Time series statistical analysis: A powerful tool to evaluate the variability of resistive switching memories

Abstract

Time series statistical analyses (TSSA) have been employed to evaluate the variability of resistive switching memories, and to model the set and reset voltages for modeling purposes. The conventional procedures behind time series theory have been used to obtain autocorrelation and partial autocorrelation functions and determine the simplest analytical models to forecast the set and reset voltages in long series of resistive switching processes. To do so, and for the sake of generality in our study, a wide range of devices have been fabricated and measured. Different oxides and electrodes have been employed, including bilayer dielectrics in devices such as:

Resistive Switching and Charge Transport in Laser-Fabricated Graphene Oxide Memristors: A Time Series and Quantum Point Contact Modeling Approach

“…The Autocorrelation (ACF) and Partial Autocorrelation functions (PACFs) have been calculated and represented in Figure 3 (see also Supplementary Materials). As can be observed, the degree of correlation between the measurements of previous cycles is very high with respect to other technologies (see, for instance, Reference [24] for other technologies with transition metal oxides as a dielectric).…”

“…The TSSA has been employed to characterize the statistical features of the device operation variables through a long RS series [24]. In particular, the resistances in the LRS and HRS have been studied.…”

“…We have employed TSSA to analytically describe the dependencies of the LRS and HRS resistances on previous cycles throughout the complete RS series (see in the Supplementary Material a summary of the steps needed to develop a TSSA model). The general expression employed was based on an Autoregressive (AR) approach [24], as seen in Equation (1):R LRS/HRS(t) = Φ 1 × R LRS/HRS(t-1) + Φ 2 × R LRS/HRS(t-2) + … + Φ p × R LRS/HRS(t-p) + ε t where t stands for the cycle number within a long resistive switching series. In this modeling technique, the order ( p ) is linked to the physics governing RS process in these devices.…”

“…The device variability has also been considered in this study, specifically by using Time Series Statistical Analysis (TSSA) [24,25,26,27]. From the statistical viewpoint, information can be extracted that is related to the correlation of successive RS cycles and the inherent stochasticity of RS memristors operation.…”

Incorporating Variability of Resistive RAM in Circuit Simulations Using the Stanford–PKU Model

“…analysing the degree of variability in LRS, HRS, V SET , and V RESET cycle-to-cycle and device-to-device; and including it in the model. Therefore, our approach is agnostic to the cause of variability 2 , and, the inherent correlation of variability observed in devices (V SET , V RESET exhibited correlation between consecutive cycles [29] and a similar phenomenon was observed in HRS [30]). We pursued this approach due to the following reasons:…”