Semiconductor light converting constructions are disclosed. The semiconductor light converting construction includes a semiconductor potential well for converting at least a portion of light at a first wavelength to light at a longer second wavelength; an outer layer that is disposed on the semiconductor potential well and has a first index of refraction; and a structured layer that is disposed on the outer layer and has a second index of refraction that is smaller than the first index of refraction. The structured layer includes a plurality of structures that are disposed directly on the outer layer and a plurality of openings that expose the outer layer. The semiconductor light converting construction further includes a structured overcoat that is disposed directly on at least a portion of the structured layer and a portion of the outer layer in the plurality of openings. The overcoat has a third index of refraction that is greater than the second index of refraction.