Simulation is used to study how the external quantum efficiency changes with the change in parameters of the unit hemisphere for GaN-based light emitting diodes (LEDs) fabricated on hemispherical patterned sapphire substrates. Through a series of experiments, we reveal the most effective pattern to improve the external quantum efficiency of LEDs on hemispherical patterned sapphire substrates. We also want to demonstrate a convenient way for pattern design and checking.
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