A Seminar Report on

““MEMRISTORMEMRISTOR” ”

Submitted for partial fulfillment of requirement of award of

BACHELOR OF TECHNOLOGYDegree

In

Electronics & Communication Engineering

By

ARPIT

Roll No.:- 0706331021

G.L.A. INSTITUTE OF TECHNOLOGY AND MANAGEMENT,MATHURA

SESSION: 2010-2011

ACKNOWLEDGEMENT

Many lives & destinies are destroyed due to the lack of proper guidance,

directions & opportunities. It is in this respect I feel that I am in much better

condition today due to continuous process of motivation & focus provided by

my parents & faculty in general. The process of selection of this topic for my

seminar was a tedious job & requires care & support at all stages. I would like

to highlight the role played by individuals towards this.

I am eternally grateful to Mr. Abhay Chaturvedi, Seminar In charge, for

providing us the suggestion & opportunity to present the seminar on this topic

as a partial fulfillment of requirement of award of Bachelor of Technology

degree in Electronics & Communication Engineering.

I would like to express my sincere thanks, with deep sense of gratitude to the

librarian of Electronics Departmental Library for providing me help in the

creation of this report. I also thank all my faculty members of my institute &

friends for their valuable help in my seminar presentation.

I am also thankful to all visible & invisible hands which helped us to

complete this seminar with a feeling of success.

Arpit (0706331021)

2

3

DEPARTMENTOF

ELECTRONICS & COMMUNICATION ENGINNERING

CERTIFICATE

We hereby certify that the work which is being presented in the seminar

report entitled “MEMRISTOR” by me in the partial fulfillment of the

requirement for the award of Bachelor Of Technology Degree in Electronics &

Communication Engineering Department at G.L.A. Institute Of Technology &

Management, Mathura from Uttar Pradesh Technical University, Lucknow.

The matter embodied in this dissertation has not been submitted by me for

award of any other degree.

DATED:. 16th August,2010

This is to certify that the above statement made by the candidate is correct to the

best of my knowledge.

SUBMITTED BY

ARPIT

B.TECH. IV YEAR (EC) (MR.ABHAY CHATURVEDI)

ROLL NO.: 0706331021 SEMINAR INCHARGE

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. Thus, a Memristors resistance varies according to a devices memristance

function. 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.

The memristor--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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CONTENTS

5

LIST OF FIGURES

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INTRODUCTION

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.

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. Missing was a link between

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Fig:1 Fundamental Circuit Components: Resistors,Inductors,Capacitors

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.

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.

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Figure 2:

Fourth Fundamental Component

17 memristors in a row are visible on this AFM image. 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. Image credit: J.J. Yang / HP Labs

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.

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TIMELINE OF MEMRISTOR & MEMRISTIVE SYSTEMS DEVELOPMENT

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 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

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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)

1993

Ju. H. Krieger, N.F. Yudanov, I.K. Igumenov and S.B. Vaschenko publish an article entitled "Study of Test Structures of a Molecular Memory Element" The article describe manufacturing of a resistance switching memory cell based on a conjugated polymer. (November 3)

Katsuhiro Nichogi, Akira Taomoto, Shiro Asakawa, Kunio Yoshida of the Matsushita Research Institute receive U.S. Patent 5,223,750 describing an artificial neural function circuit formed using two-terminal organic thin film resistance switches which appear to have some properties similar to the memristor. However, no specific mention of memristors is made.

1994

F. A. Buot and A. K. Rajagopal publish in the Journal of Applied Physics an article entitled "Binary information storage at zero bias in quantum-well diodes". The article demonstrates the existence of memristor-’bow-tie’ current-voltage characteristics in AlAs/GaAs/AlAs quantum-well diodes with special spacer-layer doping design. The analysis does not involve magnetic interaction and the authors were not aware of Chua's publications on memristor. It appears that the analysis bears no direct connection to the memristor of Chua.

1998

Michael Kozicki and William West receive U.S. Patent 5,761,115 (assigned to Axon Technologies Corp. and the Arizona Board of Regents) describing the Programmable metallization cell, a device which consists of an ion conductor between two or more electrodes and whose resistance or capacitance can be programmed via the growth and dissolution of a metal "dendrite". No connection to memristors is made but the functionality is similar. (June 2)

Bhagwat Swaroop, William West, Gregory Martinez, Michael Kozicki, and Lex Akers publish a paper entitled "Programmable Current Mode Hebbian Learning Neural Network Using Programmable Metallization Cell" in the Proceedings of the IEEE International Symposium on Circuits and Systems, (vol. 3, pp 33–36, 1998), demonstrating that the complexity of an artificial synapse can be minimized by using an ionic programmable resistance device. (June 3)

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James Heath, Philip Kuekes, Gregory Snider, and Stan Williams, of HP Labs, publish a paper in Science entitled "A Defect-Tolerant Computer Architecture:Opportunities for Nanotechnology." The article discusses how the possibility of a chemically fabricated 2-terminal configurable bit element can be implemented in a crossbar configuration and provide for defect tolerant computing. No connection to memristors is yet identified. (June 12)

Ju. H. Krieger, N.F. Yudanov, I.K. Igumenov and S.B. Vaschenko publish an article entitled "Molecular Analogue Memory Cell" in the Proceedings of the Sixth Foresight Conference on Molecular Nanotechnology, Santa Clara, California, Nov. 12-15, 1998. (November 12)

2000

A. Beck, J. G. Bednorz, Ch. Gerber, C. Rossel, and D. Widmer of IBM’s Zurich Research Laboratory describe reproducable resistance switching effects in thin oxide films in the article "Reproducible switching effect in thin oxide films for memory applications" published in Applied Physics Letters. The switches are noted as having hysteretic features similar to memristors but no connection to memristors is yet noted. (July 3)

Philip Kuekes, Stanley Williams, and James Heath, of HP Labs, receive U.S. Patent 6,128,214 (assigned to Hewlett-Packard) describing a nanoscale crossbar using a rotaxane molecular structure as a 2-terminal non-linear resistance switch. The connection to the memristor theory is not yet recognized. (October 3)

2001

Shangqing Liu, NaiJuan Wu, Xin Chen, and Alex Ignatiev, researchers in the Space Vacuum Epitaxy Center of the University of Houston, present results during a non-volatile memory conference held in San Diego, California on Nov. 6-7 in the article "A New Concept for Non-Volatile Memory: The Electric Pulse Induced Resistive Change Effect in Colossal Magnetoresistive Thin Films." This appears to be the first identification of the importance of oxide bilayers to achieve a high to low resistance ratio. Data is provided indicative of the zero-crossing Lissajous curves discussed by Chua and Kang but no connection to memristors is yet noted and no explanation for the underlying mechanism is provided.

Ju. H. Krieger, S.V. Trubin S.B., Vaschenko and N.F. Yudanov publish an article entitled "Molecular analogue memory cell based on electrical switching and memory in molecular thin films". The article describe manufacturing of a two-terminal resistance switching array (8x8) based on a soluble oligomers of a conjugated polymer and an ionic complex (sodium salt). This principle allows creating memory cells with several bits per one cell and will allow working out the artificial neuron for neural networks and neural computers. (May 1)

Ju. H. Krieger and N.F. Yudanov have a pending PCT International Application PCT/RU01/00334 describing memory cells having active and passive layers may

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store multiple information bits. 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. (August 13)

2004

Ju. H. Krieger and N.F. Yudanov receive U.S. Patent 6,768,157 (July 27), 6,806,526 (October 19) 6,815,286 (November 9) (assigned to Advanced Micro Devices) describing memory cells having active and passive layers may store multiple information bits. 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.

Ju. H. Krieger and Stuart M. Spitzer publish a paper in the IEEE Proceeding 2004 Non-Volatile Memory Technology Symposium entitled "Non-traditional, Non-volatile Memory Based on Switching and Retention Phenomena in Polymeric Thin Films". This work describes the process of dynamic doping of polymer and inorganic dielectric-like materials in order to improve the switching characteristics and retention required to create functioning nonvolatile memory cells. (15-17 Nov)

2005

Darrell Rinerson, Christophe Chevallier, Steven Longcor, Wayne Kinney, Edmond Ward, and Steve Kuo-Ren Hsia receive U.S. Patent 6,870,755 (assigned to Unity Semiconductor) including basic patent claims to reversible 2-terminal resistance switching materials based on metal oxides. (March 22)

Ju. H. Krieger and N.F. Yudanov receive U.S. Patent 6,838,720 (January 4) 6,855,977 (February 15), 6,858,481 (February 22), 6,864,522 (March 8), 6,873,540 (March 29) (assigned to Advanced Micro Devices) describing manufacturing of a two-terminal resistance switching memory cells having active and passive layers. Employing self-assembly produces polymer memory cells at the precise locations of the contacts of the transistor array. The mechanism of inducing the conductivity change of the polymer by changing its doping concentration provides a promising approach to make various memory devices.

Zhida Lan, Colin Bill, and Michael A. VanBuskirk receive U.S. Patent 6,960,783 (assigned to Advanced Micro Devices) teaching a resistance switching memory cell formed from a layer of organic material and a layer of metal oxides or sulfides. The I-V characteristic (Fig. 14) is similar to the memristor but no mention of the memristor is included in the description. (November 1)

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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)

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)

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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)

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)

Blaise Mouttet, a graduate student at George Mason University, presents a poster entitled "Logicless Computational Architectures with Nanoscale Crossbar Arrays" describing analog computational architectures using 2-terminal resistance switching materials similar to the memristor at the 2008 NSTI Nanotechnology Conference and Trade Show in Boston. (June 1-5)

Victor Erokhin and M.P. Fontana claim to have developed a polymeric memristor before the titanium dioxide memristor of Stan Williams group in the article "Electrochemically controlled polymeric device: a memristor (and more) found two years ago." (July 7)

J. Joshua Yang, Matthew D. Pickett, Xuema Li, Douglas A. A. Ohlberg, Duncan R. Stewart and R. Stanley Williams publish an article in Nature Nanotechnology "Memristive switching mechanism for metal/oxide/metal nano-devices" demonstrating the memristive switching behavior and mechanism in nanodevices. (July 15)

Stefanovich Genrikh, Choong-rae Cho, In-kyeong Yoo, Eun-hong Lee, Sung-il Cho, and Chang-wook Moon, receive U.S. Patent 7,417,271 (assigned to Samsung) including basic patent claims to a bilayer oxide 2-terminal resistance switch having memristive properties. However, the connection to Leon Chua's theory is not recognized in the patent description. (August 26)

Blaise Mouttet, a graduate student at George Mason University, presents a poster entitled "Proposal for Memristors in Signal Processing" at Nano-Net 2008, a nanotechnology conference in Boston. (September 14-16)

Yu V. Pershin and M. Di Ventra of UC San Diego publish an article in Physical Review Letters entitled "Spin memristive systems: Spin memory effects in semiconductor spintronics" which notes memristive behavior in spintronics. (September 23)

Yu V. Pershin, S. La Fontaine, M. Di Ventra publish an article entitled "Memristive model of amoeba's learning" identifying memristive behavior in amoeba's learning. (October 22)

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Duncan Stewart, Patricia Beck, and Doug Ohlberg, researchers at HP Labs, receive U.S. Patent 7,443,711 (assigned to Hewlett-Packard) including basic patent claims to a tunable nanoscale 2-terminal resistance switch. (October 28)

Blaise Mouttet, a graduate student at George Mason University, receives U.S. Patent 7,447,828 including various patent claims to using 2-terminal resistance switching materials in adaptive signal processing. (November 4)

Leon Chua, Stan Williams, Greg Snider, Rainer Waser, Wolfgang Porod, Massimiliano Di Ventra, and Blaise Mouttet speak at a Symposium on Memristors and Memristive Systems held at UC Berkeley. Discussion includes the theoretical foundations of memristors and memristive systems of Leon Chua and Sung Mo Kang and the prospects of memristors for RRAM and neuromorphic electronic architectures. (November 21)

Blaise Mouttet receives U.S. Patent 7,459,933 including various patent claims to using 2-terminal hysteretic resistance materials for image processing and pattern recognition. (December 2)

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)

Blaise Mouttet published a Google knol article entitled: "An Introduction to Memimpedance and Memadmittance Systems Analysis" which is an explanation on "Circuit elements with memory: memristors, memcapacitors and meminductors" and Chua's memristor paper. (January 30, 2009)

HP Labs group publish an article entitled "A hybrid nanomemristor/transistor logic circuit capable of self-programming" in the Proceedings of the National Academy of Sciences. (February 10, 2009)

An article is published in NanoLetters entitled "Nanoparticle Assemblies as Memristors" describing a newly discovered memristor material based on magnetite nanoparticles and proposing an extended memristor model including both time-dependent resistance and time-dependent capacitance. (May 1, 2009)

Yuriy Pershin and Massimiliano Di Ventra published a preliminary article in Nature Precedings entitled "Experimental demonstration of associative memory

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with memristive neural networks" in which a memristor emulator demonstrates properties of a neural synapse. (May 19, 2009)

Scientists at NIST published an article in IEEE Electron Device Letters entitled "A Flexible Solution-Processed Memristor". NIST's memristor is based on TiO2 like HPLabs but is fabricated using a less expensive room temperature deposition process and deposits the memristive material on flexible polymer sheets with potential applications as components of biosensors or RFID. (June 3, 2009)

At the 2nd International Multi-Conference on Engineering and Technological Innovation, Blaise Mouttet of George Mason University described a memristor-based pattern recognition circuit performing an analog variation of the exclusive nor function. The circuit architecture is proposed as a way to circumvent Von Neumann's bottleneck for processors used in robotic control systems. (July 13, 2009)

The physical realization of an electrically modifiable array of memristive neural synapses is achieved by reseachers at the Gwangju Institute of Science and Technology as reported in the journal Nanotechnology. (August 4, 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)

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MEMRISTOR

When & How it came 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 one. 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

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application in nanoelectronic memories, computer logic, and neuromorphic computer

architectures.

What is it?

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.

Why it is 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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Fig.3: Symbol Of Memristor

Analogy Of Memristor with a Pipe

The classic analogy for a resistor is a pipe through which water (electricity) runs. The

width of the pipe is analogous to the resistance of the flow of current--the narrower the

pipe, the greater the resistance. Normal resistors have an unchanging pipe size. A

memristor, on the other hand, changes with the amount of water that gets pushed through.

If you push water through the pipe in one direction, the pipe gets larger (less resistive). If

you push the water in the other direction, the pipe gets smaller (more resistive). And the

memristor remembers. When the water flow is turned off, the pipe size does not change.

Such a mechanism could technically be replicated using transistors and capacitors, but,

Williams says, ”it takes a lot of transistors and capacitors to do the job of a single

memristor.”

Consequences of Memristor’s Memory

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 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.”

Mathematical Analysis Of Its Existence

Chua deduced the existence of memristors from the mathematical relationships between

the circuit elements. The four circuit quantities (charge, current, voltage, and magnetic

flux) can be related to each other in six ways. Two quantities are covered by basic physical

laws, and three are covered by known circuit elements (resistor, capacitor, and inductor),

says Columbia University electrical engineering professor David Vallancourt. That leaves

one possible relation unaccounted for. Based on this realization, Chua proposed the

memristor purely for the mathematical aesthetics of it, as a class of circuit element based

on a relationship between charge and flux.

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Fig. 4:Mathematical relation between all four basic quantities in terms of fundamental components in electronics.It list the proof of existence of “Memristor” as an elemt relating charge and flux.

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.

22

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.

Magnetic flux in a passive device

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

23

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.

Physical restrictions on M ( q )

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.

Memristive Systems

The memristor was generalized to memristive systems in a 1976 paper by Leon Chua.

Whereas a memristor has mathematically scalar state, a system has vector state. The

number of state variables is independent of, and usually greater than, the number 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.

In the more general concept of an n-th order memristive system the defining equations are

24

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.

Physics Behind Memristive Device

    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 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.

  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

25

Fig.5(a):Current Vs Voltage Curve demonstrating hysteretic effects of memristance

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.     

Chemistry Behind Memristive Device

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

26

Fig.5(b):Idealized Hysteresis Model Of Resistance Vs Voltage for memristance switch

hybrid silicon CMOS memristor chip ”sitting on a chip tester in our lab right now,” says

Williams.

Memristor: 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 a desired change in resistance. Here we will assume that

the applied voltage remains constant and solve for the energy dissipation during a single

switching event. For a memristor to switch from Ron to Roff in time Ton to Toff, the charge

must change by ΔQ = Qon−Qoff.

To arrive at the final expression, substitute V=I(q)M(q), and then ∫dq/V = ∆Q/V for

constant V. This power characteristic differs fundamentally from that of a metal oxide

semiconductor transistor, which is a capacitor-based device. Unlike the transistor, the final

state 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."

Another kind of switch would have a cyclic M(q) so that each off-on event would be

27

Fig:5(c)O Vacancy Drift Model for TiOv(2-x) Switch (Developed by R. Stanley Williams of HP Labs, 2008)

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

under all conditions, but would be less practical.

Manufacturing Techniques

One of the key fabrication advantages of the crossbar architecture is that the structure is a

well ordered, periodic and simple structure. However, to achieve nanoscale resolutions the

standard lithography approaches are insufficient. The manufacturing techniques for the

nanoscale crossbar devices developed by Hewlett-Packard include nanoimprint

lithography, which uses a stamp-like structure with nanometer resolution to transfer a

pattern of nanoscale resolution to a substrate. Additional nanoscale fabrication approaches

can include self-assembly techniques in which a mixture of polymers or other materials

can form periodic structures on a surface based on processes of energy minimalization.

These self-assembly techniques can be used to form a periodic mask structure over a metal

film which can act as a resist to control removal of metal layers in regions not covered by

the mask resulting in the desired metal nanowires required for the crossbar structure. 

 

     But while the nanoscale fabrication approches may be critical to high density memory

design, the problem of defects become more pronounced. In addition, compatibility with

conventional fabrication approaches will likely be necessary for mass production of

memristor based electronics. Several applications in pattern recognition and signal

processing, as detailed above, may in fact not yet require nanometer scale resolution to

provide competitive solutions and applications in robotics and artificial intelligence since

in these areas it is the reconfigurability of the memristor material rather than the scalability

that can provide the key benefits. Figs. 27 and 28 below illustrate a basic outline for one

possible fabrication procedure using the typical processes of film deposition, lithography,

and etching from semiconductor manufacture. In Fig. 27, a metal film, a p-doped

polysilicon layer, and an n-doped polysilicon layer are deposited on an oxidized Si wafer

and a resist film is coated and lithographically patterned followed by etching to

form electrically isolated input wiring columns of the crossbar. The p-type and n-type

polysilicon layers are included to establish a rectification layer which help to avoid

feedback within the crossbar structure. As illustrated in Fig. 28 a dielectric filler is

deposited in the etched region followed by planarization and a thin film deposition of

28

TiO2/TiO2-x or other resistance switching material. Output metal wiring perpendicular to

the input wiring is then deposited and patterned above the memristor material to complete

the crossbar structure. 

 

 

 

29

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.

Creating a Computer that never has to boot up.

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

Faster and less expensive than DRAM and Flash Memory.

Allow digital cameras to take pictures with no delay inbetween.

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

NOT PERFECT YET

Though hundreds of thousands of memristor semiconductors have already been

built, there is still much more to be perfected.

Dissipates heat when being written to or read.

Needs more defect engineering.

No design standards (rules).

Fair endurance (overlookable e.g.. Transistors).

30

POTENTIAL APPLICATIONS OF MEMRISTOR

Williams' solid-state memristors can be combined into devices called crossbar latches,

which could replace transistors in future computers, taking up a much smaller area.

They can also be fashioned into non-volatile solid-state memory, which would allow

greater data density than hard drives with access times potentially similar to DRAM,

replacing both components. HP prototyped a crossbar latch memory using the devices that

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

memristor is about one-tenth the speed of DRAM. The devices' resistance would be read

with alternating current 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 network and a memristor was

used to model experiments on adaptive behavior of unicellular organisms. It was shown

that the electronic circuit subjected to a train of periodic pulses learns and anticipates the

next pulse to come, similarly to the behavior of slime molds Physarum polycephalum

subjected to periodic changes of environment. Such a learning circuit may find

applications, e.g., in pattern recognition.

ARITHMETIC PROCESSING WITH MEMRISTORS

     Modern computational systems are based on logic gates which perform elementary

operation on bit values (0 or 1) in order to perform operations of addition, subtraction,

multiplication, etc. This has been a highly successful methodology for

computation, however it has some drawbacks. One disadvantage of logic based

computation is that for many operations data has to be repeatedly transferred between

memory and the arithmetic logic unit which can be very time consuming for some complex

computational problems. For example, multiplication is actually performed by repeated

retrieval and storage step for accumulating sums. Another disadvantage is that logic gates

are formed from transistors and are subject to the ultimate limits of miniaturization which

31

could eventually end Moore's law. Memristors could offer some solutions which may

expand the capabilities of computation beyond tranditional logic gates.

 

    One approach to using memristors in computational processes has already been

suggested by Hewlett-Packard researcher Greg Snider in his patent US 7,203,789. The

approach is based on programmable logic architectures which are similar to the designs

found in reconfigurable computing. However, ultimately his approach may have some

drawbacks in that multiple crossbar tiles need to be configured and interconnected for a

full arithmetic logic unit design and the problem of segmentation between memory and

computation components is not solved. An alternative approach may be based on a hybrid

analog/digital computational system approach.

 

    Figs. 6a-6c below show examples of a memristor crossbar array inclusing a horizontal

wire intersected by eight vertical wires in which memristor material is sandwiched

between the horizontal wire and the vertical wires. An input voltage below the threshold

necessary for altering the resistance of the memristance material is applied to the vertical

wires. Assuming that the memristor material may be approximated as a fuse (i.e. high

resistance is approximately an open circuit and low resistance is a low resistance), the total

output current in the horizontal wire may be calculated based on the ratio of the input

voltage and the parallel combination of the number of number of low resistances. Thus if

one low resistance state produces a current of I, two low resistance states will produce a

current of 2I, three low resistance states will produce a current of 3I, etc. This system is

essentially a unary analog computer and by providing the output current to and analog-to-

digital converter (ADC) a binary output can be produced.

32

 

    Fig. 7 illustrates an example of how such an analog computational system can be made

more practical and provide integration between memory and computational systems.  In

the illustrated system each column of the crossbar is configured to store the equivalent of a

binary numerical value where low resistance states are indicated as a closed connection

and high resistance states are open connections. Thus the first column stores the binary

value 0001 (=1), the second column stores the binary value 0010 (=2), the third column

stores binary value 0011 (=3), etc. Each row wire includes a weighting resistor set to be

sufficiently larger than the low resistance state of the memristance material so that each

row has an associated bit significance ranging from a least significant bit row (uppermost

row) to a most significant bit row (lowermost row). By selecting particular columns (i.e.

applying a positive voltage Vin less than the threshold necessary to alter the resistance of

the memristor material) the binary numerical values of these columns may be added

together. In the example of Fig. 7, the first, fifth, and sixth column values are summed. In

the first column only the upper row crosspoint is in a low resistance state so this

contributes a current of approximately (Vin/R). In the fifth column, the first and third row

crosspoints are in the low resistance states which contribute (V in/R + Vin/(R/4)=5Vin/R) to

the current. In the sixth column the second and third row crosspoints are in the low

resistance states which contribute (Vin/(R/2)+Vin/(R/4)=6Vin/R) to the current. The overall

current is thus (Vin/R+5Vin/R+6Vin/R=12Vin/R). Using an analog-to-digital convertor with a

33

resolution set to Vin/R the output is converted to 1100 which is the expected sum

(0001+0101+0110).

 

Note: the above description is simplified for ease of explanation. It is noted that for proper

operation a pn junction layer or rectification material would preferably be provided

between the column and row wiring to prevent feedback paths in the crossbar wiring. Also

the low resistance values of the memristor material should be compensated for by tuning of

the fixed weighting resistors (e.g. the fixed resistor R in the first row should be changed to

R-r, in the second row R/2 should be R/2 - r, etc. where r is the value of the low resistance

state). 

34

     While the above configuration has some deficiencies of its own, such as the reliance on

analog circuitry which can be more sensitive than purely digital electronics to noise

and environmental effects, it has the advantage of integrating memory with computation. If

three, four, or more numbers need to be summed the sum can be performed directly based

on binary numbers stored as resistance states in a memristor crossbar array rather than

based on a repeated storage and retrieval from a separate memory. In some applications

where the relative magnitude of a large number of possible numerical sum is of interest

this approach may be even more advantage without the necessity of analog to digital

conversion. For example, in the Travelling Salesman Problem it is desirable to optimize

the traveling path for visiting a group of cities so that each city is visited exactly once. By

defining all the possible distances between the cities and setting the binary resistance states

of each column of the memristor crossbar in accordance with these distances, the optimum

sums may be compared in accordance with the selection of the input columns. By looking

for the lowest possible output current for a set of inputs the optimum travel path can be

sought with a less reliance on processor speed.  

PATTERN COMPARISON WITH MEMRISTORS

    In conventional digital electronics comparisons between stored bit patterns and sensed

bit patterns is required for a variety of applications in information processing such as

image recognition and memory addressing. Often logic gates called Exclusive NOR

(XNOR) are used to perform individual bit comparisons to identify matching bits in a

pattern. However, such logic gates can be inefficient when dealing with large array bit

patterns associated with visual images, digitalized voice data, or other complex patterns

since each bit comparison requires its own logic circuit. A variety of computer software

tricks exist to make data comparisons more efficient but these tricks can have a detrimental

effect on the overall speed of the pattern comparison. Memristor crossbar arrays offer the

potential to bridge the gap between hardware solutions based on logic gates and software

solutions based on computing power offering faster and more efficient pattern comparison

operations. Fig. 8 below illustrates one possible configuration for such a memristor

crossbar array used for pattern comparison in which two 4x4 crossbar arrays are included

with logic inverters connected to the right crossbar array and voltage converters provided

for selective amplification of the input voltage levels. The crossbar arrays initially includes

35

memristance material configured to be at a high resistance state between the column and

row wiring (a rectification layer may also be provided to avoid feedback between

the crossbars). 

 

 

     

    Figs. 9-12 illustrate the programming (writing) of the resistance states in the memristor

crossbar in which each row is selected via a correponding output transistor. For

programming the resistance states the voltage convertor circuitry is used to amplify a

binary input logic voltage into a range sufficient for switching the memristance material

from the high resistance state to the low resistance state. For simplicity of explanation the

low resistance state is approximated as a short circuit.

 

    In Fig. 9 below the first crossbar rows are written with resistance states corresponding to

a 1010 in the left crossbar array and a 0101 in the right crossbar array (1=low resistance

state, 0=high resistance state).  

 

36

 

    In Fig. 10 below the second crossbar rows are written with resistance states

corresponding to a 0111 in the left crossbar array and a 1000 in the right crossbar array

(1=low resistance state, 0=high resistance state).  

 

 

37

    In Fig. 11 below the third crossbar rows are written with resistance states corresponding

to a 1100 in the left crossbar array and a 0011 in the right crossbar array (1=low resistance

state, 0=high resistance state).

 

  

    In Fig. 12 below the fourth crossbar rows are written with resistance states

corresponding to a 0010 in the left crossbar array and a 1101 in the right crossbar array

(1=low resistance state, 0=high resistance state).  

 

38

 

    After storing the resistance states in the crossbar rows the voltage converter can be

swiched to a comparison mode by reducing the amplification factor so as to be below the

threshold which alters the memristance material. By selecting all of the rows an

input binary pattern van be compared to all of the rows simultaneously. In Fig. 13 the bit

pattern 0111 is input to the crossbar array producing relative current outputs for each row

in accordance with the number of matching resistance states. For example, the first row

stores 1010/0101 which only matches a single bit with the input pattern 0111 and transmits

a single unit of current from the left crossbar array. In contrast row 2 stores 0111/1000 and

thus transmits three units of current from the left crossbar array and one unit of current

from the right crossbar array providing a total of four units of current. Thus the magnitude

of the output currents between the input bit pattern and the stored bit pattern for each row

provide an indication which is somewhat related to the Hamming distance used in

information theory (i.e. a higher current magnitude corresponds to a lower Hamming

distance).  

 

 

39

 

    The output currents of Fig. 13 may be transmitted to a comparison circuit with a

threshold set in accordance with the degree of precision desired between the input and

stored bit pattern. A reduced threshold allowing for a certain percentage of bit errors could

be useful to a variety of applications such as voice recognition and image sensing in which

the closest match rather than exact match between bit patterns is important. In other

applications, such as robotics, a motor or actuator may be connected to each row output

and the input pattern may correspond to a control word used to generate a response for the

motor or actuator of a corresponding row. Artificial intelligence is another potential

application in which the digitial input patterns may correspond to visual or audio cues used

to "train" the memristor crossbar arrays as indicated in Figs.8-12. At a subsequent time

these same visual or audio cues can then be used to solicit the trained responses in the

comparison mode.  

 

    This type of crossbar architecture could of course be scaled up to crossbar arrays having

hundreds or even thousands of rows and columns allowing for comparison of more

lengthy bit patterns and a higher degree of parallel processing.

40

PROGRAMMABLE SIGNAL FILTERS WITH MEMRISTORS

    As discussed in the above section on signal processing with memristors, operational

amplifiers combined with memristors can produce some useful applications in

reconfigurable signal processing. These capacities may be extending by including

capacitors in the circuit construction. Capacitors are electrical elements that have the

property that the current flow through the capacitor is based on both the magnitude of the

voltage signal applied across the capacitor as well as the frequency of the voltage signal.

For low frequency signals, capacitors act as high impedance elements which means that

very little current is transmitted and the capacitors act like an open circuit. For high

frequency signals, capacitors act as low impedance elements which means that the

capacitors act as a short circuit allowing for a lot of current flow. At intermediate

frequencies capacitors act to tune the magnitude of the transferred current. These

capabilites provide capacitors with the ability to selectively transmit signals which is very

useful to applications in communications and control systems. 

 

    The combination of capacitors with operational amplifiers is already known to produce

some very useful circuit designs. For example, the circuit of Fig. 14 illustrated below

utilizes a resistor R1 as a negative feedback element of the operational amplifier and a

capacitor C1 as an input element. In this case the magnitude of the ratio between the output

voltage    Vout(t) and input voltage Vin(t) is equal to the ratio of the impedance of the

resistor R1 and capacitor C1. For capacitors this impedance is expressable in terms of the

input frequency f and capacitance C1 as 1/(2f x C1). Thus the magnitude of the

ratio Vout(t)/Vin(t) =  2f x R1 x C1 and the transmission ratio is proportional to the

frequency. This type of behavior is used to create a high pass filter useful for

communication applications. In control systems applications this same circuit is used as a

differentiator in which case the output signal is related to the mathematical derivative of

the input signal.

 

41

 

 

    Fig. 15 provides another example of the use of capacitors with operational amplifiers in

which the positions of the capacitor and resistor of Fig. 14 is reversed. In this case the

magnitude of the ratio of the voltage output to input is equal to the ratio of the impedances

of C1 to R1 which is expressed as 1/(2f x R1 x C1). In this case the circuit acts to transmit

low frequency signals and attenuate high frequency signals and is thus referred to as a low

pass filter. In control systems applications this same circuit acts as an integrator in which

case the output signal is related to the mathematical integral of the input signal.  

 

42

        While the above circuits are useful to communication and control systems there are a

variety of circumstances where variations in temperature or other conditions can change

the characteristics of the resistors and capacitors. In addition selective tuning of the

resistors and capacitors is desirable for communication applications. While variable

resistors and capacitors may be used to serve this function the analog behavior of these

devices can be difficult to regulate with digital precision. This is where memristance

crossbars can offer an advantage. Fig. 16 below illustrates an operational amplifier

connected to an array of fixed capacitors having values set in multiples of 2. Memristor

crossbar arrays are connected between the capacitor arrays and the inverting input of the

operational amplifier which may provide for programmable interconnections for selected

capacitors. This configuration allow for reconfiguration of the circuit to act as an amplifier

(Fig. 17), a high pass filter (Fig. 18), or a low pass filter (Fig. 19) by applying the

appropriate voltages via memristance programming circuitry. In addition, different

capacitors or combinations of capacitors can be included in the circuit via a reconfiguration

of the memristance states to tune the cutoff frequency of the circuit. Assumming that the

low resistance state of the memristance material is suitably low so as to approximated by a

short circuit, the capacitors may be treated as being in parallel when multiple crosspoints

are set to a low resistance state. Since the capacitors are set in multiples of two this results

in the possibility of creating a wide range of cutoff frequency for a low or high pass circuit

according to the digital pattern stored in the crossbars. For example, Fig. 17 would

43

correspond to the state (10000 10000), Fig. 18 would correspond to the state (01000

10000), and Fig. 19 would correspond to the state (10000 01000). The resolution of such a

system would be set by the minimum capacitor values (C/8 in the examples of Fig. 16-18)

but could be increased by adding more columns to the crossbar arrays with associated

capacitors. Connecting two of the circuits of Fig. 16 in series can provide for a

programmable bandpass filter in which case one of the filters can set the lowpass cutoff

frequency and the other can set the highpass cutoff frequency.  In another application a

reconfigurable PID controller may be implemented by connecting three circuits such as

Fig. 16 in parallel. This can provide for a tunable control system that can adjust itself to

different conditions or applications and may be particularly useful in adaptive robotic

systems.   

 

 

 

 

44

MEMRISTORS AND ARTIFICIAL INTELLIGENCE

        In the last sentence of the Nature article “The Missing Memristor Found” a mention is

made of the synapse-like function of memristors. This capability of memristors may open

the door to physical implementations of neural networks. One possible construction of

such a neural network in the form of crossbar arrays has already been worked out by Greg

Snider, a co-author of the Nature article, who has patented the basic design (US Patent

7,359,888). While neural networks themselves are nothing new, the implementation is

typically in the form of software to simulate the behavior of synapse networks. However,

software solutions to Artificial Intelligence have a fundamental drawback in that the data

needs to be transferred between a memory, which stores the software data, and a processor,

which computes based on the data. This requirement of data transfer generates an intrinsic

delay and inefficiency which limits all software based A.I. A physical neural network can

overcome this deficiency be merging data storage and processing into a single electronic

device.

    More general ways are also conceivable to implement A.I. using memristor crossbars in

the form of morphware. Conventionally electronic systems may broadly be defined into

two distinct classes - hardware systems and software systems. Hardware-based electronic

systems are formed using specialized circuitry and are typically faster than software-based

electronics but lack adaptability. In contrast, software-based systems, which are based on

programs run on a general purpose microprocessor, are more adaptable but lack the speed

of specialized hardware. Morphware bridges the gap between hardware and software by

using the 0’s and 1’s, which typically defines the software instructions, to instead define

the interconnections between basic circuit elements forming the hardware. Programmable

logic systems such as FPGAs already take advantage of this approach and memristor

crossbar arrays can improve the adaptability of such systems.

    Fig. 20 illustrates one possible implementation of a memristor crossbar array as

morphware. The crossbar array is formed from a vertical array of p-doped wiring and a

horizontal array of n-doped wiring. Memristance material is formed between the two

wiring arrays. The p-type and n-type doping generates a diode structure at each junction of

the crossbar array which prevents feedback  paths within the crossbar and the memristance

material may be configured to a high or low resistance using programming circuitry. By

45

representing the high resistance state of a memristor material as a logic value 0 and a low

resistance state of a memristor material as a logic value 1 the crossbar effectively acts as a

binary matrix transformation on a set of input signals A, B, C, and D. The input signals A,

B, C, and D may correspond to sensory signals based on vision, hearing, touch, etc.

received from arrays of detection devices. The output signals may correspond to signals

used to actuate motors or visual/audio output devices. The particular state of the binary

crossbar matrix thus defines a particular action such as a robotic movement based on

sensory signals.

The implementation of Fig. 20 may be especially useful for A.I. when combined with

software techniques such as hill climbing or genetic algorithms. In a hill climbing

approach the resistance state of each crosspoint can be switched one at a time and the

signal outputs of the crossbars can be tested against a threshold to determine if the

behavior is improved over the previous iteration. By maintaining alterations which

improve the quality of the output and reversing alterations that diminish the quality of the

output, repeated iterations can gradually improve the behavior of the system. However, for

large crossbar arrays this method can be time consuming. For example, a moderately small

100x100 binary crossbar array having 100 input wires and 100 output wires a total of 210000

possible states (approx. equivalent to a number represented by 103000 which is 1 followed

by 3000 zeros). Programming based on genetic algorithms may be used to more quickly

optimize the binary states of the crossbar array. Genetic algorithms use steps of selection,

46

crossbreeding, and mutation on binary strings of data to “evolve” better solutions to

computational problems. When applied to the two dimensional binary resistance states of a

crossbar memristor array, signal transformations may be optimized to perform particular

tasks. The use of genetic algorithms in memristor crossbars may be further optimized by

providing communication between large numbers of memristor crossbar arrays each of

which may be representative of a “species” competing to best perform a particular task.

MEMRISTORS AND ROBOTICS

    Most robotic systems include three basic elements - sensors, actuators, and processors.

The sensors detect the surrounding environment and, depending on the complexity of the

robots design, can include simple sensors such as photodiodes, microphones, thermistors to

detect the basic light, sound, and temperature or more complex sensors such as imaging

sensors, voice recognition devices, and tactile interfaces. Actuators are a generic term for

motion inducing devices and, when applied to robotics, often take the form of motors used

for translational and/or rotary motion of the robotic system. A key problem of robotics is to

find a way to map a set of sensor signals commonly detected by the robot to appropriate

responses by the actuators. For example, if one were to design a robotic arm simulating a

human arm one could use motors to rotate a plurality of joints with one joint representing

the elbow, one joint representing the wrist, three joints representing each finger, and two

joints representing the thumb. Assuming an independent motor is used for each joint a total

of 16 motors would be required for this particular design. If one wanted to provide this

robotic hand with the ability to pick up an object it would be useful to include an imaging

sensor for the robotic system. However, in order for the robotic arm to properly respond to

the detection of an object by the imaging sensor an additional component is necessary to

process the information and generate the appropriate control signals to the

motors. Conventionally this additional component is either a microprocessor performing

under software or application specific hardware designed for a specific function. However,

software based control can have reduced reaction times due to the delay required

to transfer instructions between a memory storing the instructions and the processor.

Hardware based solutions may be faster but are less adaptable to different situations.

However, memristor based robotics may be able to bridge the gap allowing for both

47

adaptability and quick response times. One example of such an implementation is

described below.

 

 

    Fig. 21 above illustrates the basic components for a robotic system. The sensors may be

provided to detect images, sounds, temperatures, or any other desirable environmental

condition. If necessary analog-to-digital conversion may be used to digitalize these signals

and the digitalized signals may be combined in an overall bit pattern identifying the state

of the environment. This bit pattern may then be input to a sensor/memory decoder

configured as described in the prior section on pattern comparison with memristors. As

previously described, this bit pattern can be directly stored in a dual crossbar array

structure having complementary high/low resistance states. Thus during a programming or

learning stage a robotic system can "learn" different environmental condition states and

map them into the resistance states of the crossbar junctions. At a later time during a non-

programming stage (i.e. input voltage<threshold voltage for memristance switching) a

similar environmental pattern will produce maximum current output for the row having

resistance bit values that match the input binary pattern (for example in Fig. 22 row 2 is the

best match to an environmental input state of "0111"). One key benefit of this system is

that there is a certain degree of tolerance to bit errors when a large number of columns are

used to construct the crossbar and the associated environmental bit state. For example, if

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10 bits are unmatched in a 100 column crossbar this would still provide 90% of maximum

current output. This flexibility which focuses on a closest rather than exact match may be

very useful to pattern recognition.  

 

 

 

    In order to properly control the movement of a robotic system the actuation timing of the

motors used to drive movement should be sequenced in a particular fashion. In the robotic

arm example in order for the arm to pick up an object detected by a visual sensor it may

need to actuate the elbow motor first for a specific amount of time followed by the wrist

motor followed by certain finger joints, etc. In order to achieve proper sequencing matched

to the environmental input state a memristor crossbar may be configured as described in

the previous section on Artificial Intelligence applications. In this case time delay elements

may be provided between each column of the crossbar to generate an actuation sequence

for an array of motors. In the example of Fig. 23 at time t=0, motor 3 is activated, at time

t=T, motors 2 and 3 are activated, at time t=2T motors 1, 3, and 4 are activated, and at time

t=3T motor 2 is activated. The states for an appropriate sequencing may be programmed by

a user if it is easy to identify a correct pattern. However, it may be preferable to simply

configure a resistance bit pattern into the crossbar that is only an approximately good

sequence and use automated techniques such as hill climbing and genetic algorithms, as

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described in the previous section, to optimize the sequencing. Once discovered, the

optimized crossbar resistance bit sequencing patterns corresponding to particular

environmental input bit patterns could be shared between robotic systems having the same

design type.   

 

 

 

  MEMRISTORS AND VIRTUAL REALITY

     Virtual reality is a common theme in numerous science fiction novels and movies and

usually is associated with an immersive interactive simulated environment providing at

least audio and visual stimulation. To some degree many technologies developed over the

past century can be classified as virtual reality to some extent. Radio for example can

provide a “virtual” presentation of live musical performances while television and movies

present the “virtual” presentation of dramas and comedies which were limited to live

theatrical performances in previous centuries. However, radio and television provide only a

one-sided virtual performance and do not provide for the interactivity usually associated

with virtual reality. In the past decade this has begun to rapidly change with the growth of

the internet and improvements in interactive video and video gaming technologies. But all

of these technologies are still indirect forms of virtual reality clearly distinguishable from

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real world interaction. In order to generate a truly immersive virtual reality a more direct

interface between computers and the human brain would be desirable. Steps in this

direction have already begun and are starting to appear in commercial products such as

produced by the company Emotiv which has designed a video gaming interface system

which can directly sense a user’s emotional state to control game characters. However, this

type of interface system is still at a crude stage of development and in order to improve this

type of system, and generate a more immersive virtual reality, memristor crossbars may

offer some advantages.

    Fig. 24 above illustrates a basic system diagram for a virtual reality system including a

neural input interface connecting computer inputs to the human brain via a plurality of

microelectrodes or nanoelectrodes and a neural output interface connecting the human

brain via a plurality of microelectrodes or nanoelectrodes to computer outputs. One key

problem to this type of system (besides physically establishing the electrode connections to

the brain) is that the waveforms defining brain activity can be very complex and the virtual

production of signal waveforms capable of producing the same effect as the actual signals

received from sense organs (i.e. eyes, ears, nerve endings, etc.) may be very difficult to

accomplish. Brain waveforms have typically been defined by electroencephalography in

terms of Delta, Theta, Alpha, Beta, and Gamma wave patterns which are all relatively low

frequency (<100 Hz) signals but can include complex wave shapes. In order to

manufacture the complex brain wave pattern which accurately corresponds to real

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experiences or sensations one strategy is to start with a set of primitive simple waveforms.

This same type of strategy is often employed in communication systems which employ a

technique called Fourier series to decompose any complex periodic waveform into a

weighted sum of simple sinusoidal functions and their harmonics. Based on the weighted

sum of these simple basis waveforms more complex waveforms can be constructed. Figs.

25 and 26 provide examples of how memristor crossbars may be used to accomplish such a

construction.

     In Fig. 25 a crossbar arrangement is illustrated as an input neural interface in which

simple input voltage signals from a computer are transmitted to the column wires of the

crossbar and currents are received from the row wires of the crossbar. Memristor material

is deposited between the column and row wires which may be programmed to have one of

a plurality of possible resistance states based on the application of voltages or currents

above a minimum threshold necessary for change in the memristance states. To avoid

feedback with the crossbar structure the column wires may be formed from p-doped

semiconductor material while the row wires may be formed from n-doped semiconductor

material which establishes in each crossbar junction a diode junction allowing signal

current flow only in the direction from the column wires to the row wires. The net effect of

this type of configuration produces output current signals (I1, I2, I3, I4) based on both the

input voltage signals (V1, V2, V3, V4) and the particular conductivity states of the

52

memristance material at the crossbar junctions. Assuming that losses due to parasitic and

rectification effects are minimal the overall transfer function between the input voltages

and output currents may be compactly expressed as (using Kirchhoff's current law):

Ij(t) = ∑ Gij x Vi(t)

where ∑ is a summation operator with respect to index i, i and j represent the column and

row indices (each ranging from 1 to 4 in the illustrated example) and Gij is a matrix

representing the programmed conductances of the crossbar at the intersection of the ith

column and jth row. The benefit of this approach is that a large range of complex wave

signals can be generated based on a relatively small set of simpler signals serving as basis

functions. Using a programming circuit to periodically change the states of the memristors

in the crossbar junctions can effectively alter visual, audio, or other stimulated experiences

which a particular combination of brain waves may represent.   

    Fig. 26 illustrates a similar configuration as that of Fig. 25 except that the memristor

crossbar is configured as an output device to detect brain waves and translate the brain

waves into signals suitable for a computer or microcontroller. In this case the row wires

may be formed from p-doped semiconductor material and the column wires may be formed

from n-doped semiconductor material to avoid feedback paths within the crossbar. The

53

output currents may similarly be expressed (again assuming that losses due to parasitic and

rectification effects are minimal) as

Ii(t) = ∑ Gji x Vj(t)

where ∑ is a summation operator with respect to index j, i and j represent the column and

row indices (each ranging from 1 to 4 in the illustrated example) and Gji is a matrix

representing the programmed conductances of the crossbar at the intersection of the ith

column and jth row.  In this case instead of attempting to generate a complex waveform

replicating the function of a brain wave from simple waveforms the memristor crossbar

could be used to filter complex waveforms generated by the human brain and produce

simpler waveform patterns which may be easier for a computer to interpret.

INTERCONNECTING NANOSCALE MEMRISTOR

CROSSBARS WITH MICROELECTRONICS

     One key difficulty in implementing nanoscale memristor crossbars is interfacing the

crossbars with more conventional electronics systems. Since the interconnect wiring

in most electronic designs may have widths on the order of microns some type of

addressing system will be necessay to encode and decode data between the microscale

wires of the conventional electronics and the nanoscale wires of the crossbars. A

demultiplexer system was invented by researchers at Hewlett-Packard in 1999 to deal with

this problem. While this type of addressing system has been improved over the past several

years by various reseachers at HP and elsewhere, the addition of the demultiplexing

circuitry make the crossbar design more complex. 

 

    Another difficulty in the integration of nanoscale memristor crossbars and conventional

electronics systems is that different manufacturing techniques are used for making

conventional electronics such as CMOS and the nanoscale crossbars. CMOS fabrication

typically involves steps of film deposition, lithography, etching, doping, etc. which usually

occur at specific temperatures and pressures in a clean room environment. Meanwhile

nanoscale crossbar fabrication steps often employ techniques such as nanoimprint

lithography and self-assembly which usually occur under very different environmental

54

conditions. Researchers have considered fabricating crossbars on top of CMOS circuitry in

a system called "CMOL" however this may not be a promising approach since CMOS

structures often have a top protective layer which is non-planer leading to an increase in

defects if the nanowires were to be patterned on the surface.

 

    A better solution to the problem of interconnecting nanoscale crossbars to

microelectronics may emerge from a tool well known for use in inspecting nanoscale

structures - the atomic force microscope. While originally invented to inspect matter on the

nanoscale, the uses of this tool have been expanded in recent years to include fabrication

on the nanoscale and massive arrays of microfabricated AFMs have been developed by a

company called Nanoink as a way to coat nanoscale line width patterns on a substrate.

By forming the AFM tips of an electrically conductive material this same type of

technology may be used to address individual input and output nanowires of nanoscale

crossbar arrays. This implementation of AFM tips to nanowire crossbar arrays is covered

by my patent US 7,342,413 which teaches selectively forming connections between

microcircuitry and particlular row and column wires of the crossbar using the

micropositioning elements associated with the AFM. Taking this concept a step further an

arrangement of nanoscale interconnect tips formed of a resilient material (such as high

density arrays of vertical multiwall carbon nanotubes) may be fabricated to extend from

a second substrate separately from a first substrate on which nanoscale crossbars are

formed. This first and second substrate may then be affixed relative to one another in an

opposing fashion aligned via piezo based nanopositioning techniques. Such a technique

may be used to interconnect plural crossbar arrays without using complex demultiplexing

or multiplexing circuits as discussed in this pending patent application.

SIGNAL PROCESSING WITH MEMRISTORS

     One advantage of memristors to electronics is their ease of configurability. Since

memristors can be switched between high and low resistances they may be used in a

similar manner as fuses used to selectively open and close connections between electronic

circuit components. However, in contrast to many conventional fuses the switching may be

repeatedly  reconfigured. In addition, when combined with nanowire crossbar interconnect

technology previously developed by Hewlett Packard millions of memristor

interconnects may be formed in a microscopic amount of space. One powerful application

55

of such reconfigurability is in signal processing which may offer the potential to create

electronic devices more capable of adapting to different situations and exhibiting a form of

learning which may advance efforts in artificial intelligence. 

 

    However, in order to use memristors in signal processors a suitable architecture needs to

be created. One circuit element which may be very useful to the construction of memristor

based signal processors is the operational amplifier, or op-amp for short. In one

configuration, as illustrated in Fig. 3, an op-amp is provided with negative feedback which

produces an inverting amplifier. Such a configuration results in the inverting and non-

inverting input terminals to be forced to a common potential and the input current

flowing through R1 is balanced by the current flowing through R2 . Combined with Ohm's

Law this results in an amplication factor between the output and input voltages set to the

ratio between resistances R2 and R1.  

 

     Since memristors have the capacity to switch between high and low resistance states an

array of memristors may be provided in a crossbar configuration to enhance the operability

and configurability of op-amps. Crossbars are basically formed from a first array

of vertical conductive wires and a second array of horizontal conductive wires. Between

the two arrays is formed the memristance material so that any particular wire in the vertical

array can be connected to a wire in the horizontal array by switching the resistance of a

particular intersection (i.e. crosspoint) to a low state (essentially a short circuit) with the

remainder of the crosspoints remaining in a high resistance state (essentially an open

circuit). By separating adjacent vertical wires of the crossbar array with time delay

elements and connecting different resistance values between the horizontal wires and the

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inverting terminal of the op-amp both the amplitude and time delay of the output signal

Vout(t) relative to the input signal Vin(t) can be determined by the crosspoints configured to

be in the low resistance state. Fig 4 illustrates such a configuration in which the

upperleftmost crosspoint is at a low resistance state and all of the other crosspoints are in

the high resistance state. Fig. 5 illustrates a reconfiguration of the crossbar array so that a

different crosspoint is in the low resistance state. This configuration results in a doubling

of the amplification factor compared to the configuration of Fig. 4 (i.e. R/(R/2) = 2) and a

relative delay of the signal.

  

     By configuring a single crosspoint to a low resistance state 16 different possible signal

outputs are possible, however by allowing for the configuration of multiple crosspoints a

maximum of 216 = 65,536 possible signal transformations are possible (note: in order to

prevent unwanted feedback paths within the crossbar a rectification layer may be provided

or p-type and n-type doping may be performed creating diode junctions at each

crosspoint). By using a periodic pulse as the input signal and providing a larger crossbar

array with finer time delay between adjacent columns of the crossbar and a larger range of

resistances for the different rows there is potential to create a universal waveform

generator capable of adapting the amplitude and timing of signals in accordance with a

variety of desired applications. An alternative example of a memristor signal

processor could include applying signal harmonics (i.e. sin t, sin 2t, sin 3t, ..) instead

of time delays to establish a programmable waveform based on Fourier series.

57

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External links

Technical FAQ by Memristor lead scientist, Stan Williams of HP Labs May 20, 2008

"Talk of the Nation" interview with co-discover Stan Williams of HP May 10, 2008 HP Reveals Memristor, The Fourth Passive Circuit Element April 30, 2008 BBC News - Electronics' 'missing link' found May 1, 2008 Nature News - Found: the missing circuit element Apr 30, 2008 Wired.com - Scientists Create First Memristor: Missing Fourth Electronic Circuit

Element April 30, 2008 EE Times - 'Missing link' memristor created: Rewrite the textbooks? April 30, 2008 IEEE Spectrum - The Mysterious Memristor, by Sally Adee May 2008 IEEE Spectrum - How We Found the Missing Memristor, by R. Stanley Williams

Dec 2008 Solid-state thin-film memristor for electronic neural networks - Journal of Applied

Physics, vol. 67 March 1990 A knol on memristors discussing applications in signal processing and filtering,

artificial intelligence, computer/brain interfaces, etc. Memristive switching mechanism for metal/oxide/metal nanodevices July 15, 2008 Java simulations of memristor circuits Dec 3, 2008 Youtube video of 2008 Memristor and Memristive Systems Symposium at UC

Berkeley Circuit elements with memory: memristors, memcapacitors and meminductors

January 23, 2009 An Introduction to Memimpedance and Memadmittance Systems Analysis A knol discussing companies involved in memristor electronics

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