A method for making a bipolar junction transistor (BJT) may include forming a first superlattice on a substrate defining a collector region therein. The first superlattice may include a plurality of stacked groups of layers, with each group of layers comprising a plurality of 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 a base on the first superlattice, and forming a second superlattice on the base comprising a plurality of stacked groups of layers, with each group of layers comprising a plurality of 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 also include forming an emitter on the second superlattice.