Date of Award

Fall 2022

Document Type

Open Access Dissertation


Physics and Astronomy

First Advisor

Yuriy Pershin


Resistance random access memory (ReRAM) cells are emerging passive components showing great promise for applications in non-volatile storage, in-memory computing, and neuromorphic circuits, to name a few. Various experimental ReRAM cells have demonstrated excellent characteristics. This includes nanoscale size, short read and write times, and small energy requirements needed to manipulate the information. The main obstacles preventing the widespread adoption of ReRAM technology are significant device-to-device and cycle-to-cycle variability.

In essence, ReRAM cells are resistors with memory whose state (resistance) can be changed by an applied signal such as voltage. Many models were developed for describing their response. These range from the ideal memristor model – loosely adequate but responsible for the name used by many authors – to multi-parameter memristive models to stochastic differential equation based models. In this thesis, after a short introduction, a novel memristive model is presented that was developed based off of the master equation. Various implementations and simulations of stochastic ReRAM cells (memristors, for short) and their circuits will be given using the master equation model. Finally, a link to a very prominent physics model, the Ising model, will be developed.The work of this dissertation focuses primarily on the modeling of stochastic memristors and their potential application to the Ising model. The contributions are three-fold:

1. A new probabilistic model for stochastic memristors is created by use of the master equation for the first time. This model is solved for a variety of binary stochastic memristor based circuits numerically, as well as analytically.

2. The approach to simulate binary and multi-state stochastic memristors under the master equation model has also been developed in the SPICE environment. SPICE being a general purpose software that allows for the simulation of a wide range of circuits.

3. Finally, a circuit composed of stochastic memristor-resistor units is constructed to act as an electronic analog of the Ising model. The results for numerical simulations of the distribution of network configurations have excellent agreement with the statistical probabilities of the Ising Hamiltonian. A key feature of this realization is the simultaneous co-existence of ferromagnetic and anti-ferromagnetic interactions between two neighboring spins – an extraordinary property not available in nature. The ability to realize both ferromagnetic and antiferromagnetic ordering in the resistance states of stochastic memristors is shown.

This work has resulted in two published manuscripts [29, 26] and a conference paper [28]. The most recent paper has been accepted for publication [27]. There have also been contributions to experimental work on a novel approach to the memristor fabrication [44].


© 2022, Vincent James Dowling

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