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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.