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Memristor

Memristor

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Memristor is a passive
Passivity (engineering)
Passivity is a property of engineering systems, used in a variety of engineering disciplines, but most commonly found in analog electronics and control systems...

 two-terminal
Terminal (electronics)
A terminal is the point at which a conductor from an electrical component, device or network comes to an end and provides a point of connection to external circuits. A terminal may simply be the end of a wire or it may be fitted with a connector or fastener...

 electrical component
Electronic component
An electronic component is a basic electronic element and may be available in a discrete form having two or more electrical terminals . These are intended to be connected together, usually by soldering to a printed circuit board, in order to create an electronic circuit with a particular function...

 envisioned by Leon Chua as a fundamental non-linear circuit element relating charge and magnetic flux linkage. The memristor is currently under development by a team at Hewlett Packard.

When current flows in one direction through the device, the electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

 increases; and when current flows in the opposite direction, the resistance decreases. When the current is stopped, the component retains the last resistance that it had, and when the flow of charge starts again, the resistance of the circuit will be what it was when it was last active. It has a regime of operation with an approximately linear charge-resistance relationship as long as the time-integral of the current stays within certain bounds.

Memristor theory was formulated and named by Leon Chua in a 1971 paper.
In 2008, a team at HP Labs
HP Labs
HP Labs is the exploratory and advanced research group for Hewlett-Packard. The lab has some 600 researchersin seven locations throughout the world....

 announced the development of a switching memristor based on a thin film
Thin film
A thin film is a layer of material ranging from fractions of a nanometer to several micrometers in thickness. Electronic semiconductor devices and optical coatings are the main applications benefiting from thin film construction....

 of titanium dioxide
Titanium dioxide
Titanium dioxide, also known as titanium oxide or titania, is the naturally occurring oxide of titanium, chemical formula . When used as a pigment, it is called titanium white, Pigment White 6, or CI 77891. Generally it comes in two different forms, rutile and anatase. It has a wide range of...

. These devices are being developed for application in nanoelectronic memories, computer logic, and neuromorphic
Neuromorphic
Neuromorphic engineering or neuromorphic computing is a concept developed by Carver Mead, in the late 1980s, describing the use of very-large-scale integration systems containing electronic analog circuits to mimic neuro-biological architectures present in the nervous system...

 computer architectures. In October 2011, the same team announced the commercial availability of memristor technology within 18 months, as a replacement for Flash
Flash memory
Flash memory is a non-volatile computer storage chip that can be electrically erased and reprogrammed. It was developed from EEPROM and must be erased in fairly large blocks before these can be rewritten with new data...

, SSD
Solid-state drive
A solid-state drive , sometimes called a solid-state disk or electronic disk, is a data storage device that uses solid-state memory to store persistent data with the intention of providing access in the same manner of a traditional block i/o hard disk drive...

, DRAM and SRAM.


Background


In his 1971 paper, Chua extrapolated the conceptual symmetry between the resistor, inductor, and capacitor, and inferred the memristor was a similarly fundamental device. However, it has a nonlinear relationship between current and voltage, like the varistor
Varistor
A varistor is an electronic component with a "diode-like" nonlinear current–voltage characteristic. The name is a portmanteau of variable resistor...

. Other scientists had already proposed fixed nonlinear flux-charge relationships, but Chua's theory introduced generality.

The resistance of a memristor depends on the integral of the input applied to the terminals (rather than on the instantaneous value of the input as in a varistor). Since the element "remembers" the amount of current that has passed through it in the past, it was tagged by Chua with the name "memristor". Another way of describing a memristor is that it is any passive two-terminal circuit elements that maintains a functional relationship
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

 between the time integral of current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

 (called charge) and the time integral of voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

 (often called flux, as it is related to magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...

). The slope of this function is called the memristance M and is similar to variable resistance. Batteries
Galvanic cell
A Galvanic cell, or Voltaic cell, named after Luigi Galvani, or Alessandro Volta respectively, is an electrochemical cell that derives electrical energy from spontaneous redox reaction taking place within the cell...

 can be considered to have memristance, but they are not passive devices.

The definition of the memristor is based solely on the fundamental circuit variables of current and voltage and their time-integrals, just like the resistor
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...

, capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

, and inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...

. Unlike those three elements however, which are allowed in linear time-invariant or LTI system theory
LTI system theory
Linear time-invariant system theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas. It investigates the response of a linear and time-invariant...

, memristors of interest have a nonlinear function and may be described by any of a variety of functions of net charge. There is no such thing as a standard memristor. Instead, each device implements a particular function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

, wherein the integral of voltage determines the integral of current, and vice versa. A linear time-invariant memristor, with a constant value for M, is simply a conventional resistor. Like other two-terminal components (e.g., resistor, capacitor, inductor), real-world devices are never purely memristors ("ideal memristor"), but will also exhibit some amount of capacitance, resistance, and inductance.

Theory


The memristor is essentially a two-terminal variable resistor, with resistance dependent upon the amount of charge q that has passed between the terminals.


To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term M(q), which characterizes the device, and write it as a differential equation:


where Q is defined by , and is defined by . Note that the above table covers all meaningful ratios of I, Q, Φm, and V. No device can relate I to Q, or Φm to V, because I is the derivative of Q and Φm is the integral of V.

The variable Φm ("magnetic flux linkage
Flux linkage
Flux linkage is a property of a coil of conducting wire and the magnetic field through which it passes. It is determined by the number of turns in the coil and the flux of the magnetic field....

") is generalized from the circuit characteristic of an inductor. It does not represent a magnetic field here, and its physical meaning is discussed below. The symbol Φm may simply be regarded as the integral of voltage over time.

Thus, the memristor is formally defined as a two-terminal element in which the flux linkage (or integral of voltage) Φm between the terminals is a function of the amount of electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

 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.


Substituting that the flux is simply the time integral of the 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
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

. If M(q(t)) is a constant, then we obtain Ohm's Law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...

 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 M does not vary with charge. Of course, nonzero current implies time varying charge. Alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

, 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
Small signal model
Small-signal modeling is a common analysis technique in electrical engineering which is used to approximate the behavior of nonlinear devices with linear equations...

 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 constant resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop.

Derivation of "flux linkage" in a passive device


In an inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...

, magnetic flux Φm relates to Faraday's law of induction
Faraday's law of induction
Faraday's law of induction dates from the 1830s, and is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators...

, which states that the energy to push charges around a loop (electromotive force
Electromotive force
In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a...

, in units of Volts) equals the negative derivative of the flux through the loop:


This notion may be extended by analogy to a single device. Working against an accelerating force (which may be EMF, or any applied voltage), a resistor produces a decelerating force, and an associated "flux linkage" varying with opposite sign. For example, a high-valued resistor will quickly produce flux linkage. The term "flux linkage" is generalized from the equation for inductors, where it represents a physical magnetic flux: If 1 Volt is applied across an inductor for 1 second, then there is 1 V·s of flux linkage in the inductor, which represents energy stored in a magnetic field that may later be obtained from it. The same voltage over the same time across a resistor results in the same flux linkage (as defined here, in units of V·s), but the energy is dissipated, rather than stored in a magnetic field — there is no physical magnetic field involved as a link to anything. Voltage for passive devices is evaluated in terms of energy lost by a unit of charge, so generalizing the above equation simply requires reversing the sense of EMF.



Observing that Φm is simply equal to the integral over time of the potential drop between two points, we find that it may readily be calculated, for example by an operational amplifier
Operational amplifier
An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output...

 configured as an integrator
Integrator
An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus.The integration function is often part of engineering, physics, mechanical, chemical and scientific calculations....

.

Two unintuitive concepts are at play:
  • Magnetic flux is defined here as generated by a resistance in opposition to an applied field or electromotive force. In the absence of resistance, flux due to constant EMF, and the magnetic field
    Superconducting magnet
    A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled to cryogenic temperatures during operation. In its superconducting state the wire can conduct much larger electric currents than ordinary wire, creating intense magnetic fields...

     within the circuit, would increase indefinitely. The opposing flux induced in a resistor must also increase indefinitely so the sum with applied EMF remains finite.
  • Any appropriate response to applied voltage may be called "magnetic flux", as the term is used here.


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
Negative resistance
Negative resistance is a property of some electric circuits where an increase in the current entering a port results in a decreased voltage across the same port. This is in contrast to a simple ohmic resistor, which exhibits an increase in voltage under the same conditions. Negative resistors are...

, 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)


M(q) is physically restricted to be positive for all values of q (assuming the device is passive and does not become superconductive at some q). A negative value would mean that it would perpetually supply energy when operated with alternating current.

An applied constant voltage potential results in uniformly increasing Φm. It is not realistic for the function M(q) to contain an infinite amount of information over this infinite range. Three alternatives avoid this physical impossibility:
  • M(q) approaches zero, such that Φm = ∫M(q)dq = ∫M(q(t))I(t) 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 periodic, so that M(q) = M(q − Δq) for all q and some Δq, e.g. sin2(q/Q).
  • The device enters hysteresis
    Hysteresis
    Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...

     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
Scalar (mathematics)
In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector....

 state, a system has vector
Tuple
In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...

 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
Hodgkin-Huxley model
The Hodgkin–Huxley model is a mathematical model that describes how action potentials in neurons are initiated and propagated....

 of the axon
Axon
An axon is a long, slender projection of a nerve cell, or neuron, that conducts electrical impulses away from the neuron's cell body or soma....

 and a thermistor
Thermistor
A thermistor is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors. The word is a portmanteau of thermal and resistor...

 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
Resistive random-access memory
Resistive random-access memory is a new non-volatile memory type being developed by many companies. The technology bears some similarities to CBRAM and phase change memory....

 and phase-change memory
Phase-change memory
Phase-change memory is a type of non-volatile computer memory. PRAMs exploit the unique behavior of chalcogenide glass. Heat produced by the passage of an electric current switches this material between two states, crystalline and amorphous...

, relating the theory to active areas of research.

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


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 f is not an explicit function of I.

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 = QonQoff.


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
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

, 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
Hysteresis
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...

, 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.

Titanium dioxide memristor


Interest in the memristor revived when an experimental solid state version was reported by R. Stanley Williams
R. Stanley Williams
Richard Stanley Williams is research scientist in the field of nanotechnology and a Senior Fellow and the founding director of the Quantum Science Research laboratory at HP. He has over 57 patents, with 40 more patents pending...

 of Hewlett Packard. The article was the first to demonstrate that a solid-state device could have the characteristics of a memristor based on the behavior of nanoscale thin films. 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.

Although not cited in HP's initial reports on their TiO2 memristor, the resistance switching characteristics of titanium dioxide was originally described in the 1960s.

The HP device is composed of a thin (50 nm) titanium dioxide
Titanium dioxide
Titanium dioxide, also known as titanium oxide or titania, is the naturally occurring oxide of titanium, chemical formula . When used as a pigment, it is called titanium white, Pigment White 6, or CI 77891. Generally it comes in two different forms, rutile and anatase. It has a wide range of...

 film between two 5 nm thick electrode
Electrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...

s, one Ti, the other Pt. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...

 atoms. The oxygen vacancies act as charge carrier
Charge carrier
In physics, a charge carrier is a free particle carrying an electric charge, especially the particles that carry electric currents in electrical conductors. Examples are electrons and ions...

s, 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
Fast ion conductor
In solid-state ionics, fast ion conductors, also known as solid electrolytes and superionic conductors, are materials that act as solid state ion conductors and are used primarily in solid oxide fuel cells. As solid electrolytes they conduct due to the movement of ions through voids, or empty...

), 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 as a nanoionic device
Nanoionic device
Nanoionic devices belong to a new class of solid state devices operating due to fast ion transport at nano-scale. The examples of such devices are nano-switches with quantum conductance, and nanoionic supercapacitors with coherent heterojunctions....

.

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
Hysteresis
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...

. It ceases to integrate q=∫Idt, but rather keeps q at an upper bound and M fixed, thus acting as a constant resistor until current is reversed.

Memory applications of thin-film oxides had been an area of active investigation for some time. IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

 published an article in 2000 regarding structures similar to that described by Williams. Samsung
Samsung
The Samsung Group is a South Korean multinational conglomerate corporation headquartered in Samsung Town, Seoul, South Korea...

 has a U.S. patent for oxide-vacancy 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
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

. Although the small dimensions of the device seem to imply fast operation, the charge carriers move very slowly, with an ion mobility
Electron mobility
In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor, when pulled by an electric field. In semiconductors, there is an analogous quantity for holes, called hole mobility...

 of 10−10 cm2/(V
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

s
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

). In comparison, the highest known drift
Drift current
In condensed matter physics and electrochemistry, drift current is the electric current, or movement of charge carriers, which is due to the applied electric field, often stated as the electromotive force over a given distance.When an electric field is applied across a semiconductor material,the...

 ionic mobilities occur in advanced superionic conductors, such as rubidium silver iodide
Rubidium silver iodide
Rubidium silver iodide is a ternary inorganic compound with the formula RbAg4I5. It is an unusual solid where the electrical conductivity involves movement of silver ions within the crystal lattice...

 with about 2×10−4 cm2/(Vs) conducting silver ions at room temperature
Room temperature
-Comfort levels:The American Society of Heating, Refrigerating and Air-Conditioning Engineers has listings for suggested temperatures and air flow rates in different types of buildings and different environmental circumstances. For example, a single office in a building has an occupancy ratio per...

. Electrons and holes in silicon have a mobility ~1000 cm2/(Vs), a figure which is essential to the performance of transistors. However, a relatively low bias of 1 volt was used, and the plots appear to be generated by a mathematical model rather than a laboratory experiment.

In April 2010, HP labs announced that they had practical memristors working at 1 ns
Nanosecond
A nanosecond is one billionth of a second . One nanosecond is to one second as one second is to 31.7 years.The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns....

 (~1 GHz) switching times and 3 nm by 3 nm sizes, with electron/hole mobility of 1 m/s, which bodes well for the future of the technology. At these densities it could easily rival the current sub-25 nm flash memory
Flash memory
Flash memory is a non-volatile computer storage chip that can be electrically erased and reprogrammed. It was developed from EEPROM and must be erased in fairly large blocks before these can be rewritten with new data...

 technology.

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.

In 2004, Juri H. Krieger and Stuart M. Spitzer published a paper "Non-traditional, Non-volatile Memory Based on Switching and Retention Phenomena in Polymeric Thin Films" at the IEEE Non-Volatile Memory Technology Symposium, describing 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 ions from the electrode. It is possible to use fast ion conductor
Fast ion conductor
In solid-state ionics, fast ion conductors, also known as solid electrolytes and superionic conductors, are materials that act as solid state ion conductors and are used primarily in solid oxide fuel cells. As solid electrolytes they conduct due to the movement of ions through voids, or empty...

 as this passive layer, which allows to significantly decrease the ionic extraction field.

Spintronic Memristor


Yiran Chen and Xiaobin Wang, researchers at disk-drive manufacturer Seagate Technology, in Bloomington, Minnesota, described three examples of possible magnetic memristors in March, 2009 in IEEE Electron Device Letters. In one of the three, resistance is caused by the spin of electrons in one section of the device pointing in a different direction than those in another section, creating a "domain wall", a boundary between the two states. Electrons flowing into the device have a certain spin, which alters the magnetization state of the device. Changing the magnetization, in turn, moves the domain wall and changes the device's resistance.

This work attracted significant attention from the electronics press, including an interview by IEEE Spectrum.

Spin Torque Transfer Magnetoresistance


Spin Torque Transfer
Spin Torque Transfer
Spin-transfer torque is an effect in which the orientation of a magnetic layer in a tunnel magnetoresistance or spin valve can be modified using a spin-polarized current....

 MRAM
MRAM
Magnetoresistive Random-Access Memory is a non-volatile computer memory technology that has been under development since the 1990s. Continued increases in density of existing memory technologies – notably flash RAM and DRAM – kept it in a niche role in the market, but its proponents...

 is a well-known device that exhibits memristive behavior. The resistance is dependent on the relative spin orientation between two sides of a magnetic tunnel junction. This in turn can be controlled by the spin torque induced by the current flowing through the junction. However, the length of time the current flows through the junction determines the amount of current needed, i.e., the charge flowing through is the key variable.
Additionally, as reported by Krzysteczko et al., MgO
MGO
MGO may refer to:*Magnesium oxide, the chemical formula MgO*Methylglyoxal, abbreviated MGO*Metal Gear Online, a PlayStation 3 online multiplayer spin-off of the Metal Gear video game series...

 based magnetic tunnel junctions show memristive behavior based on the drift of oxygen vacancies within the insulating MgO layer (resistive switching
Resistive random-access memory
Resistive random-access memory is a new non-volatile memory type being developed by many companies. The technology bears some similarities to CBRAM and phase change memory....

). Therefore, the combination of spin transfer torque and resistive switching leads naturally to a second-order memristive system with w=(w1,w2) where w1 describes the magnetic state of the magnetic tunnel junction and w2 denotes the resistive state of the MgO barrier. Note that in this case the change of w1 is current-controlled (spin torque is due to a high current density) whereas the change of w2 is voltage-controlled (the drift of oxygen vacancies is due to high electric fields).

Spin Memristive System


A fundamentally different mechanism for memristive behavior has been proposed by Yuriy V. Pershin and Massimiliano Di Ventra in their paper "Spin memristive systems". The authors show that certain types of semiconductor spintronic structures belong to a broad class of memristive systems as defined by Chua and Kang. The mechanism 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
Manganite
Manganite is a mineral. Its composition is manganese oxide-hydroxide, MnO, crystallizing in the monoclinic system . Crystals of manganite are prismatic and deeply striated parallel to their length; they are often grouped together in bundles. The color is dark steel-grey to iron-black, and the...

 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 characteristic of a memristor although the term memristor was not explicitly used 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 latch
Crossbar latch
The cross-bar latch is a technology invented by Hewlett-Packard in October 2001, that potentially could replace transistors in some applications. Transistors are essential components of logic gates and memory cells in digital electronic systems...

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

They can also be fashioned into non-volatile
Non-volatile memory
Non-volatile memory, nonvolatile memory, NVM or non-volatile storage, in the most basic sense, is computer memory that can retain the stored information even when not powered. Examples of non-volatile memory include read-only memory, flash memory, ferroelectric RAM, most types of magnetic computer...

 solid-state memory, which would allow greater data density than hard drives with access times potentially similar to DRAM
Dynamic random access memory
Dynamic random-access memory is a type of random-access memory that stores each bit of data in a separate capacitor within an integrated circuit. The capacitor can be either charged or discharged; these two states are taken to represent the two values of a bit, conventionally called 0 and 1...

, replacing both components. HP prototyped a crossbar latch
Crossbar latch
The cross-bar latch is a technology invented by Hewlett-Packard in October 2001, that potentially could replace transistors in some applications. Transistors are essential components of logic gates and memory cells in digital electronic systems...

 memory using the devices that can fit 100 gigabit
Gigabit
The gigabit is a multiple of the unit bit for digital information or computer storage. The prefix giga is defined in the International System of Units as a multiplier of 109 , and therefore...

s in a square centimeter, and has designed a highly scalable 3D design (consisting of up to 1000 layers or 1 petabit
Petabit
The petabit is a multiple of the unit bit for digital information or computer storage. The prefix peta is defined in the International System of Units as a multiplier of 1015 , and therefore...

 per cm3). HP has reported that its version of the memristor is currently about one-tenth the speed of DRAM. The devices' resistance would be read with alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

 so that the stored value would not be affected.

Some patents related to memristors appear to include applications in programmable logic
Programmable logic device
A programmable logic device or PLD is an electronic component used to build reconfigurable digital circuits. Unlike a logic gate, which has a fixed function, a PLD has an undefined function at the time of manufacture...

, signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, neural networks
Neural Networks
Neural Networks is the official journal of the three oldest societies dedicated to research in neural networks: International Neural Network Society, European Neural Network Society and Japanese Neural Network Society, published by Elsevier...

, and control systems
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

. Memristive devices can be potentially used for stateful logic implication, allowing a replacement for CMOS-based logic computation. Several early works in this direction is reported.
In the mid 2000's, 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
Physarum polycephalum
Physarum polycephalum belongs to the supergroup Amoebozoa, phylum Mycetozoa, and class Myxogastria. P. polycephalum, often referred to as the “many-headed slime,” is a slime mold that inhabits shady, cool, moist areas, such as decaying leaves and logs...

where the viscosity of channels in the cytoplasm respond to periodic changes of environment. Such a learning circuit may find applications, e.g., in pattern recognition. The DARPA’s SyNAPSE
SyNAPSE
SyNAPSE is a DARPA program that aims to develop electronic neuromorphic machine technology that scales to biological levels. More simply stated, it is an attempt to build a new kind of computer with similar form, function, and architecture to the mammalian brain...

 project has funded HP Labs, in collaboration with the Boston University
Boston University
Boston University is a private research university located in Boston, Massachusetts. With more than 4,000 faculty members and more than 31,000 students, Boston University is one of the largest private universities in the United States and one of Boston's largest employers...

 Neuromorphics Lab, to develop neuromorphic architectures which may be based on memristive systems. In 2010, Massimiliano Versace
Massimiliano Versace
Massimiliano Versace is a senior research scientist in the Neuromorphics Lab at Boston University in the Department of Cognitive and Neural Systems, where he founded and is currently the director of the Neuromorphics Lab. He is co-leading the Boston University neural modeling team working with...

 and Ben Chandler co-wrote an article describing the MoNETA (Modular Neural Exploring Traveling Agent) model. MoNETA is the first large-scale neural network model to implement whole-brain circuits to power a virtual and robotic agent compatibly with memristive hardware computations. The software used to implement MoNETA, Cog Ex Machina, has been featured on the cover page of IEEE Computer in February 2011 in a joint article by HP Labs and the Boston University Neuromorphics Lab. Application of the memristor crossbar structure in the construction of analog soft computing system is demonstrated by Farnood Merrikh-Bayat and Saeed Bagheri Shouraki . They have also shown in 2011 how memristor crossbars can be combined with fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...

 to create analog memristive neuro-fuzzy
Neuro-fuzzy
In the field of artificial intelligence, neuro-fuzzy refers to combinations of artificial neural networks and fuzzy logic. Neuro-fuzzy was proposed by J. S. R. Jang...

 computing system with fuzzy input and output terminals. Learning of this system is based on the creation of fuzzy relations inspired from Hebbian learning rule
Hebbian theory
Hebbian theory describes a basic mechanism for synaptic plasticity wherein an increase in synaptic efficacy arises from the presynaptic cell's repeated and persistent stimulation of the postsynaptic cell...

.

Memcapacitors and meminductors


In 2009, Massimiliano Di Ventra, Yuriy Pershin and Leon Chua co-wrote 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.

Historical timeline


1960
Bernard Widrow
Bernard Widrow
Bernard Widrow is a U.S. professor of electrical engineering at Stanford University. He is the co-inventor of the Widrow–Hoff least mean squares filter adaptive algorithm with his then doctoral student Ted Hoff...

 develops a 3-terminal device called a "memistor" as a new fundamental circuit component forming the basis of a neural network circuit called ADALINE
ADALINE
ADALINE is a single layer neural network. It was developed by Professor Bernard Widrow and his graduate student Ted Hoff at Stanford University in 1960. It is based on the McCulloch–Pitts neuron...

 (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.


1968
F. Argall publishes an article in Solid-State Electronics entitled "Switching Phenomena in Titanium Oxide Thin Films". Although the article is not cited in HP's memristor papers the article describes substantially similar experimental data.


1969
G. Dearnaley A. M. Stoneham and D.V. Morgan 1969 J. Non Cryst. Sol. 4, 593 612 suggest the filamentary model for switching. They showed there were no injected gold ions in the silicon oxide films. Their 1970 paper G. Dearnaley A. M. Stoneham and D.V. Morgan 1970 Rep. Prog. Phys. 33, 1129 1191 reviewed and compared the several mechanisms proposed. This paper was translated into Russian as Uspekhi Fizicheskikh Nauk 112 83 128 (1974).


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
Lissajous curve
In mathematics, a Lissajous curve , also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equationswhich describe complex harmonic motion...

 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
Journal of Applied Physics
The Journal of Applied Physics is a peer-reviewed scientific journal published since 1931 by the American Institute of Physics. Its emphasis is on the understanding of the physics underpinning modern technology....

. The article teaches a tungsten oxide electrically reprogrammable variable resistance device, but it is unclear whether the "memistor" referred to in the title has any connection to the memristor of Chua. In addition, the cited references of this article do not include any of Chua's publications on the memristor so this appears to be a coincidence.


1992
(August 27) 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.


1993
(November 3) 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.

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
Journal of Applied Physics
The Journal of Applied Physics is a peer-reviewed scientific journal published since 1931 by the American Institute of Physics. Its emphasis is on the understanding of the physics underpinning modern technology....

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
Aluminium arsenide
Aluminium arsenide or aluminum arsenide is a semiconductor material with almost the same lattice constant as gallium arsenide and aluminium gallium arsenide and wider band gap than gallium arsenide.-Properties:...

/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
(June 2) Michael Kozicki and William West receive U.S. Patent 5,761,115 (assigned to Axon Technologies Corp. and the Arizona Board of Regents
Arizona Board of Regents
The Arizona Board of Regents is the governing body of Arizona's public university system, providing policy guidance to Arizona State University, Northern Arizona University, the University of Arizona and their branch campuses.-Organization:...

) describing the Programmable metallization cell
Programmable metallization cell
The programmable metallization cell, or PMC, is a new form of non-volatile computer memory being developed at Arizona State University and its spinoff, Axon Technologies....

, 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 3) 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, demonstrating that the complexity of an artificial synapse can be minimized by using an ionic programmable resistance device.

(June 12) James R. Heath
James R. Heath
James R. Heath is an American chemist and the Elizabeth W. Gilloon Professor of Chemistry at the California Institute of Technology.- Early years :...

, Philip Kuekes, Gregory Snider, and Stan Williams, of HP Labs
HP Labs
HP Labs is the exploratory and advanced research group for Hewlett-Packard. The lab has some 600 researchersin seven locations throughout the world....

, publish a paper in Science
Science (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....

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.

(November 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
Santa Clara, California
Santa Clara , founded in 1777 and incorporated in 1852, is a city in Santa Clara County, in the U.S. state of California. The city is the site of the eighth of 21 California missions, Mission Santa Clara de Asís, and was named after the mission. The Mission and Mission Gardens are located on the...

.


2000
(July 3) A. Beck, J. G. Bednorz, Ch. Gerber, C. Rossel, and D. Widmer of IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

's Zurich Research Laboratory describe reproducible 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
Applied Physics Letters
Applied Physics Letters is a peer-reviewed scientific journal that is published 52 times per year by the American Institute of Physics. Its focus is rapid publication and dissemination of new experimental and theoretical papers regarding applications of physics in all disciplines of science,...

. The switches are noted as having hysteretic features similar to memristors, but no connection to memristors is yet noted.

(October 3) Philip Kuekes, Stanley Williams, and James Heath, of HP Labs
HP Labs
HP Labs is the exploratory and advanced research group for Hewlett-Packard. The lab has some 600 researchersin seven locations throughout the world....

, 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.


2001
Shangqing Liu, NaiJuan Wu, Xin Chen, and Alex Ignatiev, researchers in the Space Vacuum Epitaxy Center
Space Vacuum Epitaxy Center
Space Vacuum Epitaxy Center is the of laboratory space in 3 buildings on the University of Houston campus. The SVEC facilities contains equipment dedicated to thin film deposition, processing and characterization of III-V compound semiconductor, high temperature superconductor and ferroelectric...

 of the University of Houston
University of Houston
The University of Houston is a state research university, and is the flagship institution of the University of Houston System. Founded in 1927, it is Texas's third-largest university with nearly 40,000 students. Its campus spans 667 acres in southeast Houston, and was known as University of...

, present results during a non-volatile memory conference held in San Diego, California
San Diego, California
San Diego is the eighth-largest city in the United States and second-largest city in California. The city is located on the coast of the Pacific Ocean in Southern California, immediately adjacent to the Mexican border. The birthplace of California, San Diego is known for its mild year-round...

 on November 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.

(May 1) 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.

(August 13) 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 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.


2003
A. Bandyopadhyay and A. J. Pal from Indian Association for the Cultivation of Science
Indian Association for the Cultivation of Science
The Indian Association for the Cultivation of Science, established in July 1876 at 210 Bowbazar street, Calcutta, is a national institution for higher learning whose primary purpose is to foster high quality fundamental research in frontier disciplines of the basic sciences. Founded by Dr. Mahendra...

 demonstrated Large conductance switching and memory effects in organic molecules for data-storage applications, in Appl. Phys. Lett. 82, 1215 (2003). They demonstrated current-voltage characteristics similar to the prediction of Chua's memristor and they demonstrated Random Access Memory for millions of times and Read Only memory for hours. They tuned the memristive property using functional groups, A. Bandyopadhyay and A. J. Pal, J. Phys. Chem. B. 107, 2531 (2003). They tuned memristive features via Self-assembled Supramolecular Structures, A. Bandyopadhyay, A. J. Pal, Adv. Mater. 15, 1949 (2003).


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
Advanced Micro Devices
Advanced Micro Devices, Inc. or AMD is an American multinational semiconductor company based in Sunnyvale, California, that develops computer processors and related technologies for commercial and consumer markets...

) 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.

(15–17 November) Ju. H. Krieger and Stuart M. Spitzer publish a paper in the IEEE Proceeding 2004 Non-Volatile Memory Technology Symposium entitled "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.


2005
(March 22) 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.

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
Advanced Micro Devices
Advanced Micro Devices, Inc. or AMD is an American multinational semiconductor company based in Sunnyvale, California, that develops computer processors and related technologies for commercial and consumer markets...

) 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.

(November 1) Zhida Lan, Colin Bill, and Michael A. VanBuskirk receive U.S. Patent 6,960,783 (assigned to Advanced Micro Devices
Advanced Micro Devices
Advanced Micro Devices, Inc. or AMD is an American multinational semiconductor company based in Sunnyvale, California, that develops computer processors and related technologies for commercial and consumer markets...

) 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 is similar to the memristor, but no mention of the memristor is included in the description.


2006
(February 14) 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.

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
Advanced Micro Devices
Advanced Micro Devices, Inc. or AMD is an American multinational semiconductor company based in Sunnyvale, California, that develops computer processors and related technologies for commercial and consumer markets...

) describing manufacturing of a two-terminal resistance switching memory cells.

(September 11) 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.


2007
(January 2) Juri H. Krieger and Stuart M. Spitzer receive U.S. Patent 7,157,732 (assigned to Spansion
Spansion
Spansion Inc. is a Flash memory chip maker that designs, develops and manufactures NOR flash memory products. The company has over 3,400 employees and is headquartered in Sunnyvale, California. Spansion is a former joint-venture between AMD and Fujitsu....

) 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.

(February 27) Vladimir Bulovic, Aaron Mandell, and Andrew Perlman, receive U.S. Patent 7,183,141 (assigned to Spansion
Spansion
Spansion Inc. is a Flash memory chip maker that designs, develops and manufactures NOR flash memory products. The company has over 3,400 employees and is headquartered in Sunnyvale, California. Spansion is a former joint-venture between AMD and Fujitsu....

), including basic claims to methods of programming 2-terminal ionic complex resistance switches to act as a fuse or anti-fuse.

(April 10) Gregory Snider of HP Labs receives U.S. Patent 7,203,789, assigned to Hewlett-Packard, describing implementations of 2-terminal resistance switches similar to memristors in reconfigurable computing architectures.

(August 10) Gregory Snider of HP Labs publishes the article "Self-organized computation with unreliable, memristive nanodevices" in the Journal of Nanoscience and Nanotechnology
Journal of Nanoscience and Nanotechnology
-See also:*Nature Nanotechnology*International conference on Physics of Light-Matter Coupling in Nanostructures*International Journal of Nanoscience*Journal of Nanoparticle Research*Nano Letters*NANO...

discussing memristive nanodevices useful to pattern recognition and reconfigurable circuit architectures.

(November 27) Blaise Mouttet, a graduate student at George Mason University
George Mason University
George Mason University is a public university based in unincorporated Fairfax County, Virginia, United States, south of and adjacent to the city of Fairfax. Additional campuses are located nearby in Arlington County, Prince William County, and Loudoun County...

, receives U.S. Patent 7,302,513 describing uses for 2-terminal resistance switching materials in signal processing, control systems, communications, and pattern recognition.


2008
(April 15) Greg Snider of HP Labs
HP Labs
HP Labs is the exploratory and advanced research group for Hewlett-Packard. The lab has some 600 researchersin seven locations throughout the world....

 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
Neural network
The term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...

.

(May 1) Dmitri Strukov, Gregory Snider, Duncan Stewart, and Stan Williams, of HP Labs
HP Labs
HP Labs is the exploratory and advanced research group for Hewlett-Packard. The lab has some 600 researchersin seven locations throughout the world....

, 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.

(June 1–5) Blaise Mouttet, a graduate student at George Mason University
George Mason University
George Mason University is a public university based in unincorporated Fairfax County, Virginia, United States, south of and adjacent to the city of Fairfax. Additional campuses are located nearby in Arlington County, Prince William County, and Loudoun County...

, 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
Boston
Boston is the capital of and largest city in Massachusetts, and is one of the oldest cities in the United States. The largest city in New England, Boston is regarded as the unofficial "Capital of New England" for its economic and cultural impact on the entire New England region. The city proper had...

.

(July 7) Victor Erokhin and M.P. Fontana claim to have developed a polymeric memristor before the titanium dioxide
Titanium dioxide
Titanium dioxide, also known as titanium oxide or titania, is the naturally occurring oxide of titanium, chemical formula . When used as a pigment, it is called titanium white, Pigment White 6, or CI 77891. Generally it comes in two different forms, rutile and anatase. It has a wide range of...

 memristor of Stan Williams group in the article "Electrochemically controlled polymeric device: a memristor (and more) found two years ago".

(July 15) 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
Nature Nanotechnology
Nature Nanotechnology is a monthly, peer-reviewed, scientific journal, which is published by Nature Publishing Group. It was established in October 2006. The editor in chief is Peter Rodgers, a full-time professional editor who is employed by Nature Publishing Group...

"Memristive switching mechanism for metal/oxide/metal nano-devices" demonstrating the memristive switching behavior and mechanism in nanodevices.

(August 26) 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
Samsung
The Samsung Group is a South Korean multinational conglomerate corporation headquartered in Samsung Town, Seoul, South Korea...

) 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.

(September 14–16) Blaise Mouttet, a graduate student at George Mason University
George Mason University
George Mason University is a public university based in unincorporated Fairfax County, Virginia, United States, south of and adjacent to the city of Fairfax. Additional campuses are located nearby in Arlington County, Prince William County, and Loudoun County...

, presents a poster entitled "Proposal for Memristors in Signal Processing" at Nano-Net 2008, a nanotechnology conference in Boston.

(September 23) Yu V. Pershin and M. Di Ventra of University of California, San Diego
University of California, San Diego
The University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...

 publish an article in Physical Review Letters
Physical Review Letters
Physical Review Letters , established in 1958, is a peer reviewed, scientific journal that is published 52 times per year by the American Physical Society...

entitled "Spin memristive systems: Spin memory effects in semiconductor spintronics" which notes memristive behavior in spintronics
Spintronics
Spintronics , also known as magnetoelectronics, is an emerging technology that exploits both the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices.An additional effect occurs when a spin-polarized current is...

.

(October 22) 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 28) Duncan Stewart, Patricia Beck, and Doug Ohlberg, researchers at HP Labs
HP Labs
HP Labs is the exploratory and advanced research group for Hewlett-Packard. The lab has some 600 researchersin seven locations throughout the world....

, receive U.S. Patent 7,443,711 (assigned to Hewlett-Packard) including basic patent claims to a tunable nanoscale 2-terminal resistance switch.

(November 4) Blaise Mouttet, a graduate student at George Mason University
George Mason University
George Mason University is a public university based in unincorporated Fairfax County, Virginia, United States, south of and adjacent to the city of Fairfax. Additional campuses are located nearby in Arlington County, Prince William County, and Loudoun County...

, receives U.S. Patent 7,447,828 including various patent claims to using 2-terminal resistance switching materials in adaptive signal processing.

(November 21) 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 University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

. 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.

(December 2) 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.


2009
(January 21) Sung Hyun Jo, Kuk-Hwan Kim, and Wei Lu of the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus 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
CMOS
Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...

 devices.

(January 23) Massimiliano Di Ventra, Yuriy V. Pershin, Leon O. Chua
Leon O. Chua
Leon Ong Chua is an IEEE Fellow and a professor in the electrical engineering and computer sciences department at the University of California, Berkeley, which he joined in 1971...

 submit an article in arXiv
ArXiv
The arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...

 entitled "Circuit elements with memory: memristors, memcapacitors and meminductors". which extends the notion of memristive systems to capacitive and inductive elements, namely capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

s and inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...

s whose properties depend on the state and history of the system.

(January 30) 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.

(February 10) 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.

(May 1) 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 19) Yuriy Pershin and Massimiliano Di Ventra published a preliminary article in Nature Precedings
Nature Precedings
Nature Precedings is an open access electronic preprint repository of scholarly work in the fields of biomedical sciences, chemistry, and earth sciences. Submissions to Nature Precedings are not peer reviewed...

entitled "Experimental demonstration of associative memory with memristive neural networks" in which a memristor emulator demonstrates properties of a neural synapse.

(June 2) A. Delgado published a paper entitled "Input Output Linearization of Memristive Systems" in the Proceedings of the 2009 IEEE Nanotechnology Materials and Devices Conference; this work demonstrates that feedback linearization can be applied to the memristor producing a linear device.

(June 3) 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 radio-frequency identification (RFID).

(July 13) At the 2nd International Multi-Conference on Engineering and Technological Innovation, Blaise Mouttet of George Mason University
George Mason University
George Mason University is a public university based in unincorporated Fairfax County, Virginia, United States, south of and adjacent to the city of Fairfax. Additional campuses are located nearby in Arlington County, Prince William County, and Loudoun County...

 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
Von Neumann architecture
The term Von Neumann architecture, aka the Von Neumann model, derives from a computer architecture proposal by the mathematician and early computer scientist John von Neumann and others, dated June 30, 1945, entitled First Draft of a Report on the EDVAC...

 for processors used in robotic control systems.

(August 4) The physical realization of an electrically modifiable array of memristive neural synapses is achieved by researchers at the Gwangju Institute of Science and Technology
Gwangju Institute of Science and Technology
Gwangju Institute of Science and Technology , formerly known as the Kwangju Institute of Science and Technology , is a leading research oriented institute of Korea located in Gwangju, South Korea...

 as reported in the journal Nanotechnology.

(September 17) Memristive behavior of magnetic tunnel junctions
Tunnel magnetoresistance
The Tunnel magnetoresistance is a magnetoresistive effect that occurs in magnetic tunnel junctions . This is a component consisting of two ferromagnets separated by a thin insulator. If the insulating layer is thin enough , electrons can tunnel from one ferromagnet into the other...

 is reported by researchers from the Bielefeld University
Bielefeld University
Bielefeld University is a university in Bielefeld, Germany. Founded in 1969, it is one of the country's newer universities, and considers itself a "reform" university, following a different style of organization and teaching than the established universities...

, Germany. A combination of resistive
Resistive random-access memory
Resistive random-access memory is a new non-volatile memory type being developed by many companies. The technology bears some similarities to CBRAM and phase change memory....

 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).


2010
(February, 17) A review on memristor and its modeling approaches is accepted to be published in the Proceedings of the Royal Society
Proceedings of the Royal Society
Proceedings of the Royal Society is the parent title of two scientific journals published by the Royal Society, whereas its initial journal, Philosophical Transactions, is now devoted to special thematic issues...

.

The 2nd Memristor and Memristive Systems Symposium was held on Tuesday, February 2, 2010 at Sutardja Dai Hall, UC Berkeley.

(April 8) An array of memristors is demonstrated to perform logical functions.

Memristor-based Content Addressable Memory (MCAM) is introduced and accepted in IEEE Transactions on Very Large Scale Integration (VLSI) Systems.
(June 1) At the 2010 International Symposium on Circuits and Systems
International Symposium on Circuits and Systems
Initiated in 1968, by a small group of distinguished circuit theorists, IEEE ISCAS has grown into a premier annual conference reflecting the diversity, richness, and significance of the circuits and systems fields, as well as the growing technological applications and knowledge economy that is...

, there were two special sessions on memristor devices and fabrication. One of the presentations entitled "The mythology of the memristor" by Blaise Mouttet argued that the interpretation of the memristor as a fourth fundamental was incorrect and that the device discovered by HPLabs was not actually a memristor, but part of a broader class of memristive systems.

(August 31) HP announced they teamed up with Hynix
Hynix
Hynix Semiconductor Inc. chips and flash memory chips. Founded in 1983, Hynix is the world's second-largest memory chipmaker, the largest being Samsung Electronics. Formerly known as Hyundai Electronics, the company has manufacturing sites in Korea, the U.S., China and Taiwan...

 to produce a commercial product dubbed "ReRam".

(October 15) At the 2010 IEEE Nanotechnology Materials and Devices Conference, A. Delgado presented the paper "The Memristor as Controller". This work introduces the memristor as a programmable gain for closed loop systems and derives an approximate describing function for the pinched hysteresis loop.

(December 7) Ju-Hee So and Hyung-Jun Koo of North Carolina State University
North Carolina State University
North Carolina State University at Raleigh is a public, coeducational, extensive research university located in Raleigh, North Carolina, United States. Commonly known as NC State, the university is part of the University of North Carolina system and is a land, sea, and space grant institution...

 announced a hydrogel form of memristor which is speculated to be useful to construct a brain-computer interface
Brain-computer interface
A brain–computer interface , sometimes called a direct neural interface or a brain–machine interface , is a direct communication pathway between the brain and an external device...

.


2013
The first products using memristor technology are expected to become available.


See also


  • Chua (unit)
  • Memistor
    Memistor
    - History :Although the memristor is defined in terms of a 2-terminal circuit element, there was an implementation of a 3-terminal device called a memistor developed by Bernard Widrow in 1960...

  • Electrical element
    Electrical element
    Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks...

  • List of emerging technologies
  • Physical neural network
    Physical neural network
    A physical neural network is a type of artificial neural network in which an electrically adjustable resistance material is used to emulate the function of a neural synapse. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as opposed to...

  • RRAM

External links