Group III nitride diodes on carrier substrates with low index

A light emitting diode is disclosed which includes a layer of p-type group III nitride and a layer of n-type group III nitride on a transparent support substrate having a refractive index lower than that of the layer group III nitride adjacent the carrier substrate. A layer of transparent adhesive bonds the transparent substrate with the group III-nitride layers and the transparent adhesive having a refractive index lower than the layer of group III-nitride. The diode includes respective ohmic contacts to the p-type group III nitride layer and the n-type Group III nitride layer.