A two-terminal memory cell including a Schottky metal-semiconductor contact as a non-ohmic device (NOD) allows selection of two-terminal cross-point memory array operating voltages that eliminate “half-select leakage current” problems present when other types of non-ohmic devices are used. The NOD structure can comprise a “metal/oxide semiconductor/metal” or a “metal/lightly-doped single layer polycrystalline silicon.” The memory cell can include a two-terminal memory element including at least one conductive oxide layer (e.g., a conductive metal oxide—CMO, such as a perovskite or a conductive binary oxide) and an electronically insulating layer (e.g., yttria-stabilized zirconia—YSZ) in contact with the CMO. The NOD can be included in the memory cell and configured electrically in series with the memory element. The memory cell can be positioned in a two-terminal cross-point array between a pair of conductive array lines (e.g., a bit line and a word line) across which voltages for data operations are applied.