A method for making a FINFET may include forming spaced apart source and drain regions in a semiconductor fin with a channel region extending therebetween. At least one of the source and drain regions may be divided into a lower region and an upper region by a dopant diffusion blocking superlattice, with the upper region having a same conductivity and higher dopant concentration than the lower region. The dopant diffusion blocking 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 gate on the channel region.