In this research, we presented the theoretical discussion on the efficiency of light extraction for the design parameter optimization of light-emitting diodes (LEDs). Several photonic systems using two-dimensional photonic crystals (PhCs) are investigated based on a simple design method for an efficient light output from the viewpoint of Bragg diffraction. The influence of several factors on the enhancement of light extraction was investigated via the plane wave method and the finite element method. In the simulation results, the optimized Archimedean tiling pattern incorporated into the LED device could increase the emission efficiency by a factor of approximately 3 compared to an LED without the PhC pattern of an Archimedean tiling of circular pillars in the device.