Other (4)

J. Piprek, Semiconductor Optoelectronic Devices (Academic Press, 2003), chap. 9.

APSYS by Crosslight Software, Inc., Burnaby, Canada, http://www.crosslight.com

E. F. Schubert, Light-Emitting Diodes, 2nd ed. (Cambridge University Press, 2006), chap. 9.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Inc., 1995).

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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of the simulated vertical LED structure.
Fig. 2
Fig. 2 Computational domain of the vertical LED structure for finite-difference time-domain (FDTD) simulations.
Fig. 3
Fig. 3 Absorption coefficient of blue light by the free-carrier absorption as a function of electron concentration.
Fig. 4
Fig. 4 (a) Electron concentration in the horizontal direction of the QW plane for several doping concentration from 1018 to 1019 cm−3 when the thickness of the n-GaN is 3 μm. (b) Electron concentration in the horizontal direction of the QW plane for the n-GaN thickness of 2, 3, and 4 μm when doping concentration at the n-GaN is 5 × 1018 cm−3.
Fig. 5
Fig. 5 (a) Voltage versus current relations (I-V curves) for several doping concentration from 1018 to 1019 cm−3 when the n-GaN thickness is 3 μm. (b) Electrical efficiency (EE) at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three n-GaN thicknesses of 2, 3, and 4 μm.
Fig. 6
Fig. 6 (a) Internal quantum efficiency (IQE) versus current relations for several doping concentration from 1018 to 1019 cm−3 when the n-GaN thickness is 3 μm. (b) IQE at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three n-GaN thicknesses of 2, 3, and 4 μm.
Fig. 7
Fig. 7 Light extraction efficiency (LEE) at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three n-GaN thicknesses of 2, 3, and 4 μm when αb is (a) 5 and (b) 20 cm−1.
Fig. 8
Fig. 8 Wall-plug efficiency (WPE) at 350 mA is plotted as a function of doping concentration at the n-GaN layer for three thicknesses of 2, 3, and 4 μm when αb is (a) 5 and (b) 20 cm−1.

Equations (5)

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η WPE = P out IV ,
η elec = h ν ¯ eV , η int = P int /h ν ¯ I/e , η extraction = P out P int ,
η WPE = η elec η int η extraction .
α= α b + α f ,
n e =7.2× 10 13 cm -1 [ α f (0.6 eV)] 2 +2.2× 10 15 cm -2 α f (0.6 eV)

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