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We performed a theoretical analysis on improved light extraction efficiency of LEDs with photonic crystals (PCs). The light propagation and extraction of PC LEDs were simulated using the finite-difference time-domain method for various PC LED structures. LEDs with both top and bottom PCs and PC LEDs grown on patterned substrates were considered to maximize light extraction efficiency. The design parameters of the PC were varied, and optimized values were obtained. A disordered PC was simulated, and we showed that the light extraction efficiency of a disordered PC was nearly equivalent to that of an ordered PC with the same pattern periodicity. This result revealed that the increased light extraction of PC LEDs was mainly due to scattering. Moreover, by comparing the enhancement of PC LEDs with different shapes of air holes, we showed that only the density of holes and the area occupied by holes play important roles in light extraction. The shapes of the holes have no strong effect on the enhancement of light extraction.