A nonvolatile memory cell comprising doped semiconductor material and a diode can store memory states by changing the resistance of the doped semiconductor material by application of a set pulse (decreasing resistance) or a reset pulse (increasing resistance.) Set pulses are of short duration and above a threshold voltage, while reset pulses are longer duration and below a threshold voltage. In some embodiments multiple resistance states can be achieved, allowing for a multi-state cell, while restoring a prior high-resistance state allows for an rewriteable cell. In some embodiments, the diode and a switchable memory formed of doped semiconductor material are formed in series, while in other embodiments, the diode itself serves as the semiconductor switchable memory element.