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 grat- ing height from 100 nm to 1000 rim, 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.
We have fabricated a series of square-lattice hole photonic crystal (2PhC) arrays simultaneously at the un-current injection region on a special sample of GaN based light emitting diode (LED) by using focus ion beam milling (FIBM). The lattice constants of the 2PhC arrays vary from 230 to 1500 nm,while the 2PhC arrays have a constant area of about 9 μm×18 μm and a fixed depth of 150±10 nm which approaches but does not penetrate the active layer. Microscopic electroluminescence images and spectral measurements consistently confirm that the top emitting intensities from different 2PhCs are all enhanced compared with the unpatterned region. It is demonstrated that the output coupling of propagating guided modes is realized by the diffracted transmission of the 2PhCs. The enhancement factors of the guided modes compared with the unpatterned region are plotted as function of the lattice constant. It is found that the highest enhancements for the extraction of guided modes were obtained for the lattice constant of 230 and 460 nm of 2PhCs. The results are discussed by the two-dimensional rigorous coupled wave analysis (RCWA).
FU XingXingZHANG BeiKANG XiangNingXU JunXIONG ChangZHANG GuoYi
