A nonvolatile memory device with a first conductor extending in a first direction and a semiconductor element above the first conductor. The semiconductor element includes a source, a drain and a channel of a field effect transistor (JFET or MOSFET). The nonvolatile memory device also includes a second conductor above the semiconductor element, the second conductor extending in a second direction. The nonvolatile memory device also includes a resistivity switching material disposed between the first conductor and the semiconductor element or between the second conductor and the semiconductor element. The JFET or MOSFET includes a gate adjacent to the channel, and the MOSFET gate being self-aligned with the first conductor.