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Sub-wavelength photonic crystal can effectively improve the light extraction efficiency (LEE) of the light emitting diode (LED). However, it is inevitable to have defects, (namely disorder structures) during its fabrication. In this study, the LED model with ideal quadrate photonic crystal is optimized by using the finite-different time domain method. Three different LED structures with various disordered photonic crystals are further simulated. We investigate the influences of several stochastic variables (including position, radius, and depth of an air hole) of the photonic crystal on the LEE of GaN based blue LEDs. It can be found that regarding photonic crystal LED whose air hole radius is optimized to 80 nm, the stochastic variables of the position and radius will reduce its LEE. However, an opposite trend is found when this radius is replaced by 60 nm, which is not optimized. Furhermore, the LEE fluctuates inside to an extent of 53.8% as two stochastic variables (including the randomized position and the randomized radius) change from 0 nm to ±20 nm. The influence of the stochastic variables of the depth of air hole can be neglected since this variation is very small. The results in this paper have an important reference value for designing and fabricating high-performance blue light photonic crystal LED.
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Keywords:
- light emitting diode /
- disorder photonic crystals /
- light extraction efficiency /
- finite-difference time-domain method
[1] Schubert E F 2006 Light-Emitting Diodes (New York: Cambridge University Press) p21
[2] Fang Z l, Qin J M 1992 Semiconductor Light-Emitting Material and Device (Shanghai: Fudan Univerty Press) [方志烈, 秦金妹 1992 半导体发光材料和器件 (上海:复旦大学出版社)]
[3] Department of Energy 2008 Solid State Lighting Research and Development Multi-Year Program Plan FY'09-FY'14 2012.2.7
[4] Wierer J J, Steigerwald D A, Krames M R, O'Shea J J, Ludowise M J, Christenson G, Shen Y C, Lowery C, Martin P S, Subramanya S, Gotz W, Gardne N F, Kern R S, Stockman S A 2001 Appl. Phys. Lett. 78 3379
[5] Shchekin O B, Epler J E, Trottier T A, Margalith T, Steigerwald D A, Holcomb M O, Martin P S, Krames M R 2006 Appl. Phys. Lett. 89 071109
[6] Chao C H, Chuang S L, Wu T L 2006 Appl. Phys. Lett. 89 091116
[7] Krames M R, Ochiai-Holcomb M, Höfler G E, Carter-Coman C, Chen E I, Tan I H, Tan T S, Kocot C P, Hueschen M, Posselt J, Loh B, Sasser G, Collins D 1999 Appl. Phys. Lett. 75 2365
[8] Fujii T, Gao Y, Sharma R, Hu E L, Denbaars S P, Nakamura S 2004 Appl. Phys. Lett. 84 855
[9] Matioli E, Weisbuch C 2010 J. Phys. D: Appl. Phys. 43 354005
[10] Xu X S, Chen H D, Zhang D Z 2006 Acta Phys. Sin. 55 6433 (in Chinese) [许兴胜, 陈宏达, 张道中 2006 55 6433]
[11] Raedt H D, Lagendijk A, Vries P D 1989 Phys. Rev. Lett. 62 47
[12] Wang B W, Jin Y, He S L 2009 J. Appl. Phys. 106 014508
[13] Savona V 2011 Phys. Rev. B 85 085301
[14] Long D H, Hwang I K, Ryu S W 2009 IEEE J. Sel. Top. Quan. Elec. 15 1257
[15] Long D H, Kag H I, Wan S 2008 Jpn. J. Appl. Phys. 47 4527
[16] Wiesmann C 2009 Ph. D. Dissertation (Regensburg: Regensburg Universität)
[17] Köhler U, As D J, Schöttker B, Frey T, Lischka K, Scheiner J, Shokhovets S, Goldhahn R 1999 J. Appl. Phys. 85 404
[18] Ryu H Y 2009 J. Kore Phys. Soci. 55 2644
[19] Matiolio E, Fleury B, Rangel E, Melo T, Hu E, Speck J, Weisbuch C 2010 Appl. Phys. Exp. 3 032103
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[1] Schubert E F 2006 Light-Emitting Diodes (New York: Cambridge University Press) p21
[2] Fang Z l, Qin J M 1992 Semiconductor Light-Emitting Material and Device (Shanghai: Fudan Univerty Press) [方志烈, 秦金妹 1992 半导体发光材料和器件 (上海:复旦大学出版社)]
[3] Department of Energy 2008 Solid State Lighting Research and Development Multi-Year Program Plan FY'09-FY'14 2012.2.7
[4] Wierer J J, Steigerwald D A, Krames M R, O'Shea J J, Ludowise M J, Christenson G, Shen Y C, Lowery C, Martin P S, Subramanya S, Gotz W, Gardne N F, Kern R S, Stockman S A 2001 Appl. Phys. Lett. 78 3379
[5] Shchekin O B, Epler J E, Trottier T A, Margalith T, Steigerwald D A, Holcomb M O, Martin P S, Krames M R 2006 Appl. Phys. Lett. 89 071109
[6] Chao C H, Chuang S L, Wu T L 2006 Appl. Phys. Lett. 89 091116
[7] Krames M R, Ochiai-Holcomb M, Höfler G E, Carter-Coman C, Chen E I, Tan I H, Tan T S, Kocot C P, Hueschen M, Posselt J, Loh B, Sasser G, Collins D 1999 Appl. Phys. Lett. 75 2365
[8] Fujii T, Gao Y, Sharma R, Hu E L, Denbaars S P, Nakamura S 2004 Appl. Phys. Lett. 84 855
[9] Matioli E, Weisbuch C 2010 J. Phys. D: Appl. Phys. 43 354005
[10] Xu X S, Chen H D, Zhang D Z 2006 Acta Phys. Sin. 55 6433 (in Chinese) [许兴胜, 陈宏达, 张道中 2006 55 6433]
[11] Raedt H D, Lagendijk A, Vries P D 1989 Phys. Rev. Lett. 62 47
[12] Wang B W, Jin Y, He S L 2009 J. Appl. Phys. 106 014508
[13] Savona V 2011 Phys. Rev. B 85 085301
[14] Long D H, Hwang I K, Ryu S W 2009 IEEE J. Sel. Top. Quan. Elec. 15 1257
[15] Long D H, Kag H I, Wan S 2008 Jpn. J. Appl. Phys. 47 4527
[16] Wiesmann C 2009 Ph. D. Dissertation (Regensburg: Regensburg Universität)
[17] Köhler U, As D J, Schöttker B, Frey T, Lischka K, Scheiner J, Shokhovets S, Goldhahn R 1999 J. Appl. Phys. 85 404
[18] Ryu H Y 2009 J. Kore Phys. Soci. 55 2644
[19] Matiolio E, Fleury B, Rangel E, Melo T, Hu E, Speck J, Weisbuch C 2010 Appl. Phys. Exp. 3 032103
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