In a novel rewriteable nonvolatile memory cell formed above a substrate, a diode is paired with a reversible resistance-switching material, preferably a metal oxide or nitride such as, for example, NiO, Nb2O5, TiO2, HfO2, Al2O3, MgOx, CrO2, VO, BN, and AlN. In preferred embodiments, the diode is formed as a vertical pillar disposed between conductors. Multiple memory levels can be stacked to form a monolithic three dimensional memory array. In some embodiments, the diode comprises germanium or a germanium alloy, which can be deposited and crystallized at relatively low temperatures, allowing use of aluminum or copper in the conductors.