Nonvolatile memory cells and methods of forming the same are provided, the methods including forming a first conductor at a first height above a substrate; forming a first pillar-shaped semiconductor element above the first conductor, wherein the first pillar-shaped semiconductor element comprises a first heavily doped layer of a first conductivity type, a second lightly doped layer above and in contact with the first heavily doped layer, and a third heavily doped layer of a second conductivity type above and in contact with the second lightly doped layer, the second conductivity type opposite the first conductivity type; forming a first dielectric antifuse above the third heavily doped layer of the first pillar-shaped semiconductor element; and forming a second conductor above the first dielectric antifuse.