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Light extraction efficiency (LEE) in thin-film InGaN vertical light-emitting diode (LED) structures with photonic crystal patterns is studied using the three-dimensional finite-difference time-domain simulation. We systematically investigate the dependence of LEE on various structural parameters of photonic crystal vertical LEDs such as the thickness of the p-GaN and n-GaN layers, and air-hole depth and size. It is found that high LEE of > 80% is obtainable from unencapsulated photonic crystal LEDs for a wide range of structural parameters. In particular, higher LEE is observed for the structures with relatively long-period photonic crystal patterns and possible mechanisms for the large enhancement of LEE are discussed.