Extracting light out of LEDs

Abstract

‘External quantum efficiency’, that is, the number of photons generated per electron passing through the p-n junction of an LED is probably the most important number to quantify the performance of an LED chip. Although advances in epitaxy have increased the fraction of radiative recombination to extremely high values, the extraction of the precious photons that are trapped in a high refractive index crystal is still tricky. In this brief tutorial, we look at the physics of light extraction both from a geometrical optics/thermodynamic and a wave optics point of view, discussing both random and deterministic surface structures.

The Limits of Transmittance of an Interface and Their Effects on Light Extraction

“…[15][16][17] Thus, both the first and second laws of thermodynamics require that in thermal equilibrium,…”

“…15,16 This conclusion was arrived at using thermodynamic arguments. For a typical optical material of refractive index equal to 1.6, the corresponding value of transmittance is almost 40%.…”

Thermodynamics of Light Extraction from Luminescent Materials

“…In particular, several authors [5][6][7] have pointed out, in various degrees of generality, that surface structures (including nano-optic structures) have strong limits for transmission of radiation. These limits depend on the ratio of the refractive indexes of the output medium n 1 < n 2 , the refractive index of the input medium and, more generally, on the ratios of the combined angular-area phase spaces, orétendues.…”

“…While great progress has been made in solving the light extraction problem for SSL using various approaches both commercially and in the literature, a general theoretical understanding still seems lacking. In particular, several authors [5][6][7] have pointed out, in various degrees of generality, that surface structures (including nano-optic structures) have strong limits for transmission of radiation. These limits depend on the ratio of the refractive indexes of the output medium n 1 < n 2 , the refractive index of the input medium and, more generally, on the ratios of the combined angular-area phase spaces, or étendues.…”

“…One of the main goals of this work is to derive an extension of the surface extraction limit developed in Muschaweck and Wiesmann 5 and Lenef 6 to include the case where the output light can have a limited angular extent, or limited étendue more generally. As in Ref.…”