The Memristor

Abstract

In September 1971 Leon Chua, a circuit theorist at the University of California, Berkeley, argued from symmetry that electronics was missing a fourth basic element. Besides the resistor, the capacitor and the inductor there should be a “memristor,” a resistor whose resistance depends on how much charge has flowed through it and which remembers that value when the power is off. Nobody built one on purpose for 37 years. In May 2008 a team at HP Labs led by R. Stanley Williams announced in Nature that a thin film of titanium dioxide was “the missing memristor found,” and HP spent the next seven years promising memristor memory that would replace flash and DRAM. The products did not arrive. HP’s flagship project switched to conventional memory in 2015, and a series of papers argued that the 2008 device was not Chua’s memristor at all and that the fourth fundamental element may not exist.

Leon Chua, 2018. Image: Leon Chua, CC BY 4.0, via Wikimedia Commons.

The Missing Element

Circuit theory works with four quantities: voltage, current, charge and magnetic flux. Charge is the integral of current over time, and flux the integral of voltage, so two of the six possible pairings are definitions. The other relations each define an element. A resistor relates voltage to current, a capacitor charge to voltage, and an inductor flux to current. One pairing was left: flux and charge.

Chua, who had been arguing against the restriction of circuit theory to linear elements, published “Memristor: The Missing Circuit Element” in the IEEE Transactions on Circuit Theory in September 1971. An element linking flux to charge, he showed, would behave as a resistor whose value depended on the total charge that had passed through it, and it would keep that value when the current stopped. Plotted as current against voltage under an alternating signal, its characteristic would be a loop pinched at the origin. He also noticed that such an element would behave something like a synapse, which strengthens with use.

Chua and Sung Mo Kang generalised the idea in 1976 in “Memristive Devices and Systems” in the Proceedings of the IEEE. A memristive system was any device whose resistance depended on an internal state that changed with the current through it. The generalisation was broad enough to include many physical systems already known, and it was later at the centre of the argument about what HP had found.

Devices that did something similar had existed before Chua named them. In 1960 Bernard Widrow and his student Marcian Hoff at Stanford built the memistor, a three-terminal electroplating cell whose resistance between two terminals was set by the time integral of the current through the third, to store the adjustable weights of their ADALINE neuron. The Memistor Corporation sold the circuitry briefly in the 1960s, but the cells could not be made with integrated-circuit processes. The resistance switching of thin oxide films, including titanium dioxide, was also described in the 1960s.

HP Labs, 2008

Williams joined HP Labs in 1995 to start a fundamental research group that David Packard had proposed, with instructions to have something useful in about ten years. The group worked on crossbar circuits, grids of crossing nanowires with a switch at each junction, intended to keep shrinking logic and memory after transistors stopped shrinking. In late 2002 Greg Snider, a colleague from HP’s Teramac project, handed Williams a copy of Chua’s 1971 paper. “I don’t know what you guys are building,” he said, “but this is what I want.”

The paper sat on Williams’s desk for months. The group’s switches were meant to be molecules between platinum and titanium electrodes. In 2004 they pried devices apart and found that the switching layer was titanium dioxide, partly depleted of oxygen near the top electrode, and that the molecules were not needed. The oxygen vacancies are positively charged and make the depleted layer conduct. An applied voltage moves them, shifting the boundary between the conducting and insulating layers and with it the resistance of the device, and the boundary stays where it was left. On 20 August 2006, after a literature search turned up about 300 relevant papers on titanium dioxide, Williams wrote down the equations that connected the device’s physics to Chua’s memristance.

Dmitri Strukov, Gregory Snider, Duncan Stewart and Williams published “The missing memristor found” in Nature on 1 May 2008. The paper, and Williams’s account in IEEE Spectrum that December, promised dense non-volatile memory, crossbar logic that a 2007 paper had shown could reduce the area of programmable circuits by nearly a factor of ten, and circuits in which memristors act as synapses. Williams compared the memristor to the transistor in its first decade, an academic curiosity before its killer application, the hearing aid.

The Product That Kept Slipping

At the end of August 2010 HP and the Korean memory maker Hynix announced a three-year joint development agreement to manufacture memristors as resistive RAM (ReRAM), with a product announcement targeted for 2013. HP claimed the memory would be about ten times faster than flash and use about a tenth of the power, without the limited write endurance of flash. The date then moved. In 2011 HP promised a flash replacement by the summer of 2013, in 2012 it moved the target to 2014, and in 2013 Martin Fink, HP’s chief technology officer, spoke of 100-terabyte memristor drives in 2018.

In June 2014 at its Discover conference in Las Vegas, HP announced The Machine, a computer architecture built around a large pool of memristor memory shared by many specialised processors and connected by silicon photonics. Chief executive Meg Whitman said it would be available by the end of the decade, and BusinessWeek reported that three quarters of HP Labs’ researchers were working on it. In December 2014 Fink said memristor memory would sample in 2015 and launch in 2016; in February 2015 he said sampling would most likely come in 2016. In June 2015 HP announced a rethink. The first versions of The Machine would use DRAM and phase-change memory, memristors were moved to the long term, and the company stopped predicting when they would be ready. The prototype that Hewlett Packard Enterprise showed in May 2017 had 160 terabytes of memory across 40 nodes, built from ordinary DRAM.

The Existence Debate

The first objection was priority. Resistive switching in oxides had been studied for decades, and ReRAM was an active field before 2008; what HP had added was the link to Chua’s theory. Chua accepted the link. In 2011 he went further and argued in Applied Physics A that all two-terminal non-volatile memories based on resistance switching were memristors, whatever their physics, and his test for a memristor became the pinched hysteresis loop.

The second objection was that the broad definition had given up the original idea. In 2015 Sascha Vongehr and Xiangkang Meng of Nanjing University argued in Scientific Reports that the 1971 paper had predicted a real device grounded in electromagnetism, by symmetry with the inductor, which would need magnetism to work. HP’s device needed none and would work in a world without magnetic fields; it was a memristive system in the 1976 sense, a different and older category. “The originally hypothesized real memristor device is missing and likely impossible,” they concluded. Paul Meuffels and Rohit Soni had raised thermodynamic objections in 2012, and Massimiliano Di Ventra and Yuriy Pershin argued in 2013 that an ideal memristor controlled by current would be unstable against noise.

In 2018 Isaac Abraham, an engineer at Intel, made the strongest version of the case in Scientific Reports: “the 2008 memristor is not the 1971 postulate and neither of them is fundamental.” The ideal memristor, he argued, would be an unphysical active device, any realisable memristor is a nonlinear combination of resistors with hysteresis, and there are only three fundamental passive circuit elements.

Dead End: Universal Memory

HP’s promise was a universal memory, as fast as DRAM, as dense and persistent as flash, and cheap enough to replace both. Making single devices switch was not the hard part. Experts quoted by MIT Technology Review in 2015 said the difficulty was making reliable memristors in large, dense arrays. Intel and Micron’s 3D XPoint memory, announced in 2015, attacked the same gap between DRAM and flash with a different mechanism; Intel wound down its Optane products based on it in July 2022, writing off $559 million.

Resistive memory survived in smaller roles. Panasonic began mass production of 8-bit microcontrollers with embedded ReRAM, based on a metal-oxide redox reaction, in August 2013, and research groups use crossbars of resistive cells to perform the multiply-and-add operations of neural networks in analogue form inside the memory. Whether those devices are memristors depends on which of Chua’s definitions one accepts.