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In this paper, we investigate the effect of omni-directional reflectors (ODRs) on the light extraction efficiency (LEE) for flip-chip near-ultraviolet light-emitting diodes (LEDs) on patterned (PSS) and flat sapphire substrate (FSS) using three-dimensional finite-difference time-domain method. Different design principles of ODR for the flip-chip LEDs on PSS and FSS are proposed to attain optimum LEE. For the flip-chip LED on FSS, the LEE curve is oscillatory with changing the thickness of the SiO₂ layer as a result of the coherent interference in the ODR and the optical cavity tuning effect for light source. Therefore, the thickness of the p-GaN needs to satisfy even times of quarter wave and the thickness of SiO₂ needs to be quarter wave. However, for the flip-chip LED on PSS, both the total internal reflection and the surface plasmon polariton resonance absorption play a major role leading to LEE increasing as the thickness of SiO₂ layer increases. As a result, SiO₂ layer with a thickness of over one wavelength is better, because the energy of evanescent wave decays to sufficiently negligible when it reaches the Al metal.