In embodiments of the invention, a semiconductor structure comprising a III-nitride light emitting layer disposed between an n-type region and a p-type region is grown on a substrate. The substrate is a non-III-nitride material. The substrate has an in-plane lattice constant asubstrate. At least one III-nitride layer in the semiconductor structure has a bulk lattice constant alayer and [(|asubstrate−alayer|)/asubstrate]100% is no more than 1%. A surface of the substrate opposite the surface on which the semiconductor structure is grown is textured.