A memory device can include a plurality of memory elements formed over a substrate, including a plurality of first electrodes, each having a top surface and opposing side surfaces, a plurality of second electrodes formed on different vertical levels, each aligned with a corresponding first electrode in a lateral direction, and a memory material formed between each first electrode and an adjacent second electrode, the memory material being in contact with the opposing side surfaces of each first electrode and not in contact with the top surface of the first electrodes; wherein the memory material is electrically programmable between at least two different resistance states, and the lateral direction is parallel to a top surface of the substrate.