A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories

Abstract

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance.