A semiconductor device may include a semiconductor substrate and at least one metal oxide semiconductor field-effect transistor (MOSFET). The MOSFET may include spaced apart source and drain regions on the semiconductor substrate, and a superlattice including a plurality of stacked groups of layers on the semiconductor substrate between the source and drain regions. The superlattice may have upper portions extending above adjacent upper portions of the source and drain regions, and lower portions contacting the source and drain regions so that a channel is defined in lower portions of said superlattice. Furthermore, each group of layers of the superlattice may include 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. A gate may overly the superlattice.