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(a) Illustration of the vertical layer structure of LED with pillar structure fabricated on top of sapphire. (b) Schematics of three-dimensional view of the etched sapphire with pillar structure and top view of the hexagonal array configuration of pillar structure. The angle corresponds to the angle between the vertical axis and the direction of diffracted light by bottom pillar structure; parameters and directly correspond to the spacing and the pitch of pillars.
Scanning electron microscope of the side view of etched sapphire substrate having a sidewall angle of 111.9°. The top side diameter and the height of the pillar are 1378.1 and , respectively. For theoretical calculations, the diameter of the pillar is , the spacing of the pillar is , and the pitch of the pillars is assigned as with .
Comparisons of the normalized light power extraction against pitch to spacing ratio between the theoretical calculations and experimental results (sample A: , sample B: , and sample C: ). The normalized light intensity is evaluated by the light power of LED with BP structure to that of LED without BP structure.
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