In the present invention, a metal oxide or nitride compound which is a wide-band-gap semiconductor abuts a silicon, germanium, or alloy of silicon and/or germanium of the opposite conductivity type to form a p-n heterojunction. This p-n heterojunction can be used to advantage in various devices. In preferred embodiments, one terminal of a vertically oriented p-i-n heterojunction diode is a metal oxide or nitride layer, while the rest of the diode is formed of a silicon or silicon-germanium resistor. For example, a diode may include a heavily doped n-type silicon region, an intrinsic silicon region, and a nickel oxide layer serving as the p-type terminal. Many of these metal oxides and nitrides exhibit resistivity-switching behavior, and such a heterojunction diode can be used in a nonvolatile memory cell, for example in a monolithic three dimensional memory array.