A light-emitting device includes a semiconductor diode structure and a multi-layer reflector (MLR) structure. The diode structure includes first and second doped semiconductor layers and an active layer between them; the active layer emits output light at a nominal emission vacuum wavelength λ0 to propagate within the diode structure. The MLR structure is positioned against a back surface of the second semiconductor layer, includes two or more layers of dielectric materials of two or more different refractive indices, reflects incident output light within the diode structure, and is in near-field proximity to the active layer relative to λ0. At least a portion of the output light, propagating perpendicularly within the diode structure relative to a device exit surface, exits the diode structure as device output light. The MLR structure can include scattering elements that scatter some laterally propagating output light to propagate perpendicularly.