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The authors demonstrate, using finite-difference time-domain modeling, an enhancement in the extraction efficiency of flip-chip GaN light-emitting diodes (LEDs) using photonic crystals. The authors compare the extraction efficiencies of four configurations of a flip-chip GaN LED: with and without photonic crystal (PhC) layers, with a perfect reflecting mirror, and a bottom PhC reflector on GaN in combination with a top PhC extractor on sapphire. The authors show that, by using a photonic crystal layer as a bottom reflector, they can enhance the extraction efficiency similar to that of a mirror, yet the PhC reflector has the advantage that the metallic mirror loss can be avoided.