Disclosed re-emitting semiconductor constructions (RSCs) may provide full-color RGB or white-light emitting devices that are free of cadmium. Some embodiments may include a potential well that comprises a III-V semiconductor and that converts light of a first photon energy to light of a smaller photon energy, and a window that comprises a II-VI semiconductor having a band gap energy greater than the first photon energy. Some embodiments may include a potential well that converts light having a first photon energy to light having a smaller photon energy and that comprises a II-VI semiconductor that is substantially Cd-free. Some embodiments may include a potential well that comprises a first III-V semiconductor and that converts light having a first photon energy to light having a smaller photon energy, and a window that comprises a second III-V semiconductor and that has a band gap energy greater than the first photon energy.