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INTRODUCTION
Generally when most people think about electronics, they may initially think of products such as cell phones, radios, laptop computers, etc. others, having some engineering background, may think of resistors, capacitors, etc. which are the basic components necessary for electronics to function. Such basic components are fairly limited in number and each having their own characteristic function.
Memristor theory was formulated and named by Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual symmetry with the resistor, inductor, and capacitor. This symmetry follows from the description of basic passive circuit elements as defined by a relation between two of the four fundamental circuit variables. A device linking charge and flux (themselves defined as time integrals of current and voltage), which would be the memristor, was still hypothetical at the time. However, it would not be until thirty-seven years later, on April 30, 2008, that a team at HP Labs led by the scientist R. Stanley Williams would announce the discovery of a switching memristor. Based on a thin film of titanium dioxide, it has been presented as an approximately ideal device.
The reason that the memristor is radically different from the other fundamental circuit elements is that, unlike them, it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That's an effect that can't be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element.
The arrangement of these few fundamental circuit components form the basis of almost all of the electronic devices we use in our everyday life. Thus the discovery of a brand new fundamental circuit element is something not to be taken lightly and has the potential to open the door to a brand new type of electronics. HP already has plans to implement memristors in a new type of non-volatile memory which could eventually replace flash and other memory systems.
HISTORY
The transistor was invented in 1925 but lay dormant until finding a corporate champion in BellLabs during the 1950s. Now another groundbreaking electronic circuit may be poised for the same kind of success after laying dormant as an academic curiosity for more than three decades. Hewlett-Packard Labs is trying to bring the memristor, the fourth passive circuit element after the resistor, and the capacitor the inductor into the electronics mainstream. Postulated in 1971, the memory resistor represents a potential revolution in electronic circuit theory similar to the invention of transistor.
The history of the memristor can be traced back to nearly four decades ago when in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that there should be a fourth passive circuit element in addition to the other three known passive elements namely the resistor, the capacitor and the inductor. He called this fourth element a memory resistor or a memristor. Examining the relationship between charge, current, voltage and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that
value even after the current disappeared.
Fig1. The Simplest Chuaâ„¢s Circuit. Fig2. Realization of Four Element Chuaâ„¢s Circuit, NR is Chua Diode. Fig3. Showing Memristor as Fourth Basic Element. But the hypothetical device was mostly written off as a mathematical dalliance. However, it took more than three decades for the memristor to be discovered and come to life. Thirty years after Chuaâ„¢s Proposal of this mysterious device, HP senior fellow Stanley Williams and his group were working on molecular electronics when they started to notice strange behavior in their devices. One of his HP collaborators, Greg Snider, then rediscovered Chua's work from 1971. Williams spent several years reading and rereading Chua's papers. It was then that Williams realized that their molecular devices were really memristors.
Fig1. The Simplest Chuaâ„¢s Circuit
Fig2. Realization of Four Element Fig3. Showing Memristor as Fourth
Chuaâ„¢s Circuit Basic Element
NEED FOR MEMRISTOR
A memristor is one of four basic electrical circuit components, joining the resistor, capacitor, and inductor. The memristor, short for memory resistor was first theorized by student Leon Chua in the early 1970s. He developed mathematical equations to represent the memristor, which Chua believed would balance the functions of the other three types of circuit elements.
The known three fundamental circuit elements as resistor, capacitor and inductor relates four fundamental circuit variables as electric current, voltage, charge and magnetic flux. In that we were missing one to relate charge to magnetic flux. That is where the need for the fourth fundamental element comes in. This element has been named as memristor.
Memristance (Memory + Resistance) is a property of an Electrical Component that describes the variation in Resistance of a component with the flow of charge. Any two terminal electrical component that exhibits Memristance is known as a Memristor. Memristance is becoming more relevant and necessary as we approach smaller circuits, and at some point when we scale into nano electronics, we would have to take memristance into account in our circuit models to simulate and design electronic circuits properly. An ideal memristor is a passive two-terminal electronic device that is built to express only the property of memristance (just as a resistor expresses resistance and an inductor expresses inductance). However, in practice it may be difficult to build a 'pure memristor,' since a real device may also have a small amount of some other property, such as capacitance (just as any real inductor also has resistance).A common analogy for a resistor is a pipe that carries water. The water itself is analogous to electrical charge, the pressure at the input of the pipe is similar to voltage, and the rate of flow of the water through the pipe is like electrical current. Just as with an electrical resistor, the flow of water through the pipe is faster if the pipe is shorter and/or it has a larger diameter. An analogy for a memristor is an interesting kind of pipe that expands or shrinks when water flows through it. If water flows through the pipe in one direction, the diameter of the pipe increases, thus enabling the water to flow faster. If water flows through the pipe in the opposite direction, the diameter of the pipe decreases, thus slowing down the flow of water. If the water pressure is turned off, the pipe will retain it most recent diameter until the water is turned back on. Thus, the pipe does not store water like a bucket (or a capacitor) “ it remembers how much water flowed through it.
Possible applications of a Memristor include Nonvolatile Random Access
Memory (NVRAM), a device that can retain memory information even after being switched off, unlike conventional DRAM which erases itself when it is switched off. Another interesting application is analog computation where a memristor will be able to deal with analog values of data and not just binary 1s and 0s.
Figure 4. Fundamental circuit Elements and Variables.
Types of Memristors:
¢ Spintronic Memristor
¢ Spin Torque Transfer Magneto resistance
¢ Titanium dioxide memristor
¢ Polymeric memristor
¢ Spin memristive systems
¢ Magnetite memristive systems
¢ Resonant tunneling diode memristor
Titanium Dioxide Memristor It is a solid state device that uses nano scale thin-ilms to produce a Memristor. The device consists of a thin titanium dioxide film (50nm) in between two electrodes (5nm) one Titanium and the other latinum. 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 and this implies that the depleted layer has a much lower resistance than the no depleted layer. When an electric field is applied, the oxygen vacancies drift, 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.
MEMRISTOR THEORY AND ITS PROPERTIES:
Definition of Memristor
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.
Figure 5. Symbol of Memristor.
Chua defined the element as a resistor whose resistance level was based on the amount of charge that had passed through the memristor
Memristance
Memristance is a property of an electronic component to retain its resistance level even after power had been shut down or lets it remember (or recall) the last resistance it had before being shut off.
Theory
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. . i.e. ,
V(t) = M(q(t))*I(t)
3
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 instantaneously 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.
Current vs. Voltage characteristics
This new circuit element shares many of the properties of resistors and shares the same unit of measurement (ohms). However, in contrast to ordinary resistors, in which the resistance is permanently fixed, memristance may be programmed or switched to different resistance states based on the history of the voltage applied to the memristance material. This phenomena can be understood graphically in terms of the relationship between the current flowing through a memristor and the voltage applied across the memristor.
In ordinary resistors there is a linear relationship between current and voltage so that a graph comparing current and voltage results in a straight line. However, for memristors a similar graph is a little more complicated as shown in Fig. 3 illustrates the current vs. voltage behavior of memristance.
In contrast to the straight line expected from most resistors the behavior of a memristor appear closer to that found in hysteresis curves associated with magnetic materials. It is notable from Fig. 3 that two straight line segments are formed within the curve. These two straight line curves may be interpreted as two distinct resistance states with the remainder of the curve as transition regions between these two states.
Figure-6. Current vs. Voltage curve demonstrating hysteretic effects of memristance.
Fig. 6 illustrates an idealized resistance behavior demonstrated in accordance
with Fig.7 wherein the linear regions correspond to a relatively high resistance (RH) and lowresistance (RL) and the transition regions are represented by straight lines.
Figure 7. Idealized hysteresis model of resistance vs. voltage for memristance switch.
Thus for voltages within a threshold region (-VL2<V<VL1 in Fig. 4) either a high or low resistance exists for the memristor. For a voltage above threshold VL1 the resistance switches from a high to a low level and for a voltage of opposite polarity above threshold VL2 the resistance switches back to a high resistance.
WORKING OF MEMRISTOR
Figure 8(a). Al/TiO2 or TiOX /Al Sandwich
The memristor is composed of a thin (5 nm) titanium dioxide film between two electrodes as shown in figure 5(a) above. Initially, there are two layers to the 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 changing the boundary between the high-resistance and low-resistance layers.
POTENTIAL APPLICATIONS
Figure8(b).showing 17 memristors in a row
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 memristor displays fast ion conduction at nanoscale, it is considered a nanoionic device .Figure 5(b) shows the final memristor component
Williams' solid-state memristors can be combined into devices called crossbar latches, which could replace transistors in future computers, taking up a much smaller area. They can also be fashioned into non-volatile solid-state memory, which would allow greater data density than hard drives with access times potentially similar to DRAM, replacing both components. HP prototyped a crossbar latch memory using the devices that can fit 100 gigabits in a square centimeter. HP has reported that its version of the memristor is about one-tenth the speed of DRAM. The devices' resistance would be read with alternating current so that they do not affect the stored value. Some patents related to memristors appear to include applications in programmable logic, signal processing, neural networks, and control systems. Recently, a simple electronic circuit consisting of an LC contour and a memristor was used to model experiments on adaptive behavior of unicellular organisms. It was shown that the electronic circuit subjected to a train of periodic pulses learns and anticipates the next pulse to come, similarly to the behavior of slime molds Physarum polycephalum subjected to periodic changes of environment. Such a learning circuit may find applications, e.g., in pattern recognition.
MEMRISTOR-THE FOURTH BASICCIRCUIT ELEMENT
From the circuit-theoretic point of view, the three basic two-terminal circuit elements are defined in terms of a relationship between two of the four fundamental circuit variables, namely;the current i, the voltage v, the charge q, and the flux-linkage cp.Out of the six possible combinations of these four variables, five have led to well-known relationships . Two of these relationships are already given by 9 Q(t) = ò ˆž
I (t) dt and O (t) = ò ˆž v(t) dt.
. Three other relationships are given, respectively, by the axiomatic definition of the three classical circuit elements, namely, the resistor (defined by a relationship between v and i), the inductor (defined by a relationship between cp and i), and the capacitor defined by a relationship between q and v). Only one relationship remains undefined, the relationship between o and q. From the logical as well as axiomatic points of view, it is necessary for the sake of completeness to postulate the existence of a fourth basic two-terminal circuit element which is characterized by a o-q curve. This element will henceforth be called the memristor because, as will be shown later, it behaves somewhat like a nonlinear resistor with memory. The proposed symbol of a memristor and a hypothetical o-q curve are shown in Fig. l(a). Using a ,mutated , a memristor with any prescribed o-q curve can be realized by connecting an appropriate nonlinear resistor, inductor, or capacitor across port 2 of an M-R mutated, an M-L mutated, and an M-C mutated, as shown in Fig. l(b), ©, and (d), respectively. These mutators, of which there are two types of each, are defined and characterized in Table I.3
Hence, a type-l M-R mutated would transform the VR -IR< curve of the nonlinear resistor f(VR, IR)=O into the corresponding o-q curve f(o,q)=O of a memristor. In contrast to this, a type-2 M-R mutated would transform the IR,VR curve of the nonlinear resistor f(IR,VR)=O into the corresponding o-q curve f(o,q) = 0 of a memristor. An analogous transformation is realized with an M-L mutated (M-C mutated) with respect to the ((oL,iL) or (iL, oL) [(vC, qC) or (qC, vC)] curve of a nonlinear inductor (capacitor).10 t
(a) Memristor and its o-q curve.
(b). Memristor basic realization 1: M-R mutated terminated by nonlinear Resistor R.
© Memristor basic realization 2: M-L mutated terminated by nonlinear inductor L
(d) Memristor basic realization M-C mutated
terminated by nonlinear capacitor C
FEATURES
The reason that the memristor is radically different from the other fundamental
circuit elements is that, unlike them, it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That's an effect that can't be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element.
New 'Memristor' Could Make Computers Work like Human Brains
After the resistor, capacitor, and inductor comes the memristor. Researchers at HP Labs have discovered a fourth fundamental circuit element that can't be replicated by a11 combination of the other three. The memristor (short for "memory resistor") is unique because of its ability to, in HP's words, "[retain] a history of the information it has acquired." HP says the discovery of the memristor paves the way for anything from instant on computers to systems that can "remember and associate series of events in a manner similar to the way a human brain recognizes patterns." Such brain-like systems would allow for vastly improved facial or biometric recognition, and they could be used to make appliances that "learn from experience."
In PCs, HP foresees memristors being used to make new types of system memory that can store information even after they lose power, unlike today's DRAM. With memristor-based system RAM, PCs would no longer need to go through a boot process to load data from the hard drive into the memory, which would save time and power especially since users could simply switch off systems instead of leaving them in a "sleep" mode
Memristors Make Chips Cheaper
The first hybrid memristor-transistor chip could be cheaper and more energy efficient. Entire industries and research fields are devoted to ensuring that, every year,computers continue getting faster. But this trend could begin to slow down as the components used in electronic circuits are shrunk to the size of just a few atoms.Researchers at HP Labs in Palo Alto, CA, are betting that a new fundamental electronic component--the memristor--will keep computer power increasing at this rate for years to come.
They are nanoscale devices with unique properties: a variable resistance and the ability to remember the resistance even when the power is off.Increasing performance has
usually meant shrinking components so that more can be packed onto a circuit. But instead, Williams's team removes some transistors and replaces them with a smaller number of memristors. "We're not trying to crowd more transistors onto a chip or into a particular circuit," Williams says. "Hybrid memristor-transistor chips really have the promise for delivering a lot more performance."12 A memristor acts a lot like a resistor but with one big difference: it can change resistance depending on the amount and direction of the voltage applied and can remember its resistance even when the voltage is turned off. These unusual properties make them interesting from both a scientific and an engineering point of view. A single memristor can perform the same logic functions as multiple transistors, making them a promising way to increase computer power. Memristors could also prove to be a faster, smaller, more energy-efficient alternative to flash storage.
Memristor as Digital and Analog
A memristive device can function in both digital and analog forms, both having very diverse applications. In digital mode, it could substitute conventional solid-state memories (Flash) with high-speed and less steeply priced nonvolatile random access
memory (NVRAM). Eventually, it would create digital cameras with no delay between photos or computers that save power by turning off when not needed and then turning
back on instantly when needed.
No Need of Rebooting
The memristor's memory has consequences:The reason computers have to be rebooted every time they are turned on is that their logic circuits are incapable of holding their bits after the power is shut off. But because a memristor can remember voltages, a memristor-driven computer would arguably never need a reboot. You could leave all your Word files and spreadsheets open, turn off your computer, and go get a cup of coffee or go on vacation for two weeks, says Williams. When you come back, you turn on your computer and everything is instantly on the screen exactly the way you left it.that keeps memory powered. HP says memristor-based RAM could one day replace DRAM altogether.
FUTURE OF MEMRISTOR
Although memristor research is still in its infancy, HP Labs is working on a handful of practical memristor projects. And now Williams's team has demonstrated a
working memristor-transistor hybrid chip. "Because memristors are made of the same materials used in normal integrated circuits," says Williams, "it turns out to be very easy to integrate them with transistors." His team, which includes HP researcher Qiangfei Xia, built a field-programmable gate array (FPGA) using a new design that includes memristors made of the semiconductor titanium dioxide and far fewer transistors than normal.Engineers commonly use FPGAs to test prototype chip designs because they can
be reconfigured to perform a wide variety of different tasks. In order to be so flexible,
however, FPGAs are large and expensive. And once the design is done, engineers
generally abandon FPGAs for leaner "application-specific integrated circuits." "When
you decide what logic operation you want to do, you actually flip a bunch of switches and
configuration bits in the circuit," says Williams. In the new chip, these tasks are
performed by memristors. "What we're looking at is essentially pulling out all of the
configuration bits and all of the transistor switches," he says. According to Williams, using memristors in FPGAs could help significantly lower costs. "If our ideas work out, this type of FPGA will completely change the balance," he says. Ultimately, the next few years could be very important for memristor research.
Right now, "the biggest impediment to getting memristors in the marketplace is having [so few] people who can actually design circuits [using memristors]," Williams says. Still, he predicts that memristors will arrive in commercial circuits within the next three years.
When is it coming?
Researchers say that no real barrier prevents implementing the memristor in circuitry immediately. But it's up to the business side to push products through to commercial reality. Memristors made to replace flash memory (at a lower cost and lower 14 power consumption) will likely appear first; HP's goal is to offer them by 2012. Beyond that, memristors will likely replace both DRAM and hard disks in the 2014-to-2016 time frame. As for memristor-based analog computers, that step may take 20-plus years.
CONCLUSION
By redesigning certain types of circuits to include memristors, it is possible to obtain the same function with fewer components, making the circuit itself less expensive and significantly decreasing its power consumption. In fact, it can be hoped to combine memristors with traditional circuit-design elements to produce a device that does computation. The Hewlett-Packard (HP) group is looking at developing a memristor-based nonvolatile memory that could be 1000 times faster than magnetic disks and use much less power.
As rightly said by Leon Chua and R.Stanley Williams (originators of memristor), memrisrors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks.