PORTLAND, Ore. — The long-sought after memristor -- the "missing link" in electronic circuit theory -- has been invented by Hewlett Packard Senior Fellow R. Stanley Williams at HP Labs in Palo Alto, Calif.

Memristors -- the fourth passive component type after resistors, capacitors and inductors -- were postulated in a seminal 1971 paper in the IEEE Transactions on Circuit Theory by professor Leon Chua at the University of California (Berkeley), but their first realization was just announced today by HP. According to Williams and Chua, now virtually every electronics textbook will have to be revised to include the memristor and the new paradigm it represents for electronic circuit theory.

"My situation was similar to that of the Russian chemist Dmitri Mendeleev who invented the periodic table in 1869," said Chua. "Mendeleev postulated that there were elements missing from the table, and now all those elements have been found. Likewise, Stanley Williams at HP Labs has now found the first example of the missing memristor circuit element."

When Chua wrote his seminal paper, he used mathematics to deduce the existence of a fourth circuit element type after resistors, capacitors and inductors, which he called a memristor, because it "remembers" changes in the current passing through it by changing its resistance. Now HP claims to have discovered the first instance of a memristor, which it created with a bi-level titanium dioxide thin-film that changes its resistance when current passes through it.

"This new circuit element solves many problems with circuitry today -- since it improves in performance as you scale it down to smaller and smaller sizes," said Chua. "Memristors will enable very small nanoscale devices to be made without generating all the excess heat that scaling down transistors is causing today."

HP has already tested the material in its ultra-high-density crossbar switches, which use nanowires to pack a record 100 Gbits onto a single die -- compared with 16 Gbits for the highest density flash memory chips extant.

"We have been looking for years for the best material to use in our ultra-dense nanowire crossbar switches, which can fit 100 billion crossbars into a square centimeter. What we have finally realized is that the ideal material is a memristor," said Williams, primary inventor of the memristor's titanium-dioxide-based material and founding director of HP's 12-year-old Information and Quantum Systems Lab, where his team perfected its formulation.

The hold-up over the last 37 years, according to professor Chua, has been a misconception that has pervaded electronic circuit theory. That misconception is that the fundamental relationship in passive circuitry is between voltage and charge. What the researchers contend is that the fundamental relationship is actually between changes-in-voltage, or flux, and charge. Such is the insight that enabled HP to invent the memristor, according to Chua and Williams.

"Electronic theorists have been using the wrong pair of variables all these years -- voltage and charge. The missing part of electronic theory was that the fundamental pair of variables is flux and charge," said Chua. "The situation is analogous to what is called "Aristotle's Law of Motion, which was wrong, because he said that force must be proportional to velocity. That misled people for 2000 years until Newton came along and pointed out that Aristotle was using the wrong variables. Newton said that force is proportional to acceleration -- the change in velocity. This is exactly the situation with electronic circuit theory today. All electronic text books have been teaching using the wrong variables -- voltage and charge--explaining away inaccuracies as anomalies. What they should have been teaching is the relationship between changes in voltage, or flux, and charge." HP invited Chua to speak about his theory a few years ago, but at that time the lab did not tell Chua that they were actively seeking the memristor. Only two weeks ago did Williams tell Chua that he had used the proper variables -- flux and charge -- to invent the world's first working memristor.

A memristor works by virtue of hysteresis, whereby its rate of change accelerates as it moves from one state to the other -- "on" to "off," or vice versa. Hysteresis has been explained away by current circuit theory as an anomaly, according to Chua and Williams, whereas its existence is, in fact, a fundamental property of passive circuitry.

"Hysteresis is a tell-tale manifestation of the fourth circuit element -- the memristor," said Chua. "And Stan Williams is very smart to have realized that if you cannot explain something properly, then there must be a better explanation."

For instance, electrical engineers have known that titanium dioxide changes its resistance in the presence of oxygen -- this is the principle behind titanium dioxide oxygen sensors -- but they could not explain why.

"They traced its curve, and knew it contained hysteresis, but because they could not explain it, they could only design the simplest of devices using it -- sensors," said Chua. "But now that it has been explained, they will be able to design all types of new circuitry using it. This is a wonderful development."

Chua predicts that electrical engineers will soon begin discovering all types of new materials that manifest the hysteresis relationship between flux and charge. He predicts that this new era of electronics will be able to solve the problems with scaling -- such as using too much power and generating too much heat -- that are currently plaguing progress in circuit design.

"The memristor is our salvation, because it works better and better as you make it smaller and smaller," said Chua. "The era of nanoscale electronics will be enabled by the memristor. This is not just an invention, it is a basic scientific discovery. It has always been there -- we just had to face these nanoscale problems to realize its importance."

The memristor behaves like a non-linear resistor with memory -- a small, compact and highly energy-efficient means of creating a memory device. But Chua and Williams claim it is also a new type of circuit element that should enable the creation of new devices never before imagined.

The world's first memristor invented at HP Labs by Williams and his research team is based on a two-layer sandwich of titanium dioxide films. As a memory element, it works by changing the atomic structure of the films -- by coupling the motion of atoms in the material with the movement of electrons through the material. The bottom layer of HP's material uses a symmetrical lattice of titanium atoms and oxygen atoms, which makes it a good insulator. But the top layer has had oxygen vacancies introduced as a dopant, which makes it into a good conductor -- the more vacancies, the more conductive. HP's secret sauce for creating these oxygen vacancies in titanium dioxide involves using sputter deposition that begins with an excess of oxygen, then cuts back on the oxygen flow to create the layer with vacancies.

By placing the crossbar of nanowires above and below the sandwiched layers, charge can be passed through the material. "The way I discovered the material for our memristor was by studying how titanium dioxide oxygen sensors work -- that got me thinking about moving oxygen vacancies around in the material to create a memristor," said Williams. "By running current through the device, we can push oxygen vacancies from the layer that has them into the layer that does not, thereby changing its resistance by a factor of 1000 or even more, thus switching the memristor 'on,' then by reversing the current we can move the vacancies back into the first layer, thereby switching the memristor 'off'." As Chua predicted, Williams is already thinking about creating new types of devices with HP's crossbar architecture beyond a simple memory device.

"If we push current through it hard and fast, it acts like a digital device, but if we run current through it gently and slowly it acts as an analog device," said Williams. "We are already designing new types of circuits in both the digital and analog domains using our crossbar architecture. In the analog domain, we want to build memristor-based devices that operate in a manner similar to how the synapse works in the brain -- neuron-like analog computational elements that could perform control functions where decisions must be made involving comparisons as to whether something is larger or smaller than something else. We are not building a neural network yet, but we think that using the memristor in its analog mode with our crossbar is a pretty good representation of a neural net."

Later in 2008, HP promises to begin releasing details of how its memristor material works with its already perfected nanoscale crossbar switch architecture in these various types of circuits.

"The memristor is not just a replacement technology for existing memory devices, but will be used to make a whole range of new types of devices that no one has ever thought of before," said Williams.