A light-emitting device includes: a semiconductor structure formed on one side of a substrate, the semiconductor structure having a plurality of semiconductor layers and an active region within the layers; and first and second conductive electrodes contacting respectively different semiconductor layers of the structure; the substrate comprising a material having a refractive index n>2.0 and light absorption coefficient &agr;, at the emission wavelength of the active region, of &agr;>3 cm−1. In a preferred embodiment, the substrate material has a refractive index n>2.3, and the light absorption coefficient, &agr;, of the substrate material is &agr;