### Memristor Identity Crisis

June 11, 2012

First, a mild disclaimer. None of this article is criticism of someone's research. The problem discussed is one of nomenclature, not scientific misconduct. It's also good to realize that the greatest discoveries get the most criticism, since lesser "discoveries" are just ignored. If Alexander Graham Bell had invented a better post hole digger, I'm sure he would not have needed to defend his patents in the courts for so many years.

The controversy is about a supposed electrical circuit element called a memristor. As its name implies, it's a resistor with a memory; specifically, a memory of how much current has passed through it. In this information age, such a device would be useful. If someone asked me to make such a device, there would be various ways I could do it. If you wanted it in a day and weren't worried about its size or performance, I could combine a microcontroller and a field effect transistor to produce such a device.

To produce a more elegant device, I would likely look back into the decades old technology of tungsten oxide electrochromic devices that work by reversibly plating one material onto another in an electrochemical cell. If such a device were really important, a little research would yield far better material systems, and a better device.

The problem, however, is that the memristor is supposedly a fundamental device, not a device that depends on any material system. Its properties are predicted by looking at the symmetry of the fundamental electrical devices, resistors, capacitors and inductors, and filling in the gap.
Resistor: ∂v = R⋅∂i
Capacitor: ∂q = C⋅∂v
Inductor: ∂φ = L⋅∂i
Memristor: ∂φ = M⋅∂q
In these equations, v is the voltage, i is the current, φ is the magnetic flux; and R, C, L and M are the resistance, capacitance, inductance and memristance. The fundamental symmetry can be seen easily in the following figure, which shows these four electrical elements much like the ancients represented their four elements.

The four electrical elements.

(Via Wikimedia Commons))

Leon Chua, famous for his eponymous chaotic oscillator circuit, started people thinking about the possibility of the memrister in a 1971 paper.[1] The operation of this element is simply that its resistance will increase when current flows through it in one direction; and, it will decrease when current flows through it in the other direction.

As the equations dictate, magnetism should be involved because of the flux term, ∂φ, as Chua realized; viz.,
"The physical mechanism characterizing a memristor device must come from the instantaneous (memoryless) interaction between the first-order electric field and the first-order magnetic field."[1]
That was in 1971, and it wasn't until 2008 that the first memristors devices were described. I wrote about these in an earlier article (Memristor, May 14, 2008). Unlike my microcontroller version mentioned earlier, these were true, passive devices that didn't need electrical power. Chua was happy to acknowledge these devices as memristors.

Although these devices do have the resistance properties required of a memristor, the problem is that they don't involve magnetism in any way. Hewlett Packard's memristor device behaves mathematically as a memristor, but its action is via a chemical effect and not the faster, and more useful, electromagnetic effect of Chua's original proposal.

Atomic force microscope (AFM) image of seventeen memristors. The wires are 50 nm wide, which is only 150 atoms.

Photo by J. J. Yang, HP Labs, via Wikimedia Commons)

The original Hewlett Packard device functioned through ionic migration in a 5 nanometer film of titanium dioxide sandwiched between electrodes. As electrical charge is accumulated in this film, it becomes charged with oxygen vacancies that increase its conductance. The conductance effect of vacancies in bulk titanium dioxide was known for years prior to its use in memristors. It's used in some types of oxygen gas sensors.

An analysis of the true nature of the memristor has been published on the arXiv Preprint Server by Sascha Vongehr of the Department of Philosophy, Nanjing University, China.[6] Vongehr is skilled to comment in this area, since he also has an appointment at the National Laboratory of Solid-State Microstructures (Nanjing, China), and he has a physics Ph.D. from the University of Southern California.

Vongehr writes that true memristor devices may not exist at all, since there are reasons that they might be unstable. Says Vongehr, "The memristor is either impossible or still to be discovered."[6] And it's not just he who has doubts. Devices that perform as memristors were produced earlier than 2008,[7] but the discoverers of these devices did not claim them to be memristors, nor did they claim prior discovery after publication of the 2008 work.

Vongehr writes that "memristor" was a catchy label, so there was a flood of memristors papers without any critical thought as to what a memristor really is. I can relate to that, since I once worked in the area of magnetic bubbles, which seemed to persist long after its utility, perhaps because it, too, had a catchy label. Vongehr's hope is that the mis-definition of memristors doesn't stop its actual discovery; or, proof that memristors, indeed, don't exist.[6]

### References:

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