A method for making a semiconductor device may include forming a hyper-abrupt junction region above a substrate and including a first semiconductor layer having a first conductivity type, a first superlattice layer on the first semiconductor layer, a second semiconductor layer on the first superlattice layer and having a second conductivity type different than the first conductivity type, and a second superlattice layer on the second semiconductor layer. The method may further include forming a gate dielectric layer on the second superlattice layer of the hyper-abrupt junction region, forming a gate electrode on the gate dielectric layer, and forming spaced apart source and drain regions adjacent the hyper-abrupt junction region.