Photonic-crystal (PhC)-assisted light extraction is a promising method for ultrahigh efficiency, planar light-emitting diodes (LEDs). However, modeling of such structures is challenging due to the variety of their parameters and the heavy computational burden they represent. We present a thorough theoretical discussion of the optimization of PhC LEDs, which relies both on approximate treatments and on rigorous 3-D calculations. Two material systems (GaAs and GaN) are investigated, leading to quite different optimal regimes. Notably, it appears that besides the properties of the 2-D PhC itself, design of the vertical structure plays a major role in optimization.
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