A method for making a radio frequency (RF) semiconductor device may include forming an RF ground plane layer on a semiconductor-on-insulator substrate and including a conductive superlattice. The conductive superlattice may include stacked groups of layers, with each group of layers including stacked doped base semiconductor monolayers defining a doped base semiconductor portion, and at least one non-semiconductor monolayer constrained within a crystal lattice of adjacent doped base semiconductor portions. The method may further include forming a body above the RF ground plane layer, forming spaced apart source and drain regions adjacent the body and defining a channel region in the body, and forming a gate overlying the channel region.