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Sided Patterned Sapphire Substrate to Improve The Operation of The Light Emitting Diode Emulation

To run the simulation, the light source and receiver must be set up after the structure is designed. As the light source, the active MQW layer is set up as the cubic light source. A total of 100 million sample light rays are emitted randomly in all directions from an arbitrary position in the MQW layer. The receiver measured the far field radiation power in order to detect the rays and measure the light extraction efficiency of the LEDs.In order to observe the change of the light extraction efficiency according to the shape of the pattern created on top of the sapphire substrate, patterns for seven different shapes: hemispheric, conical, truncated-cone, pyramidal, truncated-pyramid, square pillar, and cylindrical were designed. Each shape was designed considering the bumps and holes in regards to the etching of the sapphire substrate.

The height, depth, diameter, and spacing between the patterns were changed for each pattern shape in order to observe the changes in the light extraction efficiency. To obtain large changes in value, hole-shaped patterns were used for the simulations. Bump-shape patterns were excluded since they cannot be higher than the GaN layer formed on top of the sapphire substrate.The changes in the light extraction efficiency according to the shape of the pattern on the sapphire substrate layer. The bump and hole shapes for the hemisphere, cone, truncated-cone, pyramid, truncated-pyramid, square pillar, and cylinder patterns  were compared. The PSS pattern used in the simulation had a diameter of 3 μm, pitch of 6 μm, and a height of 3 μm.The cone-shaped bump had the largest light extraction efficiency at around 36.5%. The hemisphere also had a high light extraction efficiency of around 35.4%. The first insight would indicate that the hemisphere would have the highest efficiency because all of the incidental light would be perpendicular to the surface. However, since the numerous light rays that are emitted in a three-dimensional structure are determined by the minimization of the reflection that reduces the probability of it passing through the absorption layer resulting in the probability of the reflection angle changed by the pattern stays within the critical angle between the GaN and the epoxy. Therefore, there are differences according to the pattern shape, which is why the cone structure had the highest light extraction efficiency. The differences between the bumps and holes were relatively higher in the cone pattern and cylinder patterns. This is probably because of the difference of the bump and hole shapes, as the number of light rays crashing to the sidewall was smaller for the hole shape. Since the diameter of the pattern plays the role of the aperture that lets the light pass through the hole shape, the circular structure hole shape had the lowest efficiency because its area was the smallest for the same diameter.


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