Is the memristor always a passive device?

Scientific Reports

The memory resistor with the moniker memristor was a harmless postulate in 1971. Since 2008 a device that claims to be the memristor is on the prowl, seeking recognition as a fundamental circuit element, sometimes wanting electronics textbooks to be rewritten, always promising remarkable digital, analog and neuromorphic computing possibilities. A systematic discussion about the fundamental nature of the device is almost absent within the memristor community. Advocates use incomplete constitutive relationships, ignore concepts of activity/passivity and aver that nonlinearity is central to their case. Few researchers have examined these claims. Our report investigates the assertion that the memristor is a fundamental passive circuit element, from the fresh perspective that electrical engineering is the science of charge management. We demonstrate with a periodic table of fundamental elements that the 2008 memristor is not the 1971 postulate and neither of them is fundamental. The ideal memristor is an unphysical active device and any physically realizable memristor is a nonlinear composition of resistors with active hysteresis. We also show that there exists only three fundamental passive circuit elements.

2018

The memory resistor abbreviated memristor was a harmless postulate in 1971. In the decade since 2008, a device claiming to be the missing memristor is on the prowl, seeking recognition as a fundamental circuit element, sometimes wanting electronics textbooks to be rewritten, always promising remarkable digital, analog and neuromorphic computing possibilities. A systematic discussion about the fundamental nature of the device is almost universally absent. This report investigates the assertion that the memristor is a fundamental passive circuit element, from the perspective that electrical engineering is the science of charge management. With a periodic table of fundamental elements, we demonstrate that there can only be three fundamental passive circuit elements. The ideal memristor is shown to be an unphysical active device. A vacancy transport model further reveals that a physically realizable memristor is a nonlinear composition of two resistors with active hysteresis.

ArXiv, 2014

It is noticed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence in the resistive characteristic v = f(i) of the voltage and current state variables, associated by their electrodynamics sense with electrical and magnetic fields, forces any resister to cause to accumulate some magnetic and electrostatic fields and energies around itself. The present version is strongly extended in the sense of the circuit theory discussion.

2016

It is observed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence of the voltage and current state variables, associated by their electrodynamics sense with electrical and magnetic fields, in the resistive characteristic v = f(i), forces any resister to accumulate some magnetic and electrostatic fields and energies around itself, i.e. L and C elements are always present. From the circuit-theoretic point of view, the role of the memristor is seen, first of all, in the elimination of the use of a unique v(i). This makes circuits with hysteresis characteristics relevant, and also suggests that the concept of memristor should influence the basic problem of definition of nonlinearity. Since the memristor mainly originates from the resistor, it was found necessary to overview some unusual cases of resistive circuits. The present opinion is that the framework of basic circuit theory and its connec...

2021

In this paper we revisit the memristor concept within circuit theory. We start from the definition of the basic circuit elements, then we introduce the original formulation of the memristor concept and summarize some of the controversies on its nature. We also point out the ambiguities resulting from a non rigorous usage of the flux linkage concept. After concluding that the memristor is not a fourth basic circuit element, prompted by recent claims in the memristor literature, we look into the application of the memristor concept to electrophysiology, realizing that an approach suitable to explain the observed inductive behavior of the giant squid axon had already been developed in the 1960s, with the introduction of “time-variant resistors.” We also discuss a recent memristor implementation in which the magnetic flux plays a direct role, concluding that it cannot strictly qualify as a memristor, because its v − i curve cannot exactly pinch at the origin. Finally, we present numeric...

ECS Meeting Abstracts, 2017

Memristors, which are the fourth kind of passive element, along with resistors, inductances and capacitors, were first explicitly described in [1]. Their main characteristics are: (i) if there is no voltage across its terminals, there is no current; and (ii) the I-V curve shows a hysteresis that depends on the frequency of the forcing signal. Equations (1)-(3) describe the most general class of memristors [2], including a “hidden” set of controlling variables (for instance, temperature). v(t)=R(Q,X)i(t) (1) dX/dt=g(Q,I,X) (2) dQ/dt=i(t) (3) v(t) and i(t) are respectively the voltage and the current in the device, R(Q,X) is the memristance of the device, X is the set of controlling variables. A special case of (2) is the POP equation (power-off portrait), which is the case of no external forcing stimuli. For a memristor to be used as a memory (as ReRAMs or PCM are), the POP equation must be zero. Otherwise, X and, as a consequence, R(Q,X) will change with time. An example of this are synapses, that show plasticity, this meaning that they are capable of forgetting past stimuli.

In 2008, researchers at the Hewlett–Packard (HP) laboratories published a paper in Nature reporting the development of a new basic circuit element that completes the missing link between charge and flux linkage, which was postulated by Chua in 1971 (Chua 1971 IEEE Trans. Circuit Theory 18, 507–519 (doi:10.1109/TCT.1971.1083337)). The HP memristor is based on a nanometre scale TiO2 thin film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and non-volatile RAM, they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application-specific integrated circuits and field programmable gate arrays. A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for integrated circuits. This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell’s equations. We also review Chua’s arguments based on electromagnetic theory.

arXiv preprint arXiv:1207.7319, 2012

In 2008, researchers at the Hewlett-Packard (HP) laboratories claimed to have found an analytical physical model for a genuine memristor device [1]. The model is considered for a thin TiO � film containing a region which is highly self-doped with oxygen vacancies and a region which is less doped, i.e., a single-phase material with a built-in chemical inhomogeneity sandwiched between two platinum electrodes. On base of the proposed model, Strukov et al. [1] were able to obtain the characteristic dynamical state equation and current-voltage relation for a genuine memristor. However, some fundamental facts of electrochemistry have been overlooked by the authors while putting forward their model, namely the coupling of diffusion currents at the boundary between both regions. The device will operate for a certain time like a "chemical capacitor" until the chemical inhomogeneity is balanced out, thus violating the essential requirement on a genuine memristor, the so-called "no energy discharge property". Moreover, the dynamical state equation for the HP-memristor device must fail as this relation violates by itself Landauer's principle of the minimum energy costs for information processing. Maybe, such an approach might be upheld if one introduces an additional prerequisite by specifying the minimum amount of electric power input to the device which is required to continuously change internal, physical states of the considered system. However, we have reasonable doubts with regard to this.

Oscillating LRC-circuits have mechanical analogies such as the damped harmonic oscillator made from a mass attached to a spring. We first construct the mechanical counterpart of the electrical basic circuit element M = d{\phi}/dQ, namely the ideal mechanical memristance M = dp/dx. We then construct a mechanical memory resistor: a very light (effectively m = 0), 1 cm radius sphere dragged by a 1mN amplitude periodic force inside a heavy fuel oil with a 10 degrees Celsius per meter gradient, leading to a pinched hysteretic loop that collapses at high frequency. It is a perfect memristor. However, memristor devices hypothesized on grounds of physical symmetries require more. The mechanical missing memristor needs to be crucially mass-involving (MI); the 1971 implied memristor device needs magnetism. Discussing MI memristive systems clarifies why such perfect MI memristors and EM memristors have not been discovered and may be impossible.

2013

There are three theoretical models which purport to relate experimentallymeasurable or fabrication-controllable device properties to the memristor's operation: 1. Strukov et al's phenomenological model; 2. Georgiou et al's Bernoulli rewrite of that phenomenological model; 3. Gale's memory-conservation model. They differ in their prediction of the effect on memristance of changing the electrode size and factors that affect the hysteresis. Using a batch of TiO2 sol-gel memristors fabricated with different top electrode widths we test and compare these three theories. It was found that, contrary to model 2's prediction, the 'dimensionless lumped parameter', β, did not correlate to any measure of the hysteresis. Contrary to model 1, memristance was found to be dependent on the three spatial dimensions of the TiO2 layer, as was predicted by model 3. Model 3 was found to fit the change in resistance value with electrode size. Simulations using model 3 and experimentally derived values for contact resistance gave hysteresis values that were linearly related to (and only one order of magnitude out) from the experimentally-measured values. Memristor hysteresis was found to be related to the ON state resistance and thus the electrode size (as those two are related). These results offer a verification of the memory-conservation theory of memristance and its association of the vacancy magnetic flux with the missing magnetic flux in memristor theory. This is the first paper to experimentally test various theories pertaining to the operation of memristor devices. arXiv:1312.4422v1 [cond-mat.mtrl-sci]