近年來，由於石油的能源危機與環保意識的抬頭，因此發光二極體的重要性也日漸增加。近期由於磊晶技術的成長與突破，所以在內部量子效率的部分已經有長足的上升，但由於材料得侷限，使的其發光效率仍有相當的進步空間，因此有許多的技術被發展來改善此問題，但在這些技術的製程中，往往也會使的磊晶結構受到一定的傷害。因此本論文的研究方向主要以不破壞到磊晶結構的方式來提升出光效率為目標。
本文利用自組式多孔陽極氧化鋁的奈米孔洞製作在發光二極體之表面作為粗化層來提升光輸出。為了瞭解孔洞結構特性與光取出效率所對應之趨勢，因此本論文首先將多孔陽極氧化鋁薄膜實際應用於磷化鋁鎵銦發光二極體上，藉由改變孔洞寬化時間來調變孔洞的大小和結構。奈米孔洞的直徑從30 nm 變化到60 nm，當孔洞大小為45nm 時，可以得到最佳的光輸出為39 %。因此多孔陽極氧化鋁薄膜扮演為中介層和散射中心在空氣和半導體材料之間，導致低的臨界角損失和Fresnel 損失，而得到提升光取出效率的成果。之後利用有限時域差分法(FDTD)建立一個三維的理論計算模型，研究發光二極體結構在添加多孔氧化鋁薄膜後其對光亮度提升的影響，經由理論計算的結果，AlGaInP 發光二極體可藉由多孔性陽極氧化鋁薄膜得到約35%的光亮度提升。因此藉著此結果可以驗證理論模擬的準確性，同時可對未來的實驗參數結構作一推測。
另一方面，以底層蝕刻週期性柱狀結構的圖案化基材之GaN 發光二極體也是另一個不傷害磊晶層更甚提升磊晶品質的方法之一。透過以傳統結構LED 計算出的光亮度做規一化，評估結構的改善對光亮度提升的量值，用以討論底層柱狀結構參數變化的影響。
在實驗與模擬上可以得到當GaN 發光二極體圖案化基材的底層柱狀結構，也對光亮度提升有30%的增強效果。這些結構對光亮度的作用，可藉由光學行為上相互影響的物理機制加以解釋。

In this article, the investigation is light-output enhancement of light emitting-diode by a technique of non-encroached epitaxial layer. First, a porous anodic alumina (PAA) film with nanoroughening is added on the top window layer of AlGaInP light-emitting diodes (LEDs) to improve the light extraction of the device. The PAA film has a natural porosity, allowing an increase of light emission intensity with no loss of damage to the semiconductor material.
Because of more light to be effectively scattered into the air by the nano-pores of PAA film and a large critical angle to avoid a high level of internal light reflection by inserting PAA between air and the GaP window layer, these benefits favor the LED to have the light output
improvement by 1.29 times than the conventional device. For the same sample followed by pore-widening at 40 min, the light output intensity is optimally achieved to 1.39 times.
Therefore, without increasing any complexity or expense of the manufacturing processes, the PAA film and with a suitable pore-widening could substantially enhance the light extraction efficiency of a LED. One the other hand, we using a three-dimensional model with finite-difference and time-domain was established to investigate the enhancement of the light output intensity of AlGaInP light-emitting diodes (LEDs) for getting optimum parameter and realized this resolution in experiment.
Second, GaN-based light-emitting diodes (LEDs) with bottom pillar (BP) structure were investigated. In this structure, a three-dimensional model with finite-difference and time-domain was established to investigate the enhancement of the light output intensity.
Through comparing the normalized light extraction intensity of GaN LEDs with or without BP in different dimensions, the theoretical results show that the light output intensity in the LED with BP structure involved could be enhanced by about 30%. The influence of BP structure on the light output intensity of a LED could be explained by the physical model of light interaction. In addition, the experimental results also show the same trend to the theoretical calculations.

[1] D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, Y. S. Park, J. Cho, et al.,
“Enhanced light extraction from GaN-based light-emitting diodes with
holographically generated two-dimensional photonic crystal patterns,” Appl.
Phys. Lett., vol. 87, pp. 203508-1~203508-3, 2005.
[2] C. C. Liu, W. T. Wang, M. P. Houng, Y. H. Wang, and S. M. Chen, “Titanium
nitride as spreading layers for AlGaInP visible LEDs,” IEEE Photo. Techno.
Lett., vol. 14, no. 12, pp. 1665-1667, 2002.
[3] C.-C. Liu, Y.-H. Chen, M.-P. Houng, Y.-H. Wang, Y.-K. Su, W.-B. Chen,
and S.-M. Chen, “Improved Light-Output Power of GaN LEDs by Selective
Region Activation”, IEEE Photonics Technol. Lett. vol. 16, pp. 1444-1446,
2004.
[4] M. Yamada, T. Mitani, Y. Narukawa, S. Shioji, I. Niki, S. Sonobe, K.
Deguchi, M. Sano, and T. Mukai, “InGaN-Based Near-Ultraviolet and
Blue-Light-Emitting Diodes with High External Quantum Efficiency Using
a Patterned Sapphire Substrate and a Mesh Electrode”, Jpn. J. Appl. Phys.,
Part 2, vol. 41, pp. L1431-L1433, 2002.
[5] Y. J. Lee, J. M. Hwang, T. C. Hsu, M. H. Hsieh, M. J. Jou, B. J. Lee, T. C. Lu,
H. C. Kuo, and S. C. Wang, “Enhancing the Output Power of GaN-Based
LEDs Grown on Wet-Etched Patterned Sapphire Substrates”, IEEE
Photonics Technol. Lett. vol. 18, pp. 1154-1152, 2006.
[6] M. R. Krames, M. Ochiai-Holcomb, G. E. Höfler, C. Carter-Coman, E. I.
Chen, I.-H. Tan, P. Grillot, N. F. Gardner, H. Chui, J.-W. Huang, S. A.
115
Stockman, F. A. Kish, M. G. Crawford, T. S. Tan, C. P. Kocot, M. Hueschen,
J. Posselt, B. P. Loh, G. Sasser, and D. Collins, “High-power
truncated-inverted-pyramid AlxGa12x…0.5In0.5P/GaP light-emitting
diodes exhibiting >50% external quantum efficiency ”, Appl. Phys. Lett. vol.
75, pp. 2365-2637, 1999.
[7] M. Borodilsky, T. F. Kraus, R. Coccioli, R. Vrijen, R. Bhat, and E.
Yablonovitch, “Light extraction from optically pumped light-emitting diode
by thin-slab photonic crystals ”, Appl. Phys. Lett. vol. 75, pp. 1036-1038,
1999.
[8] R. Windisch, C. Rooman, S. Meinlschmidt, P. Kiesel, D. Zipperer, G. H.
Döhler, B. Dutta, M. Kuijk, G. Borghs, and P. Heremans, “Impact of
texture-enhanced transmission on high-efficiency surface-textured
light-emitting diodes ”, Appl. Phys. Lett. vol. 79, pp. 2315-2317, 2001.
[9] J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes,
“Bragg scattering from periodically microstructured light emitting diodes ”,
Appl. Phys. Lett. vol. 77, pp. 3340-3342, 2000.
[10] K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato,
and T. Taguchi, “High Output Power InGaN Ultraviolet Light-Emitting
Diodes Fabricated on Patterned Substrates Using Metalorganic Vapor Phase
Epitaxy ”, Jpn. J. Appl. Phys., Part 2 vol. 40, pp. L583-L585, 2001.
[11] D. S. Wuu, W. K. Wang, W. C. Shin, R. H. Horng, C. E. Lee, W. Y. Lin, and
J. S. Fang, “Enhanced Output Power of Near-Ultraviolet InGaN–GaN LEDs
Grown on Patterned Sapphire Substrates ”, IEEE Photonics Technol. Lett.
vol. 17, pp. 288-290, 2005.
[12] C. C. Sun, C. Y. Lin, T. X. Lee, and T. H. Yang, “Enhancement of light
extraction of GaN-based light-emitting diodes with a microstructure array ”,
116
Opt. Eng. Vol. 43, pp. 1700-1702, 2004.
[13] W. J. Choi, Q-H. Park, D. Kim, H. Jeon, C. Sone, and Y. Park, “FDTD
Simulation for Light Extraction in a GaN-Based LED ”, J. Korean Phys. Soc.
Vol. 49, pp. 877-879, 2006.
[14] I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30
% external quantum efficiency from surface textured thin-film
light-emitting diodes”, Appl. Phys. Lett., Vol. 63, No. 16, pp. 2174-2176,
1993.
[15] C. P. Kuo, R. M. Fletcher, T. D. Osentowski, M. C. Lardizabal, M. G.
Craford, and V. M. Robbins,” High performance AlGaInP visible
light-emitting diodes”, Appl. Phys. Lett., Vol. 57, pp. 2937-2939, 1990.
[16] K. J. Knopp, R. P. Mirin, K. A. Bertness, K. L. Silverman, and D. H.
Christensen,” Compound semiconductor oxide antireflection coatings”, J.
Appl. Phys., Vol. 87, pp. 7169-7175, 2000.
[17] A. K. Chin, G. Zydzik, S. Singh, L. G. Van Uitert, and G. Minneci,” Al2O3
as an antireflection coating for InP/lnGaAsP LEDs”, J. Vac. Sci. Technol. B,
vol.1, pp. 72-73, 1983.
[18] R. Windisch, B. Dutta, M. Kuijk, A. Knobloch, S. Meinlschmidt, S.
Schoberth, P. Kiesel, G. Borghs, G. H. Döhler, and P. Heremans,” 40%
Efficient Thin-Film Surface-Textured Light-Emitting Diodes by
Optimization of Natural Lithography”, IEEE Trans. Electron Devices, vol.
47, pp., 1492-1498, 2000.
[19] T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura,
117
“Increase in the extraction efficiency of GaN-based light-emitting diodes via
surface roughening”, Appl. Phys. Lett., Vol. 84, No. 6, pp. 855-857, 2004.
[20] C. C. Wang, H. Ku, C. C. Liu, K. K. Chong, C. I Hung, Y. H. Wang and M.
P. Houng,” Enhancement of the Output Power of GaN-based Light-Emitting
Diodes by Bottom Pillar Structure”, Appl. Phys. Lett., Vol. 91,
pp.121109-1~121109-3, Sep., 2007.
[21] C. C. Wang, F. L. Jenq, C. C. Liu, C. I Hung , Y. H. Wang and M. P.
Houng,” Selective high resistivity region formation by a Ni catalyst on GaN
light-emitting diodes,” Semicon. Sci. Technol., Vol.23, pp.025012-1 ~
025012-4, Jan., 2008.
[22] C. C. Wang, H. C. Lu, C. C. Liu, F. L. Jenq, Y. H. Wang and M. P. Houng,”
Improved Extraction Efficiency of Light Emitting Diodes by Modifying
Surface Roughness with Anodic Aluminum Oxide Film,” IEEE Photo.
Technol. Lett., Vol. 20, pp.428-430, 2008.
[23] Y. C. Ting, and S. L. Shy, “Pore size control of alumina membrane mask”,
Proc. of SPIE, Vol. 6283, pp. 62833I~1-62833I~9, May, 2006
[24] H. Masuda, K. Nishio, and N. Baba, “Fabrication of a one-dimensional
microhole array by anodic oxidation of aluminum”, Appl. Phys. Lett., Vol.
63, No.23, pp. 3155-3157, 1993.
[25] C. A. Huber, T. E. Huber, M. Sadoqi, J. A. Lubin, S. Manalis, and C. B.
Prater, “Nanowire array composites”, Science, Vol. 263, no. 5148, pp.
800-802, 1994.
[26] S. Shingubara, O. Okino, Y. Sayama, H. Sakaue, and T. Takahagi, “Ordered
118
two-dimesion nanowire array formation using self-organized nanoholes of
anodically oxidized aluminum”, Jpn. J. Appl. Phys. Part1, Vol. 36, No. 12B,
pp. 7791-7795, 1997
[27] S. Shingubara, Y. Murakami, H. Sakaue, T. Takahagi, Kagamiyama, and H.
Hiroshima, “Aluminum nanodot array formed by anodic oxidation and its
conduction properties”, Proc. of SPIE, Vol. 4999, pp. 387-395, 2003.
[28] K. Nielsch, F. Muller, A. P. Li, and U. Gusele, “Uniform nickel deposition
into ordered alumina pores by pulsed electrodeposition”, Adv. Mater., Vol.
12, No. 8, pp. 582-586, 2000.
[29] F. Keller, M. S. Hunter, and D. L. Robinson, “Structural features of oxide
coatings on aluminum”, J. Electrochem. Soc., Vol. 100, 411, 1953.
[30] H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a
two-step replication of honeycomb structure of anodic alumina”, Science,
Vol. 268, p.146, 1995
[31] H. Masuda, F. Hasegwa, S. Ono, “Self-ordering of cell arrangement of
anodic porous alumina formed in sulfuric acid solution”, J. Electrochem.
Soc., Vol. 144, No. 5, pp. L127-L130, 1997
[32] H. Masuda, K. Yada, and A. Osaka, “Self-ordering of cell configuration of
anodic porous alumina with large-size pores in phosphoric acidsolution”,
Jpn. J. Appl. Phys., Vol. 37, pp. L1340-L1342, 1998.
[33] Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon
antireflection structures fabricated using a porous alumina membrane mask”,
Appl. Phys. Lett., Vol. 78, No. 2, pp. 142-143, 2001.
119
[34] H. Masuda, H. Yamada, M. Satoh, and H. Asoh, M. Nakao, and T.
Tamamura, “Highly ordered nanochannel-array architecture in anodic
alumina”, Appl. Phys. Lett., Vol. 71, No. 19, pp. 2770-2772, 1997.
[35] C. Y. Liu, A. Datta, and Y. L. Wang, “Ordered anodic alumina nanochannels
on focused-ion-beam-prepatterned aluminum surfaces”, Appl. Phys. Lett.,
Vol. 78, No. 1, pp. 120-122, 2001.
[36] H. Masuda, M. Ohya, H. Asoh, M. Nakao, M. Nohtomi, and T. Tamamura,
“Photonic crystal using anodic porous alumina”, Jpn. J. Appl. Phys Part 2.,
Vol. 38, pp. L1403-L1405, 1999.
[37] H. Masuda, M. Ohya, K. Nishio, H. Asoh, M. Nakao1, M. Nohtomi, A.
Yokoo and T. Tamamura, “Photonic band gap in anodic porous alumina with
extremely high aspect ratio formed in phosphoric acid solution”, Jpn. J. Appl.
Phys. Part 2, Vol. 39, pp. L1039-L1041, 2000.
[38] H. Masuda, M. Ohya, H. Asoh, and K. Nishio, “Photonic band gap in
naturally occurring ordered anodic porous alumina”, Jpn. J. Appl. Phys. Part
2, Vol. 40, pp. L1217-L1219, 2001.
[39] F. Li, L. Zhang, and R. M. Metzger, “On the growth of highly ordered pores
in anodized aluminum axide”, Chem. Mater., Vol. 10, pp. 2470-2480, 1998.
[40] A. P. Li, F. Muller, A. Birner, K. Nielsch, and U. Gosele, “Hexagonal pore
arrays with a 50-420 nm interpore distance formed by self-organization in
anodic alumina”, J. Appl. Phys., Vol. 84, No. 11, pp.6023-6026, 1998.
[41] S. K. Hwang, S. H. Jeong, H. Y. Hwang, O. J. Lee and K. H. Lee,
“Fabrication of highly ordered pore array in anodic aluminum oxide”,
120
Korean J. Chem. Eng., Vol. 19, No.3, pp. 467-473, 2002.
[42] E. Fred Schubert, “Light-Emitting Diodes” 2nd, pp. 86-87, 2006.
[43] S. Illek, U. Jacob, A. Plossl, P. Stauss, K. Streubel, W. Wegleiter, and R.
Wirth, “Burried micro-reflectors boost performance of AlGaInP LEDs,”
Compound Semicond., Vol. 8, pp. 39-42, 2002.
[44] E. Hecht, “OPTICS” 4th, Addison Wesley, New York, pp.117-120, 2002.
[45] E. Hecht, “OPTICS” 4th, Addison Wesley, New York,pp.120-123, 2002.
[46] Neamen, “Semiconductor Physics and Devices Basic Principles” 3rd, 2003.
[47] N. Linder, S. Kugler, P. Stauss, K. P. Streubel, R. Wirth, and H. Zull,
“High-brightness AlGaInP light-emitting diodes using surface”, Proc. of
SPIE, Vol. 4278, pp. 19-25, 2001.
[48] C. Huh, K. S. Lee, E. J. Kang, and S. J. Parka, “Improved light-output and
electrical performance of InGaN-based light-emitting diode by
microroughening of the p-GaN surface”, J. Appl. Phys., Vol. 93, No. 11, pp.
9383-9385, 2003.
[49] C.H. Liu, R.W. Chuang, S.J. Chang, Y.K. Su, L.W. Wu, and C.C. Lin,
“Improved light output power of InGaN/GaN MQW LEDs by lower
temperature p-GaN rough surface”, Mater. Sci. Eng., B, Vol. 112, pp. 10-13,
2004.
[50] T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura,
“Increase in the extraction efficiency of GaN-based light-emitting diodes via
surface roughening”, Appl. Phys. Lett., Vol. 84, No. 6, pp. 855-857, 2004.
[51] Y. J. Lee, H. C. Kuo, S. C. Wang, T. C. Hsu, M. H. Hsieh, M. J. Jou, and B. J.
121
Lee, “Increasing the extraction efficiency of AlGaInP LEDs via n-side
surface roughening”, IEEE Photonics Technol. Lett., Vol. 17, No. 11, pp.
2289-2291, 2005.
[52] T. H. Hsueh, J. K. Sheu, H. W. Huang, J. Y. Chu, C. C. Kao, and S. C. Wang,
“Enhancement in light output of InGaN-based microhole array light-emitting
diodes”, I IEEE Photonics Technol. Lett., Vol. 17, No. 6, pp. 1163-1165,
2005.
[53] H. W. Huang, C. C. Kao, J. T. Chu, H. C. Kuo, S.C. Wang, and C. C. Yu,
“Improvement of InGaN-GaN light-emitting diode performance with a
nano-roughened p-GaN surface”, IEEE Photonics Technol. Lett., Vol.17, No.
5, pp.983-985, 2005.
[54] M. Iwaya, H. Kasugai, T. Kawashima, K. Iida, A. Honshio, Y. Miyake, S.
Kamiyama, H. Amano, and I. Akasaki, “Improvement in light extraction
efficiency in group III nitride-based light-emitting diodes using moth-eye
structure”, Thin Solid Films, Vol. 515, pp. 768-770, 2006
[55] H. W. Huang, H. C. Kuo, C. F. Lai, C. E. Lee, C. W. Chiu, T. C. Lu, S. C.
Wang, C. H. Lin, and K. M. Leung. “High-performance GaN-based
vertical-injection light-emitting diodes with TiO2–SiO2 omnidirectional
reflector and n-GaN roughness”, IEEE Photonics Technol. Lett., Vol. 19, No.
8, pp. 565-567, 2007.
[56] H. W. Huang, C. C. Kao, J. T. Chu, W. C. Wang, T. C. Lu, H. C. Huo, S.C.
Wang, C. C. Yu, and S. Y. Kuo, “Investigation of InGaN/GaN light emitting
diodes with nano-roughened surface by excimer laser etching method”,
122
Mater. Sci. Eng., B, Vol. 136, pp. 182-186, 2007.
[ 57 ] K. Tsakmakidis, B. Weiss and O. Hess, “Full-wave electromagnetic
modelling of an InP/InGaAs traveling-wave heterojunction phototransistor”
J. Phys. D: Appl. Phys., vol. 39, p. 1805, 2006.
[58] W. J. Choi, Q-H. Park, D. Kim, H. Jeon, C. Sone, and Y. Park, “FDTD
Simulation for Light Extraction in a GaN-Based LED” Journal of the Korean
Physical Society, vol. 49, p. 877, 2006.
[59] M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous
Inhibition and Redistribution of Spontaneous Light Emission in Photonic
Crystals” Science, vol. 308, p. 1296, 2005.
[60] S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High
Extraction Efficiency of Spontaneous Emission from Slabs of Photonic
Crystals” Phys. Rev. Lett., vol. 78, p. 3294, 1997.
[61] D. K. Cheng, Field and Wave Electromagnetics, 2th ed. (Addison-Wesley
Publishing Company, Chap. 8, pp.379-380, 1989.
[62] Fullwave 5.0 User Manual (RSoft Design Group Inc., Ossining, NY, USA,
2006.
[63] V. P. Parkhutik and V. I. Shershulsky, “Theoretical modeling of porous oxide
growth on aluminum”, J. Phys. D: Appl. Phys., Vol. 25, pp. 1258-1263,
1992.
[64] O. Jessensky, F. Muller, and U. Gosele, “Self-organized formation of
hexagonal pore arrays in anodic alumina”, Appl. Phys. Lett., Vol. 72, No.
10, pp. 1173-1175, 1998
123
[65] H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a
two-step replication of honeycomb structure of anodic alumina”, Science,
Vol. 268, 146, 1995.
[66] H. Masuda, F. Hasegwa, S. Ono, “Self-ordering of cell arrangement of
anodic porous alumina formed in sulfuric acid solution”, J. Electrochem.
Soc., Vol. 144, No. 5, L127-L130, 1997.
[67] H. Masuda, K. Yada, and A. Osaka, “Self-ordering of cell configuration of
anodic porous alumina with large-size pores in phosphoric acidsolution”,
Jpn. J. Appl. Phys., Vol. 37, L1340-L1342, 1998.
[68] H. Masuda and M. Satoh, “Fabrication of gold nanodot array using anodic
porous alumina as an evaporation mask”, Jpn. J. Appl. Phys. Part 2, Vol. 35,
pp. L126-L129, 1996.
[69] H. Masuda, H. Yamada, M. Satoh, and H. Asoh, M. Nakao, and T.
Tamamura, “Highly ordered nanochannel-array architecture in anodic
alumina”, Appl. Phys. Lett., Vol. 71, No. 19, pp. 2770-2772, 1997.
[70] C. Y. Liu, A. Datta, and Y. L. Wang, “Ordered anodic alumina nanochannels
on focused-ion-beam-prepatterned aluminum surfaces”, Appl. Phys. Lett.,
Vol. 78, No. 1, pp. 120-122, 2001.
[71] K.-H. Jung, J.-W. Yoon, N. Koshizaki and Y.-S. Kwon, “Fabrication of Gold
Dot and Tubular Gold Arrays Using Anodic Aluminum Oxide Film as
Template” Jpn. J. Appl. Phys., vol. 44, p. 5300, 2005.
[72] P. G. Miney, P. E. Colavita, M. V. Shiza, R. J. Priore, F. G. Haibach, and M. L.
Myrick, “Growth and Characterization of a Porous Aluminum Oxide Film
124
Formed on an Electrically Insulating Support” Electrochem. Solid-State Lett.,
vol. 6, p. B42, 2003.
[73] A. P. Li, F. Müller, A. Birner, and U. Gösele, “Hexagonal pore arrays with a
50–420 nm interpore distance formed by self-organization in anodic
alumina” J. Appl. Phys., vol. 84, p. 6023, 1998.
[ 74 ] S. Z. Chu, K. Wada, S. Inoue, and S. Todoroki, “Formation and
Microstructures of Anodic Alumina Films from Aluminum Sputtered on
Glass Substrate” J. Electrochem. Soc., vol. 149, p. B321, 2002.
[75] S. Van Gils, Th. Dimogerontakis, G. Buytaert, E. Stijns, H. Terryn, P.
Skeldon, G. E. Thompson, and M. R. Alexander, “Optical properties of
magnetron-sputtered and rolled aluminum” J. Appl. Phys., vol. 98, p. 083505,
2005.
[76] E. S. Kooij, H. Wormeester, A. C. Galca, and B. Poelsema, “Optical
Anisotropy and Porosity of Anodic Aluminum Oxide Characterized by
Spectroscopic Ellipsometry” Electrochem. Solid-State Lett., vol. 6, p. B52,
2003.
[77] B.E. Yoldas, “Investigations of porous oxides as an antireflective coating for
glass surfaces” Appl. Opt., vol. 19, p. 1425, 1980.
[78] T. V. Cuong, H. S. Cheong, and C.-H. Hong, “Calculation of the external
quantum efficiency of light emitting diodes with different chip designs” phys.
stat. sol. (c), vol. 1, p. 2433, 2004.
[79] Fullwave 5.0 User Manual (RSoft Design Group Inc., Ossining, NY, USA,
2006)
125
[80] L. A. Coldren, S. W. Corzine, Diode Lasers and Photonic Integrated Circuits
(Wiley, New York, 1995), p. 148–153 and p. 518–525
[81] J. Shakya, K. Knabe, K. H. Kim, J. Li, J. Y. Lin, and H. X. Jiang, Appl. Phys.
Lett. 86, 091107 (2005)
[82] C.H. Jeong, D.W. Kim, H.Y. Lee, H.S. Kim, Y.J. Sung and G.Y. Yeom,
“Sapphire etching with BCl3/HBr/Ar plasma” Surf. Coat. Technol., vol. 171,
p. 280, 2003.
[83] F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed. McGraw-Hill,
New York, p. 338, 1976.
[84] R. W. Ditchburn, Light, 2nd ed., London, Blackie, 1963, pp582–585.
[85] “Interference coatings” Wikimedia Foundation, Inc., http://en.wikipedia.org/
wiki/Anti-reflective
[86] C.-H. Chao, S. L. Chuang, and T.-L. Wu, “Theoretical demonstration of
enhancement of light extraction of flip-chip GaN light-emitting diodes with
photonic crystals” Appl. Phys. Lett., vol. 89, pp. 091116-1~091116-2, 2006.