Memristor is a passive two-terminal electrical component envisioned as a fundamental non-linear circuit

element relating charge and magnetic flux linkage. The memristor is currently under development by a team at

Hewlett Packard.

When current flows in one direction through the device, the electrical resistance increases; and when current

flows in the opposite direction, the resistance decreases. When the current is stopped, the component retains the

last resistance that it had, and when the flow of charge starts again, the resistance of the circuit will be what it was

when it was last active. It has a regime of operation with an approximately linear charge-resistance relationship as

long as the time-integral of the current stays within certain bounds.

Memristor theory was formulated and named by Leon Chua in a 1971 paper. In 2008, a team at HP Labs

announced the development of a switching memristor based on a thin film of titanium dioxide. These devices are

being developed for application in nanoelectronics memories, computer logic, and neuromorphic computer

architectures. In October 2011, the same team announced the commercial availability of memristor technology

within 18 months, as a replacement for Flash, SSD, DRAM and SRAM.

WHAT IS MEMRISTOR?

Derivation of "flux linkage" in a passive device

In an inductor, magnetic flux Φm relates to Faraday's law of induction, which states that the energy topush charges around a loop (electromotive force, in units of Volts) equals the negative derivative of the fluxthrough the loop:

This notion may be extended by analogy to a single device. Working against an accelerating force(which may be EMF, or any applied voltage), a resistor produces a decelerating force, and an associated "fluxlinkage" varying with opposite sign. For example, a high-valued resistor will quickly produce flux linkage. Theterm "flux linkage" is generalized from the equation for inductors, where it represents a physical magneticflux: If 1 Volt is applied across an inductor for 1 second, then there is 1 V·s of flux linkage in theinductor, which represents energy stored in a magnetic field that may later be obtained from it. The samevoltage over the same time across a resistor results in the same flux linkage (as defined here, in units ofV·s), but the energy is dissipated, rather than stored in a magnetic field — there is no physical magnetic fieldinvolved as a link to anything. Voltage for passive devices is evaluated in terms of energy lost by a unit ofcharge, so generalizing the above equation simply requires reversing the sense of EMF.

Observing that Φm is simply equal to the integral over time of the potential drop between twopoints, we find that it may readily be calculated, for example by an operational amplifier configured as anintegrator.

Physical restrictions on M(q)

M(q) is physically restricted to be positive for all values of q (assuming the device is passive and does not become superconductive at some q). A negative value would mean that it would perpetually supply energy when operated with alternating current.

Memristive systems

The memristor was generalized to memristive systems in a 1976 paper by Leon Chua. Whereas a memristor has mathematically scalar state, a system has vector state. The number of state variables is independent of, and usually greater than, the number of terminals.

In the more general concept of an n-th order memristive system the defining equations are

where the vector w represents a set of n state variables describing the device

Operation as a switch

The type of memristor described by Williams ceases to be ideal after switching over its

entire resistance range and enters hysteresis, also called the "hard-switching regime".

Titanium dioxide memristor

The HP device is composed of a

thin (50 nm) titanium dioxide film between two

5 nm thick electrodes, one Ti, the other Pt.

Initially, there are two layers to the titanium

dioxide film, one of which has a slight depletion

of oxygen atoms. The oxygen vacancies act as

charge carriers, meaning that the depleted

layer has a much lower resistance than the

non-depleted layer. When an electric field is

applied, the oxygen vacancies drift ,changing

the boundary between the high-resistance and

low-resistance layers. Thus the resistance of

the film as a whole is dependent on how much

charge has been passed through it in a

particular direction, which is reversible by

changing the direction of current. Since the HP

device displays fast ion conduction at

nanoscale, it is considered as a nanoionic

device.

Polymeric memristor

In 2004, Juri H. Krieger and Stuart M. Spitzer published a paper

"Non-traditional, Non-volatile Memory Based on Switching and Retention

Phenomena in Polymeric Thin Films" at the IEEE Non-Volatile Memory

Technology Symposium, describing the process of dynamic doping of polymer

and inorganic dielectric-like materials in order to improve the switching

characteristics and retention required to create functioning nonvolatile memory

cells. Described is the use of a special passive layer between electrode and

active thin films, which enhances the extraction of ions from the electrode.

Spin memristive system

Spintronic Memristor

Yiran Chen and Xiaobin

Wang, researchers at disk-drive

manufacturer Seagate Technology, in

Bloomington, Minnesota, described

three examples of possible magnetic

memristors in March, 2009 in IEEE

Electron Device Letters. In one of the

three, resistance is caused by the spin

of electrons in one section of the

device pointing in a different direction

than those in another section, creating

a "domain wall", a boundary between

the two states. Electrons flowing into

the device have a certain spin, which

alters the magnetization state of the

device. Changing the magnetization, in

turn, moves the domain wall and

changes the device's resistance.

Spin Torque Transfer Magnetoresistance

Spin Torque Transfer Magnetoresistance is a well-known device that

exhibits memristive behavior. The resistance is dependent on the relative

spin orientation between two sides of a magnetic tunnel junction. This in turn

can be controlled by the spin torque induced by the current flowing through

the junction. However, the length of time the current flows through the

junction determines the amount of current needed, i.e., the charge flowing

through is the key variable.

The mechanism of memristive

behavior in such structures is based

entirely on the electron spin degree of

freedom which allows for a more

convenient control than the ionic transport

in nanostructures. When an external

control parameter (such as voltage) is

changed, the adjustment of electron spin

polarization is delayed because of the

diffusion and relaxation processes causing

a hysteresis-type behavior.

A fundamentally different mechanism for memristive behavior has been proposed by

Yuriy V. Pershin and Massimiliano Di Ventra in their paper "Spin memristive systems".

Spin Memristive System

Manganite memristive systems

Although not described using the word "memristor", a study was

done of bilayer oxide films based on manganite for non-volatile memory by

researchers at the University of Houston in 2001. Some of the graphs

indicate a tunable resistance based on the number of applied voltage

pulses similar to the effects found in the titanium dioxide memristor

materials described in the Nature paper "The missing memristor found

Resonant tunneling diode memristor

In 1994, F. A. Buot and A. K. Rajagopal of the U.S. Naval Research Laboratory

demonstrated that a 'bow-tie' current-voltage (I-V) characteristics occurs in AlAs/GaAs/AlAs

quantum-well diodes containing special doping design of the spacer layers in the source and

drain regions, in agreement with the published experimental results. This 'bow-tie' current-

voltage (I-V) characteristic is characteristic of a memristor although the term memristor was

not explicitly used in their papers. No magnetic interaction is involved in the analysis of the

'bow-tie' I-V characteristics.

Potential applications

Some patents related to memristors appear to

include applications in programmable logic, signal

processing, neural networks, and control systems.

Memristive devices can be potentially used for stateful

logic implication, allowing a replacement for CMOS-

based logic computation. Several early works in this

direction is reported.

Memristor Milestones

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