The Fourth Element: Characteristics, Modelling, and Electromagnetic Theory of the Memristor

TL;DR

This paper reviews the characteristics, modeling, and electromagnetic theory of memristors, highlighting their potential in nanoelectronics, reconfigurable circuits, and their foundational basis in Maxwell's equations.

Contribution

It provides comprehensive mathematical and SPICE models of memristors and discusses their electromagnetic foundations and applications.

Findings

Memristors enable high-density, low-area integrated circuits.

Mathematical and SPICE models for memristors are developed.

Electromagnetic theory underpins memristor operation and design.

Abstract

In 2008, researchers at HP Labs published a paper in {\it Nature} reporting the realisation of a new basic circuit element that completes the missing link between charge and flux-linkage, which was postulated by Leon Chua in 1971. The HP memristor is based on a nanometer scale TiO$_2$ thin-film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and nonvolatile RAM (NVRAM), they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application specific integrated circuits (ASICs) and field programmable gate arrays (FPGAs). A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for Integrated Circuits (ICs). This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.