# Memristor

## Memristor Background

The Memristor is the fourth fundamental 2 terminal electronic component alongside the Resistor, Capacitor and Inductor. IEEE Spectrum magazine had a feature article on this 'new' component in  May 2008.

THE STORY OF THE MEMRISTOR is truly one for the history books. When Leon Chua, nowan IEEE Fellow, wrote his seminal paper predicting the memristor, he was a newly minted and rapidly rising professor at DC Berkeley. Chua had been fighting for years against what he considered the arbitrary restriction of electronic circuit theory to linear systems. He was convinced that nonlinear electronics had much more potential than the linear circuits that dominate electronics technology to this day.
Chua discovered a missing link in the pairwise mathematical equations that relate the four circuit quantities-charge, current, voltage, and magnetic flux to one another.

These can be related in six ways. Two are connected through the basic physical laws of electricity and magnetism, and three are related by the known circuit elements:

• resistors connect voltage and current,
• inductors connect flux and current, and
• capacitors connect voltage and charge.

But one equation is missing from this group:

• the relationship between charge moving through a circuit and the magnetic flux surrounded by that circuit-or more subtly, a mathematical doppelganger defined by Faraday's Law as the time integral of the voltage across the circuit.

This distinction is the crux of a raging Internet debate about the legitimacy of our memristor. Chua's memristor was a purely mathematical construct that had more than one physical realization. What does that mean?
Consider a battery and a transformer. Both provide identical voltages for example, 12 volts of direct current but they do so by entirely different mechanisms:

• the battery by a chemical reaction going on inside the cell and
• the transformer by taking a mains ac input, stepping that down to 12 V ac, and then transforming that into 12 V dc.

The end result is mathematically identical-both will run an electric shaver or a cellphone, but the physical source of that 12 V is completely different.
Conceptually, it was easy to grasp how electric charge could couple to magnetic flux, but there was no obvious physical interaction between charge and the integral over the voltage. Chua demonstrated mathematically that his hypothetical device would provide a relationship between flux and charge similar to what a nonlinear resistor provides between voltage and current. In practice, that would mean the device's resistance would vary according to the amount of charge that passed through it. And it would remember that new resistance value even after the current was turned off.

We now know that memristance is an intrinsic property of any electronic circuit. Its existence could have been deduced by Gustav Kirchhoff or by James Clerk Maxwell, if either had considered nonlinear circuits in the 1800s. But the scales at which electronic devices have been built for most of the past two centuries have prevented experimental observation of the effect. It turns out that the influence of memristance obeys an inverse square law:

• memristance is a million times as important at the nanometre scale as it is at the micrometer scale, and it's essentially unobservable at the millimeter scale and larger.

As we build smaller and smaller devices, memristance is becoming more noticeable and in
some cases dominant. That's what accounts for all those strange results researchers have described. Memristance has been hidden in plain sight all along.

This needs some input from an academic.. but here is rough Dimensional Analysis.

 R = dV.dT/dI.dT C=dV/dT L=dI.dT MEM= dT/dI or dV.dT

## Units

Electronic theorists have been using the wrong pair of variables to define devices, ie voltage and charge. The missing part of electronic theory was that the fundamental pair of variables is flux and charge.

The situation is analogous to what is called "Aristotle's Law of Motion, which was wrong, because he said that force must be proportional to velocity. That misled people until Newton came along and pointed out that Aristotle was using the wrong variables. Newton said that force is proportional to acceleration, ie the change in velocity.

This is exactly the situation with electronic circuit theory today. All electronic textbooks have been teaching using the wrong variables of voltage and charge; explaining away inaccuracies as anomalies. What they should have been teaching is the relationship between changes in voltage, or flux, and charge.

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 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.
1993
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 a 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)
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)
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.
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)
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)
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.
2007
Vladimir Bulovic, Aaron Mandell, and Andrew Perlman, receive U.S. Patent 7,183,141 (assigned to Spansion), including basic claims to methods of programming 2-terminal ionic complex resistance switches to act as a fuse or anti-fuse. (February 27)
Gregory Snider of HP Labs receives U.S. Patent 7,203,789, assigned to Hewlett-Packard, describing implimentations of 2-terminal resistance switches similar to memristors in reconfigurable computing architectures. (April 10)
Gregory Snider of HP Labs publishes the article "Self-organized computation with unreliable, memristive nanodevices" in the journal Nanotechnology discussing memristive nanodevices useful to pattern recognition and reconfigurable circuit architectures. (August 10)
Blaise Mouttet, a graduate student at George Mason University, receives U.S. Patent 7,302,513 describing uses for 2-terminal resistance switching materials in signal processing, control systems, communications, and pattern recognition. (November 27)
2008
Greg Snider of HP Labs receives U.S. Patent 7,359,888 (assigned to Hewlett-Packard) including basic claims to a nanoscale 2-terminal resistance switch crossbar array formed as a neural network. (April 15)
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)
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)

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