A display may be provided with light sources. The light sources may include light-emitting diodes. The light sources may have packages formed from package bodies to which the light-emitting diodes are mounted. Layers such as quantum dot layers, light-scattering layers, spacer layers, and diffusion barrier layers may be formed over the package bodies and light-emitting diodes. Quantum dots of different colors may be stacked on top of each other. A getter may be incorporated into one or more of the layers to getter oxygen and water. Quantum dots may be formed from semiconductor layers that are doped with n-type and p-type dopant to adjust the locations of their conduction and valance bands and thereby enhanced quantum dot performance.