The out-coupling efficiency of planar organic light emitting diodes (OLEDs) is only about 20% due to factors, such as, the total internal reflection, surface plasmon coupling, and metal absorption. Two-dimensional periodic nanostructures, such as, photonic crystals (PhCs) and microlenses arrays offer a potential method to improve the out-coupling efficiency of OLEDs. In this work, we employed the finite-difference time-domain (FDTD) method to explore different mechanisms that embedded PhCs and surface PhCs to improve the out-coupling efficiency. The effects of several parameters, including the filling factor, the depth, and the lattice constant were investigated. The result showed that embedded PhCs play a key role in improving the out-coupling efficiency, and an enhancement factor of 240% was obtained in OLEDs with embedded PhCs, while the enhancement factor of OLEDs with surface PhCs was only 120%. Furthermore, the phenomena was analyzed using the mode theory and it demonstrated that the overlap between the mode and PhCs was related to the distribution of vertical mode profiles. The enhancement of the extraction efficiency in excess of 290% was observed for the optimized OLEDs structure with double PhCs. This proposed structure could be a very promising candidate for high extraction efficiency OLEDs.