Modeling and Simulation of Correlated Cycle-to- Cycle Variability in the Current-Voltage Hysteresis Loops of RRAM Devices

Resistive RAMs or memristors are nowadays considered serious candidates for the implementation of energy efficient and scalable neuromorphic computing systems. However, a major drawback of this technology is the instability of the device current-voltage (I-V) characteristic as is clearly revealed by the so-called cycle-to-cycle (C2C) variability. This lack of complete reproducibility is a consequence of the spontaneous or induced morphological changes of the filamentary conducting structure occurring at atomic level. Variability is an essential issue any compact model for the conduction characteristics of RRAM devices should be able to cope with to be considered realistic. In this work, a thorough investigation of the C2C variability in the I-V loops of HfO₂-based memristive structures was carried out with the aim of incorporating this information into the equations of the Dynamic Memdiode Model. From the compact modeling viewpoint, C2C correlation effects are achieved using model parameters expressed as mean-reverting stochastic processes driven by Wiener noise (Ornstein-Uhlenbeck process). The direct and indirect links between the random behavior of the model parameters and the observable magnitudes (high and low resistance states, set and reset voltages, etc.) are discussed. The agreement between simulation and experimental results is statistically assessed using the Wasserstein's distance metric.