[Paper Review] The Memory-Conservation Theory of Memristance

Ella Gale|arXiv (Cornell University)|Jun 16, 2011

Advanced Memory and Neural Computing6 references4 citations

TL;DR

This paper proposes a memory-conservation theory of memristance that resolves the long-standing inconsistency between Chua's memristor definition and the Strukov memristor model by identifying the magnetic flux in Chua's equation as arising from the motion of oxygen vacancies (non-electronic charge carriers) in TiO₂. By modeling the ions' magnetostatics and separating their dynamics from electronic conduction, the theory shows the Strukov memristor is a true Chua memristor with a single state variable (ion boundary position w), linking device physics directly to memristor theory for the first time.

ABSTRACT

The memristor, the recently discovered fundamental circuit element, is of great interest for neuromorphic computing, nonlinear electronics and computer memory. It is usually modelled either using Chua's equations, which lack material device properties, or using Strukov's phenomenological model (or models derived from it), which deviates from Chua's definitions due to the lack of a magnetic flux term. It is shown that by modelling the magnetostatics of the memory-holding ionic current (oxygen vacancies in the Strukov memristor), the memristor's magnetic flux can be identified as the flux arising from the ions. This leads to a novel theory of memristance consisting of two components: 1. A memory function which describes how the memristance, as felt by the ions, affects the conducting electrons located in the `on' part of the device; 2. A conservation function which describes the time-varying resistance in the `off' part of the device. This model allows for a straight-forward incorporation of the ions within the electronic theory and relates Chua's constitutive definition of a memristor with device material properties for the first time.

Motivation & Objective

• To resolve the inconsistency between Chua’s constitutive definition of a memristor and the phenomenological Strukov model, which lacks a physical origin for magnetic flux.
• To identify the physical source of magnetic flux in the memristor, which has been missing in prior models.
• To demonstrate that the Strukov memristor satisfies Chua’s definition of a memristor by showing it depends on a single state variable (w), the boundary position of the doped TiO₂₋ₓ region.
• To unify electronic conduction with ionic dynamics by introducing a two-system model: one for electrons and one for ions.
• To provide a physically grounded, material-property-based explanation of memristance that enables future device design.

Proposed method

• Model the magnetostatics of oxygen vacancies (non-electronic charge carriers) in the TiO₂ memristor to identify their contribution to magnetic flux.
• Separate the system into two subsystems: the electronic system (conducting electrons) and the magnetic system (ions and their flux).
• Define a memory function that describes how the ion-induced resistance affects electron flow, based on the ion boundary position w.
• Define a conservation function that models the time-varying resistance in the 'off' region due to ion movement, linking it to the total resistance R_tot.
• Express total resistance R_tot as a function of w only, proving the system is a Chua memristor with a single state variable.
• Use the derived equations to show that the magnetic flux φ in Chua’s equation dφ = M(q)dq arises from the ionic current and its associated magnetic field.

Experimental results

Research questions

• RQ1 What physical mechanism generates the magnetic flux required by Chua’s memristor definition in the Strukov memristor?
• RQ2 Why does the Strukov model, which lacks a magnetic flux term, still exhibit memristive behavior such as a pinched hysteresis loop?
• RQ3 Can the memristor be shown to satisfy Chua’s definition of a fundamental circuit element with a single state variable, despite the presence of two charge carriers?
• RQ4 How can the motion of oxygen vacancies be consistently incorporated into the electronic theory of memristance?
• RQ5 What is the relationship between the ion boundary position w and the state variable q in Chua’s equation?

Key findings

• The magnetic flux in Chua’s memristor equation arises from the magnetostatics of moving oxygen vacancies in the TiO₂, not from electronic currents.
• The memory function is defined by the resistance felt by electrons due to the ion boundary position w, which modulates the effective conductance.
• The conservation function describes the time-varying resistance in the 'off' region due to ion movement, contributing to the total resistance R_tot.
• The total resistance R_tot depends only on the single state variable w, confirming the Strukov memristor as a true Chua memristor.
• The model is experimentally verified and provides a physically consistent link between device material properties (oxygen vacancies) and memristor theory.
• The theory resolves the long-standing issue of missing magnetic flux in the Strukov model by identifying the ionic current as the source of flux, satisfying Chua’s constitutive equation.