Abstract

We demonstrate the high efficiency of InGaN/GaN multiple quantum wells (MQWs) light-emitting diode (LED) grown on the electrochemically etched nanoporous (NP) GaN. The photoluminescence (PL) and Raman spectra show that the LEDs with NP GaN have a strong carrier localization effect resulting from the relaxed strain and reduced defect density in MQWs. Also, the finite-difference time-domain (FDTD) simulation shows that the light extraction efficiency (LEE) is increased by light scattering effect by nanopores. The output power of LED with NP GaN is increased up to 123.1% at 20 mA, compared to that of LED without NP GaN. The outstanding performance of LEDs with NP GaN is attributed to the increased internal quantum efficiency (IQE) by the carrier localization in the indium-rich clusters, low defect density in MQWs, and increased LEE owing to the light scattering in NP GaN.

© 2014 Optical Society of America

1. Introduction

Recently, GaN-based light-emitting diodes (LEDs) have been rapidly developed because of their tremendous potential for energy-efficient lighting and widespread LED applications. Many researchers have focused on improving the external quantum efficiency (EQE) of LEDs. Unfortunately, the optical performance of GaN-based LEDs still suffers from low internal quantum efficiency (IQE) and light extraction efficiency (LEE) [15]. Generally, it is believed that the low IQE is related to the poor crystal quality of the GaN epilayer and the polarization field in LEDs [69]. The large mismatch of lattice constants and thermal expansion coefficients between the GaN epilayer and sapphire substrate reduce the crystal quality of GaN layers by introducing threading dislocations that act as non-radiative recombination centers [10,11]. Furthermore, the quantum confined Stark effect induced by the strong built-in piezoelectric field in InGaN/GaN multiple quantum wells (MQWs) lowers carrier recombination rate by increasing the spatial separation between the electron and hole wavefunctions [12]. Another important reason for the low EQE of such devices is their low LEE, which results from the total internal reflection of light emitted from MQWs because of the large difference in the refractive indices of GaN (n = 2.5) and air (n = 1) [1315]. Recently, NP GaN formed by electrochemical (EC) etching has shown promise as a way to improve the crystal quality of overgrown GaN [16,17]. Soh et al. [18] reported that a low defect density and stress relaxation of GaN regrown on NP GaN were achieved by the presence of NP GaN and effect of dislocation annihilation. Although it has been shown that a NP GaN underlayer is a simple and effective method to reduce the defect density and compressive stress state of regrown GaN layers, the electroluminescence and electrical properties of LEDs grown on a NP GaN underlayer have not been reported. In this paper, we reveal that the optical and electrical characteristics of LEDs can be improved by growth on a NP GaN layer.

2. Experimental details

InGaN/GaN MQW LEDs were grown on a c-plane (0001) sapphire substrate by metal-organic chemical vapor deposition. Figure 1(a) shows a schematic diagram of a LED grown on a NP GaN layer. A 2.5 μm-thick undoped GaN layer and a 1.5 μm-thick n-type GaN layer with a doping concentration of 6 × 1018 cm−3 were deposited on the sapphire substrate. To obtain a NP GaN layer, the n-type GaN layer was etched in 0.2 M oxalic acid electrolyte at room temperature for 10 min using a platinum rod as the cathode. NP GaN layers with different porosities were obtained at applied voltages of 11, 17, and 30 V. Then, a 500 nm-thick undoped GaN layer was grown on NP GaN as a current-blocking layer to prevent current leakage to NP GaN. A 2 μm-thick n-type GaN layer and six periods of InGaN/GaN (2.3/7.7 nm) MQWs were grown on the undoped GaN current-blocking layer, followed by growth of a 200 nm-thick p-type GaN layer. Figure 1(b) shows that nanosized air voids formed in the NP GaN layer after an InGaN/GaN MQW LED was grown on NP GaN that was electrochemically etched at an applied voltage of 17 V.

 

Fig. 1 (a) Schematic diagram of LEDs grown on a NP GaN layer, (b) SEM image of NP GaN-embedded LED structure etched at an applied voltage of 17 V. (c) Top and (d) cross-sectional SEM images of NP GaN etched at an applied voltage of 17 V.

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3. Results and discussion

Figures 1(c) and 1(d) show top and cross-sectional scanning electron microscopy (SEM) images of NP GaN layers fabricated by EC etching at an applied voltage of 17 V. Figure 1(c) shows that the size distribution of nanopores is in the range of 23–53 nm and the area of pores on the surface is ~11.0%. Other two samples showed the size distribution of nanopores and area of pores on the surface in the range of 12–24 nm and ~1.1% at 11 V, and in the range of 28–240 nm and ~23.3% at 30 V, respectively. These results indicate that the size distribution and surface area of nanopores are increased with increasing the applied voltage in the EC etching of n-type GaN. The nanopores in the NP GaN layers had a columnar structure with a height of 1.5 μm, as shown in Fig. 1(d). The nanopores in NP GaN changed to nanosized sphere-like voids after regrowth of the LED epilayer (Fig. 1(b)). The NP GaN layer has a metastable morphology after EC etching because of its high surface area and high curvature, as reported for porous materials including NP silicon [1921]. The marked shape transformation from columnar- to nanosphere-like voids occurs in NP GaN to minimize the surface energy of nanospheres by surface diffusion and atomic migration during the regrowth of LEDs on NP GaN.

Figure 2 shows the Raman spectra of GaN epilayers regrown on NP GaN layers. The NP GaN layers were etched at applied voltages of 11, 17, and 30 V. The E2 phonon mode peak of the as-grown GaN and regrown GaN layers on NP GaN etched at 11, 17, and 30 V (denoted GaN(NP GaN)-1, GaN(NP GaN)-2, and GaN(NP GaN)-3, respectively), appear at 568.3, 568.3, 567.6, and 567.1 cm-1, respectively. The shift of the E2 phonon mode peak is related to the relaxation of residual strain and can be calculated using the following equation [22]:

Δωγ=ωγωo=Kγσxx
where ωγ and ωo represent the Raman peaks of the 500 nm-thick regrown undoped GaN layer with and without a NP GaN underlayer, respectively. A proportionality factor Kγ of 4.2 cm−1 GPa−1 is used for hexagonal GaN [22]. GaN(NP GaN)-3 shows the largest red shift of 1.2 cm−1 with respect to that of as-grown GaN, as shown in Fig. 2. This corresponds to a relaxation of compressive stress (σxx) of 0.286 GPa. Figure 2 also shows that the relaxation of the residual strain of the GaN layer regrown on NP GaN is increased with increasing porosity of the NP GaN layer. This indicates that the compressive stress in the regrown GaN layer on NP GaN is relaxed because of shape transformation and atomic migration in the nanovoids of NP GaN.

 

Fig. 2 Raman spectra of GaN grown on an NP GaN layer.

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Room-temperature photoluminescence (PL) and temperature-dependent PL (TD-PL) spectra of LEDs grown on the NP GaN layers were measured. The LEDs grown on as-grown GaN, and GaN(NP GaN)-1, −2, and −3 are denoted reference LED and LED(NP GaN)-1, −2, and −3, respectively. Figure 3(a) shows that the integrated PL intensity is increased by 92% for LED(NP GaN)-1, 194% for LED(NP GaN)-2, and 235% for LED(NP GaN)-3 compared with that of the reference LED. Figure 3(b) shows the peak position and full width at half-maximum (FWHM) of the PL spectra of the NP GaN LEDs. The PL peak position exhibits a red shift from 2.81 to 2.68 eV with increasing porosity of NP GaN. In addition, FWHM increases as the integrated PL intensity of the NP GaN LEDs increases, indicating a high indium content and fluctuation of indium distribution in InGaN/GaN MQWs grown on the GaN(NP GaN) layers.

 

Fig. 3 (a) Room-temperature PL spectra of a MQW structure grown on a NP GaN layer. (b) Peak position and FWHM of PL for reference LED, and LED(NP GaN)-1, −2, and −3. (c) Peak shift of TDPL spectra of LEDs grown on NP GaN layers. (d) Arrhenius plot for LEDs grown on NP GaN layers.

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To further examine the inhomogeneity of indium in InGaN/GaN MQWs, the band-tail model is considered. The temperature-induced shift of the PL peak energy can be described by [23]:

Eg(T)=Eg(0)αT2Tβσ2kBT
where Eg(T) is the PL emission energy at temperature T, Eg(0) is peak energy at 0 K, α and β are Varshni coefficients, and kB is the Boltzmann constant. The third term originates from the composition inhomogeneity, in which σ indicates the Gaussian broadening parameter of carrier localization states in MQWs induced by the fluctuation of indium. Figure 3(c) shows the shift of PL peak position and a fitting curve as a function of temperature. The fitting curve shows that σ = 22.5 meV for the reference LED, and σ = 24.1, 27.8, and 30.5 meV for LED(NP GaN)-1, −2, and −3, respectively. These results show that the carrier localization effect increases with increasing porosity in NP GaN because of the increased indium content and fluctuation in MQWs caused by the partially relaxed residual strain in the undoped GaN regrown on the NP GaN layers.The Arrhenius plots of PL intensities of the NP GaN LEDs in Fig. 3(d) show the thermal quenching of PL intensity with increasing temperature. The TD-PL intensity is described by the following equation based on the non-radiative recombination process [24]:
I(T)=I(0)1+Cexp(Ea/kBT)
where I(T) is the integrated PL intensity at temperature T, and I(0) is the integrated intensity of the emission at 10 K in this study. Ea and C are the activation energy and a constant related to the density of the non-radiative recombination centers, respectively. The fitting curves in Fig. 3(d) show Ea is 35.5, 36.1, and 36.2 meV for LED(NP GaN)-1, −2, and −3, respectively, and 26.2 meV for the reference LED. C is 8.3, 7.2, and 7.1 for LED(NP GaN)-1, −2, and −3, respectively and 12.2 for the reference LED. The large Ea for the NP GaN LEDs are ascribed to the deep potential wells of indium-rich regions in MQWs; a large Ea leads to a high energy barrier for carrier capture by defects such as threading dislocations [24]. The larger Ea of the NP GaN LEDs than that of the reference LED indicate that they have higher indium contents in their InGaN/GaN MQWs. The smaller C for the NP GaN LEDs means that they have a lower density of non-radiative recombination centers such as threading dislocations in MQWs than in the reference LED. In addition, the estimated IQEs of the LEDs are 28.2, 38.5, and 36.3% for LED(NP GaN)-1, −2, and −3, respectively, and 19.2% for the reference LED according to Fig. 3(d), assuming that IQE is 100% at a low temperature of 10 K [25]. These results show that the distribution of carrier localization states in MQWs is enhanced by the reduced strain in MQWs grown on the regrown NP GaN layer. This results in a high IQE because of increased carrier localization and reduced defect densities in the NP GaN LEDs.

To analyze the contribution of the nanovoids in NP GaN to LEE, finite-difference time-domain (FDTD) simulations were performed using the FullWAVETM program. Figures 4(a) and 4(b) show the calculated electric-field distributions of LEDs without and with a NP GaN layer, respectively. A single dipole source was used to simulate the LEE of LED. The peak wavelength of light source was set at 450 nm. The light intensity in FDTD simulation was obtained by adding the results of 3 orthogonal polarizations states along the x, y, and z direction incoherently [26]. The light intensity was measured by a detector located on top of the LED. The size distribution of nanovoids used in the simulation was extracted from the SEM image of LED(NP GaN)-3 shown in the inset of Fig. 4(c). Figure 4(c) reveals the size distribution of nanovoids over an area of 2.5 × 2.5 μm of NP GaN-3 in LED(NP GaN-3). Figure 4(d) shows the light intensity of LEDs with and without NP GaN as a function of simulation time. The light intensity of the LED with NP GaN is increased by 50.7% compared with that of the LED without NP GaN. This means that the photons emitted from the active region can escape more easily into the air in LEDs with NP GaN than in those without NP GaN because of the light scattering effect. In addition, the FDTD simulation for LED(NP GaN)-1 and LED(NP GaN)-2 show that the LEE is also increased by 20.7% and 38.2%, respectively. The LEE is linearly increased with increasing pore size and density in nanoporous GaN, as shown in FDTD simulation of Fig. 4(e). However, IQE is linearly increased and then decreased, showing a maximum value at 17 V of applied voltage. Even though the increased pore size and density in nanoporous GaN decrease the residual stress and defects in the overgrown GaN layer and increase IQE, the larger pore size and density can deteriorate the GaN overgrowth condition, decreasing IQE at a higher voltage of 30 V. The calculated enhancement of output power (IQE × enhanced LEE) of LED(NP GaN)-3 (54.7%) was slightly higher than the enhancement of output power of LED(NP GaN)-2 (53.2%) and this is well agreed with the measured optical output values at 20 mA as shown in Fig. 5(b).

 

Fig. 4 Schematic diagrams with calculated electric-field distributions of (a) LED without NP GaN, and (b) LED with NP GaN. (c) The size distribution of nanovoids used in FDTD simulations over an area of 2.5 × 2.5 μm of NP GaN-3 in LED(NP GaN-3). The inset shows an SEM image of NP GaN in LED(NP GaN-3). (d) Calculated light intensity as a function of simulation time for LEDs with and without NP GaN. (e) The IQE and enhanced LEE of reference LED and LED(NP GaN)s assuming that the LEE of LED without nanoporous GaN is 100%.

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Fig. 5 (a) I-V curve and (b) optical output power of reference LED and LED(NP GaN)-1, −2, and −3.

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Figure 5(a) shows the current-voltage (I-V) characteristics of the reference LED and NP GaN LEDs. The forward voltages of the reference LED and LED(NP GaN)-1, −2, and −3 are 3.86, 3.52, 3.66, and 3.59 V at 20 mA, respectively. The low forward voltages of the NP GaN LEDs are attributed to the large degree of indium fluctuation and the higher crystal quality achieved by using a NP GaN underlayer. The total voltage at forward bias is given by [27]:

VF=nkBTqln(IFA)+Eg(T)q+IFRS
where IF is the forward current, Eg(T) is the band gap at temperature T, Rs is the series resistance, q is the elementary charge, A is a constant related to the materials of the p-n junction, and n is the ideality factor. Equations (2) and (4) show that the bias voltage is affected by Eg(T) and the crystal quality related to Rs. Equation (2) reveals that Eg(T) decreases as σ, which is associated with carrier localization, increases. This indicates that VF can be decreased by increasing the indium fluctuation in MQWs. Wu et al. [28] also reported that indium fluctuation in MQWs strongly affects IQE, I-V curve, and droop behavior because carrier transport occurs along local potential minimum paths when the indium composition is varied in MQWs. Furthermore, Rs estimated from the I-V curves of the reference LED and LED(NP GaN)-1, −2, and −3 are 15.96, 15.39, 15.31, and 15.61 Ω, respectively. These values indicate that decreasing the density of defects such as threading dislocations would improve the crystal quality of regrown MQWs, resulting in a reduction of Rs and forward voltage. Figure 5(b) shows that the optical output powers of LED(NP GaN)-1, −2, and −3 are increased by 72.7%, 117.3%, and 123.1% at 20 mA, respectively, compared with that of the reference LED. The large increase of optical power is partly attributed to the increased indium content in MQWs with a lower density of threading dislocations because of the decrease of residual strain in MQWs grown on an NP GaN layer. The localized states caused by indium fluctuation can enhance the confinement of carriers at the potential minimum, and increase IQE [28,29]. Therefore, the large increase in optical output power can be attributed to an improvement of IQE caused by the increased rate of radiative recombination induced by the enhanced carrier localization in indium-rich regions of MQWs, reduction of defects such as threading dislocations, and increased light extraction by the nanopores in the NP GaN layer.

4. Conclusion

In summary, we report the enhanced optical and electrical properties of InGaN/GaN MQW LEDs grown on electrochemically etched NP GaN layers. The Raman spectra of regrown undoped GaN layers on NP GaN show relaxation of compressive stress caused by nanosphere-like shape transformation and atomic migration in the NP GaN layer. The PL peak position of LEDs with NP GaN undergoes a red shift from 2.81 to 2.68 eV because of the increase of indium content and inhomogeneity in MQWs as the residual strain is relaxed in GaN regrown on NP GaN. Increases in output power of 72.7%, 117.3%, and 123.1% at 20 mA for LED(NP GaN)-1, −2, and −3 compared with that of the reference LED are attributed to the increased IQE caused by the strong carrier localization in the indium-rich regions in MQWs, low defect density in MQWs, and the increased LEE allowed by the nanopores in the NP GaN layer.

Acknowledgment

This work was supported by Samsung Electronics Co. Ltd., Industrial Strategic technology development program (Project No. 10041878) funded by the Ministry of Trade, Industry and Energy (MOTIE/KEIT, Korea).

References and links

1. E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2003), pp 145–162.

2. S. Nakamura, “The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes,” Science 14(281), 956–961 (1998). [CrossRef]   [PubMed]  

3. C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007). [CrossRef]  

4. K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010). [CrossRef]  

5. B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012). [CrossRef]  

6. F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), 10024–10027 (1997). [CrossRef]  

7. S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008). [CrossRef]  

8. M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007). [CrossRef]  

9. J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273, 24–32 (1999). [CrossRef]  

10. M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009). [CrossRef]  

11. J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96(22), 221106 (2010). [CrossRef]  

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

13. J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012). [CrossRef]   [PubMed]  

14. C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012). [CrossRef]  

15. C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010). [CrossRef]  

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References

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  1. E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2003), pp 145–162.
  2. S. Nakamura, “The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes,” Science 14(281), 956–961 (1998).
    [CrossRef] [PubMed]
  3. C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
    [CrossRef]
  4. K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
    [CrossRef]
  5. B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
    [CrossRef]
  6. F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), 10024–10027 (1997).
    [CrossRef]
  7. S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
    [CrossRef]
  8. M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
    [CrossRef]
  9. J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273, 24–32 (1999).
    [CrossRef]
  10. M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009).
    [CrossRef]
  11. J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96(22), 221106 (2010).
    [CrossRef]
  12. S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleischer, J. E. Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBaars, and T. Sota, “Effective band gap inhomogeneity and piezoelectric field in InGaN/GaN multiquantum well structures,” Appl. Phys. Lett. 73(14), 2006 (1998).
    [CrossRef]
  13. J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
    [CrossRef] [PubMed]
  14. C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
    [CrossRef]
  15. C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
    [CrossRef]
  16. Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
    [CrossRef]
  17. H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
    [CrossRef]
  18. C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
    [CrossRef]
  19. T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
    [CrossRef]
  20. K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
    [CrossRef]
  21. M. Y. Ghannam, A. S. Alomar, J. Poortmans, and R. P. Mertens, “Interpretation of macropore shape transformation in crystalline silicon upon high temperature processing,” J. Appl. Phys. 108(7), 074902 (2010).
    [CrossRef]
  22. C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
    [CrossRef] [PubMed]
  23. P. G. Eliseev, P. Perlin, L. Lee, and M. Osinski, “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569 (1997).
    [CrossRef]
  24. D. Bimberg, M. Sondergeld, and E. Grobe, “Thermal dissociation of excitons bounds to neutral acceptors in high-purity GaAs,” Phys. Rev. B 4(10), 3451–3455 (1971).
    [CrossRef]
  25. S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
    [CrossRef]
  26. J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
    [CrossRef]
  27. B. Li, Y. Feng, and Y. Liu, “An electrical model of InGaN based high power light emitting diodes with self-heating effect,” proc. SPIE 6669, 66691 (2007).
    [CrossRef]
  28. Y. R. Wu, R. Shivaraman, K. C. Wang, and J. S. Speck, “Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure,” Appl. Phys. Lett. 101(8), 083505 (2012).
    [CrossRef]
  29. S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
    [CrossRef]

2012 (4)

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
[CrossRef]

Y. R. Wu, R. Shivaraman, K. C. Wang, and J. S. Speck, “Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure,” Appl. Phys. Lett. 101(8), 083505 (2012).
[CrossRef]

2011 (1)

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

2010 (5)

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96(22), 221106 (2010).
[CrossRef]

M. Y. Ghannam, A. S. Alomar, J. Poortmans, and R. P. Mertens, “Interpretation of macropore shape transformation in crystalline silicon upon high temperature processing,” J. Appl. Phys. 108(7), 074902 (2010).
[CrossRef]

K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
[CrossRef]

2009 (2)

M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009).
[CrossRef]

K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
[CrossRef]

2008 (1)

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

2007 (5)

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
[CrossRef]

C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
[CrossRef]

B. Li, Y. Feng, and Y. Liu, “An electrical model of InGaN based high power light emitting diodes with self-heating effect,” proc. SPIE 6669, 66691 (2007).
[CrossRef]

2005 (1)

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

2004 (1)

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

2003 (1)

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

1999 (1)

J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273, 24–32 (1999).
[CrossRef]

1998 (2)

S. Nakamura, “The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes,” Science 14(281), 956–961 (1998).
[CrossRef] [PubMed]

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

1997 (2)

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), 10024–10027 (1997).
[CrossRef]

P. G. Eliseev, P. Perlin, L. Lee, and M. Osinski, “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569 (1997).
[CrossRef]

1996 (1)

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

1971 (1)

D. Bimberg, M. Sondergeld, and E. Grobe, “Thermal dissociation of excitons bounds to neutral acceptors in high-purity GaAs,” Phys. Rev. B 4(10), 3451–3455 (1971).
[CrossRef]

Abare, A. C.

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

Ager, J. W.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Alomar, A. S.

M. Y. Ghannam, A. S. Alomar, J. Poortmans, and R. P. Mertens, “Interpretation of macropore shape transformation in crystalline silicon upon high temperature processing,” J. Appl. Phys. 108(7), 074902 (2010).
[CrossRef]

Baik, J. M.

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

Bernardini, F.

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), 10024–10027 (1997).
[CrossRef]

Bhattacharya, A.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Bimberg, D.

D. Bimberg, M. Sondergeld, and E. Grobe, “Thermal dissociation of excitons bounds to neutral acceptors in high-purity GaAs,” Phys. Rev. B 4(10), 3451–3455 (1971).
[CrossRef]

Bowers, J. E.

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

Bremers, H.

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

Bremser, M. D.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Cao, H.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Chen, K. T.

C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
[CrossRef]

Chichibu, S. F.

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

Cho, C. Y.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

Choi, Y. S.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

Chow, S. Y.

H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
[CrossRef]

C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
[CrossRef]

Chowdhury, A.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Chua, S. J.

C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
[CrossRef]

H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
[CrossRef]

Coldren, L. A.

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

Dai, Q.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Davis, R. F.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

De, S.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

de Sousa Pereira, S. M.

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

DenBaars, S. P.

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

Dhar, S.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Eliseev, P. G.

P. G. Eliseev, P. Perlin, L. Lee, and M. Osinski, “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569 (1997).
[CrossRef]

Feng, Y.

B. Li, Y. Feng, and Y. Liu, “An electrical model of InGaN based high power light emitting diodes with self-heating effect,” proc. SPIE 6669, 66691 (2007).
[CrossRef]

Fiorentini, V.

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), 10024–10027 (1997).
[CrossRef]

Fitzgerald, E. A.

H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
[CrossRef]

C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
[CrossRef]

Fleischer, S. B.

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

Fuhrmann, D.

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

Ghannam, M. Y.

M. Y. Ghannam, A. S. Alomar, J. Poortmans, and R. P. Mertens, “Interpretation of macropore shape transformation in crystalline silicon upon high temperature processing,” J. Appl. Phys. 108(7), 074902 (2010).
[CrossRef]

Gokhale, M. R.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Grobe, E.

D. Bimberg, M. Sondergeld, and E. Grobe, “Thermal dissociation of excitons bounds to neutral acceptors in high-purity GaAs,” Phys. Rev. B 4(10), 3451–3455 (1971).
[CrossRef]

Hader, J.

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96(22), 221106 (2010).
[CrossRef]

Han, J.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Han, S. H.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

Hangleiter, A.

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

Hartono, H.

H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
[CrossRef]

C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
[CrossRef]

Hatano, M.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Hayashi, H.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Hiruta, R.

K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
[CrossRef]

Hoffmann, L.

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

Hu, E.

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

Humphreys, C. J.

M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009).
[CrossRef]

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

Iwasaki, H.

K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
[CrossRef]

Jeong, H.

K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
[CrossRef]

Jeong, M. S.

K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
[CrossRef]

Jiang, H. X.

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

Jiang, R. H.

C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
[CrossRef]

Jones, E.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Jung, G. Y.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
[CrossRef]

Kadir, A.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Kang, S. E.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

Kappers, M. J.

M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009).
[CrossRef]

Keller, S.

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

Kim, B. J.

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

Kim, J. K.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Kim, J. U.

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

Kim, K. H.

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

Kim, K. S.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
[CrossRef]

Kim, M. H.

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Kim, S. M.

K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
[CrossRef]

Kisielowski, C.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Knabe, K.

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

Koch, S. W.

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96(22), 221106 (2010).
[CrossRef]

Krüger, J.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Kudo, H.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Kuribayashi, H.

K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
[CrossRef]

Layek, A.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Lee, J. L.

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

Lee, L.

P. G. Eliseev, P. Perlin, L. Lee, and M. Osinski, “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569 (1997).
[CrossRef]

Lee, S. J.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

Leung, B.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Li, B.

B. Li, Y. Feng, and Y. Liu, “An electrical model of InGaN based high power light emitting diodes with self-heating effect,” proc. SPIE 6669, 66691 (2007).
[CrossRef]

Li, J.

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

Liliental-Weber, Z.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Lin, C. F.

C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
[CrossRef]

Lin, C. M.

C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
[CrossRef]

Lin, J. Y.

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

Liu, Y.

B. Li, Y. Feng, and Y. Liu, “An electrical model of InGaN based high power light emitting diodes with self-heating effect,” proc. SPIE 6669, 66691 (2007).
[CrossRef]

Martins, M. A.

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

Mertens, R. P.

M. Y. Ghannam, A. S. Alomar, J. Poortmans, and R. P. Mertens, “Interpretation of macropore shape transformation in crystalline silicon upon high temperature processing,” J. Appl. Phys. 108(7), 074902 (2010).
[CrossRef]

Minsky, M. S.

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

Mishra, U. K.

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

Mizushima, I.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Moloney, J. V.

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96(22), 221106 (2010).
[CrossRef]

Moram, M. A.

M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009).
[CrossRef]

Nagashima, M.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Nakamura, S.

S. Nakamura, “The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes,” Science 14(281), 956–961 (1998).
[CrossRef] [PubMed]

Netzel, C.

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

Okagawa, H.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Oliver, R. A.

M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009).
[CrossRef]

Osinski, M.

P. G. Eliseev, P. Perlin, L. Lee, and M. Osinski, “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569 (1997).
[CrossRef]

Park, S. J.

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

Park, Y. J.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Perlin, P.

P. G. Eliseev, P. Perlin, L. Lee, and M. Osinski, “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569 (1997).
[CrossRef]

Piprek, J.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Poortmans, J.

M. Y. Ghannam, A. S. Alomar, J. Poortmans, and R. P. Mertens, “Interpretation of macropore shape transformation in crystalline silicon upon high temperature processing,” J. Appl. Phys. 108(7), 074902 (2010).
[CrossRef]

Raja, A.

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Rosner, S. J.

J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273, 24–32 (1999).
[CrossRef]

Rossow, U.

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

Rubin, M.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Ruvimov, S.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Ryu, C. J.

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

Ryu, S. W.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Sasaki, C.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Sato, T.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Schubert, E. F.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Schubert, M. F.

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Shakya, J.

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

Shimizu, R.

K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
[CrossRef]

Shimonishi, S.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Shivaraman, R.

Y. R. Wu, R. Shivaraman, K. C. Wang, and J. S. Speck, “Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure,” Appl. Phys. Lett. 101(8), 083505 (2012).
[CrossRef]

Soh, C. B.

H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
[CrossRef]

C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
[CrossRef]

Son, J. H.

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

Sondergeld, M.

D. Bimberg, M. Sondergeld, and E. Grobe, “Thermal dissociation of excitons bounds to neutral acceptors in high-purity GaAs,” Phys. Rev. B 4(10), 3451–3455 (1971).
[CrossRef]

Song, Q.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Song, Y. H.

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

Sota, T.

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

Speck, J. S.

Y. R. Wu, R. Shivaraman, K. C. Wang, and J. S. Speck, “Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure,” Appl. Phys. Lett. 101(8), 083505 (2012).
[CrossRef]

J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273, 24–32 (1999).
[CrossRef]

Sudoh, K.

K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
[CrossRef]

Sugihara, K.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Sun, Q.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Suski, T.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Tadatomo, K.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Taguchi, T.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Takenaka, K.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Taniguchi, S.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Trindade, T.

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

Tsunashima, Y.

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Ueki, Y.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Vanderbilt, D.

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), 10024–10027 (1997).
[CrossRef]

Wang, K. C.

Y. R. Wu, R. Shivaraman, K. C. Wang, and J. S. Speck, “Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure,” Appl. Phys. Lett. 101(8), 083505 (2012).
[CrossRef]

Watanabe, S.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Watson, I. M.

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

Weber, E. R.

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Wu, Y. R.

Y. R. Wu, R. Shivaraman, K. C. Wang, and J. S. Speck, “Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure,” Appl. Phys. Lett. 101(8), 083505 (2012).
[CrossRef]

Yamada, N.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Yamada, Y.

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

Yang, C. C.

C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
[CrossRef]

Ye, B. U.

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

Yerino, C.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Yu, H. K.

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

Zhang, Y.

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Zhu, D.

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

Adv. Funct. Mater. (3)

K. S. Kim, S. M. Kim, H. Jeong, M. S. Jeong, and G. Y. Jung, “Enhancement of light extraction through the wave-guiding effect of ZnO sub-microrods in InGaN blue light-emitting diodes,” Adv. Funct. Mater. 20(7), 1076–1082 (2010).
[CrossRef]

B. U. Ye, B. J. Kim, Y. H. Song, J. H. Son, H. K. Yu, M. H. Kim, J. L. Lee, and J. M. Baik, “Enhancing light emission of nanostructured vertical light-emitting diodes by minimizing total internal reflection,” Adv. Funct. Mater. 22(3), 632–639 (2012).
[CrossRef]

S. De, A. Layek, A. Raja, A. Kadir, M. R. Gokhale, A. Bhattacharya, S. Dhar, and A. Chowdhury, “Two distinct origins of highly localized luminescent centers within InGaN/GaN quantum-well light-emitting diodes,” Adv. Funct. Mater. 21(20), 3828–3835 (2011).
[CrossRef]

Adv. Mater. (3)

S. M. de Sousa Pereira, M. A. Martins, T. Trindade, I. M. Watson, D. Zhu, and C. J. Humphreys, “Controlled integration of nanocrystals in inverted hexagonal nano-pits at the surface of light-emitting heterostructures,” Adv. Mater. 20(5), 1038–1043 (2008).
[CrossRef]

M. A. Moram, R. A. Oliver, M. J. Kappers, and C. J. Humphreys, “The spatial distribution of threading dislocations in gallium nitride films,” Adv. Mater. 21(38–39), 3941–3944 (2009).
[CrossRef]

J. H. Son, J. U. Kim, Y. H. Song, B. J. Kim, C. J. Ryu, and J. L. Lee, “Design rule of nanostructures in light-emitting diodes for complete elimination of total internal reflection,” Adv. Mater. 24(17), 2259–2262 (2012).
[CrossRef] [PubMed]

Appl. Phys. Lett. (10)

C. Y. Cho, S. E. Kang, K. S. Kim, S. J. Lee, Y. S. Choi, S. H. Han, G. Y. Jung, and S. J. Park, “Enhanced light extraction in light-emitting diodes with photonic crystal structure selectively grown on p-GaN,” Appl. Phys. Lett. 96(18), 181110 (2010).
[CrossRef]

H. Hartono, C. B. Soh, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Reduction of threading dislocation density in GaN grown on strain relaxed nanoporous GaN template,” Appl. Phys. Lett. 90(17), 171917 (2007).
[CrossRef]

C. B. Soh, H. Hartono, S. Y. Chow, S. J. Chua, and E. A. Fitzgerald, “Dislocation annihilation in regrown GaN on nanoporous GaN template with optimization of buffer layer growth,” Appl. Phys. Lett. 90(5), 053112 (2007).
[CrossRef]

J. Hader, J. V. Moloney, and S. W. Koch, “Density-activated defect recombination as a possible explanation for the efficiency droop in GaN-based diodes,” Appl. Phys. Lett. 96(22), 221106 (2010).
[CrossRef]

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

M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. J. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91(18), 183507 (2007).
[CrossRef]

Y. R. Wu, R. Shivaraman, K. C. Wang, and J. S. Speck, “Analyzing the physical properties of InGaN multiple quantum well light emitting diodes from nano scale structure,” Appl. Phys. Lett. 101(8), 083505 (2012).
[CrossRef]

P. G. Eliseev, P. Perlin, L. Lee, and M. Osinski, “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett. 71(5), 569 (1997).
[CrossRef]

S. Watanabe, N. Yamada, M. Nagashima, Y. Ueki, C. Sasaki, Y. Yamada, T. Taguchi, K. Tadatomo, H. Okagawa, and H. Kudo, “Internal quantum efficiency of highly-efficient InxGa1−xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett. 83(24), 4906 (2003).
[CrossRef]

J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, “Polarization of III-nitride blue and ultraviolet light-emitting diodes,” Appl. Phys. Lett. 86(9), 091107 (2005).
[CrossRef]

IEEE Elec. Dev. Lett. (1)

C. C. Yang, C. F. Lin, K. T. Chen, R. H. Jiang, and C. M. Lin, “Direct-grown air-void structure in the InGaN light-emitting diodes,” IEEE Elec. Dev. Lett. 33(12), 1738–1740 (2012).
[CrossRef]

J. Appl. Phys. (2)

K. Sudoh, H. Iwasaki, R. Hiruta, H. Kuribayashi, and R. Shimizu, “Void shape evolution and formation of silicon-on-nothing structures during hydrogen annealing of hole arrays on Si(001),” J. Appl. Phys. 105(8), 083536 (2009).
[CrossRef]

M. Y. Ghannam, A. S. Alomar, J. Poortmans, and R. P. Mertens, “Interpretation of macropore shape transformation in crystalline silicon upon high temperature processing,” J. Appl. Phys. 108(7), 074902 (2010).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Sato, I. Mizushima, S. Taniguchi, K. Takenaka, S. Shimonishi, H. Hayashi, M. Hatano, K. Sugihara, and Y. Tsunashima, “Fabrication of silicon-on-nothing structure by substrate engineering using the empty-space-in-silicon formation technique,” Jpn. J. Appl. Phys. 43(1), 12–18 (2004).
[CrossRef]

Phys. Rev. B (3)

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), 10024–10027 (1997).
[CrossRef]

D. Bimberg, M. Sondergeld, and E. Grobe, “Thermal dissociation of excitons bounds to neutral acceptors in high-purity GaAs,” Phys. Rev. B 4(10), 3451–3455 (1971).
[CrossRef]

C. Netzel, H. Bremers, L. Hoffmann, D. Fuhrmann, U. Rossow, and A. Hangleiter, “Emission and recombination characteristics of Ga1−xInxN/GaN quantum well structures with nonradiative recombination suppression by V-shaped pits,” Phys. Rev. B 76(15), 155322 (2007).
[CrossRef]

Phys. Rev. B Condens. Matter (1)

C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. W. Ager, E. Jones, Z. Liliental-Weber, M. Rubin, E. R. Weber, M. D. Bremser, and R. F. Davis, “Strain-related phenomena in GaN thin films,” Phys. Rev. B Condens. Matter 54(24), 17745–17753 (1996).
[CrossRef] [PubMed]

Phys. Stat. Solidi B (1)

Y. Zhang, S. W. Ryu, C. Yerino, B. Leung, Q. Sun, Q. Song, H. Cao, and J. Han, “A conductivity-based selective etching for next generation GaN devices,” Phys. Stat. Solidi B 247(7), 1713–1716 (2010).
[CrossRef]

Physica B (1)

J. S. Speck and S. J. Rosner, “The role of threading dislocations in the physical properties of GaN and its alloys,” Physica B 273, 24–32 (1999).
[CrossRef]

proc. SPIE (1)

B. Li, Y. Feng, and Y. Liu, “An electrical model of InGaN based high power light emitting diodes with self-heating effect,” proc. SPIE 6669, 66691 (2007).
[CrossRef]

Science (1)

S. Nakamura, “The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes,” Science 14(281), 956–961 (1998).
[CrossRef] [PubMed]

Other (1)

E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2003), pp 145–162.

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic diagram of LEDs grown on a NP GaN layer, (b) SEM image of NP GaN-embedded LED structure etched at an applied voltage of 17 V. (c) Top and (d) cross-sectional SEM images of NP GaN etched at an applied voltage of 17 V.

Fig. 2
Fig. 2

Raman spectra of GaN grown on an NP GaN layer.

Fig. 3
Fig. 3

(a) Room-temperature PL spectra of a MQW structure grown on a NP GaN layer. (b) Peak position and FWHM of PL for reference LED, and LED(NP GaN)-1, −2, and −3. (c) Peak shift of TDPL spectra of LEDs grown on NP GaN layers. (d) Arrhenius plot for LEDs grown on NP GaN layers.

Fig. 4
Fig. 4

Schematic diagrams with calculated electric-field distributions of (a) LED without NP GaN, and (b) LED with NP GaN. (c) The size distribution of nanovoids used in FDTD simulations over an area of 2.5 × 2.5 μm of NP GaN-3 in LED(NP GaN-3). The inset shows an SEM image of NP GaN in LED(NP GaN-3). (d) Calculated light intensity as a function of simulation time for LEDs with and without NP GaN. (e) The IQE and enhanced LEE of reference LED and LED(NP GaN)s assuming that the LEE of LED without nanoporous GaN is 100%.

Fig. 5
Fig. 5

(a) I-V curve and (b) optical output power of reference LED and LED(NP GaN)-1, −2, and −3.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Δ ω γ = ω γ ω o = K γ σ x x
E g ( T )= E g ( 0 ) α T 2 Tβ σ 2 k B T
I( T )= I( 0 ) 1+Cexp( E a / k B T )
V F = n k B T q ln( I F A )+ E g (T) q + I F R S

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