Tuesday, September 8, 2009


One frustrating aspect of science writing is that there's little market for stories that are skeptical about a new advance, but there's a big market for stories that run with the hype.

One widely covered "beyond Moore's law" story last year was the announcement from HP Labs that they had discovered the "fourth basic circuit element," the "memristor," which "could transform computing." As I've complained before, lots of researchers think they can solve industry's problems even though they don't know what they are, but in this case I think the strategy is more deliberate.

HP, in fact, has a history of visionary claims. In 2005, for example, they announced the "crossbar latch": "Who Needs Transistors? HP Scientists Create New Computing Breakthrough at Molecular Scale." They described dense arrays of devices whose resistance depends on previous voltages. But their claims, such as their ability to "restore" signal levels, were quite misleading, since the depend on surrounding their structure with normal transistors. The devices themselves, although densely packed, were slow and passive and certainly not a threat to transistors.

In spite of this history, most news coverage of the memristor repeated the framing in the HP press release: this was the "fourth element" that researchers had sought for decades. U.C. Berkeley electrical engineering professor Leon Chua authoritatively endorsed this view.

Unfortunately, it was Chua who had made the original claim about the memristor, in a 1971 paper that was cited only about 20 times over the next 37 years. In reality, no researchers were beating down the bushes looking for this device; most had never heard of it. Meanwhile many experimenters, including those at HP, had made devices that had the special properties of memristors, but didn't need see a need for that language. Now the crossbar latch appears to contain memristors.

So what elite group is the memristor supposed to be the fourth member of? The other three members are the resistor, capacitor, and inductor. These are the passive, linear, two-terminal circuit elements found in every textbook. Passive means they don't provide power, and two-terminal means they just have two wires coming out. Linear means that output is proportional to input, but for reasons I'll explain below that word was left out of the HP descriptions.

In his 1971 paper, Chua argued that these elements relate either the current or its integral over time (the charge) to the voltage or its integral (which he somewhat surprisingly calls the magnetic flux). The resistance relates current to voltage. The capacitance relates the charge to the voltage. The inductance relates the current to the flux. And one thing is missing….

This unusual description of these familiar devices is a little unnerving. But as Chua modestly explains to Information Week:

"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."

What seems to be missing is something that relates charge (the integral of the current) to flux (the integral of the voltage). He postulated, and HP says they found, this missing element, called the memristor.

But remember that omitted word "linear"? The device that is in the same club as the resistor, capacitor, and inductor would have, like them, a proportionality between the quantities it relates. This simple linear relationship is what makes these devices fundamental. And if the integral of the current is proportional to the integral of the voltage, then their derivatives, the current and voltage, are also proportional. In other words, in this linear case--the only case for which a memristor can legitimately join the ranks of the other three devices--"the memristor reduces to a linear time-invariant resistor," in Chua's own words.

So the memristor only exists, as a fundamental circuit element, when it is just a resistor.

Of course, there are nonlinear generalizations of all of these devices, and things get complicated really fast. And real devices aren't purely one device or another. Capacitors, have some series resistance and some leakage resistance, for example.

Still, maybe thinking in terms of a general, nonlinear "memristivity" makes some observations easier to understand. Even if it doesn't, people may discover some cool stuff by exploring this area. And to their credit, HP researchers seem to be seriously pursuing this, as exemplified by this September 1 Nano Letter. But there's an awful lot of noise and hype that makes it hard to get a bead on the real issues. Certainly the story is much more complex than, say, finding a missing element predicted to be at a particular spot in the periodic table. It's more like deciding that Pluto wasn't really a planet after all--and we know how complicated that story gets.

Once a story like this gets out there, though, unless it's so widespread that virtually everybody has heard of it, it's very hard to sell a story that tries to put it back in the bottle, or even to give it some perspective. (I've tried.)

After all, why would you want to put a lot of effort into understanding something that not worth learning about in the first place?

I'll bet you haven't even read this whole post.


  1. I read the whole post and I can relate to your concerns. You might be interested in an online article I wrote which attempts to give some historical perspective for the memristor theory and which attempts to point out some similar holes in the idea of the memristor as a "fourth fundamental circuit element".


  2. Thanks, Blaise!
    that's a very thorough and useful analysis.

  3. I, too, read the whole thing :-) I agree with you completely about this. When the memristor paper came out, and I heard one of my colleagues interviewed about it on NPR on my way to work, I was very curious. Then I read the thing, and realized that there wasn't any new device physics that wasn't there previously in their resistive switching latches (which, to their credit, they figured out were based on electrochemistry of TiOx, rather than molecular effects as originally claimed when they were getting DARPA moletronics money). What they had done was come up with a clever interpretive angle for resistive switching phenomena, and marketed it full bore. Many other people have been playing with resistive memory over the years, but these folks clearly found the secret to getting lots of attention for it.

  4. Thanks, anonymous.
    It looks like you need to include the "/7#" at the end. Here's a link.

  5. Your complaint is 100% valid for *linear* circuit theory, where there is no difference between resistors and memristors.

    However, Chua is dealing with nonlinear circuit theory. A much better presentation than his 1971 paper is this:

    Leon O. Chua, "Nonlinear Circuit Foundations for Nanodevices, Part I: The Four-Element Torus," Proc. IEEE 91, 1830-1859 (2003)

    Interestingly, there is actually an infinite periodic table of nonlinear elements that are required as a basis set to model all possible circuits. This table of elements is parameterized by two integers than run from -inf to +inf. The 2-terminal elements we are familiar with are just 4 points in this infinite plane. Capacitors are at (0,-1), inductors (-1,0), memristors (-1,-1), and resistors, diodes, voltage sources, current sources, voltage controlled current sources, and current controlled voltage sources are all at (0,0). See figure 31.

    I am sympathetic to your complaints about the marketing around this. But whether or not memristors deserve to be elected to the Pantheon is a non issue for me.

    The real issue is that restricting ourselves to the world of linear circuit elements is like restricting ourselves to linear physics - a reasonable approximation for many applications - but insufficient for the real world. Given nonlinear circuit theory, we need not continue publishing papers about "anomalous capacitance/resistance/inductance". Results in solid state physics over the past 50 years demand this theory.


    P.S. A formal proof of the independence of R,L,C, and M (which I haven't read) is here:

    L. O. Chua, “Device modeling via basic nonlinear circuit elements,”
    IEEE Trans. Circuits Syst., vol. CAS-27, no. 11, pp. 1014–1044,
    Nov. 1980.

  6. Thanks, Forrest.

    I'm happy to think of memristors as members of an infinite class of devices, but that does rather undercut their status as the single missing fundamental circuit element.

    I also have no doubt that nonlinear elements can do important things that should be studied and could be very useful. An interesting example is stochastic resonance, in which adding noise can increase the sensitivity of a nonlinear system.

    Unfortunately, for me anyway, the noise around memristors makes it more difficult to figure out what the real potential is.