A semiconductor device may include a substrate, an insulating layer adjacent the substrate, and a semiconductor layer adjacent a face of the insulating layer opposite the substrate. The device may further include source and drain regions on the semiconductor layer, a superlattice adjacent the semiconductor layer and extending between the source and drain regions to define a channel, and a gate overlying the superlattice. The superlattice may include a plurality of stacked groups of layers, with each group of layers including a plurality of stacked base semiconductor monolayers defining a base semiconductor portion and an energy band-modifying layer thereon. The energy band-modifying layer may include at least one non-semiconductor monolayer constrained within a crystal lattice of adjacent base semiconductor portions.