Variable impedance memory element structures, methods of manufacture, and memory devices containing the same

A memory device can include at least one cathode formed in first opening of a first insulating layer; at least one anode formed in a second opening of second insulating layer, the second insulating layer being a different vertical layer than the first insulating layer; and a memory layer comprising an ion conductor layer extending laterally between the at least one anode and cathode on the first insulating layer, the ion conductor layer having a thickness in the vertical direction less than a depth of the first opening.