Probabilistic Resistive Switching Device modeling based on Markov Jump processes

TL;DR

This paper introduces a new probabilistic mathematical framework combining memristor models and Markov jump processes to accurately describe multi-state resistive switching devices over time.

Contribution

It presents a novel, generic probabilistic modeling approach for multi-state resistive switching devices using master equations, applicable to any number of states.

Findings

Qualitative and quantitative match with existing models

Effective modeling for both two-state and multi-state devices

Framework demonstrated with N=2 and N=4 states

Abstract

In this work, a versatile mathematical framework for multi-state probabilistic modeling of Resistive Switching (RS) devices is proposed for the first time. The mathematical formulation of memristor and Markov jump processes are combined and, by using the notion of master equations for finite-states, the inherent probabilistic time-evolution of RS devices is sufficiently modeled. In particular, the methodology is generic enough and can be applied for $N$ states; as a proof of concept, the proposed framework is further stressed for both two-state RS paradigm, namely $N=2$, and multi-state devices, namely $N=4$. The presented I-V results demonstrate in a qualitative and quantitative manner, adequate matching with other modeling approaches.