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This is a very good article of the memristor: Read first. http://memristor.ucmerced.edu/docs/EETimesArticle.pdf Common FAQ http://www.hpl.hp.com/news/2008/apr-jun/memristor_faq.html What is memristance? Memristance is a property of an electronic component. If charge flows in one direction through a circuit, the resistance of that component of the circuit will increase, and if charge flows in the opposite direction in the circuit, the resistance will decrease. If the flow of charge is stopped by turning off the applied voltage, the component will 'remember' 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. Why is memristance important? It turns out that memristance is becoming stronger as the feature sizes in circuits are getting smaller. At some point as we scale into the realm of nanoelectronics, it will be necessary to explicitly take account of memristance in our circuit models in order to simulate and design electronic circuits properly. Have people seen memristance before? Yes, we are aware of over 100 published papers going back to at least the early 1960's in which researchers observed and reported unusual 'hysteresis' in their current-voltage plots of various devices and circuits based on many different types of materials and structures. In retrospect, we can understand that those researchers were actually seeing memristance, but they were apparently not aware of it. What is a memristor? 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). What is an analogy for a memristor? 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. Who first predicted the existence of memristance and memristors? Prof. Leon Chua had just moved to the Electrical Engineering Department of UC Berkeley when he published his seminal paper, "Memristor - The missing circuit element." IEEE Trans. Circuit Theory CT-18, 507-519 (1971). In this paper, Prof. Chua proved a number of theorems to show that there was a 'missing' two-terminal circuit element from the family of "fundamental" passive devices: resistor, capacitor and inductor (e.g. elements that do not add energy to a circuit). He proved that no combination of nonlinear resistors, capacitors and inductors could duplicate the properties of a memristor. The most recognizable signature of a memristor is that when an AC voltage is applied to the device, the current-voltage (I-V) plot is a Lissajous figure (the curve formed by combining two oscillations that are perpendicular to each other). The most commonly observed I-V trace is a 'figure 8', or a 'pinched loop' for which the current is zero when the voltage is zero. This inability to duplicate the properties of a memristor with the other passive circuit elements is what makes the memristor fundamental. However, this original paper requires a considerable effort for a non-expert to follow. In a later paper, Prof. Chua introduced his 'periodic table' of circuit elements. This was a visually pleasing illustration that we borrowed and modified for our Nature paper on finding memristors. Aren't there other fundamental passive devices that don't add energy to a circuit? What about diodes? No, there are only four fundamental types of passive circuit elements. Diodes are just non-linear resistors - the resistance of a diode changes with the applied voltage, but if you turn off the voltage and start back at 0 volts, the resistance of the diode is the same as it was before at 0 volts, not what it was when the voltage was turned off. This is also true of a resistor that heats up and increases its resistance because of a temperature increase. Thus, neither a diode nor a heated resistor 'remember' their history. However, each type of fundamental circuit element is actually a family of devices with essentially an infinite number of higher order members. To see all the members of the four families of fundamental devices, see the following paper: Leon O. Chua, "Nonlinear Circuit Foundations for Nanodevices, Part I: The Four-Element Torus," Proc. IEEE 91, 1830-1859 (2003). This is a very educational paper, but requires a significant investment in effort to appreciate. Note: Part II has not appeared in the literature yet. What was the contribution of HP Labs? We were the first to understand that the hysteresis that was being observed in the I-V curves of a wide variety of materials and structures was actually the result of memristance and something more general that can be called 'memristive behavior' [see L.O. Chua & S. M. Kang, "Memristive devices and systems," Proc. IEEE 64, 209-223 (1976)]. We then went on to create an elementary circuit model that was defined by exactly the same mathematical equations as those predicted by Chua for the memristor, with the exception that this model had an upper bound to the resistance (which means that at large bias or long times, it is a memristive device). We then showed that this simple model could reproduce a wide variety of eccentric and complex I-V curves that have been observed and reported over the years by many researchers, including ourselves. Most of these did not look much like the 'figure 8' curves of Chua, but rather 'S' and 'N' curves that have erroneously been attributed to negative differential resistance, which is one reason why the connection to memristive behavior had not been made earlier. We also showed that in a highly simplified form appropriate for a general audience journal like Nature or for a basic undergraduate course, the equations for the drift of oxygen vacancies in TiO2 and their influence on the electronic conduction in the material were also identical with our equivalent circuit model, and thus Chua's memristor equations. From this, we could for the first time write down a formula for the memristance of a device in terms of material and geometrical properties of the device (just as the resistance is the resistivity of the material times the length divided by the cross sectional area of the resistor). Our memristance formula immediately showed that the size of the most important term in the memristance gets larger the smaller the device – thus showing that it was not very important for micron-scale electronics but is becoming very important for nanoscale devices. We have developed more sophisticated and accurate models that will be published at a future date, and we have used our models to design and build better memristors. What types of applications could memristors have? We see two types of applications for memristors and memristive devices. The first, as the name "memory resistor" implies, is for a type of non-volatile random access memory, or NVRAM. Such a memory would have very useful properties, in that it would not 'forget' the data that it stores when the power is turned off. We think that NVRAM made with the types of memristor materials that are currently being studied by many groups around the world could be a strong competitor to the flash memory market in about five years. The great thing is that the various metal oxides that have been identified as having a memory function are highly compatible with present chip fabrication facilities, so they can be made in existing foundries without a lot of changes being required. The major contribution of our work to this effort at this point is to make the connection to the non-linear circuit theory of Leon Chua – without the fundamental understanding that comes from his circuit equations, the devices themselves are fairly useless. Another interesting application is as an 'artificial synapse' in a circuit designed for analog computation. Prof. Chua himself pointed out the connection between the properties of his proposed memristor and those of a synapse in his earliest papers, and he has performed a lot of research in the area of neural computing. We also think that this is a very interesting and potentially valuable research direction. However, as experience shows, the most valuable applications of memristors will most likely come from some young student who learns about these devices and has an inspiration for something totally new. How it works 1. A memristor effectively stores information because the level of its electrical resistance changes when current is applied. A typical resistor provides a stable level of resistance. By contrast, a memristor can have a high level of resistance, which can be interpreted as a computer as a "1" in data terms, and a low level can be interpreted as a "0." Thus, data can be recorded and rewritten by controlling current. In a sense, a memristor is a variable resistor that, through its resistance, reflects its own history, Williams said. 2. Think of a resistor as a pipe through which water flows. The water is electric charge. The resistor’s obstruction of the flow of charge is comparable to the diameter of the pipe: the narrower the pipe, the greater the resistance. For the history of circuit design, resistors have had a fixed pipe diameter. But a memristor is a pipe that changes diameter with the amount and direction of water that flows through it. If water flows through this pipe in one direction, it expands (becoming less resistive). But send the water in the opposite direction and the pipe shrinks (becoming more resistive). Further, the memristor remembers its diameter when water last went through. Turn off the flow and the diameter of the pipe ”freezes” until the water is turned back on. That freezing property suits memristors brilliantly for computer memory. The ability to indefinitely store resistance values means that a memristor can be used as a nonvolatile memory. That might not sound like very much, but go ahead and pop the battery out of your laptop, right now—no saving, no quitting, nothing. You’d lose your work, of course. But if your laptop were built using a memory based on memristors, when you popped the battery back in, your screen would return to life with everything exactly as you left it: no lengthy reboot, no half-dozen auto-recovered files. 3. Williams found an ideal memristor in titanium dioxide--the stuff of white paint and sunscreen. Like silicon, titanium dioxide (TiO 2 ) is a semiconductor, and in its pure state it is highly resistive. However, it can be doped with other elements to make it very conductive. In TiO 2 , the dopants don't stay stationary in a high electric field; they tend to drift in the direction of the current. Such mobility is poison to a transistor, but it turns out that's exactly what makes a memristor work. Putting a bias voltage across a thin film of TiO 2 semiconductor that has dopants only on one side causes them to move into the pure TiO 2 on the other side and thus lowers the resistance. Running current in the other direction will then push the dopants back into place, increasing the TiO 2 's resistance. 6. What is it? As its name implies, the memristor can "remember" how much current has passed through it. And by alternating the amount of current that passes through it, a memristor can also become a one-element circuit component with unique properties. Most notably, it can save its electronic state even when the current is turned off, making it a great candidate to replace today's flash memory. Memristors will theoretically be cheaper and far faster than flash memory, and allow far greater memory densities. They could also replace RAM chips as we know them, so that, after you turn off your computer, it will remember exactly what it was doing when you turn it back on, and return to work instantly. This lowering of cost and consolidating of components may lead to affordable, solid-state computers that fit in your pocket and run many times faster than today's PCs. Someday the memristor could spawn a whole new type of computer, thanks to its ability to remember a range of electrical states rather than the simplistic "on" and "off" states that today's digital processors recognize. By working with a dynamic range of data states in an analog mode, memristor-based computers could be capable of far more complex tasks than just shuttling ones and zeroes around. History 1. It’s time to stop shrinking. Moore’s Law, the semiconductor industry’s obsession with the shrinking of transistors and their commensurate steady doubling on a chip about every two years, has been the source of a 50-year technical and economic revolution. Whether this scaling paradigm lasts for five more years or 15, it will eventually come to an end. The emphasis in electronics design will have to shift to devices that are not just increasingly infinitesimal but increasingly capable. Earlier this year, I and my colleagues at Hewlett-Packard Labs, in Palo Alto, Calif., surprised the electronics community with a fascinating candidate for such a device: the memristor. It had been theorized nearly 40 years ago, but because no one had managed to build one, it had long since become an esoteric curiosity. That all changed on 1 May, when my group published the details of the memristor in Nature. For nearly 150 years, the known fundamental passive circuit elements were limited to the capacitor (discovered in 1745), the resistor (1827), and the inductor (1831). Then, in a brilliant but underappreciated 1971 paper, Leon Chua, a professor of electrical engineering at the University of California, Berkeley, predicted the existence of a fourth fundamental device, which he called a memristor. He proved that memristor behavior could not be duplicated by any circuit built using only the other three elements, which is why the memristor is truly fundamental. memristor is truly one for the history books. When Leon Chua, now an IEEE Fellow, wrote his seminal paper predicting the memristor, he was a newly minted and rapidly rising professor at UC Berkeley. Chua had been fighting for years against what he considered the arbitrary restriction of electronic circuit theory to linear systems. He was convinced that nonlinear electronics had much more potential than the linear circuits that dominate electronics technology to this day. Chua discovered a missing link in the pairwise mathematical equations that relate the four circuit quantities—charge, current, voltage, and magnetic flux—to one another. These can be related in six ways. Two are connected through the basic physical laws of electricity and magnetism, and three are related by the known circuit elements: resistors connect voltage and current, inductors connect flux and current, and capacitors connect voltage and charge. But one equation is missing from this group: the relationship between charge moving through a circuit and the magnetic flux surrounded by that circuit—or more subtly, a mathematical doppelgänger defined by Faraday’s Law as the time integral of the voltage across the circuit. This distinction is the crux of a raging Internet debate about the legitimacy of our memristor [see sidebar, ”Resistance to Memristance ”]. Chua’s memristor was a purely mathematical construct that had more than one physical realization. What does that mean? Consider a battery and a transformer. Both provide identical voltages—for example, 12 volts of direct current—but they do so by entirely different mechanisms: the battery by a chemical reaction going on inside the cell and the transformer by taking a 110â¿¿V ac input, stepping that down to 12 V ac, and then transforming that into 12 V dc. The end result is mathematically identical—both will run an electric shaver or a cellphone, but the physical source of that 12 V is completely different. Conceptually, it was easy to grasp how electric charge could couple to magnetic flux, but there was no obvious physical interaction between charge and the integral over the voltage. Chua demonstrated mathematically that his hypothetical device would provide a relationship between flux and charge similar to what a nonlinear resistor provides between voltage and current. In practice, that would mean the device’s resistance would vary according to the amount of charge that passed through it. And it would remember that resistance value even after the current was turned off. He also noticed something else—that this behavior reminded him of the way synapses function in a brain. Even before Chua had his eureka moment, however, many researchers were reporting what they called ”anomalous” current-voltage behavior in the micrometer-scale devices they had built out of unconventional materials, like polymers and metal oxides. But the idiosyncrasies were usually ascribed to some mystery electrochemical reaction, electrical breakdown, or other spurious phenomenon attributed to the high voltages that researchers were applying to their devices. As it turns out, a great many of these reports were unrecognized examples of memristance. After Chua theorized the memristor out of the mathematical ether, it took another 35 years for us to intentionally build the device at HP Labs, and we only really understood the device about two years ago. So what took us so long? It’s all about scale. We now know that memristance is an intrinsic property of any electronic circuit. Its existence could have been deduced by Gustav Kirchhoff or by James Clerk Maxwell, if either had considered nonlinear circuits in the 1800s. But the scales at which electronic devices have been built for most of the past two centuries have prevented experimental observation of the effect. It turns out that the influence of memristance obeys an inverse square law: memristance is a million times as important at the nanometer scale as it is at the micrometer scale, and it’s essentially unobservable at the millimeter scale and larger. As we build smaller and smaller devices, memristance is becoming more noticeable and in some cases dominant. That’s what accounts for all those strange results researchers have described. Memristance has been hidden in plain sight all along. But in spite of all the clues, our finding the memristor was completely serendipitous What can it be used for 1. If memristors can be commercialized, it could lead to very dense, energy-efficient memory chips. Scientists have made devices that function like memristors, but it took a good number of transistors and several capacitors, Williams said. Memristor chips would function like flash memory and retain data even after a computer is turned off, but require less silicon, consume less energy, and require fewer transistors. 2. Combined with transistors in a hybrid chip, memristors could radically improve the performance of digital circuits without shrinking transistors. Using transistors more efficiently could in turn give us another decade, at least, of Moore’s Law performance improvement, without requiring the costly and increasingly difficult doublings of transistor density on chips. In the end, memristors might even become the cornerstone of new analog circuits that compute using an architecture much like that of the brain. But the memristor’s potential goes far beyond instant-on computers to embrace one of the grandest technology challenges: mimicking the functions of a brain. Within a decade, memristors could let us emulate, instead of merely simulate, networks of neurons and synapses. Many research groups have been working toward a brain in silico: IBM’s Blue Brain project, Howard Hughes Medical Institute’s Janelia Farm, and Harvard’s Center for Brain Science are just three. However, even a mouse brain simulation in real time involves solving an astronomical number of coupled partial differential equations. A digital computer capable of coping with this staggering workload would need to be the size of a small city, and powering it would require several dedicated nuclear power plants. Memristors can be made extremely small, and they function like synapses. Using them, we will be able to build analog electronic circuits that could fit in a shoebox and function according to the same physical principles as a brain. A hybrid circuit—containing many connected memristors and transistors—could help us research actual brain function and disorders. Such a circuit might even lead to machines that can recognize patterns the way humans can, in those critical ways computers can’t—for example, picking a particular face out of a crowd even if it has changed significantly since our last memory of it. 4. Possible replacement for D-RAM By providing a mathematical model for the physics of a memristor, the team makes possible for engineers to develop integrated circuit designs that take advantage of its ability to retain information. "This opens up a whole new door in thinking about how chips could be designed and operated," Williams says. Engineers could, for example, develop a new kind of computer memory that would supplement and eventually replace today's commonly used dynamic random access memory (D-RAM). Computers using conventional D-RAM lack the ability to retain information once they are turned off. When power is restored to a D-RAM-based computer, a slow, energy-consuming "boot-up" process is necessary to retrieve data stored on a magnetic disk required to run the system. Memristor-based computers wouldn't require that process, using less power and possibly increasing system resiliency and reliability. Chua believes the memristor could have applications for computing, cell phones, video games - anything that requires a lot of memory without a lot of battery-power drain. Brain-like systems? As for the human brain-like characteristics, memristor technology could one day lead to computer systems that can remember and associate patterns in a way similar to how people do. This could be used to substantially improve facial recognition technology or to provide more complex biometric recognition systems that could more effectively restrict access to personal information. These same pattern-matching capabilities could enable appliances that learn from experience and computers that can make decisions. Nanoscale electronics experience In the memristor work, the researchers built on their extensive experience - Williams founded the precursor lab to IQSL in 1995 - in building and studying nanoscale electronics and architectures. One goal of this work has been to move computing beyond the physical and fiscal limits of conventional silicon chips. For decades, increases in chip performance have come about largely by putting more and more transistors on a circuit. Higher densities, however, increase the problems of heat generation and defects and affect the basic physics of the devices. "Instead of increasing the number of transistors on a circuit, we could create a hybrid circuit with fewer transistors but the addition of memristors - and more functionality," Williams says. Alternately, memristor technologies could enable more energy-efficient high-density circuits. In 2007, the team developed an architecture for such a hybrid chip using conventional CMOS technology and nanoscale switching devices. "What we now know," Williams says, "is that these switches have a name - memristor." 6. 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 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.