Stochastic modeling of Random Access Memories reset transitions

TL;DR

This paper addresses the stochastic variability of resistive RAM reset transitions by applying Functional Data Analysis to current–voltage curves. Using Functional Principal Component Analysis based on the Karhunen-Loève expansion, the authors decompose reset curves into an orthogonal set of components and show that the current can be effectively modeled with a single dominant random variable, after aligning curves via curve registration and smoothing with P-splines. The method achieves a compact representation where the first principal component explains most of the variability (over 97%), and the distribution of its score is modeled with a Gumbel distribution after a simple transformation, enabling straightforward stochastic circuit simulations. The approach offers a principled, simple, and scalable way to capture device variability in RRAMs, with potential extensions to higher-order components and functional regression techniques for richer design analyses.

Abstract

Resistive Random Access Memories (RRAMs) are being studied by the industry and academia because it is widely accepted that they are promising candidates for the next generation of high density nonvolatile memories. Taking into account the stochastic nature of mechanisms behind resistive switching, a new technique based on the use of functional data analysis has been developed to accurately model resistive memory device characteristics. Functional principal component analysis (FPCA) based on Karhunen-Loeve expansion is applied to obtain an orthogonal decomposition of the reset process in terms of uncorrelated scalar random variables. Then, the device current has been accurately described making use of just one variable presenting a modeling approach that can be very attractive from the circuit simulation viewpoint. The new method allows a comprehensive description of the stochastic variability of these devices by introducing a probability distribution that allows the simulation of the main parameter that is employed for the model implementation. A rigorous description of the mathematical theory behind the technique is given and its application for a broad set of experimental measurements is explained.

Figures (8)

• Figure 1: Experimental current versus applied voltage for several set/reset transitions in a long set-reset series for devices based on a Ni/Hf$O_{2}/Si-n^{+}$ structure. Although the Ni electrode had a negative voltage applied while the substrate was grounded gonzalez2014analysis, we have considered absolute values for the applied voltage in order to ease the modeling process for curves in the first quadrant. The curves have been plotted on a logarithmic scale for the current.
• Figure 2: Experimental current versus applied voltage for a set and reset transitions for a device based on a Ni/Hf$O_{2}/Si-n^{+}$ structure. The ($V_{Reset}$, $I_{Reset}$) and ($V_{Set}$, $I_{Set}$) points are highlighted.
• Figure 3: Sample of 3057 reset curves obtained for the same device under successive set-reset cycles registered in the interval [0,1].
• Figure 4: Functional mean of reset curves and confidence bands computed as $\pm$ 2 times the standard deviation at each current.
• Figure 5: First four principal components weigh functions of the registered curves.