  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.
