Memristor

Chua in his 1971 paper identified a theoretical symmetry between the non-linear resistor (voltage vs. current), non-linear capacitor (voltage vs. charge), and non-linear inductor (magnetic flux linkage vs. current). From this symmetry he inferred the characteristics of a fourth fundamental non-linear circuit element, linking magnetic flux and charge, which he called the memristor. In contrast to a linear (or non-linear) resistor, the memristor has a dynamic relationship between current and voltage, including a memory of past voltages or currents. Other scientists had proposed dynamic memory resistors such as the memistor of Bernard Widrow, but Chua introduced a mathematical generality. Derivation and characteristics The memristor was originally defined in terms of a non-linear functional relationship between magnetic flux linkage and the amount of electric charge that has flowed, : In the relationship between and , the derivative of one with respect to the other depends on the value of one or the other, and so each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge: M(q)=\frac{\mathrm d\Phi_{\rm m}}{\mathrm dq} \,. Substituting the flux as the time integral of the voltage, and charge as the time integral of current, the more convenient forms are: M(q(t)) = \cfrac{\mathrm d\Phi_{\rm}/\mathrm dt}{\mathrm dq/\mathrm dt}=\frac{V(t)}{I(t)}\,. To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term , which characterizes the device, and write it as a differential equation. The above table covers all meaningful ratios of differentials of , , , and . No device can relate to , or to , because is the time derivative of and is the time derivative of . It can be inferred from this that memristance is charge-dependent resistance. If is a constant function (i.e. has the same value for all ), then we obtain Ohm's law: . If is nontrivial, however, the equation is not equivalent because and thus vary with time. Solving for voltage as a function of time produces V(t) =\ M(q(t)) \cdot I(t)\,. This equation reveals that memristance defines a linear relationship between current and voltage, as long as does not vary with charge. Non-zero 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 value of does not cause much change in compared to the initial value . Furthermore, the memristor has a constant memristance if no current is applied. If , is constant due to being constant. This is the essence of the memory effect. Analogously, we can define a as memductance (portmanteau of memory and conductance): I(t) = W(\phi(t)) \cdot V(t)\,. Memductance with respect to flux is the inverse of memristance with respect to charge, i.e. W(\phi(t)) = \frac{1}{M(q(t))}, and therefore the unit of memductance is the same as the unit of conductance ‒ Siemens. The power consumption characteristic recalls that of a resistor, : P(t) =\ I(t) \cdot V(t) =\ I^2(t) \cdot M(q(t))\,. As long as varies little, such as under alternating current, the memristor will appear as a constant resistor. If increases rapidly, however, current and power consumption will quickly stop. is physically restricted to be positive for all values of (assuming the device is passive and does not become superconductive at some ). A negative value for some charge implies it acts as a power source at this charge level. A negative value for all charges would mean that it would perpetually supply energy when operated with alternating current. ==Modelling and validation==

In order to understand the nature of memristor function, some knowledge of fundamental circuit theoretic concepts is useful, starting with the concept of device modeling. Engineers and scientists seldom analyze a physical system in its original form. Instead, they construct a model which approximates the behaviour of the system. By analyzing the behaviour of the model, they hope to predict the behaviour of the actual system. The primary reason for constructing models is that physical systems are usually too complex to be amenable to a practical analysis. In the 20th century, work was done on devices where researchers did not recognize the memristive characteristics. This has raised the suggestion that such devices should be recognised as memristors. mentions the memristor in connection with Josephson junctions. This was an early use of the word memristor in the context of a circuit device. One of the terms in the current through a Josephson junction is of the form: \begin{align} i_M(v) &= \epsilon\cos(\phi_0)v \\ &=W(\phi_0)v \end{align} where is a constant based on the physical superconducting materials, is the voltage across the junction and is the current through the junction. Through the late 20th century, research regarding this phase-dependent conductance in Josephson junctions was carried out. A more comprehensive approach to extracting this phase-dependent conductance appeared with Peotta and Di Ventra's seminal paper in 2014. Memristor circuits Due to the practical difficulty of studying the ideal memristor, we will discuss other electrical devices which can be modelled using memristors. For a mathematical description of a memristive device (systems), see . A discharge tube can be modelled as a memristive device, with resistance being a function of the number of conduction electrons . Thermistors can be modeled as memristive devices: The memristor plays a crucial role in mimicking the charge storage effect in the diode base, and is also responsible for the conductivity modulation phenomenon (that is so important during forward transients). Criticisms In 2008, a team at HP Labs found experimental evidence for Chua's memristor based on an analysis of a thin film of titanium dioxide, thus connecting the operation of ReRAM devices to the memristor concept. According to HP Labs, the memristor would operate in the following way: the memristor's electrical resistance is not constant but depends on the current that had previously flowed through the device, i.e., its present resistance depends on how much electric charge has previously flowed through it and in what direction; the device remembers its history—the so-called ''''. The HP Labs result was published in the scientific journal Nature. Chua argued that the memristor definition could be generalized to cover all forms of two-terminal non-volatile memory devices based on resistance switching effects. Chua also argued that the memristor is the oldest known circuit element, with its effects predating the resistor, capacitor, and inductor. However, there are doubts as to whether a memristor can actually exist. Additionally, some experimental evidence contradicts Chua's generalization since a non-passive nanobattery effect is observable in resistance switching memory. A simple test has been proposed by Pershin and Di Ventra to analyze whether such an ideal or generic memristor does actually exist or is a purely mathematical concept. Up to now, there seems to be no experimental resistance switching device (ReRAM) which can pass the test. These devices are intended for applications in nanoelectronic memory devices, computer logic, and neuromorphic/neuromemristive computer architectures. In 2013, Hewlett-Packard CTO Martin Fink suggested that memristor memory may become commercially available as early as 2018. In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip. -depleted titanium dioxide memristors built at HP Labs, imaged by an atomic force microscope. The wires are about , or 150 atoms, wide. Electric current through the memristors shifts the oxygen vacancies, causing a gradual and persistent change in electrical resistance. Some researchers argued that biological structures such as blood and skin fit the definition. Others argued that the memory device under development by HP Labs and other forms of ReRAM are not memristors, but rather part of a broader class of variable-resistance systems, and that a broader definition of memristor is a scientifically unjustifiable land grab that favored HP's memristor patents. In 2011, Meuffels and Schroeder noted that one of the early memristor papers included a mistaken assumption regarding ionic conduction. In 2012, Meuffels and Soni discussed some fundamental issues and problems in the realization of memristors. They indicated inadequacies in the electrochemical modeling presented in the Nature article "The missing memristor found" in 2013. Within this context, Meuffels and Soni Consequently, there is always a lower limit of energy requirement – depending on the required bit-error probability – for intentionally changing a bit value in any memory device. In the general concept of memristive system the defining equations are (see ): \begin{align} y(t) &= g(\mathbf{x},u,t) u(t), \\ \dot{\mathbf{x}} &= f(\mathbf{x},u,t), \end{align} where is an input signal, and is an output signal. The vector \mathbf{x} represents a set of state variables describing the different internal memory states of the device. \dot{\mathbf{x}} is the time-dependent rate of change of the state vector \mathbf{x} with time. When one wants to go beyond mere curve fitting and aims at a real physical modeling of non-volatile memory elements, e.g., resistive random-access memory devices, one has to keep an eye on the aforementioned physical correlations. To check the adequacy of the proposed model and its resulting state equations, the input signal can be superposed with a stochastic term , which takes into account the existence of inevitable thermal fluctuations. The dynamic state equation in its general form then finally reads: \dot{\mathbf{x}} = f(\mathbf{x}, u(t) + \xi(t), t), where is, e.g., white Gaussian current or voltage noise. On the basis of an analytical or numerical analysis of the time-dependent response of the system towards noise, a decision on the physical validity of the modeling approach can be made, e.g., whether the system would be able to retain its memory states in power-off mode. Such an analysis was performed by Di Ventra and Pershin Di Ventra and Pershin A 2014 article from researchers of ReRAM concluded that Strukov's (HP's) initial/basic memristor modeling equations do not reflect the actual device physics well, whereas subsequent (physics-based) models such as Pickett's model or Menzel's ECM model (Menzel is a co-author of that article) have adequate predictability, but are computationally prohibitive. As of 2014, the search continues for a model that balances these issues; the article identifies Chang's and Yakopcic's models as potentially good compromises. Martin Reynolds, an electrical engineering analyst with research outfit Gartner, commented that while HP was being sloppy in calling their device a memristor, critics were being pedantic in saying that it was not a memristor. Experimental tests Chua suggested experimental tests to determine if a device may properly be categorized as a memristor: all resistive switching memories including ReRAM, MRAM and phase-change memory meet these criteria and are memristors. However, the lack of data for the Lissajous curves over a range of initial conditions or over a range of frequencies complicates assessments of this claim. Experimental evidence shows that redox-based resistance memory (ReRAM) includes a nanobattery effect that is contrary to Chua's memristor model. This indicates that the memristor theory needs to be extended or corrected to enable accurate ReRAM modeling. ==Theory==

In 2008, researchers from HP Labs introduced a model for a memristance function based on thin films of titanium dioxide. For a current-controlled memristive system, the input u(t) is the current i(t), the output y(t) is the voltage v(t), and the slope of the curve represents the electrical resistance. The change in slope of the pinched hysteresis curves demonstrates switching between different resistance states which is a phenomenon central to ReRAM and other forms of two-terminal resistance memory. At high frequencies, memristive theory predicts the pinched hysteresis effect will degenerate, resulting in a straight line representative of a linear resistor. It has been proven that some types of non-crossing pinched hysteresis curves (denoted Type-II) cannot be described by memristors. Memristive networks and mathematical models of circuit interactions The concept of memristive networks was first introduced by Leon Chua in his 1976 paper "Memristive Devices and Systems." which describes the evolution of the internal memory of the network for each device. For a simple memristor model (but not realistic) of a switch between two resistance values, given by the Williams-Strukov model R(x)=R_{off} (1-x)+R_{on} x, with dx/dt=I/\beta-\alpha x, there is a set of nonlinearly coupled differential equations that takes the form: : \frac{d\vec{x}}{dt} = -\alpha \vec{x}+\frac{1}{\beta} (I-\chi \Omega X)^{-1} \Omega \vec S where X is the diagonal matrix with elements x_i on the diagonal, \alpha,\beta,\chi are based on the memristors physical parameters. The vector \vec S is the vector of voltage generators in series to the memristors. The circuit topology enters only in the projector operator \Omega^2=\Omega, defined in terms of the cycle matrix of the graph. The equation provides a concise mathematical description of the interactions due to Kirchhoff 's laws. Interestingly, the equation shares many properties in common with a Hopfield network, such as the existence of Lyapunov functions and classical tunnelling phenomena. In the context of memristive networks, the CTD equation may be used to predict the behavior of memristive devices under different operating conditions, or to design and optimize memristive circuits for specific applications. Extended systems Some researchers have raised the question of the scientific legitimacy of HP's memristor models in explaining the behavior of ReRAM. attempts to extend the memristive systems framework by including dynamic systems incorporating higher-order derivatives of the input signal u(t) as a series expansion :\begin{align} y(t) &= g_0(\textbf{x}, u)u(t) + g_1(\textbf{x}, u){\operatorname{d}^2u\over\operatorname{d}t^2} + g_2(\textbf{x}, u){\operatorname{d}^4u\over\operatorname{d}t^4} + \ldots + g_m(\textbf{x}, u){\operatorname{d}^{2m}u\over\operatorname{d}t^{2m}}, \\ \dot{\textbf{x}} &= f(\textbf{x}, u) \end{align} where m is a positive integer, u(t) is an input signal, y(t) is an output signal, the vector x represents a set of n state variables describing the device, and the functions g and f are continuous functions. This equation produces the same zero-crossing hysteresis curves as memristive systems but with a different frequency response than that predicted by memristive systems. Another example suggests including an offset value a to account for an observed nanobattery effect which violates the predicted zero-crossing pinched hysteresis effect. :\begin{align} y(t) &= g_0(\textbf{x},u)(u(t)-a), \\ \dot{\textbf{x}} &= f(\textbf{x},u) \end{align} == Implementation of hysteretic current-voltage memristors ==

There exist implementations of memristors with a hysteretic current-voltage curve or with both hysteretic current-voltage curve and hysteretic flux-charge curve. Memristors with hysteretic current-voltage curve use a resistance dependent on the history of the current and voltage and bode well for the future of memory technology due to their simple structure, high energy efficiency, and high integration. Titanium dioxide memristor Interest in the memristor revived when an experimental solid-state version was reported by R. Stanley Williams of Hewlett Packard in 2007. 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 were originally described in the 1960s. The HP device is composed of a thin (50 nm) titanium dioxide film between two 5 nm thick electrodes, one titanium, the other platinum. 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. 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=∫I dt, 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 published an article in 2000 regarding structures similar to that described by Williams. which bodes well for the future of the technology. At these densities it could easily rival the current sub-25 nm flash memory technology. Silicon dioxide memristor It seems that memristance has been reported in nanoscale thin films of silicon dioxide as early as the 1960s . More recently, beginning in 2012, Tony Kenyon, Adnan Mehonic and their group clearly demonstrated that the resistive switching in silicon oxide thin films is due to the formation of oxygen vacancy filaments in defect-engineered silicon dioxide, having probed directly the movement of oxygen under electrical bias, and imaged the resultant conductive filaments using conductive atomic force microscopy. Polymeric memristor In 2004, Krieger and Spitzer described dynamic doping of polymer and inorganic dielectric-like materials that improved the switching characteristics and retention required to create functioning nonvolatile memory cells. They used a passive layer between electrode and active thin films, which enhanced the extraction of ions from the electrode. It is possible to use fast-ion conductor as this passive layer, which allows a significant reduction of the ionic extraction field. In July 2008, Erokhin and Fontana claimed to have developed a polymeric memristor before the more recently announced titanium dioxide memristor. In 2010, Alibart, Gamrat, Vuillaume et al. introduced a new hybrid organic/nanoparticle device (the NOMFET : Nanoparticle Organic Memory Field Effect Transistor), which behaves as a memristor and which exhibits the main behavior of a biological spiking synapse. This device, also called a synapstor (synapse transistor), was used to demonstrate a neuro-inspired circuit (associative memory showing a pavlovian learning). In 2012, Crupi, Pradhan and Tozer described a proof of concept design to create neural synaptic memory circuits using organic ion-based memristors. The synapse circuit demonstrated long-term potentiation for learning as well as inactivity based forgetting. Using a grid of circuits, a pattern of light was stored and later recalled. This mimics the behavior of the V1 neurons in the primary visual cortex that act as spatiotemporal filters that process visual signals such as edges and moving lines. In 2012, Erokhin and co-authors have demonstrated a stochastic three-dimensional matrix with capabilities for learning and adapting based on polymeric memristor. Layered memristor In 2014, Bessonov et al. reported a flexible memristive device comprising a MoOx/MoS2 heterostructure sandwiched between silver electrodes on a plastic foil. The fabrication method is entirely based on printing and solution-processing technologies using two-dimensional layered transition metal dichalcogenides (TMDs). The memristors are mechanically flexible, optically transparent and produced at low cost. The memristive behaviour of switches was found to be accompanied by a prominent memcapacitive effect. High switching performance, demonstrated synaptic plasticity and sustainability to mechanical deformations promise to emulate the appealing characteristics of biological neural systems in novel computing technologies. Atomristor Atomristor is defined as the electrical devices showing memristive behavior in atomically thin nanomaterials or atomic sheets. In 2018, Ge and Wu et al. in the Akinwande group at the University of Texas, first reported a universal memristive effect in single-layer TMD (MX2, M = Mo, W; and X = S, Se) atomic sheets based on vertical metal-insulator-metal (MIM) device structure. The work was later extended to monolayer hexagonal boron nitride, which is the thinnest memory material of around 0.33 nm. These atomristors offer forming-free switching and both unipolar and bipolar operation. The switching behavior is found in single-crystalline and poly-crystalline films, with various conducting electrodes (gold, silver and graphene). Atomically thin TMD sheets are prepared via CVD/MOCVD, enabling low-cost fabrication. Afterwards, taking advantage of the low on resistance and large on/off ratio, a high-performance zero-power RF switch is proved based on MoS2 or h-BN atomristors, indicating a new application of memristors for 5G, 6G and THz communication and connectivity systems. In 2020, atomistic understanding of the conductive virtual point mechanism was elucidated in an article in nature nanotechnology. Ferroelectric memristor The ferroelectric memristor reported observing memristor effect in structure based on vertically aligned carbon nanotubes studying bundles of CNT by scanning tunneling microscope. Later it was found that CNT memristive switching is observed when a nanotube has a non-uniform elastic strain ΔL0. It was shown that the memristive switching mechanism of strained CNT is based on the formation and subsequent redistribution of non-uniform elastic strain and piezoelectric field Edef in the nanotube under the influence of an external electric field E(x,t). Biomolecular memristor Biomaterials have been evaluated for use in artificial synapses and have shown potential for application in neuromorphic systems. In particular, the feasibility of using a collagen‐based biomemristor as an artificial synaptic device has been investigated, whereas a synaptic device based on lignin demonstrated rising or lowering current with consecutive voltage sweeps depending on the sign of the voltage furthermore a natural silk fibroin demonstrated memristive properties; spin-memristive systems based on biomolecules are also being studied. In 2012, Sandro Carrara and co-authors have proposed the first biomolecular memristor with aims to realize highly sensitive biosensors. Since then, several memristive sensors have been demonstrated. Spin memristive systems Spintronic memristor Chen and Wang, researchers at disk-drive manufacturer Seagate Technology described three examples of possible magnetic memristors. In one device resistance occurs when the spin of electrons in one section of the device points in a different direction from those in another section, creating a domain wall, a boundary between the two sections. Electrons flowing into the device have a certain spin, which alters the device's magnetization state. Changing the magnetization, in turn, moves the domain wall and changes the resistance. The work's significance led to an interview by IEEE Spectrum. A first experimental proof of the spintronic memristor based on domain wall motion by spin currents in a magnetic tunnel junction was given in 2011. Memristance in a magnetic tunnel junction The magnetic tunnel junction has been proposed to act as a memristor through several potentially complementary mechanisms, both extrinsic (redox reactions, charge trapping/detrapping and electromigration within the barrier) and intrinsic (spin-transfer torque). Extrinsic mechanism Based on research performed between 1999 and 2003, Bowen et al. published experiments in 2006 on a magnetic tunnel junction (MTJ) endowed with bi-stable spin-dependent states(resistive switching). The MTJ consists in a SrTiO3 (STO) tunnel barrier that separates half-metallic oxide LSMO and ferromagnetic metal CoCr electrodes. The MTJ's usual two device resistance states, characterized by a parallel or antiparallel alignment of electrode magnetization, are altered by applying an electric field. When the electric field is applied from the CoCr to the LSMO electrode, the tunnel magnetoresistance (TMR) ratio is positive. When the direction of electric field is reversed, the TMR is negative. In both cases, large amplitudes of TMR on the order of 30% are found. Since a fully spin-polarized current flows from the half-metallic LSMO electrode, within the Julliere model, this sign change suggests a sign change in the effective spin polarization of the STO/CoCr interface. The origin to this multistate effect lies with the observed migration of Cr into the barrier and its state of oxidation. The sign change of TMR can originate from modifications to the STO/CoCr interface density of states, as well as from changes to the tunneling landscape at the STO/CoCr interface induced by CrOx redox reactions. Reports on MgO-based memristive switching within MgO-based MTJs appeared starting in 2008 While the drift of oxygen vacancies within the insulating MgO layer has been proposed to describe the observed memristive effects, on spintronics. This highlights the importance of understanding what role oxygen vacancies play in the memristive operation of devices that deploy complex oxides with an intrinsic property such as ferroelectricity or multiferroicity. Intrinsic mechanism The magnetization state of a MTJ can be controlled by Spin-transfer torque, and can thus, through this intrinsic physical mechanism, exhibit memristive behavior. This spin torque is induced by current flowing through the junction, and leads to an efficient means of achieving a MRAM. However, the length of time the current flows through the junction determines the amount of current needed, i.e., charge is the key variable. The combination of intrinsic (spin-transfer torque) and extrinsic (resistive switching) mechanisms naturally leads to a second-order memristive system described by the state vector x = (x1,x2), where x1 describes the magnetic state of the electrodes and x2 denotes the resistive state of the MgO barrier. In this case the change of x1 is current-controlled (spin torque is due to a high current density) whereas the change of x2 is voltage-controlled (the drift of oxygen vacancies is due to high electric fields). The presence of both effects in a memristive magnetic tunnel junction led to the idea of a nanoscopic synapse-neuron system. Spin memristive system A fundamentally different mechanism for memristive behavior has been proposed by Pershin and Di Ventra. The authors show that certain types of semiconductor spintronic structures belong to a broad class of memristive systems as defined by Chua and Kang. but was not described in terms of memristive behavior. On a short time scale, these structures behave almost as an ideal memristor. The SDC device is the first memristive device available commercially to researchers, students and electronics enthusiast worldwide. The SDC device is operational immediately after fabrication. In the Ge2Se3 active layer, Ge-Ge homopolar bonds are found and switching occurs. The three layers consisting of Ge2Se3/Ag/Ge2Se3, directly below the top tungsten electrode, mix together during deposition and jointly form the silver-source layer. A layer of SnSe is between these two layers ensuring that the silver-source layer is not in direct contact with the active layer. Since silver does not migrate into the active layer at high temperatures, and the active layer maintains a high glass transition temperature of about , the device has significantly higher processing and operating temperatures at and at least , respectively. These processing and operating temperatures are higher than most ion-conducting chalcogenide device types, including the S-based glasses (e.g. GeS) that need to be photodoped or thermally annealed. These factors allow the SDC device to operate over a wide range of temperatures, including long-term continuous operation at . == Implementation of hysteretic flux-charge memristors ==

There exist implementations of memristors with both hysteretic current-voltage curve and hysteretic flux-charge curve. Time-integrated Formingfree memristor Time-integrated Formingfree (TiF) memristors reveal a hysteretic flux-charge curve with two distinguishable branches in the positive bias range and with two distinguishable branches in the negative bias range. And TiF memristors also reveal a hysteretic current-voltage curve with two distinguishable branches in the positive bias range and with two distinguishable branches in the negative bias range. The memristance state of a TiF memristor can be controlled by both the flux and the charge [DOI: 10.1063/1.4775718]. A TiF memristor was first demonstrated by Heidemarie Schmidt and her team in 2011. This TiF memristor is composed of a BiFeO3 thin film between metallically conducting electrodes, one gold, the other platinum. The hysteretic flux-charge curve of the TiF memristor changes its slope continuously in one branch in the positive and in one branch in the negative bias range (write branches) and has a constant slope in one branch in the positive and in one branch in the negative bias range (read branches). the slope of the flux-charge curve corresponds to the memristance of a memristor or to its internal state variables. The TiF memristors can be considered as memristors with a constant memristance in the two read branches and with a reconfigurable memristance in the two write branches. The physical memristor model which describes the hysteretic current-voltage curves of the TiF memristor implements static and dynamic internal state variables in the two read branches and in the two write branches. The static and dynamic internal state variables of a non-linear memristors can be used to implement operations on non-linear memristors representing linear, non-linear, and even transcendental, e.g. exponential or logarithmic, input-output functions. The transport characteristics of the TiF memristor in the small current – small voltage range are non-linear. This non-linearity well compares to the non-linear characteristics in the small current – small voltage range of the basic former and present building blocks in the arithmetic logic unit of von-Neumann computers, i.e. of vacuum tubes and of transistors. In contrast to vacuum tubes and transistors, the signal output of hysteretic flux-charge memristors, i.e. of TiF memristors, is not lost when the operation power is switched off before storing the signal output to the memory. Therefore, hysteretic flux-charge memristors are said to merge the functionality of the arithmetic logic unit and of the memory unit without data transfer. The transport characteristics in the small current – small voltage range of hysteretic current-voltage memristors are linear. This explains why hysteretic current-voltage memristors are well established memory units and why they can not merge the functionality of the arithmetic logic unit and of the memory unit without data transfer. ==Potential applications==

Memristors are not yet made in sufficient numbers to gain any commercial applications. However, a potential application of memristors is in analog memories for superconducting quantum computers. HP prototyped a crossbar latch memory that can fit 100 gigabits in a square centimeter, and proposed a scalable 3D design (consisting of up to 1000 layers or 1 petabit per cm3). In May 2008 HP reported that its device reaches currently about one-tenth the speed of DRAM. The devices' resistance would be read with alternating current so that the stored value would not be affected. In May 2012, it was reported that the access time had been improved to 90 nanoseconds, which is nearly one hundred times faster than the contemporaneous Flash memory. At the same time, the energy consumption was just one percent of that consumed by Flash memory. Memristors have applications in programmable logic signal processing, super-resolution imaging physical neural networks, control systems, reconfigurable computing, in-memory computing, brain–computer interfaces and RFID. Memristive devices are potentially used for stateful logic implication, allowing a replacement for CMOS-based logic computation Several early works have been reported in this direction. In 2009, 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 subjected to a train of periodic pulses, the circuit learns and anticipates the next pulse similar to the behavior of slime molds Physarum polycephalum where the viscosity of channels in the cytoplasm responds to periodic environment changes. MoNETA is the first large-scale neural network model to implement whole-brain circuits to power a virtual and robotic agent using memristive hardware. Application of the memristor crossbar structure in the construction of an analog soft computing system was demonstrated by Merrikh-Bayat and Shouraki. In 2011, they showed how memristor crossbars can be combined with fuzzy logic to create an analog memristive neuro-fuzzy computing system with fuzzy input and output terminals. Learning is based on the creation of fuzzy relations inspired from Hebbian learning rule. In 2013 Leon Chua published a tutorial underlining the broad span of complex phenomena and applications that memristors span and how they can be used as non-volatile analog memories and can mimic classic habituation and learning phenomena. ==Derivative devices==

Memistor and memtransistor The memistor and memtransistor are transistor-based devices which include memristor function. Memcapacitors and meminductors In 2009, Di Ventra, Pershin, and Chua extended 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, further extended in 2013 by Di Ventra and Pershin. ==History==

Precursors Sir Humphry Davy is said by some to have performed the first experiments which can be explained by memristor effects as long ago as 1808. However the first device of a related nature to be constructed was the memistor (i.e. memory resistor), a term coined in 1960 by Bernard Widrow to describe a circuit element of an early artificial neural network called ADALINE. A few years later, in 1968, Argall published an article showing the resistance switching effects of TiO2 which was later claimed by researchers from Hewlett Packard to be evidence of a memristor. (composed of researchers from Universidad Nacional de General San Martín (Argentina), INTI, CNEA, and CONICET) put memory devices into a Low Earth orbit. Since then, seven missions with different devices are performing experiments in low orbits, onboard Satellogic's Ñu-Sat satellites. On 7 July 2015, Knowm Inc announced Self Directed Channel (SDC) memristors commercially. These devices remain available in small numbers. On 13 July 2018, MemSat (Memristor Satellite) was launched to fly a memristor evaluation payload. In 2021, Jennifer Rupp and Martin Bazant of MIT started a Lithionics research programme to investigate applications of lithium beyond their use in battery electrodes, including lithium oxide-based memristors in neuromorphic computing. In May 2023, TECHiFAB GmbH (techifab.com) announced the commercial availability of TiF memristors. These devices remain available in small and medium quantities. In the September 2023 issue of Science Magazine, Chinese scientists Wenbin Zhang et al. described the development and testing of a memristor-based integrated circuit. ==See also==