A memory cell including a memory element and a non-ohmic device (NOD) that are electrically in series with each other is disclosed. The NOD comprises a semiconductor based selection device operative to electrically isolate the memory element from a range of voltages applied across the memory cell that are not read voltages operative read stored data from the memory element or write voltages operative to write data to the memory element. The selection device may comprise a pair of diodes that are electrically in series with each other and disposed in a back-to-back configuration. The memory cell may be fabricated over a substrate (e.g., a silicon wafer) that includes active circuitry. The selection device and the semiconductor materials (e.g., poly-silicon) that form the selection device are fabricated above the substrate and are integrated with other thin film layers of material that form the memory cell.