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 first contact coupled to the hyper-abrupt junction region and a second contact coupled to the substrate to define a varactor. The first and second superlattices may each include stacked groups of layers, with each group of layers comprising stacked base semiconductor monolayers defining a base semiconductor portion, and at least one non-semiconductor monolayer constrained within a crystal lattice of adjacent base semiconductor portions.