A threshold device including a plurality of adjacent tunnel barrier layers that are in contact with one another and are made from a plurality of different dielectric materials is disclosed. A memory plug having first and second terminals includes, electrically in series with the first and second terminals, the threshold device and a memory element that stores data as a plurality of conductivity profiles. The threshold device is operative to impart a characteristic I-V curve that defines current flow through the memory element as a function of applied voltage across the terminals during data operations. The threshold device substantially reduces or eliminates current flow through half-selected or un-selected memory plugs and allows a sufficient magnitude of current to flow through memory plugs that are selected for read and write operations. The threshold device reduces or eliminates data disturb in half-selected memory plugs and increases S/N ratio during read operations.