Memristor Seminar Report[1]

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    2. HISTORY

    The transistor was invented in 1925 but lay dormant until finding a corporate

    champion in BellLabs during the 1950s. Now another groundbreaking electronic circuitmay be poised for the same kind of success after laying dormant as an academic curiosity

    for more than three decades.

    Hewlett-Packard Labs is trying to bring the memristor, the fourth passive circuit

    element after the resistor, and the capacitor the inductor into the electronics mainstream.

    Postulated in 1971, the memory resistor represents a potential revolution in electronic

    circuit theory similar to the invention of transistor.

    The history of the memristor can be traced back to nearly four decades ago

    when in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that

    there should be a fourth passive circuit element in addition to the other three known passive

    elements namely the resistor, the capacitor and the inductor. He called this fourth element a

    memory resistor or a memristor.

    Examining the relationship between charge, current, voltage and flux in

    resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of

    memristor. Such a device, he figured, would provide a similar relationship between

    magnetic flux and charge that a resistor gives between voltage and current. In practice, thatwould mean it acted like a resistor whose value could vary according to the current passing

    through it and which would remember that value even after the current disappeared.

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    3. NEED FOR MEMRISTOR

    A memristor is one of four basic electrical circuit components, joining theresistor, capacitor, and inductor. The memristor, short for memory resistor was first

    theorized by student Leon Chua in the early 1970s. He developed mathematical equations

    to represent the memristor, which Chua believed would balance the functions of the other

    three types of circuit elements.

    The known three fundamental circuit elements as resistor, capacitor and inductor

    relates four fundamental circuit variables as electric current, voltage, charge and magnetic

    flux. In that we were missing one to relate charge to magnetic flux. That is where the needfor the fourth fundamental element comes in. This element has been named as memristor.

    Memristance (Memory + Resistance) is a property of an Electrical Component that

    describes the variation in Resistance of a component with the flow of charge. Any two

    terminal electrical component that exhibits Memristance is known as a Memristor.

    Memristance is becoming more relevant and necessary as we approach smaller circuits, and

    at some point when we scale into nano electronics, we would have to take memristance into

    account in our circuit models to simulate and design electronic circuits properly. An ideal

    memristor is a passive two-terminal electronic device that is built to express only the

    property of memristance (just as a resistor expresses resistance and an inductor expresses

    inductance).

    However, in practice it may be difficult to build a 'pure

    memristor,' since a real device may also have a small amount of some other property, such

    as capacitance (just as any real inductor also has resistance).A common analogy for a

    resistor is a pipe that carries water. The water itself is analogous to electrical charge, the

    pressure at the input of the pipe is similar to voltage, and the rate of flow of the water

    through the pipe is like electrical current. Just as with an electrical resistor, the flow of

    water through the pipe is faster if the pipe is shorter and/or it has a larger diameter. An

    analogy for a memristor is an interesting kind of pipe that expands or shrinks when water

    flows through it. If water flows through the pipe in one direction, the diameter of the pipe

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    increases, thus enabling the water to flow faster. If water flows through the pipe in the

    opposite direction, the diameter of the pipe decreases, thus slowing down the flow of water.

    If the water pressure is turned off, the pipe will retain it most recent diameter until the

    water is turned back on. Thus, the pipe does not store water like a bucket (or a capacitor)

    it remembers how much water flowed through it.

    Possible applications of a Memristor include Nonvolatile Random Access

    Memory (NVRAM), a device that can retain memory information even after being

    switched off, unlike conventional DRAM which erases itself when it is switched off.

    Another interesting application is analog computation where a memristor will be able to

    deal with analog values of data and not just binary 1s and 0s.

    Figure 3.1 Fundamental circuit Elements and Variables.

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    4. TYPES OF MEMRISTOR

    Titanium dioxide memristor Polymeric memristor

    Spin memristive systems

    4.1 Titanium Doxide memristor:-

    Interest in the memristor revived in 2008 when an experimental solid state version

    was reported by R. Stanley Williams of Hewlett Packard. A solid-state device could not beconstructed until the unusual behavior of nanoscale materials was better understood. 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

    using a chemical mechanism.

    The HP device is composed of a thin (5 nm) titanium dioxide film between two

    electrodes. Initially, there are two layers to the 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 (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 aparticulardirection, 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 toresistance. 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 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

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    described by Williams.Samsung has a pending U.S. patent application for several oxide-

    layer 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. In comparison, the highest known drift ionic mobilities occur in advanced

    superionic conductors, such as rubidium silver iodide with about 2104 cm/(Vs)

    conducting silver ions at room temperature. Electrons and holes in silicon have a mobility

    ~1000 cm/(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 amathematical model rather than a laboratory experiment.

    4.2 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.

    4.3 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 ofmemristive 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

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    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

    application of the concept of memristive systems.

    .

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    5. MEMRISTOR THEORY AND ITS PROPERTIES

    5.1 Definition of Memristor:-

    The 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.

    Figure 5.1. Symbol of Memristor.

    Chua defined the element as a resistor whose resistance level was based on the

    amount of charge that had passed through the memristor

    5.2 Memristance:-

    Memristance is a property of an electronic component to retain its resistance level

    even after power had been shut down or lets it remember (or recall) the last resistance it

    had before being shut off.

    5.3 Theory:-

    Each memristor is characterized by its memristance function describing the charge-

    dependent rate of change of flux with charge.

    .5.3.1

    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

    ...............................5.3.2

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

    . i.e.

    V(t) = M (q(t))*I(t)............5.3.3

    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

    instantaneously varying charge. Alternating current, however, may reveal the linear

    dependence in circuit operation by inducing a measurable voltage without net charge

    movement as long as the maximum change in q does not cause much change in M.

    The power consumption characteristic recalls that of a resistor, I2R.

    ..5.3.4

    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.

    5.5 Current vs. Voltage characteristics:-

    This new circuit element shares many of the properties of resistors and shares the

    same unit of measurement (ohms). However, in contrast to ordinary resistors, in which the

    resistance is permanently fixed, memristance may be programmed or switched to different

    resistance states based on the history of the voltage applied to the memristance material.

    This phenomena can be understood graphically in terms of the relationship between the

    current flowing through a memristor and the voltage applied across the memristor.

    In ordinary resistors there is a linear relationship between current and voltage sothat a graph comparing current and voltage results in a straight line. However, for

    memristors a similar graph is a little more complicated as shown in Fig. 3 illustrates the

    current vs. voltage behavior of memristance.

    In contrast to the straight line expected from most resistors the behavior of a

    memristor appear closer to that found in hysteresis curves associated with magnetic

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    materials. It is notable from Fig. 3 that two straight line segments are formed within the

    curve. These two straight line curves may be interpreted as two distinct resistance states

    with the remainder of the curve as transition regions between these two states.

    Figure-5.2. Current vs. Voltage curve demonstrating hysteretic effects of memristance.

    Fig. 6 illustrates an idealized resistance behavior demonstrated in accordance

    with Fig.7 wherein the linear regions correspond to a relatively high resistance (RH) and

    lowresistance (RL) and the transition regions are represented by straight lines.

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    Figure 5.3 Idealized hysteresis model of resistance vs. voltage for memristance switch.

    Thus for voltages within a threshold region (-VL2

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    6. WORKING OF MEMRISTOR

    Figure 6.1 Al/TiO2 or TiOX /Al Sandwich

    The memristor is composed of a thin (5 nm) titanium dioxide film between two

    electrodes as shown in figure 5(a) above. Initially, there are two layers to the film, one of

    which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers,

    meaning that the depleted layer has a much lower resistance than the non-depleted layer.

    When an electric field is applied, the oxygen vacancies drift changing the boundary

    between the high-resistance and low-resistance layers.

    Analogy of Memristor:-

    A common analogy for a resistor is a pipe that carries water. The water itself is

    analogous to electrical charge, the pressure at the input of the pipe is similar to voltage, and

    the rate of flow of the water through the pipe is like electrical current. Just as with an

    electrical resistor, the flow of water through the pipe is faster if the pipe is shorter and/or it

    has a larger diameter.

    An analogy for a memristor is an interesting kind of pipe that expands or shrinks

    when water flows through it. If water flows through the pipe in one direction, the diameter

    of the pipe increases, thus enabling the water to flow faster. If water flows through the pipe

    in the opposite direction, the diameter of the pipe decreases, thus slowing down the flow of

    water. If the water pressure is turned off, the pipe will retain it most recent diameter until the

    water is turned back on. Thus, the pipe does not store water like a bucket (or a capacitor) it

    remembers how much water flowed through it.

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    7. POTENTIAL APPLICATIONS

    Figure7.1.showing 17 memristors in a row

    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 memristor displays fast ion conduction at nanoscale, it is

    considered a nanoionic device .Figure 5(b) shows the final memristor component

    Williams' solid-state memristors can be combined into devices called crossbarlatches, 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 latch memory using the devices that

    can fit 100 gigabits in a square centimeter. HP has reported that its version of the

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    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

    contour 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.

    7.1 MEMRISTOR-THE FOURTH BASIC CIRCUIT ELEMENT:-

    From the circuit-theoretic point of view, the three basic two-terminal circuit

    elements are defined in terms of a relationship between two of the four fundamental circuit

    variables, namely; the current i, the voltage v, the charge q, and the flux-linkage cp. Out of

    the six possible combinations of these four variables, five have led to well-known

    relationships . Two of these relationships are already given by 9 Q(t) =

    I (t) dt and O (t) = v(t) dt.

    . Three other relationships are given, respectively, by theaxiomatic definition of the three classical circuit elements, namely, the resistor (defined by

    a relationship between v and i), the inductor (defined by a relationship between cp and i),

    and the capacitor defined by a relationship between q and v). Only one relationship remains

    undefined, the relationship between o and q. From the logical as well as axiomatic points of

    view, it is necessary for the sake of completeness to postulate the existence of a fourth

    basic two-terminal circuit element which is characterized by a o-q curve.

    This element will henceforth be called the memristor because, as will be

    shown later, it behaves somewhat like a nonlinear resistor with memory. The proposed

    symbol of a memristor and a hypothetical o-q curve are shown in Fig. l(a). Using a

    ,mutated , a memristor with any prescribed o-q curve can be realized by connecting an

    appropriate nonlinear resistor, inductor, or capacitor across port 2 of an M-R mutated, an

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    M-L mutated, and an M-C mutated, as shown in Fig. l(b), (c), and (d), respectively. These

    mutators, of which there are two types of each, are defined and characterized in Table I.3

    Hence, a type-l M-R mutated would transform the VR -IR< curve of the nonlinear resistor

    f(VR, IR)=O into the corresponding o-q curve f(o,q)=O of a memristor. In contrast to this,

    a type-2 M-R mutated would transform the IR,VR curve of the nonlinear resistor

    f(IR,VR)=O into the corresponding o-q curve f(o,q) = 0 of a memristor. An analogous

    transformation is realized with an M-L mutated (M-C mutated) with respect to the ((oL,iL)

    or (iL, oL) [(vC, qC) or (qC, vC)] curve of a nonlinear inductor (capacitor).10 t

    (a) Memristor and its o-q curve.

    (b). Memristor basic realization 1: M-R mutated terminated by nonlinear Resistor R.

    (c) Memristor basic realization 2: M-L mutated terminated by nonlinear inductor L

    (d) Memristor basic realization M-C mutatedterminated by nonlinear capacitor C

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    8. FEATURES

    The reason that the memristor is radically different from the other fundamental

    circuit elements is that, unlike them, it carries a memory of its past. When you turn off thevoltage to the circuit, the memristor still remembers how much was applied before and for

    how long. That's an effect that can't be duplicated by any circuit combination of resistors,

    capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit

    element.

    8.1 New Memristor Could Make Computers Work like HumanBrains:-

    After the resistor, capacitor, and inductor comes the memristor. Researchers at HP

    Labs have discovered a fourth fundamental circuit element that can't be replicated by a11

    combination of the other three. The memristor (short for "memory resistor") is unique

    because of its ability to, in HP's words, "[retain] a history of the information it has

    acquired." HP says the discovery of the memristor paves the way for anything from instant

    on computers to systems that can "remember and associate series of events in a manner

    similar to the way a human brain recognizes patterns." Such brain-like systems would

    allow for vastly improved facial or biometric recognition, and they could be used to make

    appliances that "learn from experience."

    In PCs, HP foresees memristors being used to make new types of system memory

    that can store information even after they lose power, unlike today's DRAM. With

    memristor-based system RAM, PCs would no longer need to go through a boot process to

    load data from the hard drive into the memory, which would save time and power

    especially since users could simply switch off systems instead of leaving them in a "sleep"

    mode

    8.2 Memristors Make Chips Cheaper:-

    The first hybrid memristor-transistor chip could be cheaper and more energy

    efficient. Entire industries and research fields are devoted to ensuring that, every

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    year,computers continue getting faster. But this trend could begin to slow down as the

    components used in electronic circuits are shrunk to the size of just a few

    atoms.Researchers at HP Labs in Palo Alto, CA, are betting that a new fundamental

    electronic component--the memristor--will keep computer power increasing at this rate for

    years to come.

    They are nanoscale devices with unique properties: a variable resistance and the

    ability to remember the resistance even when the power is off.Increasing performance has

    usually meant shrinking components so that more can be packed onto a circuit. But instead,

    Williams's team removes some transistors and replaces them with a smaller number of

    memristors. "We're not trying to crowd more transistors onto a chip or into a particular

    circuit," Williams says. "Hybrid memristor-transistor chips really have the promise for

    delivering a lot more performance."12 A memristor acts a lot like a resistor but with onebig difference: it can change resistance depending on the amount and direction of the

    voltage applied and can remember its resistance even when the voltage is turned off. These

    unusual properties make them interesting from both a scientific and an engineering point of

    view. A single memristor can perform the same logic functions as multiple transistors,

    making them a promising way to increase computer power. Memristors could also prove to

    be a faster, smaller, more energy-efficient alternative to flash storage.

    8.3 Memristor as Digital and Analog:-

    A memristive device can function in both digital and analog forms, both having

    very diverse applications. In digital mode, it could substitute conventional solid-state

    memories (Flash) with high-speed and less steeply priced nonvolatile random access

    memory (NVRAM). Eventually, it would create digital cameras with no delay between

    photos or computers that save power by turning off when not needed and then turning

    back on instantly when needed.

    8.4 No Need of Rebooting:-

    The memristor's memory has consequences:The reason computers have to be

    rebooted every time they are turned on is that their logic circuits are incapable of holding

    their bits after the power is shut off. But because a memristor can remember voltages, a

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    memristor-driven computer would arguably never need a reboot. You could leave all your

    Word files and spreadsheets open, turn off your computer, and go get a cup of coffee or go

    on vacation for two weeks, says Williams. When you come back, you turn on your

    computer and everything is instantly on the screen exactly the way you left it.that keeps

    memory powered. HP says memristor-based RAM could one day replace DRAM

    altogether.

    8.5 MemristorsforNanoscaleelectronics:-

    The main objective in the electronic chip design is to move computingbeyond the

    physical and fiscal limits ofconventional silicon chips. For decades, increases in chip

    performance have come about largely byputting more and more transistors on a circuit.

    Higher densities, however, increase the problems of heat generation and defects and

    affect thebasicphysics of the devices.

    Instead of increasing the number of transistors on a circuit, we could create a

    hybrid circuit with fewer transistorsbutwith the addition ofmemristorswhichcouldadd

    functionality. Alternately, memristor technologies could enable more energy-efficient

    high-density circuits.

    9. FUTURE OF MEMRISTOR

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    Although memristor research is still in its infancy, HP

    Labs is working on a handful of practical memristor projects. And now Williams's team has

    demonstrated a working memristor-transistor hybrid chip. "Because memristors are made

    of the same materials used in normal integrated circuits," says Williams, "it turns out to be

    very easy to integrate them with transistors." His team, which includes HP researcher

    Qiangfei Xia, built a field-programmable gate array (FPGA) using a new design that

    includes memristors made of the semiconductor titanium dioxide and far fewer transistors

    than normal.Engineers commonly use FPGAs to test prototype chip designs because they

    can be reconfigured to perform a wide variety of different tasks.

    In order to be so flexible, however, FPGAs are

    large and expensive. And once the design is done, engineers generally abandon FPGAs forleaner "application-specific integrated circuits." "When you decide what logic operation

    you want to do, you actually flip a bunch of switches and configuration bits in the circuit,"

    says Williams. In the new chip, these tasks are performed by memristors. "What we're

    looking at is essentially pulling out all of the configuration bits and all of the transistor

    switches," he says. According to Williams, using memristors in FPGAs could help

    significantly lower costs. "If our ideas work out, this type of FPGA will completely change

    the balance," he says. Ultimately, the next few years could be very important for memristor

    research. Still, he predicts that memristors will arrive in commercial circuits within the next

    three years.

    Researchers say that no real barrier prevents implementing the memristor in

    circuitry immediately. But it's up to the business side to push products through to

    commercial reality. Memristors made to replace flash memory will likely appear first; HP's

    goal is to offer them by 2012. Beyond that, memristors will likely replace both DRAM and

    hard disks in the 2014-to-2016 time frame. As for memristor-based analog computers, that

    step may take 20-plus years.

    10. CONCLUSION

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    By redesigning certain types of circuits to include memristors, it is possible to

    obtain the same function with fewer components, making the circuit itself less expensive

    and significantly decreasing its power consumption. In fact, it can be hoped to combine

    memristors with traditional circuit-design elements to produce a device that does

    computation. The Hewlett-Packard (HP) group is looking at developing a memristor-based

    nonvolatile memory that could be 1000 times faster than magnetic disks and use much less

    power.

    As rightly said by Leon Chua and R.Stanley Williams (originators of memristor),

    memrisrors are so significant that it would be mandatory to re-write the existing electronics

    engineering textbooks.

    However, as experience shows, the most valuable applications of memristors will

    most likely come from some young student who learns about these devices and has an

    inspiration for something totally new recognition. You may think this is not an electrical

    topic but the linear elements are also used in every electrical circuit and my intension is to

    divert the minds of young future engineers to this memristor and to make there inventions

    in this topic. I am glad that I am directing all the engineers in the right way.

    11. BIBLIOGRAPHY

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    1. www.google.com

    2. www.wikipedia.com

    3. http://www.memristor.org/

    4. www.allaboutcircuits.com5. www.ieee.org

    CONTENTS

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    http://www.google.com/http://www.wikipedia.com/http://www.memristor.org/http://www.memristor.org/http://www.memristor.org/http://www.allaboutcircuits.com/http://www.google.com/http://www.wikipedia.com/http://www.memristor.org/http://www.allaboutcircuits.com/
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    1. Introduction 1

    2. History 23. Need for memristor 3

    4. Types of memristor 5

    5. Memristor theory 8

    6. Working of memristor 12

    7. Potential applications 13

    8. Features 16

    9. Future of memristor 19

    10. Conclusion 20

    11. Bibliography 21

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