Memristor – a real missing link of circuit theory or just a theoretical mirage?

On 5th May 2010, Todd Hoff posted on his blog “High Scalability” an article entitled: “How will Memristors change everything?”. One of Hoff's questions treated in this article is “What Can We Do With These Things?” And his answer ends with these words:

“Designing for memristors may be a bit like the radical shift in our sense of space, time and causality that accompanied the move from classical Newtonian physics to the relativistic quantum perspective of Modern physics. Our common sense notions of classical physics dissolve and are replaced by what? What will systems and algorithms look like when our core assumptions have shifted so radically?”

However, Hoff's own statement regarding the actual existence of a memristor, posted just above the quoted question, is following.

“It doesn't exist. Yes, there's a lot of hype about memristors, but there also seems to be a lot of confidence memristors will be real viable products. But for now they don't exist. And we don't know a lot about memristors: unit cost; IO/s per device; performance on sequential/random access operations and read/write loads; reliability; error rates; ease of system integration; persistence lifetime; ease of programming; access times; instructions per clock cycle; power use; density.”

Shortly before this article, R. Stanley Williams, a researcher at HP (Hewlett-Packard Labs), has presented his team's work (as a video “Finding the Missing Memristor”), where he recounts Leon Chua's theoretical discovery of the memristor as the fourth circuit element (after resistor, capacitor, and inductor), and explains how a memristor works. Williams said Chua is to circuit theory what Albert Einstein is to relativity. And Williams gave also a prognosis of some important developments before 2020.

This was the situation about five years ago. But still nothing great has changed. On “The 4th Memristor and Memristive Symposium” (held at the University of Notre Dame; Indiana, on 28th July 2014), R. Stanley Williams presented his newer article, where we read in abstract:

“Constructing an accurate and predictive compact mathematical model for a memristor is essential for designing and modeling complex integrated circuits. Although the fundamental equations that specify the device physics are known, they comprise a set of coupled nonlinear integro-‐differential equations that are extremely challenging and time consuming to solve numerically. On the other hand, a purely black box approach of fitting a set of experimental measurements to a convenient functional form runs the risk of poorly representing the behavior of the device. Thus, a hybrid approach is necessary, in which the mathematical formalism for a memristor provides the framework for the model and knowledge of the device physics defines the state variable(s), operating limits and asymptotic behavior necessary to make the model useful.”

If we go back to the original article by Leon Chua (“Memristor - The Missing Circuit Element”) from year 1971, we can find the simplest, but also the most important source of the theoretical problems with memristors. We read at the beginning of this article:

“Three other relationships are given, respectively, by the axiomatic definition of the three classical circuit elements, namely, the resistor (defined by a relationship between v and i), the inductor (defined by a relationship between φ and i), and the capacitor (defined by a relationship between q and v). Only one relationship remains undefined, the relationship between φ and q. From the logical as well as axiomatic points of view, it is necessary for the sake of completeness to postulate the existence of a fourth basic two-terminal circuit element which is characterized by a φ-q curve.”

Now, let us consult the Unified Family of all physical quantities. Let us note that Chua's electric potential v is U in our case of the electrodynamic plane, and his flux-linkage φ is our flux of magnetic field ΦH. Finally, let us consider the equivalence relation of the electric resistance R of a quantum to the quantum speed of light c; R = c (compare Table 2 on the related page). If we do this, we immediately see that in the unified quantum description of any integrated circuit the “missing” memristor relation between ΦH and q is the same, as between U and i, namely, ΦH = q*c (similar to U = i*c). It is because in the quantum description of the Unified Physics, ΦH*f = U, like q*f = i, where f is the quantum frequency.

As soon as we arrive experimentally at the quantum limit of the electronics at just a few nanometers, we are obliged to use our quantum description of all processes. On the other hand, we have also got the advantage of the enormous simplicity of this description. So, what is the answer to the title-question here above? In a range of the universal quantum length of about 5 nm all physical quantities collapse to the length-period (or matter-spirit) properties of each and every quantum. Electrodynamics collapses to dynamics. All what remains is just the Unified Physics. I think, it is a proper time to rethink just now.

2 Responses

  1. Peter Jakubowski
    Dear Martina, thank you for this interesting and important link. It presents some technology demos of the transistors smaller that 5 nm, indeed. But we have to remember, in Nature (as suggested by the Unified Physics) all physical properties (physical quantities) are strictly connected to each others. The dimension 5 nm, for example, corresponds roughly with the room temperature. Trying to develop 1 nm devices means to go down with their working temperature to about 60 K, which is not realizable (as I think today) in our daily applications of mobiles or laptops. The 5 nm size is really a boundary between the living and inanimate matter, the universal level of the Quantum Spectrum of all possible matter-spirit quanta in our observable Universe.
  2. Martina Schöner I think it's a helpful link and reminder what we are dealing with when it comes down to 5nm.

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