Radiation-emitting semiconductor devices include a first base region comprising an n-type III-V semiconductor material, a second base region comprising a p-type III-V semiconductor material, and a multi-quantum well structure disposed between the first base region and the second base region. The multi-quantum well structure includes at least three quantum well regions and at least two barrier regions. An electron hole energy barrier between a third of the quantum well regions and a second of the quantum well regions is less than an electron hole energy barrier between the second of the quantum well regions and a first of the quantum well regions. Methods of forming such devices include sequentially epitaxially depositing layers of such a multi-quantum well structure, and selecting a composition and configuration of the layers such that the electron hole energy barriers vary across the multi-quantum well structure.