|
|
|
|
Memristor
|
| |
|
| |
Memristors ("memory resistors") are a class 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. The definition of the memristor is based solely on fundamental circuit variables, similarly to the resistor, capacitor, and inductor.
Discussion
Ask a question about 'Memristor' Start a new discussion about 'Memristor' Answer questions from other users |
Encyclopedia
Memristors ("memory resistors") are a class 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. 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. A linear time-invariant memristor is simply a conventional resistor.
Memristor theory was formulated and named by Leon Chua in a 1971 paper.
Chua extrapolated the conceptual symmetry between the resistor, inductor, and capacitor, and inferred that the memristor is a similarly fundamental device. Other scientists had already used fixed nonlinear flux-charge relationships, but Chua's theory introduces generality.
On April 30, 2008 a team at HP Labs announced the development of a switching memristor. Based on a thin film of titanium dioxide, it has a regime of operation with an approximately linear charge-resistance relationship.
These devices are being developed for application in nanoelectronic memories, computer logic, and neuromorphic computer architectures.
Memristor theory
The memristor is formally defined as a two-terminal element in which the magnetic flux Fm 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.
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 Fm 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 Fm is simply equal to the integral of the potential drop between two points, we find that it may readily be calculated, for example by an operational amplifier configured as an integrator.
Two unintuitive concepts are at play:
- Magnetic flux is generated by a resistance in opposition to an applied field or electromotive force. In the absence of resistance, flux due to constant EMF increases indefinitely. The opposing flux induced in a resistor must also increase indefinitely so their sum remains finite.
- Any appropriate response to applied voltage may be called "magnetic flux."
The upshot is that a passive element may relate some variable to flux without storing a magnetic field. Indeed, a memristor always appears instantaneously as a resistor. As shown above, assuming non-negative resistance, at any instant it is dissipating power from an applied EMF and thus has no outlet to dissipate a stored field into the circuit. 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 Fm. 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 Fm = ?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 − ?q) for all q and some ?q, 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.
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 ?Q = 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 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.
Implementations
Titanium dioxide memristor
Interest in the memristor revived in 2008 when an experimental solid state version was reported by R. Stanley Williams of Hewlett Packard. A solid-state device could not be constructed until the unusual behavior of nanoscale materials was better understood. The device neither uses magnetic flux as the theoretical memristor suggested, nor stores charge as a capacitor does, but instead achieves a resistance dependent on the history of current using a chemical mechanism.
The HP device is composed of a thin (50 nm) titanium dioxide film between two 5 nm thick electrodes, one Ti, the other Pt. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers, meaning that the depleted layer has a much lower resistance than the non-depleted layer. When an electric field is applied, the oxygen vacancies drift (see Fast ion conductor), changing the boundary between the high-resistance and low-resistance layers. Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by changing the direction of current. Since the HP device displays fast ion conduction at nanoscale, it is considered a nanoionic device.
Memristance is displayed only when both the doped layer and depleted layer contribute to resistance. When enough charge has passed through the memristor that the ions can no longer move, the device enters hysteresis. It ceases to integrate q=?Idt but rather keeps q at an upper bound and M fixed, thus acting as a resistor until current is reversed.
Memory applications of thin-film oxides had been an area of active investigation for some time. IBM published an article in 2000 regarding structures similar to that described by Williams. Samsung has a pending U.S. patent application for several oxide-layer based switches similar to that described by Williams. Williams also has a pending U.S. patent application related to the memristor construction.
Although the HP memristor is a major discovery for electrical engineering theory, it has yet to be demonstrated in operation at practical speeds and densities. Graphs in Williams' original report show switching operation at only ~1 Hz. Although the small dimensions of the device seem to imply fast operation, the charge carriers move very slowly, with an ion mobility of 10−10 cm2/(V·s). In comparison, the highest known drift ionic mobilities occur in advanced superionic conductors, such as rubidium silver iodide with about 2×10−4 cm2/(V·s) conducting silver ions at room temperature. Electrons and holes in silicon have a mobility ~1000 cm2/(V·s), a figure which is essential to the performance of transistors. However, a relatively low bias of 1 volt was used, and the plots appear to be generated by a mathematical model rather than a laboratory experiment.
Polymeric memristor
In July 2008, Victor Erokhin and Marco P. Fontana, in Electrochemically controlled polymeric device: a memristor (and more) found two years ago, claim to have developed a polymeric memristor before the titanium dioxide memristor more recently announced.
Juri H. Krieger and Stuart M. Spitzer publish a paper in the IEEE Proceeding 2004 Non-Volatile Memory Technology Symposium entitled .
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.
Described is the use of a special passive layer between electrode and active thin films, which enhances the extraction of metal ions from the electrode. It is possible to use superionic materials as this passive layer, which allows to significantly decreasing the ionic extraction field.
Spin memristive systems
A fundamentally different mechanism for memristive behavior has been proposed by and in their paper "Spin memristive systems". The authors show that certain types of semiconductor spintronic structures belong to a broad class of memristive systems as defined by Chua and Kang. The mechanism of memristive behavior in such structures is based entirely on the electron spin degree of freedom which allows for a more convenient control than the ionic transport in nanostructures. When an external control parameter (such as voltage) is changed, the adjustment of electron spin polarization is delayed because of the diffusion and relaxation processes causing a hysteresis-type behavior. This result was anticipated in the study of spin extraction at semiconductor/ferromagnet interfaces, but was not described in terms of memristive behavior. On a short time scale, these structures behave almost as an ideal memristor. This result broadens the possible range of applications of semiconductor spintronics and makes a step forward in future practical applications of the concept of memristive systems.
Manganite memristive systems
Although not described using the word "memristor", a study was done of bilayer oxide films based on manganite for non-volatile memory by researchers at the University of Houston in 2001. Some of the graphs indicate a tunable resistance based on the number of applied voltage pulses similar to the effects found in the titanium dioxide memristor materials described in the Nature paper "The missing memristor found".
Resonant tunneling diode memristor
In 1994, F. A. Buot and A. K. Rajagopal of the U.S. Naval Research Laboratory demonstrated
that a ‘bow-tie’ current-voltage (I-V) characteristics occurs in AlAs/GaAs/AlAs quantum-well diodes containing special doping design of the spacer layers in the source and drain regions, in agreement with the published experimental results.
This ‘bow-tie’ current-voltage (I-V) characteristic is sine qua non of a memristor although the term memristor is not explicitly mentioned in their papers. No magnetic interaction is involved in the analysis of the ‘bow-tie’ I-V characteristics.
Potential applications
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 contour and a memristor was used to model experiments on adaptive behavior of unicellular organisms. It was shown that the electronic circuit subjected to a train of periodic pulses learns and anticipates the next pulse to come, similarly to the behavior of slime molds Physarum polycephalum subjected to periodic changes of environment. Such a learning circuit may find applications, e.g., in pattern recognition.
Memcapacitors and Meminductors
Leon Chua has written an article
extending the notion of memristive systems to capacitive and inductive elements in the form of memcapacitors and meminductors whose properties depend on the state and history of the system.
Timeline of memristor and memristive systems developments
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. (February 14)
- 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
- 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)
2009
- Massimiliano Di Ventra, Yuriy V. Pershin, Leon O. Chua submit an article in arXiv.org entitled "" 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)
See also
External links
- May 20, 2008
- May 10, 2008
- April 30, 2008
- May 1, 2008
- Apr 30, 2008
- April 30, 2008
- April 30, 2008
- May 2008
- Dec 2008
- March 1990
- discussing applications in signal processing and filtering, artificial intelligence, computer/brain interfaces, etc.
- July 15, 2008
- Dec 3, 2008
-
- January 23, 2009
-
|
| |
|
|
