A material such as a phosphor is optically coupled to a semiconductor structure including a light emitting region disposed between an n-type region and a p-type region, in order to efficiently extract light from the light emitting region into the phosphor. The phosphor may be phosphor grains in direct contact with a surface of the semiconductor structure, or a ceramic phosphor bonded to the semiconductor structure, or to a thin nucleation structure on which the semiconductor structure may be grown. The phosphor is preferably highly absorbent and highly efficient. When the semiconductor structure emits light into such a highly efficient, highly absorbent phosphor, the phosphor may efficiently extract light from the structure, reducing the optical losses present in prior art devices.