LED epitaxial layers (n-type, p-type, and active layers) are grown on a substrate. For each die, the n and p layers are electrically bonded to a package substrate that extends beyond the boundaries of the LED die such that the LED layers are between the package substrate and the growth substrate. The package substrate provides electrical contacts and conductors leading to solderable package connections. The growth substrate is then removed. Because the delicate LED layers were bonded to the package substrate while attached to the growth substrate, no intermediate support substrate for the LED layers is needed. The relatively thick LED epitaxial layer that was adjacent the removed growth substrate is then thinned and its top surface processed to incorporate light extraction features. There is very little absorption of light by the thinned epitaxial layer, there is high thermal conductivity to the package because the LED layers are directly bonded to the package substrate without any support substrate therebetween, and there is little electrical resistance between the package and the LED layers so efficiency (light output vs. power input) is high. The light extraction features of the LED layer further improves efficiency.