Nonstationary distributions and relaxation times in a stochastic model of memristor

We propose a stochastic model for a memristive system by generalizing known approaches and experimental results. We validate our theoretical model by experiments carried out on a memristive device based on Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti multilayer structure. In the framework of the proposed model we obtain the exact analytic expressions for stationary and nonstationary solutions. We analyze the equilibrium and non-equilibrium steady-state distributions of the internal state variable of the memristive system and study the influence of fluctuations on the resistive switching, including the relaxation time to the steady-state. The relaxation time shows a nonmonotonic dependence, with a minimum, on the intensity of the fluctuations. This paves the way for using the intensity of fluctuations as a control parameter for switching dynamics in memristive devices.