A method for making a semiconductor device may include forming at least one double-barrier resonant tunneling diode (DBRTD) by forming a first doped semiconductor layer, and forming a first barrier layer on the first doped semiconductor layer and including a superlattice. The superlattice may include stacked groups of layers, each group of layers including 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. The method may further include forming an intrinsic semiconductor layer on the first barrier layer, forming a second barrier layer on the intrinsic semiconductor layer, and forming a second doped semiconductor layer on the second superlattice layer.