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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."
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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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