Abstract
The lattice-parameter effects on the diffracted transmission of GaN square-lattice photonic crystals (2PhC) at the wavelength of 460 nm were studied by using a rigorous coupled wave analysis (RCWA). The impacts of lattice parameters on the diffracted transmission are calculated in the ranges for lattice pitch from 100 nm to 2000 nm, fill factor from 0.1 to 0.9 and grating height from 100 nm to 1000 nm, respectively. Our simulation results confirm that the lattice pitch is the dominant factor of the diffraction. It determines how many orders of diffraction occur by the 2PhCs. The larger the lattice pitch, the higher the diffraction orders come into play. Moreover, besides the first-order Bragg diffraction, higher diffraction orders from large pitches of PhCs are also beneficial to the light extraction improvement. The higher enhancement factors of the integrated transmission were obtained from a wide range of pitches with micro-scale GaN 2PhCs. Three different diffraction mechanisms through wave vector analysis were used to discuss the simulation results.
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Lai C F, Chi J Y, Kuo H C, et al. Anisotropy of light extraction from GaN two-dimensional photonic crystals. Opt Express, 2008, 16: 7285–7294
David A, Benisty H, Weisbuch C. Optimization of light diffracting photonic-crystals for high extraction efficiency LEDs. IEEE J Disp Tech, 2007, 3: 133–148
Wiesmann Ch, Bergenek K, Linder N, et al. Photonic crystal LEDs-designing light extraction. Laser Photonics Rev, 2008, 1: 1–25
Wierer J J, Krames M R, Epler J E, et al. InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures. Appl Phys Lett, 2004, 84: 3885–3887
David A, Fujii T, Sharma R, et al. Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution. Appl Phys Lett, 2006, 88: 061124-1–061124-3
Zhang Z S, Zhang B, Xu J, et al. Effects of symmetry of GaN-based two-dimensional photonic crystal with quasicrystal lattices on enhancement of surface light extraction. Appl Phys Lett, 2006, 88: 171103-1–171103-3
Oder T N, Kim K H, Lin J Y, et al. III-nitride blue and ultraviolet photonic crystal light emitting diodes. Appl Phys Lett, 2004, 84: 466–468
Orita K, Tamura S, Takizawa T, et al. High-extraction-efficiency blue light-emitting diode using extended-pitch photonic crystal. Jpn J Appl Phys, 2004, 43: 5809–5813
Kim K, Choi J, Park J B, et al. Lattice constant effect of photonic crystals on the light output of blue light-emitting diodes. IEEE Phot Tech Lett, 2008, 20: 1455–1457
Horng R H, Huang S H, Yang C C, et al. Efficiency improvement of GaN-based LEDs with ITO texturing window layers using natural lithography. IEEE J Sele Topi Quan Elec, 2006, 12:1196–1201
Chang S J, Shen C F, Chen W S, et al. Nitride-based light emitting diodes with indium tin oxide electrode patterned by imprint lithography. Appl Phys Lett, 2007, 91: 013504-1–013504-3
Xiong C, Zhang B, Kang X N, et al. Two-dimensional photonic quasicrystal on the surface of GaN-based light emitting diodes. Semicond Sci Technol, 2010, 25: 065006-1–065006-4
Wierer J J, David A, Megens M M. III-nitride photonic-crystal light-emitting diodes with high extraction efficiency. Nat Photonics, 2009, 3: 163–169
Wiesmann Ch, Bergenek K, Houdre R, et al. Theoretical investigation of the radiation pattern from LEDs incorporating shallow photonic crystals. IEEE J Quan Elec, 2009, 45: 1273–1283
Lai C F, Chao C H, Kuo H C, et al. Directional light extraction enhancement from GaN-based film-transferred photonic crystal light-emitting diodes. Appl Phys Lett, 2009, 94: 123106-1–123106-3
Bao K, Kang X N, Zhang B, et al. Improvement of light extraction from patterned polymer encapsulated GaN-based flip-chip light emitting diodes by imprinting. IEEE Phot Tech Lett, 2007, 19: 1840–1842
Bergenek K, -Wiesmann Ch, Zull H, et al. Beam-shaping properties of InGaN thin-film micro-cavity light-emitting diodes with photonic crystals. Proc of SPIE, 2009, 7231: 72310C-1–72310C-11
Dai T, Zhang B, Zhang Z S, et al. Surface light extraction mapping from two-dimensional array of 12-fold photonic quasicrystal on current injected GaN-based LEDs. Chin Phys Lett, 2007, 24: 979–982
Moharam M G, Grann E B, Pommet A, et al. Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings. J Opt Soc Am A, 1995, 12:1068–1076
Kikuta H, Hino S, Maruyama A, et al. Estimation method for the light extraction efficiency of light-emitting elements with a rigorous grating diffraction theory. J Opt Soc Am A, 2006, 23: 1207–1213
Xiong C, Zhang B, Kang X N, et al. Diffracted transmission effects of GaN and polymer two-dimensional square-lattice photonic crystals. Opt Express, 2009, 17: 23684–23689
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Xiong, C., Zhang, B., Kang, X. et al. Lattice-parameter effects on diffracted transmission of GaN two-dimensional square-lattice photonic crystals. Sci. China Technol. Sci. 54, 23–27 (2011). https://doi.org/10.1007/s11431-010-4184-0
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DOI: https://doi.org/10.1007/s11431-010-4184-0