Electron Tunneling between Vibrating Cu Atoms in a Cu Filament in a Memristive ReRAM Memory Cell

Depending on the amount of heat transport, thermal cross-talk between ReRAM cells of a crossbar array (Fig. 1) may cause permanent or transient erasure of programmed cells by a neighboring cell subject to frequent write/erase cycles. The transient erasure is explained by local temperature dependence of a 3D resistor network built of unit quantum conductance. The process of the spontaneous recovery of the electric conductivity of the conductive filament (CF) is explained as an attenuation of Cu atom vibrations in the CF with the attendant increase of electron tunneling effects for which the variation of the average tunneling distance between the vibrating Cu atoms is proportional to the square root of the absolute temperature. At high temperatures, the average tunneling distance increases, leading to a sharp decrease of the tunneling probability and, consequently, to a sharp increase in transient resistance. The thermal cross-talk allows heat to pass controllably from a neighboring cell to the target cell. The heating of the neighboring cell can be accomplished by application of frequent heating cycles, by selecting the level of compliance current level during the set process, and or by applying a low voltage ramp rate to both the set and reset operation. Here, we focus probed cells as indicated in Fig. 2 that have been set, prior to the heating of a neighboring cell and we monitor the resistance of the probed cell before and after the thermal-cross-talk with the heated cell. We observe several phenomena including a temporary erasure of the target cell and its spontaneous recovery to a preset value. Such spontaneous recovery as a function of time is shown in Fig. 3 90-110 s after the heating of the cell has ceased. The spontaneous recover is explained by 3D resistor model of the CF (see Fig. 5), consisting of identical resistors of Ro=1/Go, where Go is given by the Landauer Go=(2e2/h)×t where t is the tunneling transmission probability between two neighboring Cu atoms. The observation of quantum conductance of our memristive cell is shown in Fig. 4. The tunneling probability t depends exponentially on the local temperature T of the CF and explains the restoration of the initial resistance of the CF after the filament has cooled off. The transient and permanent erasure effects may be mitigated by the use of composite electrodes with high a thermal conductivity.