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14 March 2013 Light extraction by Lambertian sources from light emitting diodes
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Internal back-and-forth propagation of photons within a light emitting diode (LED) will naturally tend towards a Lambertian intensity profile when surface texturing is sufficiently rough. Novel designs in light extraction efficiency (LEE) can therefore benefit by optimizing under this expectation. This paper develops a framework for calculating LEE from a planar LED structure with textured surface features under the assumption of Lambertian intensity within the substrate. The method can estimate the total LEE value when given a substrate width w, an attenuation constant α, and the transmittance function T(θ,Φ) through the top interface. We demonstrate our theory on a pyramidal surface texture over a GaSb substrate at 4.5 μm wavelength by computing the expected LEE as a function of w.
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James R. Nagel "Light extraction by Lambertian sources from light emitting diodes", Proc. SPIE 8619, Physics and Simulation of Optoelectronic Devices XXI, 86190L (14 March 2013);

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