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The GaN-based blue light LED with double layer photonic crystals is designed to enhance the vertical light extraction efficiency. The effective index approximation method is proposed and used to solve the distribution of the modes in the LED model. The geometrical parameters including the depth of the top photonic crystal d, the thickness of the embedded photonic crystal T, and the distance between the active layer and the embedded photonic crystal D are optimized. Compared with other numerical optimization, the mode analysis used in this work can dramatically save computation time and reduce complexity. In addition, it can provide more theoretical details about the influence of these geometrical parameters on light extraction efficiency. It can be found that when the surface photonic crystal satisfies the condition of d / nPhCs, high order modes localized in the structure are still not cut off but the low order modes obtain less power since they are pushed away from the active layer. Hence, the light extraction efficiency reaches its maximum. The cap layer modes can be excited by the embedded photonic crystals, when this layer satisfies 100 nm T 300 nm and 100 nm D 200 nm, the cap layer modes gather much power from the active layer and interact with the surface photonic crystals more efficiently. Hence the light extraction efficiency is dramatically improved. With our optimized parameters, the light extraction efficiency can be achieved to be up 4 times that of ordinary LED. These results shows a significant promise of designing a high-efficiency GaN-based blue light LED.
[1] Schubert E F 2006 Light Emitting Diodes (Cambridge: Cambridge Univ. Press) p21
[2] Schubert E F, Kim J K 2005 Science 308 1274
[3] Fujii T, Gao Y, Sharma R, Hu E L, Denbaars S P, Nakamura S 2004 Appl. Phys. Lett 84 855
[4] Xing Y H, Han J, Deng J, Li J J, Xu C, Shen G D 2010 Acta Phys. Sin. 59 1233 (in Chinese) [刑艳辉, 韩军, 邓军, 李建军, 徐晨, 沈光地 2010 59 1233]
[5] Ma X Y 2010 The Theory and Its Application of The Photonic Crystal (Beijing: Science Press) p22 (in Chinese) [马锡英 2010 光子晶体原理及应用 (北京: 科学出版社) 第 22 页]
[6] Chen J, Li X L, Li H H, Wang Q K 2009 Acta Phys. Sin. 58 6126 (in Chinese) [陈健, 李小丽, 李海华, 王庆康 2009 58 6126]
[7] Matioli E N 2010 PhD Thesis (University of California at Santa Barbara)
[8] David A, Moran B, McGroddy K, Matioli E, Hu E L, DenBaars S P, Nakamura S, Weisbuch C 2008 Appl. Phys. Lett. 92 113514
[9] Liu S B, Zhu C X, Yuan N C 2005 Acta Phys. Sin. 54 2804 (in Chinese) [刘少斌, 朱传喜, 袁乃昌 2005 54 2804]
[10] Zhang Y Y, Fan G H 2011 Acta Phys. Sin. 60 078504 (in Chinese) [张运炎, 范广涵 2011 60 075804]
[11] Long D H, Hwang I K, Ryu S W 2009 IEEE. J. Sel. Top. Quantum Electron 15 1257
[12] Vardeny Z V, Nahata A 2011 Nat. Photonics 5 453
[13] Marcuse D 1982 Theory of delectric optical waveguides Liu Hongdu Transl. (Beijing:Posts & Telecom Press) p7-14 (in Chinese) [D· 马库塞 1982 介质光波导理论 刘弘度译 (北京: 人民邮电出版社) 第7-14页]
[14] Yariv A, Yeh P 2009 Photonics-Optical Electronics in Modern Communications Chen heming Transl. (Beijing: Publishing House of Electronics Industry) p98--112 (in Chinese) [亚里夫, 耶赫 2009 光子学-----现代通信光电子学 陈鹤鸣译 (北京: 电子工业出版社) 第98--112页]
[15] Qin Z K, Ma C S 2011 A Concise Course on Optical Waveguides (Beijing: Higher Education Press) p54--59 (in Chinese) [秦政坤, 马春生 2011 光波导简明教程 (北京: 高等教育出版社) 第54--59页]
[16] Ge D B, Yan Y B 2005 The Finite-difference time-domain Method of the Electromagetic Wave (Xi'an:Xidian Univesity Press) p11--34 (in Chinese) [葛德彪, 闫玉波 2005 电磁波时域有限差分方法 (西安: 西安电子科技大学出版社) 第 11--34 页]
[17] Wiesmann C 2009 PhD Thesis (Regensburg Universität)
[18] Berenger J P 1994 Comput. Phys. 114 185
[19] Zhang B 2005 Acta Phys. Sin. 54 5677 (in Chinese) [张波 2005 54 5677]
[20] Chen J, Wang Q K, Li H H 2010 Acta Opt. Sin. 30 233 (in Chinese) [陈健, 王庆康, 李海华 2010 光学学报 30 233 ]
[21] David. A, Fujii T, Sharma R, McGroddy K, Nakamura S, DenBaars S P, Hu E L, Weisbuch C, Benisty H 2006 Appl. Phys. Lett. 88 061124
[22] Chul S Y, Ho K D, Hong K E, Mok P J, Ming H K, Constant K, Ho C J, Park Q H, Youl R H, Hyeob B J, Tak J, Tae K 2010 IEEE. J. Sel. Top. Quantum Electron 46 116
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[1] Schubert E F 2006 Light Emitting Diodes (Cambridge: Cambridge Univ. Press) p21
[2] Schubert E F, Kim J K 2005 Science 308 1274
[3] Fujii T, Gao Y, Sharma R, Hu E L, Denbaars S P, Nakamura S 2004 Appl. Phys. Lett 84 855
[4] Xing Y H, Han J, Deng J, Li J J, Xu C, Shen G D 2010 Acta Phys. Sin. 59 1233 (in Chinese) [刑艳辉, 韩军, 邓军, 李建军, 徐晨, 沈光地 2010 59 1233]
[5] Ma X Y 2010 The Theory and Its Application of The Photonic Crystal (Beijing: Science Press) p22 (in Chinese) [马锡英 2010 光子晶体原理及应用 (北京: 科学出版社) 第 22 页]
[6] Chen J, Li X L, Li H H, Wang Q K 2009 Acta Phys. Sin. 58 6126 (in Chinese) [陈健, 李小丽, 李海华, 王庆康 2009 58 6126]
[7] Matioli E N 2010 PhD Thesis (University of California at Santa Barbara)
[8] David A, Moran B, McGroddy K, Matioli E, Hu E L, DenBaars S P, Nakamura S, Weisbuch C 2008 Appl. Phys. Lett. 92 113514
[9] Liu S B, Zhu C X, Yuan N C 2005 Acta Phys. Sin. 54 2804 (in Chinese) [刘少斌, 朱传喜, 袁乃昌 2005 54 2804]
[10] Zhang Y Y, Fan G H 2011 Acta Phys. Sin. 60 078504 (in Chinese) [张运炎, 范广涵 2011 60 075804]
[11] Long D H, Hwang I K, Ryu S W 2009 IEEE. J. Sel. Top. Quantum Electron 15 1257
[12] Vardeny Z V, Nahata A 2011 Nat. Photonics 5 453
[13] Marcuse D 1982 Theory of delectric optical waveguides Liu Hongdu Transl. (Beijing:Posts & Telecom Press) p7-14 (in Chinese) [D· 马库塞 1982 介质光波导理论 刘弘度译 (北京: 人民邮电出版社) 第7-14页]
[14] Yariv A, Yeh P 2009 Photonics-Optical Electronics in Modern Communications Chen heming Transl. (Beijing: Publishing House of Electronics Industry) p98--112 (in Chinese) [亚里夫, 耶赫 2009 光子学-----现代通信光电子学 陈鹤鸣译 (北京: 电子工业出版社) 第98--112页]
[15] Qin Z K, Ma C S 2011 A Concise Course on Optical Waveguides (Beijing: Higher Education Press) p54--59 (in Chinese) [秦政坤, 马春生 2011 光波导简明教程 (北京: 高等教育出版社) 第54--59页]
[16] Ge D B, Yan Y B 2005 The Finite-difference time-domain Method of the Electromagetic Wave (Xi'an:Xidian Univesity Press) p11--34 (in Chinese) [葛德彪, 闫玉波 2005 电磁波时域有限差分方法 (西安: 西安电子科技大学出版社) 第 11--34 页]
[17] Wiesmann C 2009 PhD Thesis (Regensburg Universität)
[18] Berenger J P 1994 Comput. Phys. 114 185
[19] Zhang B 2005 Acta Phys. Sin. 54 5677 (in Chinese) [张波 2005 54 5677]
[20] Chen J, Wang Q K, Li H H 2010 Acta Opt. Sin. 30 233 (in Chinese) [陈健, 王庆康, 李海华 2010 光学学报 30 233 ]
[21] David. A, Fujii T, Sharma R, McGroddy K, Nakamura S, DenBaars S P, Hu E L, Weisbuch C, Benisty H 2006 Appl. Phys. Lett. 88 061124
[22] Chul S Y, Ho K D, Hong K E, Mok P J, Ming H K, Constant K, Ho C J, Park Q H, Youl R H, Hyeob B J, Tak J, Tae K 2010 IEEE. J. Sel. Top. Quantum Electron 46 116
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