Memrstror

1. ABSTRACT

Since the dawn of electronics, we've had only three types of circuit component--resistors,

inductors, and capacitors. But in 1971, UC Berkeley researcher Leon Chua theorized the possibility of a

fourth type of component, one that would be able to measure the flow of electric current: the memristor.

Now, just 37 years later, Hewlett-Packard has built one. A mathematical model and a physical example

that prove the memristor's existence appear in a paper published in the April 30, 2008 issue of the

journal Nature. MEMRISTOR- A groundbreaking breakthrough in fundamental electronics!! The

memristor, a microscopic component that can "remember" electrical states even when turned off.

Memristors are basically a fourth class of electrical circuit, joining the resistor, the capacitor, and the

inductor, that exhibit their unique properties primarily within the nanoscale. the functional equivalent of

a synapse--could revolutionize circuit design. Memristors circuits lead to ultra small PCs. Williams says

these memristors can be used as either digital switches or to build a new breed of analog devices.

Memristors can be used in Signal Processing, Arithmetic Processing,Pattern Comparison, Robotics,

Artificial Intelligence and virtual reality etc.

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2. INTRODUCTION

2.1 Missing link of electronics discovered: "Memristor":

After nearly 40 years, researchers have discovered a new type of building block for electronic

circuits. And there's at least a chance it will spare you from recharging your phone every other day.

Scientists at Hewlett-Packard Laboratories in Palo Alto, California, report in Nature that a new

nanometer-scale electric switch "remembers" whether it is on or off after its power is turned off. (A

nanometer is one billionth of a meter.) Researchers believe that the memristor, or memory resistor,

might become a useful tool for constructing nonvolatile computer memory, which is not lost when the

power goes off, or for keeping the computer industry on pace to satisfy Moore's law, the exponential

growth in processing power every 18 months. You may dimly recall circuit diagrams from your middle

school science class; those little boxes with a battery on one end and a light bulb on the other. Ring any

bells? Until now, electrical engineers had only three "passive" circuit elements (those that dissipate the

energy from a power source) The capacitor accumulates electric charge; the resistor (represented by the

light bulb) resists electric current; and the inductor converts current into a magnetic field.

Fig:2.1 Fundamental Circuit Components: Resistors, Inductors, Capacitors

In 1971 researcher Leon Chua of the University of California, Berkeley, noticed a gap in that

list. Circuit elements express relationships between pairs of the four electromagnetic quantities of

charge, current, voltage and magnetic flux.

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Missing was a link between charge and flux. Chua dubbed this missing link the memristor and

created a crude example to demonstrate its key property: it becomes more or less resistive (less or more

conductive) depending on the amount of charge that had flowed through it.

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The memristor consists of two titanium dioxide layers connected to wires. When a current is

applied to one, the resistance of the other changes. That change can be registered as data, Physicist

Stanley Williams of HP Labs says that after a colleague brought Chua's work to his attention, he saw

that it would explain a variety of odd behaviors in electronic devices that his group and other nanotech

researchers had built over the years. His "brain jolt" came, he says, when he realized that "to make a

pure memristor you have to build it so as to isolate this memory function." So he and his colleagues

inserted a layer of titanium dioxide (TiO2) as thin as three nanometers between a pair of platinum layers

[see image above]. Part of the TiO2 layer contained a sprinkling of positively charged divots (vacancies)

where oxygen atoms would have normally been. They applied an alternating current to the electrode

closer to these divots, causing it to swing between a positive and negative charge.

When positively charged, the electrode pushed the charged vacancies and spread them

throughout the TiO2, boosting the current flowing to the second electrode. When the voltage reversed, it

slashed the current a million-fold, the group reports.

When the researchers turned the current off, the vacancies stopped moving, which left the

memristor in either its high- or low-resistant state. "Our physics model tells us that the memristive state

should last for years," Williams says. Chua says he didn't expect anyone to make a memristor in his

lifetime. "It's amazing," he says. "I had just completely forgotten it." He says the HP memristor has an

advantage over other potential nonvolatile memory technologies because the basic manufacturing tools

are already in place.Williams adds that memristors could be used to speed up microprocessors by

synchronizing circuits that tend to drift in frequency relative to one another or by doing the work of

many transistors at once. We will see how the textbooks choose to define it. However, there are some

good arguments for why it should be considered the Fourth Fundamental Nonlinear Circuit Element.

Chua has shown mathematically that it is not possible to construct an equivalent circuit for a memristor

using any combination of only passive nonlinear resistors, capacitors and inductors. Thus, the memristor

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represents an independent 'basis function' for constructing passive nonlinear circuits, so it has a status

similar to the nonlinear resistor, capacitor and inductor.

The figure below is an illustration of thisargument. The upper panel shows an applied voltage

sine wave (gray) versus time with the corresponding current for a resistor (blue), capacitor (red),

inductor (green) and memristor (purple). The lower figures show the current-voltage characteristics for

the four devices, with the characteristic pinched hysteresis loop of the memristor in the bottom right. It

is nearly obvious by inspection that the memristor curve cannot be constructed by combining the others.

There are also arguments that there are far more than four fundamental electronic circuit elements. In

fact, Chua has shown that there are essentially an infinite number of two-terminal circuit elements that

can be defined via various integral and differential equations that relate voltage and current to each other

[L. O. Chua, Nonlinear Circuit Foundations for Nanodevices, Part I: The Four-Element Torus. Proc.

IEEE 91, 1830-1859 (2003) – this is an interesting tutorial for the beginner], to which the memcapacitor

and eminductor belong. It comes down to whether one wants to think of all of these possible circuit

elements as being on an equal footing or choose the four lowest order relations to be a fundamental set

with a large number of higher order cousins. The memristor as a mathematical model or entity was

discovered and made rigorous by Leon Chua. Independent of and even preceding his discovery, there

were experimental observations of pinched hysteresis loops in two-terminal electrical measurements in a

variety of material systems and subsequent development of devices based on those observations.

We are not aware of any useful mathematical models presented in any of these previous works

for predicting the behavior of these devices in an electronic circuit. We never claimed to be the first to

have observed these electrical characteristics.

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Fig 2.1.2.Characterstics Of Memristror when compared with the passive components.

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3. TIMELINE OF MEMRISTOR

1960

Bernard Widrow develops a 3-terminal device called a "memistor" as a new fundamental circuit

component forming the basis of a neural network circuit called ADALINE (ADAptive LInear

NEuron).

1967

J.G. Simmons and R.R. Verderber publish an article in the Proceeding of the Royal Society of

London entitled "New conduction and reversible memory phenomena in thin insulating films."

The article notes hysteretic resistance switching effects in thin film (20-300 nm) silicon oxide

having injected gold ions. Electron trapping is suggested as the explanation for the phenomena.

1971

Leon Chua, a professor at UC Berkeley, postulates a new two-terminal circuit element

characterized by a relationship between charge and flux linkage as a fourth fundamental circuit

element in the article "Memristor-the Missing Circuit Element" published in IEEE Transactions

on Circuit Theory.

1976

Leon Chua and his student Sung Mo Kang publish a paper entitled "Memristive Devices and

Systems" in the Proceedings of the IEEE generalizing the theory of memristors and memristive

systems including a property of zero crossing in the Lissajous curve characterizing current vs.

voltage behavior.

1986

Robert Johnson and Stanford Ovshinsky receive U.S. Patent 4,597,162 describing manufacturing

of a 2-terminal reconfigurable resistance switching array based on phase changing materials.

While distinct from memristor behavior, some of the basic elements later used by Stan Williams

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group such as the use of a crossbar architecture and the basic use of a 2-terminal resistance

switch are found in this patent.

1990

S.Thakoor, A. Moopenn, T. Daud, and A.P. Thakoor publish an article entitled "Solid-state thin-

film memistor for electronic neural networks" in the Journal of Applied Physics. The article

teaches a tungsten oxide electrically reprogrammable variable resistance device but it is unclear

whether the "memistor" referred to in the title has any connection to the memristor of Chua. In

addition, the cited references of this article do not include any of Chua's publications on the

memristor so this appears to be a coincidence.

1992

Juri H. Krieger and Nikolai F. Yudanov receive RU. Patent 2,071,126 in the first describing

application of a super-ionic material with high ion mobility for creating a resistance switching

memory cell (August 27)

2006

Stanford Ovshinsky receives U.S. Patent 6,999,953 describing a neural synaptic system based on

phase change material used as a 2-terminal resistance switch. Leon Chua's original memristor

paper is cited by the U.S. Patent Office as a pertinent prior art reference but no specific reference

of connection to the memristor theory is made. (February 14)

Ju. H. Krieger and N.F. Yudanov receive U.S. Patents 6,992,323 (January 31), 7,026,702 (April

11), 7,113,420 (September 26) (assigned to Advanced Micro Devices) describing manufacturing

of a two-terminal resistance switching memory cells.

Shangquig Liu, Naijuan Wu, Alex Ignatiev, and Jianren Li publish an article entitled "Electric-

pulse-induced capacitance change effect in perovskite oxide thin films" which appears to

disclose effects similar to that of a memcapacitor. (September 11)

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2007

Juri H. Krieger and Stuart M. Spitzer receive U.S. Patent 7,157,732 (assigned to Spansion

describing manufacturing of a switchable diode with memory having a passive and active layer

with asymmetric semiconducting properties. The active layer may include conjugated polymers,

an inclusion compounds or different type of oxide that have a variable resistance based on the

movement of ions and electrons between the passive layer and the active layer. The passive layer

may be a super-ionic material that has high ion and electron mobility. (January 2)

Vladimir Bulovic, Aaron Mandell, and Andrew Perlman, receive U.S. Patent 7,183,141

(assigned to Spansion), including basic claims to methods of programming 2-terminal ionic

complex resistance switches to act as a fuse or anti-fuse. (February 27)

Gregory Snider of HP Labs receives U.S. Patent 7,203,789, assigned to Hewlett-Packard,

describing implimentations of 2-terminal resistance switches similar to memristors in

reconfigurable computing architectures. (April 10)

Gregory Snider of HP Labs publishes the article "Self-organized computation with unreliable,

memristive nanodevices" in the journal Nanotechnology discussing memristive nanodevices

useful to pattern recognition and reconfigurable circuit architectures. (August 10)

Blaise Mouttet, a graduate student at George Mason University, receives U.S. Patent 7,302,513

describing uses for 2-terminal resistance switching materials in signal processing, control

systems, communications, and pattern recognition. (November 27)

2008

Greg Snider of HP Labs receives U.S. Patent 7,359,888 (assigned to Hewlett-Packard) including

basic claims to a nanoscale 2-terminal resistance switch crossbar array formed as a neural

network. (April 15)

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Dmitri Strukov, Gregory Snider, Duncan Stewart, and Stan Williams, of HP Labs, publish an

article in Nature "The missing memristor found” identifying a link between the 2-terminal

resistance switching behavior found in nanoscale systems and Leon Chua's memristor. (May 1)

2009

Sung Hyun Jo, Kuk-Hwan Kim, and Wei Lu of the University of Michigan publish an article in

NanoLetters entitled "High-Density Crossbar Arrays Based on a Si Memristive System," which

details an amorphous silicon based memristive material capable of being integrated with CMOS

devices. (January 21)

Massimiliano Di Ventra, Yuriy V. Pershin, Leon O. Chua submit an article in arXiv.org entitled

"Circuit elements with memory: memristors, memcapacitors and meminductors" which extends

the notion of memristive systems to capacitive and inductive elements, namely capacitors and

inductors whose properties depend on the state and history of the system. (January 23, 2009)

Memristive behavior of magnetic tunnel junctions is reported by researchers from the Bielefeld

University, Germany. A combination of resistive and magnetoresistive switching leads to a

second order memristive device. The two state variables are the state of the insulating layer

(oxygen vacancy positions) and the state of the magnetic electrodes (the relative orientation of

the magnetization direction). (September 17, 2009).

2011‘

Have been running the successive characterstics based on the performance of it in the HP

Laboratory at japan

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4. MEMRISTOR

4.1 Memristor into existence:

In 1971, a University of California, Berkeley engineer predicted that there should be a fourth

element: a memory resistor, or memristor. But no one knew how to build. Now, 37 years later,

electronics have finally gotten small enough to reveal the secrets of that fourth element. The memristor,

Hewlett-Packard researchers revealed today in the journal Nature , had been hiding in plain sight all

along--within the electrical characteristics of certain nanoscale devices. They think the new element

could pave the way for applications both near- and far-term, from nonvolatile RAM to realistic neural

networks. The memristor's story starts nearly four decades ago with a flash of insight by IEEE Fellow

and nonlinear-circuit-theory pioneer Leon Chua. Examining the relationships between charge and flux in

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

called the memory resistor. 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, that would 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.

But the hypothetical device was mostly written off as a mathematical dalliance. Thirty years

later, Hewlett Packard Senior fellow Stanley Williams and his group were working on molecular

electronics when they started to notice strange behavior in their devices. ”They were doing really funky

things, and we couldn't figure out what [was going on],” Williams says. Then his HP collaborator Greg

Snider rediscovered Chua's work from 1971. ”He said, ’Hey guys, I don't know what we've got, but this

is what we want ,' ” Williams remembers. Williams spent several years reading and rereading Chua's

papers. ”It was several years of scratching my head and thinking about it.” Then Williams realized their

molecular devices were really memristors. ”It just hit me between the eyes.” 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 in nanoelectronic memories, computer logic, and neuromorphic

computer architectures.

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Fig.4.1: Symbol Of Memristor

A memristor ("memory resistor") is any of various kinds of passive two-terminal circuit

elements that maintain a functional relationship between the time integrals of current and voltage. This

function, called memristance, is similar to variable resistance. Specifically engineered memristors

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.

4.2 Different from other fundamental circuit components:

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, 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 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.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 the voltage 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.

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5.THEORY

The memristor is formally defined as a two-terminal element in which the magnetic flux Φm

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 simply charge-dependent resistance. If M(q(t)) is

a constant, then we obtain Ohm's Law R(t) = V(t)/ I(t). If M(q(t)) is nontrivial, however, the equation is

not equivalent because q(t) and M(q(t)) will vary with time. Solving for voltage as a function of time we

obtain

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

as long as charge does not vary. Of course, nonzero current implies time varying charge. Alternating

current, however, may reveal the linear dependence in circuit operation by inducing a measurable

voltage without net charge movement—as long as the maximum change in q does not cause much

change in M.

Furthermore, the memristor is static if no current is applied. If I(t) = 0, we find V(t) = 0 and M(t)

is constant. This is the essence of the memory effect.

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

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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.\

In circuit theory, magnetic flux Φm typically relates to Faraday's law of induction, which states

that the voltage in terms of electric field potential gained around a loop (electromotive force) equals the

negative derivative of the flux through the loop:

This notion may be extended by analogy to a single passive device. If the circuit is composed of

passive devices, then the total flux is equal to the sum of the flux components due to each device. For

example, a simple wire loop with low resistance will have high flux linkage to an applied field as little

flux is "induced" in the opposite direction. Voltage for passive devices is evaluated in terms of energy

lost by a unit of charge:

Observing that Φm is simply equal to the integral 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.

Two unintuitive concepts are at play:

Magnetic flux is generated by a resistance in opposition to an applied field or electromotive

force. In the absence of resistance, flux due to constant EMF increases indefinitely. The

opposing flux induced in a resistor must also increase indefinitely so their sum remains finite.

Any appropriate response to applied voltage may be called "magnetic flux."

The upshot is that a passive element may relate some variable to flux without storing a magnetic

field. Indeed, a memristor always appears instantaneously as a resistor. As shown above, assuming non-

negative resistance, at any instant it is dissipating power from an applied EMF and thus has no outlet to

dissipate a stored field into the circuit.

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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.An applied

constant voltage potential results in uniformly increasing Φm. Numerically, infinite memory 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 Φm = ∫M(q)dq = ∫M(q(t))I

dt remains bounded but continues changing at an ever-decreasing rate.

Eventually, this would encounter some kind of quantization and non-ideal behavior.

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

The device enters hysteresis once a certain amount of charge has passed through, or otherwise

ceases to act as a memristor.

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 of terminals. In this paper, Chua applied this model

to empirically observed phenomena, including the Hodgkin–Huxley 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.

where the vector w represents a set of n state variables describing the device. The pure

memristor is a particular case of these equations, namely when M depends only on charge (w=q) and

since the charge is related to the current via the time derivative dq/dt=I. For pure memristors neither R

nor f are explicit functions of I. 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 so that a graph comparing current and voltage results in a

straight line. However, for memristors a similar graph is a little more complicated. Fig. 5(a) illustrates

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the current vs. voltage behavior of memristance similar to that discussed in the paper by Stan Williams

or in this earlier study conducted in 2001 by researchers of NASA on manganite based hysteretic

resistance materials.

Fig.6.1: Current Vs Voltage Curve demonstrating hysteretic effects 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 materials. It is notable from Fig. 5(a) 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. Fig. 5(b) illustrates an idealized resistance behavior demonstrated in accordance with

Fig. 5(a) wherein the linear regions correspond to a relatively high resistance (RH) and low resistance

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

Thus for voltages within a threshold region (-VL2<V<VL1 in Fig. 5(b)) either a high or low

resistance exists for the memristor. For a voltage above threshold VL1 the resistance switches from a high

to a low level and for a voltage of opposite polarity above threshold VL2 the resistance switches back to a

high resistance.     

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Fig.6.2: Idealized Hysteresis Model Of Resistance Vs Voltage for memristance switch

Williams found an ideal memristor in titanium dioxide--the stuff of white paint and sunscreen.

Like silicon, titanium dioxide (TiO 2 ) is a semiconductor, and in its pure state it is highly resistive.

However, it can be doped with other elements to make it very conductive. In TiO 2 , the dopants don't

stay stationary in a high electric field; they tend to drift in the direction of the current. Such mobility is

poison to a transistor, but it turns out that's exactly what makes a memristor work. Putting a bias voltage

across a thin film of TiO 2 semiconductor that has dopants only on one side causes them to move into the

pure TiO 2 on the other side and thus lowers the resistance. Running current in the other direction will

then push the dopants back into place, increasing the TiO 2 's resistance.

HP Labs is now working out how to manufacture memristors from TiO 2 and other materials and

figuring out the physics behind them. They also have a circuit group working out how to integrate

memristors and silicon circuits on the same chip. The HP group has a hybrid silicon CMOS memristor

chip ”sitting on a chip tester in our lab right now,” says Williams.

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Fig 6.3: Vacancy Drift Model for TiOv(2-x) Switch (Developed by R. Stanley Williams of HP Labs, 2008)

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6. BENEFITS OF MEMRISTOR

Operating outside of 0’s and 1’s allows it to imitate brain functions.

Have great data density.

Innovating nanotechnology due to the fact that it performs better the smaller it is.

Combines the jobs of working memory and hard drives into one tiny device.

Faster and less expensive than DRAM and Flash Memory.

As non-volatile memory, memristors do not consume power when idle.

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7. CONCLUSION

We know the available RAM is implemented using capacitors & requires periodic refreshment.

But using memristor, volatile RAM can be changed into non-volatile RAM. Thus the pc can be turned

ON & OFF like a light ,This makes , possible of developing computer systems that have memories that

do not forget, consume far less power and associate information in a manner similar to that of the human

brain Cloud computing requires an IT infrastructure of hundreds of thousands of servers and storage

systems. The memory and storage systems used by today’s cloud infrastructure require significant power

to store, retrieve and protect the information of millions of web users worldwide. In contrast, a

memristor -based computer would retain its information after losing power and would not require the

boot-up process, resulting in the consumption of less power and wasted time. This functionality could

play a significant role as “cloud computing” becomes more prevalent. Thus the memristor forms a

bridge between present technology and future technology.

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8. REFERENCES

1. Bush S, "HP nano device implements memristor", Electronics Weekly 2008-05-02

2. Michael Kanellos "HP makes memory from a once-theoretical circuit" 2008-04-30 (Blog entry-

not a reliable source)

3. Chua 1971, p. 511: ... In the very special case where the memristor Φ-q curve is a straight line, ...

the memristor reduces to a linear time-invariant resistor.

4. Chua, Leon O (September 1971), "Memristor—The Missing Circuit Element", IEEE

Transactions on Circuit Theory CT-18 (5): 507–519, doi:10.1109/TCT.1971.1083337,

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

5. Tour, James M; He, Tao (2008), "Electronics: The fourth element", Nature 453: 42–43,

doi:10.1038/453042a, http://www.nature.com/nature/journal/v453/n7191/full/453042a.html

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