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MEMRISTOR

Presenters : p.manoj kumar.

Department : E.C.E

College : ESWAR COLLEGE OF ENGINEERING.

Contact : 8790161176 .

Email : popurimanoj@gmail.com.

Abstract:

A Memristor ("memory resistor") is

one of various kinds of passive two-terminal

circuit elements that maintain a functional

relationship between the time integrals of

current and voltage. This function, called

memristance, is similar to variable resistance.

Specifically engineered Memrstors provide

controllable resistance, but such devices are

not commercially available. Other devices like

batteries and varistors have memristance, but

it does not normally dominate their behavior.

The definition of the memristor is based solely

on fundamental circuit variables, similarly to

the resistor, capacitor, and inductor. Unlike

those three elements, which are allowed in

linear time-invariant or LTI system theory,

Memristor are nonlinear and may be described

by any of a variety of time-varying functions

of net charge. There is no such thing as a

generic memristor. Instead, each device

implements a particular function, wherein

either the integral of voltage determines the

integral of current, or vice versa. A linear

time-invariant memristor is simply a

conventional resistor.

Introduction:

Memristor theory was formulated and named

by Leon Chua in a 1971 paper. Chua

extrapolated the conceptual symmetry

between the resistor, inductor, and capacitor,

and inferred that the memristor is a similarly

fundamental device. Other scientists had

already used fixed nonlinear flux-chargerelationships, but Chua's theory introduces

generality.On April 30, 2008 a team at HP

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Labs announced the development of a

switching memristor. Based on a thin film of

titanium dioxide, it has a regime of operation

with an approximately linear charge-resistance

relationship. These devices are being

developed for application in nanoelectronic

memories, computer logic, and neuromorphic

computer architectures.

Theory

Memristor symbol.

The memristor is

formally defined as a two-terminal element in

which the magnetic flux m between theterminals is a function of the amount of

electric charge q that has passed through the

device. Each memristor is characterized by its

memristance function describing the charge-

dependent rate of change of flux with

charge.Noting from Faraday's law of induction

that magnetic flux is simply the time integral

of voltage, and charge is the time integral of

current, we may write the more convenient

form,It can be inferred from this that

memristance is simply charge-dependent

resistance. If M(q(t)) is a constant, then weobtain Ohm's Law R(t) = V(t)/ I(t). If M(q(t))

is nontrivial, however, the equation is not

equivalent because q(t) and M(q(t)) will vary

with time. Solving for voltage as a function of

time we obtain

This equation reveals that memristance

defines a linear relationship between current

and voltage, as long as charge does not vary.

Of course, nonzero current implies time

varying charge. Alternating current, however,

may reveal the linear dependence in circuit

operation by inducing a measurable voltage

without net charge movementas long as themaximum change in q does not cause much

change in M.Furthermore, the memristor isstatic if no current is applied. If I(t) = 0, we

find V(t) = 0 and M(t) is constant. This is the

essence of the memory effect.The power

consumption characteristic recalls that of a

resistor, I2R.As long as M(q(t)) varies little,

such as under alternating current, the

memristor will appear as a resistor. If M(q(t))

increases rapidly, however, current and power

consumption will quickly stop.

Magnetic flux in a passive device:

In circuit theory, magnetic flux m typicallyrelates to Faraday's law of induction, which

states that the voltage in terms of electric field

potential gained around a loop (electromotive

force) equals the negative derivative of the

Flux through the loop:

This notion may be extended by analogy to asingle passive device. If the circuit is

composed of passive devices, then the total

flux is equal to the sum of the flux

components due to each device. For example,

a simple wire loop with low resistance will

have high flux linkage to an applied field as

little flux is "induced" in the opposite

direction. Voltage for passive devices is

evaluated in terms of energy lostby a unit of

charge:

Observing that m is simply equal to theintegral over time of the potential drop

between two points, we find that it may

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readily be calculated, for example by an

operational amplifier configured as an

integrator.

Two unintuitive concepts are at play:

Magnetic flux is generated by aresistance in opposition to an applied

field or electromotive force. In the

absence of resistance, flux due to

constant EMF increases indefinitely.

The opposing flux induced in a resistor

must also increase indefinitely so their

sum remains finite.

Any appropriate response to appliedvoltage may be called "magnetic flux."

The upshot is that

a passive element may relate some variable to

flux without storing a magnetic field. Indeed, a

memristor always appears instantaneously as a

resistor. As shown above, assuming non-

negative resistance, at any instant it is

dissipating power from an applied EMF and

thus has no outlet to dissipate a stored field

into the circuit. This contrasts with an

inductor, for which a magnetic field stores all

energy originating in the potential across its

terminals, later releasing it as an electromotive

force within the circuit.

Physical restrictions onM(q):

An applied constant

voltage potential results in uniformly

increasing m. numerically, infinite memoryresources, or an infinitely strong field, would

be required to store a number which grows

arbitrarily large. Three alternatives avoid this

physical impossibility:

M(q) approaches zero, such that m =M(q)dq = M(q(t))I dt remainsbounded but continues changing at an

ever-decreasing rate. Eventually, this

would encounter some kind of

quantizationand non-ideal behavior.

M(q) is cyclic, so that M(q) = M(q q) for all q and some q, e.g.sin2(q/Q).

The device enters hysteresis once acertain amount of charge has passed

through, or otherwise ceases to act as a

memristor.

Memristive systems:

The memristor was

generalized to memristive systems in a 1976paper 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 this paper, Chua applied this model to

empirically observed phenomena, including

theHodgkinHuxley modelof theaxonand a

thermistor at constant ambient temperature.He also described memristive systems in terms

of energy storage and easily observed

electrical characteristics. These characteristics

match resistive random-access memory and

phase-change memory, relating the theory to

active areas of research.

In the more general concept of an n-th order

memristive system the defining equations are

where the vector w represents a set ofn state

variables describing the device. The pure

memristor is a particular case of these

equations, namely when M depends only on

charge (w=q) and since the charge is related to

the current via the time derivative dq/dt=I. For

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pure memristorsfis not an explicit function of

I.

Operation as a switch:

For somememristors, applied current or voltage will

cause a great change in resistance. Such

devices may be characterized as switches by

investigating the time and energy that must be

spent in order to achieve a desired change in

resistance. Here we will assume that the

applied voltage remains constant and solve for

the energy dissipation during a single

switching event. For a memristor to switch

fromRon to Roff in time Ton to Toff, the charge

must change by Q = QonQoff.

To arrive at the final expression, substitute

V=I(q)M(q), and then dq/V = Q/V forconstant V. This power characteristic differs

fundamentally from that of a metal oxidesemiconductortransistor, which is a capacitor-

based device. Unlike the transistor, the final

state of the memristor in terms of charge does

not depend on bias voltage.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." Another kind of

switch would have a cyclic M(q) so that eachoff-on event would be followed by an on-off

event under constant bias. Such a device

would act as a memristor under all conditions,

but would be less practical.

Spintronic Memristor:

Spintronic Memristor

Yiran Chenand 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 inanother section, creating a domain wall, aboundary 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.

This work attracted significant attention from

the electronics press, including an interviewby IEEE Spectrum.It was stated in this

interview that the proposed memristor was

easy to construct and easily integrated on top

of a CMOS device.

Spin Torque Transfer Magnetoresistance:

Spin Torque

Transfer MRAM is a well-known device that

exhibits memristive behavior. The resistanceis

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.

Additionally, as reported by Krzysteczko etal., MgO based magnetic tunnel junctions

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show memristive behavior based on the drift

of oxygen vacancies within the insulating

MgO layer (resistive switching). Therefore,

the combination of spin transfer torque and

resistive switching leads naturally to a second-order memristive system with w=(w1,w2)

where w1 describes the magnetic state of the

magnetic tunnel junction and w2 denotes the

resistive state of the MgO barrier. Note that in

this case the change ofw1 is current-controlled

(spin torque is due to a high current density)

whereas the change ofw2 is voltage-controlled

(the drift of oxygen vacancies is due to high

electric fields).

Titanium dioxide memristor:

Interest in the

memristor revived in 2008 when an

experimental solid state version was reported

by R. Stanley Williams of Hewlett Packard.

The article was the first to demonstrate that a

solid-state device could have the

characteristics of a memristor based on the

behavior of nanoscale thin films. The device

neither uses magnetic flux as the theoretical

memristor suggested, nor stores charge as a

capacitor does, but instead achieves a

resistance dependent on the history of

current.Although not cited in HP's initial

reports on their TiO2 memristor, the resistance

switching characteristics of titanium dioxide

was originally described in the 1960's.

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 oxygenvacancies drift (see Fast ion conductor),

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 reversibleby changing the direction of current. Since the

HP device displays fast ion conduction at

nanoscale, it is considered a nanoionic device.

Memristance is displayed

only when both the doped layer and depleted

layer contribute to resistance. When enough

charge has passed through the memristor that

the ions can no longer move, the device enters

hysteresis. It ceases to integrate q=Idt butrather keeps q at an upper bound and M fixed,

thus acting as a resistor until current is

reversed.

Memory applications of thin-film oxides had

been an area of active investigation for some

time. IBM published an article in 2000

regarding structures similar to that described

by Williams. Samsung has a U.S. patent for

oxide-vacancy based switches similar to that

described by Williams. Williams also has a

pending U.S. patent application related to the

memristor construction.

Although the HP

memristor is a major discovery for electrical

engineering theory, it has yet to be

demonstrated in operation at practical speeds

and densities. Graphs in Williams' original

report show switching operation at only ~1

Hz. Although the small dimensions of the

device seem to imply fast operation, the

charge carriers move very slowly, with an ion

mobility of 1010 cm2/(Vs). In comparison,the highest known drift ionic mobilities occur

in advanced superionic conductors, such as

rubidium silver iodide with about 2104cm2/(Vs) conducting silver ions at room

temperature. Electrons and holes in siliconhave a mobility ~1000 cm2/(Vs), a figure

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which is essential to the performance of

transistors. However, a relatively low bias of 1

volt was used, and the plots appear to be

generated by a mathematical model rather than

a laboratory experiment.

Polymeric memristor:

In July 2008,

Victor Erokhin and Marco P. Fontana, in

Electrochemically controlled polymeric

device: a memristor (and more) found two

years ago, claim to have developed a

polymeric memristor before the titanium

dioxide memristor more recently announced.

Juri H. Krieger and Stuart M. Spitzer publish a

paper in the IEEE Proceeding 2004 Non-

Volatile Memory Technology Symposium

entitled "Non-traditional, Non-volatile

Memory Based on Switching and Retention

Phenomena in Polymeric Thin Films". This

work describes the process of dynamic doping

of polymer and inorganic dielectric-like

materials in order to improve the switchingcharacteristics 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. It is possible to use fast ion

conductor as this passive layer, which allows

to significantly decrease the ionic extraction

field.

Spin memristive systems:

A fundamentally

different mechanism for memristive behavior

has been proposed by Yuriy V. Pershin and

Massimiliano Di Ventra in their paper "Spin

memristive systems". The authors show that

certain types of semiconductor spintronic

structures belong to a broad class of

memristive systems as defined by Chua and

Kang. 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 externalcontrol 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. This result was

anticipated in the study of spin extraction at

semiconductor/ferromagnet interfaces, but was

not described in terms of memristive behavior.

On a short time scale, these structures behave

almost as an ideal memristor. This result

broadens the possible range of applications of

semiconductor spintronics and makes a step

forward in future practical applications of the

concept of memristive systems.

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) characteristicsoccurs 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.[30] This bow-tie current-voltage (I-V) characteristic is sine qua non of a

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memristor although the term memristor is not

explicitly mentioned in their papers. No

magnetic interaction is involved in the

analysis of the bow-tie I-V characteristics.

3-terminal Memristor (Memistor):

Although the

memristor is defined in terms of a 2-terminal

circuit element, there was an implementation

of a 3-terminal device called a memistor

developed by Bernard Widrow in 1960.

Memistors formed basic components of aneural network architecture called ADALINE

developed by Widrow and Ted Hoff (who

later invented the microprocessor at Intel). In

one of the technical reports[31] the memistor

was described as follows:

Like the transistor, the memistor is a 3-

terminal element. The conductance between

two of the terminals is controlled by the time

integral of the current in the third, rather than

its instantaneous value as in the transistor.

Reproducible elements have been made which

are continuously variable (thousands of

possible analog storage levels), and which

typically vary in resistance from 100 ohms to

1 ohm, and cover this range in about 10seconds with several milliamperes of plating

current. Adaptation is accomplished by direct

current while sensing the neuron logical

structure is accomplished nondestructively by

passing alternating currents through the arrays

of memristor cells.

Since the conductance was described as being

controlled by the time integral of current as in

Chua's theory of the memristor, the memistor

of Widrow may be considered as a form of

memristor having three instead of two

terminals. However, one of the main

limitations of Widrow's memistors was that

they were made from an electroplating cell

rather than as a solid-state circuit element.

Solid-state circuit elements were required to

achieve the scalability of the integrated circuit

which was gaining popularity around the sametime as the invention of Widrow's memistor.

APPLICATIONS:

Potential applications:

Williams' solid-

state memristors can be combined into devices

called crossbar latches, which could replace

transistors in future computers, taking up a

much smaller area.

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They can also be fashioned into non-volatile

solid-state memory, which would allow

greater data density than hard drives with

access times potentially similar to DRAM,

replacing both components. HP prototyped acrossbar latch memory using the devices that

can fit 100 gigabits in a square centimeter. HP

has reported that its version of the memristor

is about one-tenth the speed of DRAM. The

devices' resistance would be read with

alternating current so that they do not affect

the stored value.

Some patents related to memristors appear to

include applications in programmable logic,signal processing, neural networks, and

control systems.

Recently, a simple electronic circuit consisting

of an LC network and a memristor was used to

model experiments on adaptive behavior of

unicellular organisms. It was shown that the

electronic circuit subjected to a train of

periodic pulses learns and anticipates the next

pulse to come, similarly to the behavior of

slime molds Physarum polycephalum

subjected to periodic changes of environment.

Such a learning circuit may find applications,

e.g., in pattern recognition.

Memcapacitors and Meminductors:

In 2009, Massimiliano Di

Ventra, Yuriy Pershin and Leon Chua co-

wrote an article [41] extending the notion ofmemristive systems to capacitive and

inductive elements in the form of

memcapacitors and meminductors whose

properties depend on the state and history of

the system.

Storage purpose:

Memristors we can use in memory storage

devices like RAM, Hard disk, Compact disk,

etc.,

The storage capacity is upto 10 peta bites. TheRAM speed will be increase up to 30GB. The

main Host servers need high speed RAMs in

their communication mechanism in which they

are using large server RAMs which are

occupying more space than the servers. It is

better to use Memristors in the storage

purpose.

Conclusions:

RRAMs can be build by different kinds of

materials.The RRAM has advantages on

today's memories.The memristor is found and

may have other applications than RRAM.For

the development in robotic as well as robonaut

technology.For the development of Nano

technology to Pico tech.High storage

capability.In RRAM ( resistive random access

memory )We can widely use in self

programming circuits.In large storage

applications.

References:

www.wikipedia.com

www.wikimedia.com

www.physicshypothesis.com

http://en.wikipedia.org/wiki/Memristor"

http://www.physicshypothesis.com/http://www.physicshypothesis.com/http://www.physicshypothesis.com/

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