Crossover From Deterministic to Stochastic Nature of Resistive-Switching Statistics in a Tantalum Oxide Thin Film

We study the voltage dependence of the SET time statistics of bipolar resistive switching in a tantalum oxide thin film. Weibull analysis reveals that the SET time statistics exhibit a crossover from deterministic to stochastic nature in a single cell as the amplitude of the applied voltage is lowered. While the Joule heating effect has a general contribution to the SET physics in both deterministic and stochastic cases, the magnitude of the positive feedback cycle of the Joule heating determines the statistical nature. Sufficient feedback effect under a voltage of large amplitude increases the SET probability with time, resulting in the SET time distribution with a deterministic nature. When amplitude of the applied voltage is small, on the other hand, the feedback effect is weak hence the SET process is controlled by randomness of the cell condition. In this case, the SET time is totally unpredictable hence its statistics has a stochastic nature. Since the crossover between the deterministic and stochastic regimes is found to occur based on the electric field rather than the current, we argue that it stems from a field-driven redox reaction at the tantalum oxide/tantalum interface.