How We Found the Missing Memristor

Thinking Machine: This artist’s conception of a memristor shows a stack of multiple crossbar arrays,…


Thinking Machine: This artist’s conception of a memristor shows a stack of multiple crossbar arrays, the fundamental structure of R. Stanley Williams’s device. Because memristors behave functionally like synapses, replacing a few transistors in a circuit with memristors could lead to analog circuits that can think like a human brain.
Image: Bryan Christie Design

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.

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.

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 a contraction of “memory resistor,” because that is exactly its function: to remember its history. A memristor is a two-terminal device whose resistance depends on the magnitude and polarity of the voltage applied to it and the length of time that voltage has been applied. When you turn off the voltage, the memristor remembers its most recent resistance until the next time you turn it on, whether that happens a day later or a year later.

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.

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.



Photo: Paul Sakuma/AP Photo

Picturing Memristance: HP Labs senior fellow R. Stanley Williams [left] and research physicist Duncan Stewart [right] explain the fourth fundamental circuit element. Williams worked with nearly 100 scientists and engineers to find the memristor.

The story of the 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 110-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.

In 1995, I was recruited to HP Labs to start up a fundamental research group that had been proposed by David Packard. He decided that the company had become large enough to dedicate a research group to long-term projects that would be protected from the immediate needs of the business units. Packard had an altruistic vision that HP should “return knowledge to the well of fundamental science from which HP had been withdrawing for so long.” At the same time, he understood that long-term research could be the strategic basis for technologies and inventions that would directly benefit HP in the future. HP gave me a budget and four researchers. But beyond the comment that “molecular-scale electronics” would be interesting and that we should try to have something useful in about 10 years, I was given carte blanche to pursue any topic we wanted. We decided to take on Moore’s Law.

At the time, the dot-com bubble was still rapidly inflating its way toward a resounding pop, and the existing semiconductor road map didn’t extend past 2010. The critical feature size for the transistors on an integrated circuit was 350 nanometers; we had a long way to go before atomic sizes would become a limitation. And yet, the eventual end of Moore’s Law was obvious. Someday semiconductor researchers would have to confront physics-based limits to their relentless descent into the infinitesimal, if for no other reason than that a transistor cannot be smaller than an atom. (Today the smallest components of transistors on integrated circuits are roughly 45 nm wide, or about 220 silicon atoms.)