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Scientists Create First Memristor: Missing Fourth Electronic Circuit Element By Bryan Gardiner

April 30, 2008 | 10:03 am | Categories: Uncategorized

Researchers at HP Labs have built the first working prototypes of an important newelectronic component that may lead to instant-on PCs as well as analog computers thatprocess information the way the human brain does.

The new component is called a memristor, or memory resistor. Up until today, the circuitelement had only been described in a series of mathematical equations written by LeonChua, who in 1971 was an engineering student studying non-linear circuits. Chua knewthe circuit element should exist he even accurately outlined its properties and how itwould work. Unfortunately, neither he nor the rest of the engineering community couldcome up with a physical manifestation that matched his mathematical expression.

Thirty-seven years later, a group of scientists from HP Labs has finally built real workingmemristors, thus adding a fourth basic circuit element to electrical circuit theory, onethat will join the three better-known ones: the capacitor, resistor and the inductor.

Researchers believe the discovery will pave the way for instant-on PCs, more energy-efficient computers, and new analog computers that can process and associateinformation in a manner similar to that of the human brain.

According to R. Stanley Williams, one of four researchers at HP Labs Information andQuantum Systems Lab who made the discovery, the most interesting characteristic of amemristor device is that it remembers the amount of charge that flows through it.

Indeed, Chuas original idea was that the resistance of a memristor would depend uponhow much charge has gone through the device. In other words, you can flow the chargein one direction and the resistance will increase. If you push the charge in the oppositedirection it will decrease. Put simply, the resistance of the devices at any point in time isa function of history of the device - or how much charge went through it either forwardsor backwards. That simple idea, now that it has been proven, will have profound effecton computing and computer science.
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"Part of whats going to come out of this is something none of us can imagine yet," saysWilliams. "But what we can imagine in and of itself is actually pretty cool."

For one thing, Williams says these memristors can be used as either digital switches orto build a new breed of analog devices.

For the former, Williams says scientists can now think about fabricating a new type ofnon-volatile random access memory (RAM) or memory chips that dont forget whatpower state they were in when a computer is shut off.

Thats the big problem with DRAM today, he says. "When you turn the power off on yourPC, the DRAM forgets what was there. So the next time you turn the power on youvegot to sit there and wait while all of this stuff that you need to run your computer isloaded into the DRAM from the hard disk."

With non-volatile RAM, that process would be instantaneous and your PC would be inthe same state as when you turned it off.

Scientists also envision building other types of circuits in which the memristor would beused as an analog device.

Indeed, Leon himself noted the similarity between his own predictions of the propertiesfor a memristor and what was then known about synapses in the brain. One of hissuggestions was that you could perhaps do some type of neuronal computing usingmemristors. HP Labs thinks thats actually a very good idea.

"Building an analog computer in which you dont use 1s and 0s and instead useessentially all shades of gray in between is one of the things were already working on,"says Williams. These computers could do the types of things that digital computersarent very good at - like making decisions, determining that one thing is larger than

another, or even learning.While a lot of researchers are currently trying to write a computer code that simulatesbrain function on a standard machine, they have to use huge machines with enormousprocessing power to simulate only tiny portions of the brain.

Williams and his team say they can now take a different approach: "Instead of writing acomputer program to simulate a brain or simulate some brain function, were actuallylooking to build some hardware based upon memristors that emulates brain-likefunctions," says Williams.

Such hardware could be used to improve things like facial recognition technology, and

enable an appliance to essentially learn from experience, he says. In principle, thisshould also be thousands or millions of times more efficient than running a program ona digital computer.

The results of HP Labs teams findings will be published in a paper in todays editionofNature. As far as when we might see memristors actually being used in actualcommercial devices, Williams says the limitations are more business oriented thantechnological.


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Ultimately, the problem is going to be related to the time and effort involved in designinga memristor circuit, he says. "The money invested in circuit design is actually muchlarger than building fabs. In fact, you can use any fab to make these things right now,but somebody also has to design the circuits and theres currently no memristor model.The key is going to be getting the necessary tools out into the community and finding a

niche application for memristors. How long this will take is more of a business decisionthan a technological one."

Read More http://www.wired.com/gadgetlab/2008/04/scientists-prov/#ixzz10ThGZ0vJ
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MemristorFrom Wikipedia, the free encyclopedia

This article may need to be updated. Please update this article to reflect

recent events or newly available information, and remove this template when

finished. Please see thetalk page for more information. (September 2010)

An array of 17 purpose-built oxygen-depletedtitanium dioxidememristors built atHP Labs, imaged by an atomic force microscope. The wires

are about 50 nm, or 150 atoms, wide.[1]Electric currentthrough the memristors shifts the oxygen vacancies, causing a gradual and persistent

change inelectrical resistance.[2]

A memristor/ m mr st r/ (aportmanteau of "memory resistor") is apassive two-terminal circuit element in which

the resistance is a functionof the time history of thecurrentandvoltage through the device. Memristor theory was

formulated and named byLeon Chuain a 1971 paper. [3]

On April 30, 2008 a team atHP Labs announced the development of a switching memristor. Based on a thin

film oftitanium dioxide, it has a regime of operation with an approximately linear charge-resistance relationship.[4][5]

[6] These devices are being developed for application in nanoelectronicmemories, computer logic,

andneuromorphiccomputer architectures.[7]
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[edit]Background

Memristor symbol.

A memristor is a passive two-terminal electronic component for which the resistance (dV/dI) is proportional to the

amount of charge that has flowed through the circuit. When current flows in one direction through the device, theresistance 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. [8].

More generally, a memristor is a two-terminal component in which the resistance depends on the integral of the input

applied to the terminals, rather than on the instantaneous value of the input at the terminals. Since the element

"remembers" the amount of current that has passed through it in the past, it was tagged by Chua with the name

"memristor." A general memristor is any of various kinds of passive two-terminal circuit elements that maintain

afunctional relationshipbetween thetime integrals ofcurrent and voltage. This function, called memristance, is

similar to variableresistance. Specifically engineered memristors provide controllable resistance, but such devices

are not commercially available. Other devices such asbatteries andvaristorshave memristance, but it does not

normally dominate their behavior. The definition of the memristor is based solely on fundamental circuit variables,

similar to theresistor, capacitor, and inductor. Unlike those three elements, which are allowed in linear time-invariant

orLTI system theory, memristors 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 particularfunction,

wherein either the integral of voltage determines the integral of current, or vice versa. A linear time-invariant

memristor is simply a conventional resistor.[9]

In his 1971 paper, memristor theory was formulated and named byLeon Chua,[3] extrapolating the conceptual

symmetry between the resistor, inductor, and capacitor, and inferring that the memristor is a similarly fundamental

device. Other scientists had already proposed fixed nonlinear flux-charge relationships, but Chua's theory introduced

generality.

Like other two-terminal components (e.g., resistor, capacitor, inductor), real-world devices are never purely

memristors ("ideal memristor"), but will also exhibit some amount of capacitance, resistance, and inductance.
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[edit]Theory

The memristor is essentially a two-terminal variable resistor, with resistance dependent upon the amount of

charge q that has passed between the terminals.

To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term M(q), which

characterizes the device, and write it as a differential equation.

where Q is defined by Q = dI/dt, and m is defined by V = dm/dt. Note that the above table covers all meaningful

ratios ofI, Q, m, and V. No device can relate Ito Q, orm to V, because Iis the integral ofQ and m is the integral

ofV.

The variable m ("magnetic flux linkage") is a generalized from the circuit characteristic of an inductor. It does

notrepresent a magnetic field here, and its physical meaning is discussed below. The symbol m may simply be

regarded as the integral of voltage over t ime.[10]

Thus, the memristor is formally defined[3] as a two-terminal element in which the flux linkage (or integral of voltage)

m between the terminals is a function of the amount ofelectric chargeQ 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.

Substituting that magnetic flux is simply the time integral of voltage, and charge is the time integral of current, we maywrite the more convenient form

It can be inferred from this that memristance is simply charge-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

This equation reveals that memristance defines a linear relationship between current and voltage, as long as Mdoes

not vary with charge. 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 the maximum change in q does not cause much change in M.
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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 as M(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.

[edit]Derivation of "flux linkage" in a passive device

In aninductor, magnetic flux m relates toFaraday's law of induction, which states that the energy to push charges

around a loop (electromotive force, in units of Volts) equals the negative derivative of the flux through 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 "flux linkage" varying with

opposite sign. For example, a high-valued resistor will quickly produce flux linkage. The term "flux linkage" is

generalized from the equation for inductors, where it represents a physical magnetic flux: If 1 Volt is applied across

an inductor for 1 second, then there is 1 Vs of flux linkage in the inductor, which represents energy stored in a

magnetic field that may later be obtained from it. The same voltage over the same time across a resistor results in the

same flux linkage (as defined here, in units of V-s), but the energy is dissipated, rather than stored in a magnetic field

there is no physical magnetic field involved as a link to anything. Voltage for passive devices is evaluated in terms

of energy lostby a unit of charge, so generalizing the above equation simply requires reversing the sense of EMF.

Observing that m is simply equal to the integral over time of the potential drop between two points, we find that it

may readily be calculated, for example by anoperational amplifierconfigured as anintegrator. Two unintuitive

concepts are at play:

Magnetic flux is defined here as generated by a resistance in

opposition to an applied field or electromotive force. In

the absence of resistance, flux due to constant EMF, and

the magnetic fieldwithin the circuit, would increase indefinitely.

The opposing flux induced in a resistor must also increase

indefinitely so the sum with applied EMF remains finite.
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Any appropriate response to applied voltage may be called

"magnetic flux," as the term is used here.

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.

[edit]Physical restrictions on M(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))Idtremains bounded but continues changing at an ever-

decreasing rate. Eventually, this would encounter some kind

ofquantizationand non-ideal behavior.

M(q) is periodic, so that M(q) = M(q q) for all q and some

q, e.g. sin2(q/Q).

The device enters hysteresisonce a certain amount of charge

has passed through, or otherwise ceases to act as a memristor.

[edit]Memristive systems

The memristor was generalized to memristive systems in a 1976

paper by Leon Chua.[11] Whereas a memristor has

mathematicallyscalarstate, a system has vectorstate. 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 theHodgkin-Huxley model of theaxon and

athermistorat constant ambient temperature. He also described
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memristive systems in terms of energy storage and easily observed

electrical characteristics. These characteristics match resistive

random-access memoryandphase-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 vectorw represents a set ofn state variables

describing the device.[12] Thepure memristor is a

particular case of these equations, namely

when Mdepends only on charge (w=q) and since thecharge is related to the current via the time derivative

dq/dt=I. Forpure memristors fis not an explicit function

ofI.[12]

[edit]Operation as a switch

For some memristors, 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 adesired 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 from Ron 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/Vfor

constant V. This power characteristic differs

fundamentally from that of a metal oxide

semiconductortransistor, which is a capacitor-

based device. Unlike the transistor, the final state
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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."[13] Another kind of

switch would have a cyclic M(q) so that each off-

on event would be followed by an on-offevent

under constant bias. Such a device would act as a

memristor under all conditions, but would be less

practical.

[edit]Implementations

[edit]Titanium dioxide memristor

Interest in the memristor revived in 2008 when an

experimental solid state version was reported

by R. Stanley WilliamsofHewlett Packard.[14][15]

[16] 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 usesmagnetic 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 1960s.[17]

The HP device is composed of a thin

(50nm)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 ofoxygenatoms. The
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oxygen vacancies act ascharge 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

(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

reversible by changing the direction of current.

[5] Since the HP device displays fast ion conduction

at nanoscale, it is considered a nanoionic device.

[18]

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=Idtbut rather keeps q at an upper

bound and Mfixed, 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.

[19]Samsunghas a U.S. patent for oxide-vacancy

based switches similar to that described by

Williams.[20] Williams also has a pending U.S.

patent application related to the memristor

construction.[21]

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 ~1Hz. Although the
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small dimensions of the device seem to imply fast

operation, the charge carriers move very slowly,

with an ionmobility of 1010 cm2/(V*s). In

comparison, the highest knowndriftionic mobilities

occur in advanced superionic conductors, such

as rubidium silver iodidewith about 2104 cm2/

(V*s) conducting silver ions at room temperature.

Electrons and holes in silicon have a mobility

~1000 cm2/(V*s), 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.

[5]

In April 2010, HP labs announced that they had

practical memristors working at 1ns switching

times and 3 nm by 3 nm sizes, with electron/hole

mobility of 1m/s[22], which bodes well for the future

of the technology.[23] At these densities it could

easily rival the current sub-25 nm flash

memorytechnology.

[edit]Polymeric memristor

In July 2008, Victor Erokhin and Marco P. Fontana,

in Electrochemically controlled polymeric device: a

memristor (and more) found two years ago,

[24] claim to have developed a polymeric memristor

before the titanium dioxide memristor more

recently announced.

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" [25] at the IEEE

Non-Volatile Memory Technology Symposium,

describing the process of dynamic doping of

polymer and inorganic dielectric-like materials in
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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

conductoras this passive layer, which allows to

significantly decrease the ionic extraction field.

[edit]Spin memristive systems

[edit]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.[26]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.

This work attracted significant attention from the

electronics press, including an interview by IEEE

Spectrum.[27]

[edit]Spin Torque Transfer

Magnetoresistance

Spin Torque TransferMRAM is a well-known

device that exhibits memristive behavior. The

resistance is dependent on the relative spin

orientation between two sides of amagnetic tunnel

junction. This in turn can be controlled by the spin
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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.[28]

Additionally, as reported by Krzysteczko et al.,

[29]MgO basedmagnetic 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 magneticstate of the magnetic tunnel junction

and w2denotes 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).

[edit]Spin Memrisitive System

A fundamentally different mechanism for

memristive behavior has been proposed byYuriy

V. PershinandMassimiliano Di Ventrain their

paper "Spin memristive systems".[30]The authors

show that certain types of

semiconductorspintronicstructures belong to a

broad class of memristive systems as defined by

Chua and Kang.[11] 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
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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,[31]but was

not described in terms of memristive behavior. On

a short time scale, these structures behave almost

as an ideal memristor.[3]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.

[edit]Manganite memristive systems

Although not described using the word

"memristor", a study was done of bilayer oxide

films based onmanganitefor non-volatile memory

by researchers at the University of Houston in

2001.[32]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".

[edit]Resonant tunneling diode

memristor

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

Naval Research Laboratory demonstrated[33] 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, inagreement with the published experimental results.

[34] This 'bow-tie' current-voltage (I-V) characteristic

is characteristic of a memristor although the term

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

of the 'bow-tie' I-V characteristics.

[edit]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 byBernard Widrow in 1960.

Memistors formed basic components of a neural

network architecture calledADALINE developed

by Widrow and Ted Hoff(who later invented the

microprocessor at Intel). In one of the technical

reports[35] 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 memistor

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
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cell rather than as a solid-state circuit element.

Solid-state circuit elements were required to

achieve the scalability of the integrated

circuitwhich was gaining popularity around the

same time as the invention of Widrow's memistor.

A Google Knol article suggests that the Floating

Gate MOSFETas well as other 3-terminal

"memory transistors" may be modeled using

memristive systems equations.[36]

[edit]Potential applications

Williams' solid-state memristors can be combined

into devices called crossbar latches, which couldreplace transistors in future computers, taking up a

much smaller area.

They can also be fashioned intonon-volatile solid-

state memory, which would allow greater data

density than hard drives with access times

potentially similar toDRAM, replacing both

components.[37]HP prototyped a crossbar

latch memory using the devices that can fit100gigabitsin a square centimeter, and has

designed a highly scalable 3D design (consisting

of up to 1000 layers or 1petabitper cm3).[7] HP has

reported that its version of the memristor is

currently about one-tenth the speed of DRAM.

[38] The devices' resistance would be read

withalternating current so that the stored value

would not be affected.[39]

Some patents related to memristors appear to

include applications inprogrammable logic,

[40] signal processing,[41] neural networks,

[42] and control systems.[43]
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memristors data

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