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.

翻译：阻变随机存取存储器（RRAM）因其被普遍认为是下一代高密度非易失性存储器的有力候选者，正受到工业界和学术界的广泛研究。考虑到阻变背后机制的随机性，本文开发了一种基于函数数据分析的新技术，以精确建模阻变存储器器件特性。基于Karhunen-Loève展开的函数主成分分析（FPCA）被用于获取复位过程的正交分解，该分解以不相关的标量随机变量表示。随后，仅利用一个变量即可精确描述器件电流，提出了一种从电路仿真角度极具吸引力的建模方法。新方法通过引入一种概率分布，允许模拟用于模型实现的主要参数，从而全面描述这些器件的随机变异性。本文对技术背后的数学理论进行了严谨阐述，并解释其在广泛实验测量中的应用。