Phase-type distributions for studying variability in resistive memories

Abstract

A new statistical approach has been developed to analyze Resistive Random Access Memory (RRAM) variability. The stochastic nature of the physical processes behind the operation of resistive memories makes variability one of the key issues to solve from the industrial viewpoint of these new devices. The statistical features of variability have been usually studied making use of Weibull distribution. However, this probability distribution does not work correctly for some resistive memories, in particular for those based on the Ni/HfO 2 /Si structure that has been employed in this work. A completely new approach based on phase-type modeling is proposed in this paper to characterize the randomness of resistive memories operation. An in-depth comparison with experimental results shows that the fitted phase-type distribution works better than the Weibull distribution and also helps to understand the physics of the resistive memories. • Reliability analysis of switching parameters in Resistive Random Access Memories (RRAMS) is developed. • The lack of fit of the Weibull model is shown with data of voltage up to the conductive filament failure (Vreset). • A new statistical modeling of Vreset based on phase-type distributions (PHDs) is introduced. • Estimation and selection of parameters of the PHD via EM algorithm provide the Erlang distribution (ED) as the best fit. • The ED has two parameters with a clear physical interpretation.