A Paper
On
MEMRISTORS
Presenters :
Name :T.HANOK
Department : E.C.E
College : K.L.UNIVERSITY,VADDESWARAM
Contact :8801355500
Email :
Name : M.YASWANTH
Department : E.C.E
College : K.L.UNIVERSITY,VADDESWARAM
Contact : 9059912340
Email :
Abstract:
A Memristor ("memory resistor") is one of various kinds of passive two-terminal circuit elements that maintain a functional relationship between the time integrals of current and voltage. This function, called memristance, is similar to variable resistance. Specifically engineered Memrstors provide controllable resistance, but such devices are not commercially available. Other devices like batteries and varistors have memristance, but it does not normally dominate their behavior. The definition of the memristor is based solely on fundamental circuit variables, similarly to the resistor, capacitor, and inductor. Unlike those three elements, which are allowed in linear time-invariant or LTI system theory, Memristor are nonlinear and may be described by any of a variety of time-varying functions of net charge. There is no such thing as a generic memristor. Instead, each device implements a particular function, wherein either the integral of voltage determines the integral of current, or vice versa. A linear time-invariant memristor is simply a conventional resistor.
Introduction:
Memristor theory was formulated and named by Leon Chua in a 1971 paper. Chua extrapolated the conceptual symmetry between the resistor, inductor, and capacitor, and inferred that the memristor is a similarly fundamental device. Other scientists had already used fixed nonlinear flux-charge relationships, but Chua's theory introduces generality.
On April 30, 2008 a team at HP Labs announced the development of a switching memristor. Based on a thin film of titanium dioxide, it has a regime of operation with an approximately linear charge-resistance relationship. These devices are being developed for application in nanoelectronic memories, computer logic, and neuromorphic computer architectures.
Theory
The memristor is formally defined as a two-terminal element in which the magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device. Each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.
Noting from Faraday's law of induction that magnetic flux is simply the time integral of voltage, and charge is the time integral of current, we may write the more convenient form It can be inferred from this that memristance is simply charge-dependent resistance. If M(q(t)) is a constant, then we obtain Ohm's Law R(t) = V(t)/ I(t).
If M(q(t)) is nontrivial, however, the equation is not equivalent because q(t) and M(q(t)) will vary with time. Solving for voltage as a function of time we obtain
This equation reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary. Of course, nonzero current implies time varying charge. Alternating current, however, may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement—as long as the maximum change in q does not cause much change in M..
Furthermore, the memristor is static if no current is applied. If I(t) = 0, we find V(t) = 0 and M(t) is constant. This is the essence of the memory effect.
The power consumption characteristic recalls that of a resistor, I2R.
As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop.
Magnetic flux in a passive device:
In circuit theory, magnetic flux Φm typically relates to Faraday's law of induction, which states that the voltage in terms of electric field potential gained around a loop (electromotive force) equals the negative derivative of the flux through the loop:
This notion may be extended by analogy to a single passive device. If the circuit is composed of passive devices, then the total flux is equal to the sum of the flux components due to each device. For example, a simple wire loop with low resistance will have high flux linkage to an applied field as little flux is "induced" in the opposite direction. Voltage for passive devices is evaluated in terms of energy lost by a unit of charge:
Observing that Φm is simply equal to the integral over time of the potential drop between two points, we find that it may readily be calculated, for example by an operational amplifier configured as an integrator.
Two unintuitive concepts are at play:
· Magnetic flux is generated by a resistance in opposition to an applied field or electromotive force. In the absence of resistance, flux due to constant EMF increases indefinitely. The opposing flux induced in a resistor must also increase indefinitely so their sum remains finite.
· Any appropriate response to applied voltage may be called "magnetic flux."
The upshot is that a passive element may relate some variable to flux without storing a magnetic field. Indeed, a memristor always appears instantaneously as a resistor. As shown above, assuming non-negative resistance, at any instant it is dissipating power from an applied EMF and thus has no outlet to dissipate a stored field into the circuit. This contrasts with an inductor, for which a magnetic field stores all energy originating in the potential across its terminals, later releasing it as an electromotive force within the circuit.
Physical restrictions on M(q):
An applied constant voltage potential results in uniformly increasing Φm. numerically, infinite memory resources, or an infinitely strong field, would be required to store a number which grows arbitrarily large. Three alternatives avoid this physical impossibility:
· M(q) approaches zero, such that Φm = ∫M(q)dq = ∫M(q(t))I dt remains bounded but continues changing at an ever-decreasing rate. Eventually, this would encounter some kind of quantization and non-ideal behavior.
· M(q) is cyclic, so that M(q) = M(q − Δq) for all q and some Δq, e.g. sin2(q/Q).
· The device enters hysteresis once a certain amount of charge has passed through, or otherwise ceases to act as a memristor.
Memristive systems:
The memristor was generalized to memristive systems in a 1976 paper by Leon Chua. Whereas a memristor has mathematically scalar state, a system has vector state. The number of state variables is independent of, and usually greater than, the number of terminals.
In this paper, Chua applied this model to empirically observed phenomena, including the Hodgkin–Huxley model of the axon and a thermistor at constant ambient temperature. He also described memristive systems in terms of energy storage and easily observed electrical characteristics. These characteristics match resistive random-access memory and phase-change memory, relating the theory to active areas of research.
In the more general concept of an n-th order memristive system the defining equations are
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 = Qon−Qoff.
To arrive at the final expression, substitute V=I(q)M(q), and then ∫dq/V = ∆Q/V for constant V. This power characteristic differs fundamentally from that of a metal oxide semiconductor transistor, which is a capacitor-based device. Unlike the transistor, the final state of the memristor in terms of charge does not depend on bias voltage.
The type of memristor described by Williams ceases to be ideal after switching over its entire resistance range and enters hysteresis, also called the "hard-switching regime." Another kind of switch would have a cyclic M(q) so that each off-on event would be followed by an on-off event under constant bias. Such a device would act as a memristor under all conditions, but would be less practical.
Spintronic Memristor:
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.It was stated in this interview that the proposed memristor was easy to construct and easily integrated on top of a CMOS device.
Spin Torque Transfer Magnetoresistance:
Spin Torque Transfer MRAM 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 based magnetic tunnel junctions show memristive behavior based on the drift of oxygen vacancies within the insulating MgO layer (resistive switching). 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).
Titanium dioxide memristor:
Interest in the memristor revived in 2008 when an experimental solid state version was reported by R. Stanley Williams of Hewlett Packard. 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 1960's.
The HP device is composed of a thin (50 nm) titanium dioxide film between two 5nm thick electrodes, one Ti, the other Pt. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers, meaning that the depleted layer has a much lower resistance than the non-depleted layer. When an electric field is applied, the oxygen vacancies drift (see Fast ion conductor), changing the boundary between the high-resistance and low-resistance layers. Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by changing the direction of current. Since the HP device displays fast ion conduction at nanoscale, it is considered a nanoionic device.
Memristance is displayed only when both the doped layer and depleted layer contribute to resistance. When enough charge has passed through the memristor that the ions can no longer move, the device enters hysteresis. It ceases to integrate q=∫Idt but rather keeps q at an upper bound and M fixed, thus acting as a resistor until current is reversed.
Memory applications of thin-film oxides had been an area of active investigation for some time. IBM published an article in 2000 regarding structures similar to that described by Williams. Samsung has a 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. Although the small dimensions of the device seem to imply fast operation, the charge carriers move very slowly, with an ion mobility of 10−10 cm2/(V·s). In comparison, the highest known drift ionic mobilities occur in advanced superionic conductors, such as rubidium silver iodide with about 2×10−4 cm2/(V·s) conducting silver ions at room temperature. Electrons and holes in silicon have a mobility ~1000cm2/(V·s), a figure which is essential to the performance of transistors. However, a relatively low bias of 1 volt was used, and the plots appear to be generated by a mathematical model rather than a laboratory experiment.
Polymeric memristor:
In July 2008, Victor Erokhin and Marco P. Fontana, in Electrochemically controlled polymeric device: a memristor (and more) found two years ago, claim to have developed a polymeric memristor before the titanium dioxide memristor more recently announced.
Juri H. Krieger and Stuart M. Spitzer publish a paper in the IEEE Proceeding 2004 Non-Volatile Memory Technology Symposium entitled "Non-traditional, Non-volatile Memory Based on Switching and Retention Phenomena in Polymeric Thin Films". This work describes the process of dynamic doping of polymer and inorganic dielectric-like materials in order to improve the switching characteristics and retention required to create functioning nonvolatile memory cells. 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 as this passive layer, which allows to significantly decrease the ionic extraction field.