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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 23702–23711
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Light extraction enhancement for InGaN/GaN LED by three dimensional auto-cloned photonics crystal

Chen-Yang Huang, Hao-Min Ku, and Shiuh Chao  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 23702-23711 (2009)
http://dx.doi.org/10.1364/OE.17.023702


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Abstract

Three dimensional (3-D) auto-cloned photonics crystal (APhC) of Ta2O5/SiO2 multi-layers was fabricated on the backside of the sapphire wafer that had InGaN/GaN multi-quantum well LED on the front side. 94% light extraction enhancement in comparison to the LED without APhC was obtained. Electrical properties of the LED did not altered by the APhC and its fabrication process. Experimental evidences showed that light extraction enhancement mechanism is two-folded: for rays that are emitted from the source and incident at lower angle of incidence to the APhC, the APhC acts as a high reflector; for rays incident at higher angle of incidence to the APhC, first order diffracted light from the APhC appears, the diffracted light is concentrated around the surface normal and is therefore capable of escaping.

© 2009 Optical Society of America

1. Introduction

Light emitting diode (LED) is on the cutting-edge of the energy saving technologies for lighting and display. Total internal reflection due to the high refractive index of the semiconductor light emitting material prohibits light being completely extracted from the device. Various means for light extraction enhancement such as photonic crystal on the front surface of the LED [1

1. H. Ichikawa and T. Baba, “Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal,” Appl. Phys. Lett. 84, 457–459, (2004). [CrossRef]

], [2

2. J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887, (2004). [CrossRef]

], patterned structure on the sapphire/GaN interface [3

3. Z. H. Feng, Y. D. Qi, Z. D. Lu, and K. M. Lau, “GaN-based blue light-emitting diodes grown and fabricated on patterned sapphire substrates by metalorganic vapor-phase epitaxy,” J. Cryst. Growth 272, 327–332, (2004). [CrossRef]

] or in the GaN [4

4. S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, “InGaN/GaN/AlGaN-based laser diodes with modulation-doped strained-layer superlattices grown on an epitaxially laterally overgrown GaN substrate,” Appl. Phys. Lett 72(2), 211–213, (1998). [CrossRef]

] or on the front surface [5

5. J.Q. Xi, H. Luo, A. J. Pasquale, J. K. Kim, and E. F. Schubert, “Enhanced light extraction in GaInN light-emitting diode with pyramid reflector,” IEEE Photonic Tech. Lett. 18, 2347–2349, (2006). [CrossRef]

], omni-reflector [6

6. T. Gessmann, E. F. Schubert, J. W. Graff, K. Streubel, and C. Karnutsch, “Omnidirectional reflective contacts for light-emitting diodes,” IEEE Electron Device Lett. 24, 683–685, (2003). [CrossRef]

], [7

7. J. K. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO2/SiO2/Ag omni-directional reflector,” Appl. Phys. Lett. 84, 4508–4510, (2004). [CrossRef]

], distributed Bragg reflector on the back side of the sapphire substrate [8

8. H. Ishikawa, B. Zhang, K. Asano, T. Egawa, and T. Jimbo, “Characterization of GaInN light-emitting diodes with distributed Bragg reflector grown on Si,” J. Cryst. Growth 272, 322–326, (2004). [CrossRef]

], [9

9. Y. S. Zhao, D. L. Hibbard, H. P. Lee, K. Ma, W. So, and H. Liu, “Efficiency enhancement of InGaN/GaN light-emitting diodes with a back-surface distributed bragg reflector,” J. of Electronic Materials 32, 1523–1526, (2003). [CrossRef]

], [10

10. J. H. Seo and J. H. Jang, “Nitride semiconductor light emitting diode and fabrication method thereof,” US patent 20050133796A1, (2005).

], just to name a few, were developed on the LED. Some of the enhancement structures require involved fabrication process, and some suffer from sacrificing the electrical properties of the LED. Auto-cloned photonics crystal (APhC) [11

11. S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electronics Lett. 33, 1260–1261, (1997). [CrossRef]

], [12

12. M. Notomi, T. Tamamura, T. Kawashima, and S. Kawakami, “Drilled alternating-layer three-dimensional photonic crystals having a full photonic band gap,” Appl. Phys. Lett. 77, 4256–4258, (2000). [CrossRef]

] is a mutilayer structure with alternated refractive index films stacked on a periodically corrugated saw-tooth shape substrate. In this paper, we employed the properties of photonics band gap and diffraction grating of the 3-D APhC for light extraction enhancement on LED. The 3-D APhC was fabricated on the back side of the sapphire wafer such that the electrical properties of the LED on the front side were expected to be intact. We report the fabrication process, the electrical and the optical properties of the APhC-LED. We also report with experimental evidences and detailed analysis the mechanism of light extraction enhancement for devices of this kind.

2. Structure and fabrication

We started with a commercial available epitaxial wafer, 2” in diameter, which has InGaN/GaN multi quantum wells (MQWs) structure on a 100µm thickness sapphire. The total thickness of the semiconductor layers was about 5µm. Array of 300µm×300µm square mesa structure with electrodes was fabricated by the standard lithographic patterning process, the device is shown schematically in Fig. 1(a). Three various enhancement structures were fabricated on the back side of the sapphire substrate, namely, Bragg reflector (BR) with Ta2O5/SiO2 multi-layers, 3-D auto-cloned photonics crystal (APhC) of Ta2O5/SiO2 multi-layers, and APhC with an aluminium reflector (APhC/Al), as shown schematically in Fig. 1(b)~(d), respectively.

The fabrication process for the 3-D APhC is introduced as follows: 250nm photo resist (THMR-M100) was deposited on the back side of the sapphire that has the InGaN/GaN multi quantum well structure on the front side. Single beam laser (He-Cd laser at 325nm) interference lithography was applied to expose the photo resist, and the substrate was rotated 90° for a second exposure. The exposed pattern on the photo resist turned out to be square-symmetrical with side length of 300nm. After the photo resist development, the substrate was subjected to inductive-coupled plasma etching (ICP) in BCl 4 +Ar mixture (50:5 sccm) to pattern the sapphire. SEM picture of the patterned sapphire is shown in Fig. 2(c); a square-symmetrical cone array with ~110nm in cone height and ~135nm in cone radius was formed on the sapphire, the square lattice has a side length of 300nm. Total of 30 layers of Ta2O5/SiO2 multi-layers were then deposited on the patterned sapphire by ion beam sputter (IBS). For high quality auto-cloning, the deposition parameters for IBS with Kaufmann ion source were found [13

13. C. Y. Huang, H. M. Ku, and S. Chao, “Surface profile control of the autocloned photonic crystal by ion-beam-sputter deposition with radio-frequency-bias etching,” Appl. Opts. 84, 69–73, (2009). [CrossRef]

] to be 1000V beam voltage, and 145mA beam current for deposition of SiO2 films, and 30W RF-bias was added for deposition of Ta2O5 films. The refractive index at 465nm wavelength for the Ta2O5 and the SiO2 films were 2.20 and 1.46, respectively. Figure 2(b) shows the SEM picture of the auto-cloned layers; the thickness for both films was ~60nm tip to tip on the saw-tooth structure. The SEM picture of the overview for the complete 3-D APhC on the patterned sapphire is shown in Fig. 2(a).

Fig. 1. (color online) (a) standard LED, (b) LED with Bragg reflector, (c) LED with APhC (d)LED with APhC/Al.
Fig. 2. SEM pictures of (a) 3-D APhC overview and its schematics, (b)cross section of the APhC, (c) The patterned sapphire.

Aluminum reflector layer of 200nm thickness was deposited on the APhC by electron beam deposition method to form the third variety of the enhancement structure, Fig. 1(d). Bragg reflector of Ta2O5/SiO2 multi-layers, 30 layers in total, was deposited on the bare back side of the sapphire by using ISB to form the first variety of the enhancement structure, Fig. 1(b). The layer thickness of the Ta2O5 and the SiO2 films were 55nm and 82nm, respectively. The BR has high reflection band (~94% reflectance) from 430nm to 530nm at normal incidence, the s-polarization was omni-reflective and the p-polarization has the high reflection band from 0° to 50° angle of incidence.

Figure 3 shows the atomic force microscope (AFM) scan of the surface of the APhC. Figures 3(b) and (c) show that the averaged periodicity along the row and the column remained the same, i.e. close to 300nm, but the averaged peak to peak height along the row and the column, 29nm and 48nm, are significantly different; the original circular cone was elongated. The AFM scans imply that the crystal symmetry of the APhC evolved from a square lattice superimposed by a circularly symmetrical cone-base on the sapphire surface to a square lattice superimposed by an rectangularly symmetrical, elongated cone-base on the top surface. In the multilayer deposition process, the substrate was not rotating and it was positioned with respect to the ion beam in a way such that the shadowing effect during the multilayer deposition was different along the row and the column of the lattice to cause the elongation of the base,

Fig. 3. (color online) AFM scan of the top surface of the APhC (a) overview (b) 45° counterclockwise rotation view and the surface profile along the dashed line (c) 45° clockwise rotation view and the surface profile along the dashed line. Averaged periodicity=298nm for scan along the dashd line in (b) and 305nm for that in (c). Averaged peak to peak height=29nm for scan along the dashed line in (b) and 48nm for that in (c).

3. Electrical and optical properties

I-V characteristics for four kinds of LED of Fig. 1 are shown in Fig. 4. Series resistance, forward voltage at 20mA forward current, and reverse current at -5V are shown in Table 1. It is clear that the electrical characteristics of the four LEDs are similar, indicating that the enhancement structures and their fabrication processes was not alter the electrical properties of the LED.

Optical output power, measured with integrating sphere, versus forward current is shown in Fig. 5 for the LEDs. Spectra of the optical output power at 20mA forward current are shown in the inset of Fig. 5. The peak position of the spectra did not change, indicating that the optical property of the light emitting semiconductors was not altered by the enhancement structures and their fabrication processes.

Light extraction enhancement at 20mA forward current, using the structure of Fig. 1(a) as the standard, can be obtained from Fig. 5 and they are found to be 58% for BR, 94% for APhC and 105% for APhC/Al as listed in the last row of Table 1.

3-D far field light intensity distributions for four kinds of LED, measured by imaging sphere for luminous intensity measurement with hemispherical array detectors, are shown in Fig. 6. The side-lobs around the edges were from the guided modes. A slight 180° rotation symmetry for APhC LED and APhC/AL LED are revealed in Fig. 6(c) and (d), it is consistent with the rectangular symmetry of the base as was shown in Fig. 3.

Fig. 4. (color online) I-V curves of the LEDs. Inset is the I-V curves in the reversed bias.

4. Mechanism for light extraction enhancement

In order to explore the mechanism for light extraction enhancement, we have measured the intensity distribution of the diffracted light from the sample that has only the sapphire substrate with the APhC structure. A He-Cd laser with 441.6nm wavelength was used as the incident light. The laser beam was incident from the side of the APhC instead of from the side of the sapphire. The set-up is shown in Fig. 7(a). First of all, we observed that, due to the small periodicity of our APhC, only one diffracted beam, i.e. first order diffracted beam, was observed in each hemisphere for a fixed angle of incidence. The incident beam Ii and the reflected beam Ir (0th order diffracted beam) form the plane of incidence and the diffracted beam Idr is not necessarily on the plan of incidence. By scanning the angle of incidence from 0° to ±90° and rotating the sample about the Z-axis with the azimuth angle of the sample changing from 0° to

Table 1. Electrical and optical properties of the LEDs.

table-icon
View This Table

IF: forward current.

360°, the 3-D intensity distribution of the diffracted lights that are generated by a hypothetical omni-directional light source, which resembles the light source in the LED, can be measured. In practice, only the intensity distribution of the diffracted light that were generated by the incident beam with 0°-90° angle of incidence and with 0°-90° for the azimuth angle of the sample orientation need to be measured and the complete 3-D distribution can be derived from these measurements due to the symmetry nature of our APhC as was discussed in section 2 with Fig. 3 and section 3 with Fig. 6. Both 3-D diffracted light distributions for the p-polarization and the s-polarization incident light were measured separately. Polarizations of the diffracted lights were found to be linear, the same as that of the incident light.

Fig. 5. (color online) Optical output power vs. forward current of the LEDs. Inset is the spectra of the optical output at 20mA.
Fig. 6. (color online) 3-D far field intensity distribution for (a) std. LED (b) BR LED (c) APhC LED (d) APhC/Al LED.

Figures 8(b) and (c) show the intensity distribution of the diffracted lights Id together with that of the reflected light Ir and the transmitted light It, normalized to the incident light Ii, for the case where the plane of incidence is parallel to the edge of the square lattice, i.e. y-axis in Fig. 7. In this case, the diffracted lights are co-planar with the incident and the transmitted lights, as shown in Fig. 8(a). The distributions shown in Figs. 8(b) and (c) are actually the distribution measured alone the meridional plane of 0° longitude in Figs. 7(b) and (c). During the measurement process of Fig. 8, when the angle of incidence was increasing from 0° toward 90°, we observed that the diffracted light in the upper-hemisphere, Idr, started to appear at θdr ~-45° as the angle of incidence θi approaching ~33°, the intensity of the diffracted light in the upper-hemisphere Idr then increasing with the increasing angle of incidence. As the angle of incidence approaching 65°-75°, the intensity of the diffracted light in the upper-hemisphere Idr started decreasing, (Noticing that the scale of the abscissa of the composite figures in Fig.8,s are not in one to one correspondence with proportion). Again, one can see that the intensity of the diffracted lights concentrated around the polar axis, and it is stronger for the p-polarization incident light than for the s-polarization incident light. For lower angle of incidence θi, Figs. 8(b) and (c) show that more than 90% of the incident intensity were reflected and there was no diffracted light, which implies that the APhC acts as a high reflector; while for higher angle of incidence Ii, Figs. 8(b) and (c) show that the diffraction appeared and was concentrated around the polar axis. The diffracted light in the lower-hemisphere Idt follows the same characteristics, qualitatively.

Fig. 7. (color online) 3-D intensity distribution of the diffracted light (a) measurement set-up and the schematic of the top view for the APhC (b) for the p-polarization incident light (c) for the s-polarization incident light.

According to these observations, the mechanism for light extraction enhancement of the APhC can therefore be deduced qualitatively as follows: referring to Fig. 9, light emitting source in the LED emits light in all directions. For the lights that incident at lower angle of incidence to the APhC, e.g. I i1 in Fig. 9, the reflected light I r1 (0th order diffracted light) can escape from the escaping zone that is defined by the total internal reflection, the low angle of incidence region in Figs. 8(b) and (c) indicates that the reflectance of the lights are high, in contrast to that for the LED without enhancement structure in Fig. 1(a), therefore, the APhC acts as a high reflector, same as the BR. For the lights that incident at higher angle of incidence, e.g. I i2 in Fig. 9, the reflected light I r2 can not escape but be trapped by the total internal reflection, however, there is diffracted light I dr and the diffracted light can escape because it concentrates around the surface normal and it is within the escape cone in contrast to that of the LED with BR structure and the LED without enhancement structure where all the reflected lights are trapped. The APhC extracts light from the total internal reflection and converts to the diffracted light that is concentrated around the surface normal to escape from the escaping cone.

The last row of Table 1 shows that the structure with APhC/Al has even higher extraction ratio, 105%, than the APhC structure. It is obvious that the transmitted light It and the diffracted light in the lower-hemisphere Idt were reflected back by the aluminum to enhance the effect as implied by Figs. 8(a), (b), and (c).

Fig. 8. 2-D intensity distribution of the diffracted light Idr and Idt, transmitted light It, reflected light Ir (a) measurement set-up, (b) for the p-polarization incident light, (c) for the s-polarization incident light.
Fig. 9. (color online) Schematic illustration for the mechanism of light extraction enhancement.

5. Conclusion

We demonstrated a 94% (or 105%) light extraction enhancement of LED by a 3-D APhC (or APhC/Al) on the back side of the sapphire substrate. The advantages of our structure are that large area, 2” wafer, enhancement structure can be fabricated on the sapphire wafer by the auto-cloning process and the electrical properties of the LED will not be altered by the enhancement structure and its fabrication process. We experimentally showed that the enhancement mechanism is two folded, firstly, the APhC serves as a high reflector for those rays generated in the LED and incident to the APhC at low angle of incidence, secondly, the APhC serves as a diffraction grating for those rays generated in the LED and incident to the APhC at high angle of incidence, the APhC creates diffracted lights, and the diffracted lights are concentrated around the LED surface normal and are therefore capable of escaping from the LED.

References and links

1.

H. Ichikawa and T. Baba, “Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal,” Appl. Phys. Lett. 84, 457–459, (2004). [CrossRef]

2.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, “InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures,” Appl. Phys. Lett. 84, 3885–3887, (2004). [CrossRef]

3.

Z. H. Feng, Y. D. Qi, Z. D. Lu, and K. M. Lau, “GaN-based blue light-emitting diodes grown and fabricated on patterned sapphire substrates by metalorganic vapor-phase epitaxy,” J. Cryst. Growth 272, 327–332, (2004). [CrossRef]

4.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, “InGaN/GaN/AlGaN-based laser diodes with modulation-doped strained-layer superlattices grown on an epitaxially laterally overgrown GaN substrate,” Appl. Phys. Lett 72(2), 211–213, (1998). [CrossRef]

5.

J.Q. Xi, H. Luo, A. J. Pasquale, J. K. Kim, and E. F. Schubert, “Enhanced light extraction in GaInN light-emitting diode with pyramid reflector,” IEEE Photonic Tech. Lett. 18, 2347–2349, (2006). [CrossRef]

6.

T. Gessmann, E. F. Schubert, J. W. Graff, K. Streubel, and C. Karnutsch, “Omnidirectional reflective contacts for light-emitting diodes,” IEEE Electron Device Lett. 24, 683–685, (2003). [CrossRef]

7.

J. K. Kim, T. Gessmann, H. Luo, and E. F. Schubert, “GaInN light-emitting diodes with RuO2/SiO2/Ag omni-directional reflector,” Appl. Phys. Lett. 84, 4508–4510, (2004). [CrossRef]

8.

H. Ishikawa, B. Zhang, K. Asano, T. Egawa, and T. Jimbo, “Characterization of GaInN light-emitting diodes with distributed Bragg reflector grown on Si,” J. Cryst. Growth 272, 322–326, (2004). [CrossRef]

9.

Y. S. Zhao, D. L. Hibbard, H. P. Lee, K. Ma, W. So, and H. Liu, “Efficiency enhancement of InGaN/GaN light-emitting diodes with a back-surface distributed bragg reflector,” J. of Electronic Materials 32, 1523–1526, (2003). [CrossRef]

10.

J. H. Seo and J. H. Jang, “Nitride semiconductor light emitting diode and fabrication method thereof,” US patent 20050133796A1, (2005).

11.

S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electronics Lett. 33, 1260–1261, (1997). [CrossRef]

12.

M. Notomi, T. Tamamura, T. Kawashima, and S. Kawakami, “Drilled alternating-layer three-dimensional photonic crystals having a full photonic band gap,” Appl. Phys. Lett. 77, 4256–4258, (2000). [CrossRef]

13.

C. Y. Huang, H. M. Ku, and S. Chao, “Surface profile control of the autocloned photonic crystal by ion-beam-sputter deposition with radio-frequency-bias etching,” Appl. Opts. 84, 69–73, (2009). [CrossRef]

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(230.3670) Optical devices : Light-emitting diodes
(310.6860) Thin films : Thin films, optical properties
(050.5298) Diffraction and gratings : Photonic crystals
(050.6875) Diffraction and gratings : Three-dimensional fabrication

ToC Category:
Optical Devices

History
Original Manuscript: August 26, 2009
Revised Manuscript: November 1, 2009
Manuscript Accepted: November 1, 2009
Published: December 11, 2009

Citation
Chen-Yang Huang, Hao-Min Ku, and Shiuh Chao, "Light extraction enhancement for InGaN/GaN LED by three dimensional auto-cloned photonics crystal," Opt. Express 17, 23702-23711 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23702


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References

  1. H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2004). [CrossRef]
  2. J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, M. G. Craford, J. R. Wendt, J. A. Simmons, and M. M. Sigalas, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004). [CrossRef]
  3. Z. H. Feng, Y. D. Qi, Z. D. Lu, and K. M. Lau, "GaN-based blue light-emitting diodes grown and fabricated on patterned sapphire substrates by metalorganic vapor-phase epitaxy," J. Cryst. Growth 272, 327-332 (2004). [CrossRef]
  4. S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, "InGaN/GaN/AlGaN-based laser diodes with modulationdoped strained-layer superlattices grown on an epitaxially laterally overgrown GaN substrate," Appl. Phys. Lett 72(2), 211-213 (1998). [CrossRef]
  5. J. Q. Xi, H. Luo, A. J. Pasquale, J. K. Kim, and E. F. Schubert, "Enhanced light extraction in GaInN light-emitting diode with pyramid reflector," IEEE Photon. Technol. Lett. 18, 2347-2349 (2006). [CrossRef]
  6. T. Gessmann, E. F. Schubert, J. W. Graff, K. Streubel, and C. Karnutsch, "Omnidirectional reflective contacts for light-emitting diodes," IEEE Electron. Dev. Lett. 24, 683-685 (2003). [CrossRef]
  7. J. K. Kim, T. Gessmann, H. Luo, and E. F. Schubert, "GaInN light-emitting diodes with RuO2/SiO2/Ag omnidirectional reflector," Appl. Phys. Lett. 84, 4508-4510 (2004). [CrossRef]
  8. H. Ishikawa, B. Zhang, K. Asano, T. Egawa, and T. Jimbo, "Characterization of GaInN light-emitting diodes with distributed Bragg reflector grown on Si," J. Cryst. Growth 272, 322-326 (2004). [CrossRef]
  9. Y. S. Zhao, D. L. Hibbard, H. P. Lee, K. Ma, W. So, and H. Liu, "Efficiency enhancement of InGaN/GaN light-emitting diodes with a back-surface distributed bragg reflector," J. Electron. Mater. 32, 1523-1526 (2003). [CrossRef]
  10. J. H. Seo and J. H. Jang, "Nitride semiconductor light emitting diode and fabrication method thereof," US patent 20050133796A1 (2005).
  11. S. Kawakami, "Fabrication of submicrometer 3D periodic structures composed of Si/SiO2," Electron. Lett. 33, 1260-1261 (1997). [CrossRef]
  12. M. Notomi, T. Tamamura, T. Kawashima, and S. Kawakami, "Drilled alternating-layer three-dimensional photonic crystals having a full photonic band gap," Appl. Phys. Lett. 77, 4256-4258 (2000). [CrossRef]
  13. C. Y. Huang, H. M. Ku, and S. Chao, "Surface profile control of the autocloned photonic crystal by ion-beamsputter deposition with radio-frequency-bias etching," Appl. Opt. 84, 69-73 (2009). [CrossRef]

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