Table 1 Comparison of the \(\hbox {LEE}_\Gamma\) into the \(\pm 15^\circ\) and \(\pm 90^\circ\) solid angles for the 3D validation of the 2D parameter sweep results and the improvement ratio to the reference. Its clear that the µHorn significantly improves the directionality. While the µHorn leads to a decrease in the \(\hbox {LEE}_{{90}}\) for the air filled case, adding a filling material within the µHorn has a large effect, both on the directional outcoupling as well as total outcoupling. In particular, filling the µHorn with a GRIN coating improves the directionality significantly. For comparison, a small spherical (r=1.5 µm) and a large elliptical (r=12 µm, h=26 µm) SiO2 lens was added on top of the bare reference chip. In particular the large lens leads to a good enhancement of directionality but at the cost of a much larger structure, shown in next to the cGRIN in subsect. A.6. The small spherical lens with a radius of 1.5 µm increases directionality to a small degree but increases the \(\hbox {LEE}_{{90}}\). More details about the small lens are presented in subsect. A.6.

From: Ultra-directional and high-efficiency µLEDs via gradient index filled micro-horn collimators