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Memristor

K.Venkatesh

09F61A04B5

Abstract:

A Memristor ("memory resistor") is one of various kinds

of passive two-terminal circuit elements that maintain afunctional relationship between the time integrals ofcurrent

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.

I. 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-charge relationships, but Chua's theory introducesgenerality.

On April 30, 2008 a team at HP 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 innanoelectronic memories, computer logic, and

neuromorphic computer architectures.

Figure 1: Location of Memristor

II. THEORYThe memristor is formally defined as a two-terminal

element in which the magnetic flux m between the

terminals 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 simplycharge-dependent resistance. IfM(q(t)) is a constant, then

we obtain Ohm's LawR(t) = V(t)/I(t).

IfM(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

Figure 2: Memristors appearance

Figure 3: Symbol of Memristor

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 netcharge movementas longas the maximum change in q does not cause much change in

M..

Furthermore, the memristor is static if no current is

applied. IfI(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 asM(q(t)) varies little, such as under alternating

current, the memristor will appear as a resistor. IfM(q(t))

increases rapidly, however, current and power consumption

will quickly stop.

III. MAGNETIC FLUX IN A PASSIVEDEVICE:

In circuit theory, magnetic flux m typically relates toFaraday'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 a single

passive device. If the circuit is composed of passive

devices, then the total flux is equal to the sum of the flux

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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 the integral overtime of the potential drop between two points, we find that

it may readily be calculated, for example by an operational

amplifier configured as an integrator.

IV. TWO UNINTUITIVE CONCEPTS ARE ATPLAY:

Magnetic flux is generated by a resistance inopposition 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 applied voltage maybe 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 appearsinstantaneously 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, laterreleasing it as an electromotive force within the circuit.

V. PHYSICAL RESTRICTIONS ONM(Q):An applied constant voltage potential

results in uniformly increasing m. numerically, infinitememory resources, 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))Idt remains bounded but continues changing at anever-decreasing rate. Eventually, this would encounter some

kind ofquantization and 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 a certain amountof charge has passed through, or otherwise ceases to act as a

memristor.

VI. 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 ofterminals.

In this paper, Chua applied this model to empiricallyobserved phenomena, including the HodgkinHuxley model

of the axon and 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 of n state variables

describing the device. The pure memristor is a particularcase 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. Forpure memristorsfis not

an explicit function ofI.

A.Operation as a switch:For some memristors, applied current or voltage will

cause a great change in resistance. Such devices may becharacterized 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 toRoff 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 for constant V. This powercharacteristic differs fundamentally from that of a metaloxide semiconductor transistor, which is a capacitor-based

device. Unlike the transistor, the final state of the memristor

in terms of charge does notdepend 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

each off-on event would be followed by an on-off eventunder constant bias. Such a device would act as a memristor

under all conditions, but would be less practical.

B. Spintronic Memristor: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 thetwo 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 interview by IEEE Spectrum.It was stated in this interview that the proposed memristor

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was easy to construct and easily integrated on top of a

CMOS device.

C.Spin Torque Transfer Magnetoresistance:Spin Torque Transfer MRAM 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 throughthe 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 et al., MgO based

magnetic tunnel junctions 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 of w1 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).

D.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 ofnanoscale 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 thickelectrodes, 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 (seeFastionconductor),

changing the boundary between the high-resistance andlow-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 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 but rather keeps q at an upperbound and Mfixed, thus acting as a resistor until current is

reversed.

Memory applications of thin-film oxides had been anarea 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 demonstratedin 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 toimply 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 2104 cm2/(Vs) conducting silver ions at room

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

Figure 4: Titanium dioxide memristor

E.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 MemoryTechnology 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 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. It is

possible to use fast ion conductor as this passive layer,which allows to significantly decrease the ionic extraction

field.

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F.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 isbased 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. This result was anticipated in the study of spin

extraction at semiconductor/ferromagnet interfaces, but wasnot 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 ofmemristive systems.

G.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".

H.Resonant Tunneling Diode Memristor:In 1994, F. A. Buot and A. K. Rajagopal of the U.S.

Naval Research Laboratory demonstrated that a bow-tiecurrent-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.[30]This bow-tie current-voltage (I-V) characteristicis sine qua non of a 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-Vcharacteristics.

Figure 5: V-I Characteristics

I. 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 a

neural 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 10 seconds 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'smemistors 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 same time as the invention of Widrow's memistor.

VII. APPLICATIONS:A. 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.

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 a crossbar latchmemory 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 sothat 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.

http://www.physics.sc.edu/~pershin/http://physics.ucsd.edu/~diventra/http://en.wikipedia.org/wiki/Spintronichttp://en.wikipedia.org/wiki/Manganitehttp://en.wikipedia.org/wiki/Memristor#cite_note-29http://en.wikipedia.org/wiki/Memristor#cite_note-29http://en.wikipedia.org/wiki/Memristor#cite_note-29http://en.wikipedia.org/wiki/Bernard_Widrowhttp://en.wikipedia.org/wiki/Bernard_Widrowhttp://en.wikipedia.org/wiki/ADALINEhttp://en.wikipedia.org/wiki/Ted_Hoffhttp://en.wikipedia.org/wiki/Memristor#cite_note-30http://en.wikipedia.org/wiki/Memristor#cite_note-30http://en.wikipedia.org/wiki/Memristor#cite_note-30http://en.wikipedia.org/wiki/Integrated_circuithttp://en.wikipedia.org/wiki/Crossbar_latchhttp://en.wikipedia.org/wiki/Non-volatile_memoryhttp://en.wikipedia.org/wiki/Dynamic_random_access_memoryhttp://en.wikipedia.org/wiki/Crossbar_latchhttp://en.wikipedia.org/wiki/Gigabithttp://en.wikipedia.org/wiki/Alternating_currenthttp://en.wikipedia.org/wiki/Programmable_logic_devicehttp://en.wikipedia.org/wiki/Signal_processinghttp://en.wikipedia.org/wiki/Neural_networkshttp://en.wikipedia.org/wiki/Control_theoryhttp://en.wikipedia.org/wiki/Physarum_polycephalumhttp://en.wikipedia.org/wiki/Physarum_polycephalumhttp://en.wikipedia.org/wiki/Physarum_polycephalumhttp://en.wikipedia.org/wiki/Physarum_polycephalumhttp://en.wikipedia.org/wiki/Physarum_polycephalumhttp://en.wikipedia.org/wiki/Control_theoryhttp://en.wikipedia.org/wiki/Neural_networkshttp://en.wikipedia.org/wiki/Signal_processinghttp://en.wikipedia.org/wiki/Programmable_logic_devicehttp://en.wikipedia.org/wiki/Alternating_currenthttp://en.wikipedia.org/wiki/Gigabithttp://en.wikipedia.org/wiki/Crossbar_latchhttp://en.wikipedia.org/wiki/Dynamic_random_access_memoryhttp://en.wikipedia.org/wiki/Non-volatile_memoryhttp://en.wikipedia.org/wiki/Crossbar_latchhttp://en.wikipedia.org/wiki/Integrated_circuithttp://en.wikipedia.org/wiki/Memristor#cite_note-30http://en.wikipedia.org/wiki/Ted_Hoffhttp://en.wikipedia.org/wiki/ADALINEhttp://en.wikipedia.org/wiki/Bernard_Widrowhttp://en.wikipedia.org/wiki/Bernard_Widrowhttp://en.wikipedia.org/wiki/Memristor#cite_note-29http://en.wikipedia.org/wiki/Manganitehttp://en.wikipedia.org/wiki/Spintronichttp://physics.ucsd.edu/~diventra/http://www.physics.sc.edu/~pershin/

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B.Memcapacito and Meminductors:In 2009, Massimiliano Di Ventra, Yuriy Pershin and

Leon Chua co-wrote an article [41] extending the notion of

memristive systems to capacitive and inductive elements in

the form of memcapacitors and meminductors whose

properties depend on the state and history of the system.

Figure 6: Memcapacitors and Meminductors

C.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. The RAM

speed will be increase up to 30GB. The main Host servers

need high speed RAMs in their communication mechanismin 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.

Figure 7: Compact disk, Hard disk, RAM

VIII. 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 robonauttechnology.

For the development of Nano technology to Picotech.

High storage capability. In RRAM ( resistive random access memory ) We can widely use in self programming circuits, In

large storage applications.

IX. REFERENCES:[1] http://www.memristor.org/

[2] http://www.memristor.org/

[3]http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1083337

[4]http://www.pdf-searchengine.com/memristor-

pdf.html ebook_pdf

[5]http://thefutureofthings.com/news/5988/hps-

memristor-on-a-chip.html

[6]http://www.nature.com/nature/journal/v453/n7191/ful

http://en.wikipedia.org/wiki/Memristor#cite_note-40http://en.wikipedia.org/wiki/Memristor#cite_note-40http://en.wikipedia.org/wiki/Memristor#cite_note-40http://www.nature.com/nature/journal/v453/n7191/fulhttp://www.nature.com/nature/journal/v453/n7191/fulhttp://www.nature.com/nature/journal/v453/n7191/fulhttp://www.nature.com/nature/journal/v453/n7191/fulhttp://en.wikipedia.org/wiki/Memristor#cite_note-40