A memory device in a 3-D read and write memory includes memory cells. Each memory cell includes a resistance-switching memory element (RSME) in series with a steering element. The RSME has a resistance-switching layer, a conductive intermediate layer, and first and second electrodes at either end of the RSME. A breakdown layer is electrically between, and in series with, the second electrode and the intermediate layer. The breakdown layer maintains a resistance of at least about 1-10 MΩ while in a conductive state. In a set or reset operation of the memory cell, an ionic current flows in the resistance-switching layers, contributing to a switching mechanism. An electron flow, which does not contribute to the switching mechanism, is reduced due to scattering by the conductive intermediate layer, to avoid damage to the steering element. Particular materials and combinations of materials for the different layers of the RSME are provided.