A nonvolatile memory cell comprising a diode formed of semiconductor material can store memory states by changing the resistance of the semiconductor material by application of a set pulse (decreasing resistance) or a reset pulse (increasing resistance.) In preferred embodiments, set pulses are applied with the diode under forward bias, while reset pulses are applied with the diode in reverse bias. By switching resistivity of the semiconductor material of the diode, a memory cell can be either one-time programmable or rewriteable, and can achieve two, three, four, or more distinct data states.