Log-Normal Statistics in Filamentary RRAM Devices and Related Systems

We present a phenomenological theory of the log-normal statistics commonly observed in filamentary resistive memory and related devices. Based on the central limit theorem that statistics are shown to emerge regardless of the underlying material properties when the processes are dominated by thermal activation or tunneling. That takes place in particular for the read-out resistances in the high-resistive (OFF) state, and the random telegraph noise amplitudes, but can be observed in the low-resistive (ON) state as well. We show that the statistics of switching times becomes log-normal when the switching is due to the field induced nucleation.