Optical extraction efficiency of electroluminescent diodes

Typical electroluminescent diodes have rough (sawed) surfaces and optically imperfect shapes, contacts, coatings, and dopants; all of which make the optical extraction efficiency (fraction of internally generated photons which actually escape from diode) difficult to calculate by conventional ray tracing. Because of the isotropic incoherent emission and the rough surfaces, the light distribution within the diode is nearly randomized and we have therefore analyzed it as a near equilibrium photon gas. Applying thermodynamic methods to the light extraction efficiency, we obtained a number of comparatively simple analytic relations and bounding expressions which we have used to optimize the optical design of GaP electroluminescent diodes. For red GaP (ZnO) diodes, design criteria were established with respect to the size, placement, and reflectivity of the contacts, the size and shape of the diode, the bulk absorption, the diffusion length, the far-field pattern and the encapsulant. Theoretical and practical limits on optical improvements were then inferred. These results explain and correlate a number of experimental observations. Similar procedures were applied to green GaP (N) diodes, but in this case the strong photon-energy-dependent self-absorption in the nitrogen-doped layer required a ray tracing supplement to the thermodynamic model and a careful measurement of the internally generated green spectrum, i.e., the spectrum prior to self-absorption distortion.