In his paper "If it's pinched it's a memristor" [Semicond. Sci. Technol. 29,
104001 (2014)] L. Chua claims to extend the notion of memristor to all
two-terminal resistive devices that show a hysteresis loop pinched at the
origin. He also states that memcapacitors and meminductors can be defined by a
trivial replacement of symbols in the memristor relations, and, therefore,
there should be a correspondence between the hysteresis curves of different
types of memory elements. This leads the author to the erroneous conclusion
that charge-voltage curves of any memcapacitive devices should be pinched at
the origin. The purpose of this Comment is to correct the wrong statements in
Chua's paper, as well as to highlight some other inconsistencies in his
reasoning. We also provide experimental evidence of a memcapacitive device
showing non-pinched hysteresis

Di Ventra, M.

Pershin, Y. V.

English

arXiv

Pershin, YV

Di Ventra, M

eScholarship - University of California

UC San DiegoUC San Diego Previously Published WorksTitleComment on 'If it's pinched it's a memristor'Permalinkhttps://escholarship.org/uc/item/50q298s9JournalSEMICONDUCTOR SCIENCE AND TECHNOLOGY, 34(9)ISSN0268-1242AuthorsPershin, YVDi Ventra, MPublication Date2019DOI10.1088/1361-6641/ab3584 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaComment on “If it’s pinched it’s a memristor” byL. Chua [Semicond. Sci. Technol. 29, 104001 (2014)]Y. V. PershinE-mail: pershin@physics.sc.eduDepartment of Physics and Astronomy, University of South Carolina, Columbia,South Carolina 29208, USAM. Di VentraE-mail: diventra@physics.ucsd.eduDepartment of Physics, University of California San Diego, La Jolla, California92093, USAMay 2019Abstract. In his paper “If it’s pinched it’s a memristor” [Semicond. Sci.Technol. 29, 104001 (2014)] L. Chua claims to extend the notion of memristorto all two-terminal resistive devices that show a hysteresis loop pinched at theorigin. He also states that memcapacitors and meminductors can be defined bya trivial replacement of symbols in the memristor relations, and, therefore, thereshould be a correspondence between the hysteresis curves of different types ofmemory elements. This leads the author to the erroneous conclusion that charge-voltage curves of any memcapacitive devices should be pinched at the origin. Thepurpose of this Comment is to correct the wrong statements in Chua’s paper, aswell as to highlight some other inconsistencies in his reasoning. We also provideexperimental evidence of a memcapacitive device showing non-pinched hysteresis.Although resistive devices and systems with memory were well known inthe literature (both experimental and theoretical) well before the 70’s, the name“memristive elements” and their formal definition introduced in 1976 by Chua andKang [1] are now widely used to describe various types of resistance switchingmemories and other kinds of memory systems and devices (see e.g., Ref. [2] foran extended review). At the same time, the “ideal memristor” (in the sense ofits original definition [3]) still remains an elusive/idealized concept, leading manyresearchers to raise serious concerns about its actual existence as a physically-realizabledevice [4, 5, 6, 7, 8]. In fact, it is doubtful that any experimental system would passthe memristor test we have recently proposed in Ref. [9], which would differentiatebetween an ideal memristor and the more general, and physically-valid concept ofmemristive element.In his paper [10], Chua has further pushed the idea of the “universality” ofmemristors, and even went a step further by claiming that memcapacitive andmeminductive [11] devices and systems can be defined by a trivial replacementof symbols in the memristor relations. Therefore, he claims there should be acorrespondence between the hysteresis curves of different types of memory elements.arXiv:1905.02254v1  [cs.ET]  6 May 2019Comment on “If it’s pinched it’s a memristor” 2In this Comment we point out several errors and misleading statements inRef. [10]. In fact, we demonstrate that it is really not necessary for the differentmemelements to show pinched characteristics to be valid memory elements. It isenough for them to have i) a specific type of response (resistive, capacitive, orinductive), and ii) a memory component. Nothing else is required of them.Our perspective rests on the fact that memristive, memcapacitive, andmeminductive devices and systems are simply generalizations of the traditionalresistors, capacitors, and inductors to the case of memory response [6]. This is not anassumption or a mathematical definition. It is a matter of physical reality: any physicalsystem shows some degree of memory in its response to external perturbations [12],whether that memory is easy to detect or not. Therefore, since theoretical modelshave to correspond to an actual physical reality to be valid models (or else what isdone is at best mathematics, at worst pseudo-science), the basic properties of memorydevice models (whether resistive, capacitive or inductive) should reflect those of thecorresponding experimental systems and devices. With these important preliminariesin mind, let us then highlight the errors and misleading statements in Ref. [10].First point: the hysteresis curves pinched at the origin need not result from non-divergent memory resistances or conductances. In fact, it is straightforward to showthat the pinching at the origin is still possible with some divergent resistance (leadingto an insulating state) and conductance (leading to a superconducting state). Whythese physically realizable situations should not be part of a well-defined memoryelement is a mystery to us.Consider, for instance, a current-controlled memristive system described byV = RM (x, I)I , (1)ẋ = f(x, I) , (2)with RM (x, I) = g(x)/√|I|. Here, V and I are the voltage across and currentthrough the memristive system, respectively, RM (x, I) is the memory resistance, xis the internal state variable, f(x, I) is the function describing the evolution of x, andg(x) ≥ 0 is a bounded function of x. It is evident that as I goes to zeroV = limI→0RM (x, I)I = 0, (3)whilelimI→0RM (x, I) =∞, (4)for g(x) > 0, and yet the above model is a valid memristive element describing atransition to an insulating state.In fact, we emphasize that Eq. (3) is a superior criterion for the I − V curvepassing through the origin compared to the criterion RM (x, 0) 6= ∞ introduced inRef. [10], which would exclude physically plausible situations.Second point: the author of Ref. [10] criticizes our prior work [13] by stating that“a memcapacitor described by a non-pinched hysteresis loop in the q versus V plane iserroneous. Their error can be traced to the associated capacitance tending to infinityat the origin” [10].Chua here reaches these erroneous conclusions due to a clear mistake in hisreasoning. His idea that memcapacitive systems and their properties can bederived/formulated by a trivial replacement of “symbols” in the memristive relationsdoes not hold since the physics of memristive and memcapacitive elements is toodifferent. In particular, the memory properties of resistors are often based on electronicComment on “If it’s pinched it’s a memristor” 3(a)-6 -4 -2 0 2 4-20-10010203040506070CCharge (nC)Voltage (V)V(t)CM(b)- 6 - 4 - 2 0 2 4- 1 . 5- 1 . 0- 0 . 50 . 00 . 51 . 01 . 5Current (arb. units)V o l t a g e  ( V )Figure 1. Experimental electric response of a ferroelectric memcapacitor. (a)q − V curve, and (b) I − V curve. The inset of (a) shows the schematic of thecapacitor-ferroelectric capacitor circuit used in our measurements. A triangularvoltage waveform was used in the measurements. In this figure, the measuredcharge, q, and current, I, are plotted as functions of the voltage across thememcapacitor. The measurement was performed using a standard capacitor ofC = 33 nF, and a lead zirconate titanate (PZT) ferroelectric capacitor with filmthickness of 255 nm and plate area of 105 µm2.and ionic transport [2]. On the other hand, memcapacitors can support memory by,for instance, micro-electro-mechanical effects [14] (e.g., changes of the relative positionof their plates) or time delay in the relative permittivity of the medium in betweenthe capacitor plates [2]. Both cases are physically possible and both lead to memoryeffects. In fact, even the basic properties of the usual resistors and capacitors, such asthe passivity of resistors and the reactance of capacitors, do not allow a transformationfrom one element to the other by a simple “replacement of symbols”.In the case of our specific memcapacitor realization [13] criticized in Ref. [10], thememory effect is caused by the delayed/nonlinear response to the applied bias of amultilayer medium positioned between the capacitor plates. This medium shifts thecharging/discharging q−V curves with respect to each other and away from the origin.Clearly, this is not even remotely similar to what occurs in memristive systems.To further support our arguments, consider the experimentally-obtained q − Vcurve of a ferroelectric capacitor as reported in Fig. 1(a). Previously we pointed outthat ferroelectric capacitors are a kind of memcapacitors [2], and there is no doubtabout such classification [15]. We have performed experimental measurements of theq − V curves of a lead zirconate titanate (PZT) ferroelectric capacitor using a simplecapacitor-ferroelectric capacitor circuit shown in the inset of Fig. 1(a). The circuit wasdriven by a triangular voltage waveform, and the charge on the ferroelectric capacitorwas measured from the voltage drop across the standard capacitor. Fig. 1(a) clearlyshows that the q−V curve of the ferroelectric memcapacitor is not pinched. The I−Vcurve obtained by the differentiation of the experimentally measured q(t) exhibits twopeaks typical of ferroelectric capacitors [16] (see Fig. 1(b)).Third point: by referring again to our work [13] Chua writes in Ref. [10] “It alsofollows that their rather intimidating quantum-mechanical arguments were incorrectlyapplied”. Chua does not seem to realize that our work [13] is based entirely onclassical electrodynamics, except for the use of the Simmons formula for the tunnelingcurrent [17]. We are surprised that the Simmons current expression was not recognizedComment on “If it’s pinched it’s a memristor” 4by the author of Ref. [10]. There should be nothing “intimidating” about usingclassical electrodynamics and standard formulas for the tunneling current: it shouldbe standard knowledge of any electrical engineer.Fourth point: the word “pinched” is not general enough to represent all kinds ofmemristive hysteresis. Semantically, a “pinched loop” is a loop obtained by the actionof pinching. In a pinched loop, the ascending and descending curves are tangent toeach other at the pinched point (see, e.g., Fig. 2(b) in [10]). To obtain the self-crossinghysteresis curves, which are the most common ones (see Fig. 2(a) in [10]), the hysteresisloop needs to be twisted not pinched.Final point: although one can loosely use the word “memristor” to indicate anymemristive elements (and we have done so sometimes as well), it is very importantto remember that an actual “ideal memristor” as originally defined in [3] has not beenfound yet. By using the same name for all resistive memories seems only an attemptto distract from this important fact. As we have already argued in our Ref. [9], beforeclaiming that such a hypothetical device had been found, researchers should submittheir devices to the test we have proposed in [9], which clearly and unambiguouslydistinguishes between an ideal memristor and actual, physically possible and well-documented memristive devices.To summarize, the present Comment corrects wrong and misleading statementsand concepts presented by Chua in Ref. [10]. In particular, we have shown that i)the hysteresis curves pinched at the origin need not result from non-divergent memoryresistances or conductances, and divergent response functions do not preclude differentphysical systems to be valid memory elements, ii) a trivial replacement of symbols inthe memristor relations leads to incorrect conclusions regarding the hysteresis curvesof memcapacitors and meminductors, iii) memcapacitors with non-pinched hysteresisdo exist, and we have even provided experimental evidence of one such case.In other words, physically realizable memristive, memcapacitive and minductiveelements are simply resistors, capacitors and inductors whose memory can be detectedexperimentally. Whether their constitutive relations are pinched at the origin or notis irrelevant. A lesson can be drawn from all this: over-reliance on mathematicaldefinitions to describe physical phenomena can easily lead to the wrong conclusionsand away from physical reality.References[1] L. O. Chua and S. M. Kang, “Memristive devices and systems,” Proceedings of IEEE, vol. 64,pp. 209–223, 1976.[2] Y. V. Pershin and M. Di Ventra, “Memory effects in complex materials and nanoscale systems,”Advances in Physics, vol. 60, pp. 145–227, 2011.[3] L. O. Chua, “Memristor - the missing circuit element,” IEEE Transactions on Circuit Theory,vol. 18, pp. 507–519, 1971.[4] B. Mouttet, “Memresistors and non-memristive zero-crossing hysteresis curves,” arXiv preprintarXiv:1201.2626, 2012.[5] P. Meuffels and R. Soni, “Fundamental issues and problems in the realization of memristors,”arXiv preprint arXiv:1207.7319, 2012.[6] M. Di Ventra and Y. V. Pershin, “On the physical properties of memristive, memcapacitive andmeminductive systems,” Nanotechnology, vol. 24, p. 255201, 2013.[7] S. Vongehr and X. Meng, “The missing memristor has not been found,” Scientific Reports, vol. 5,p. 11657, 2015.[8] K. M. Sundqvist, D. K. Ferry, and L. B. Kish, “Memristor equations: Incomplete physics andundefined passivity/activity,” Fluctuation and Noise Letters, vol. 16, p. 1771001, 2017.Comment on “If it’s pinched it’s a memristor” 5[9] Y. V. Pershin and M. Di Ventra, “A simple test for ideal memristors,” J. Phys. D: Appl. Phys.,vol. 52, p. 01LT01, 2019.[10] L. Chua, “If it’s pinched it’s a memristor,” Semicond. Sci. Technol., vol. 29, no. 10, p. 104001,2014.[11] M. Di Ventra, Y. V. Pershin, and L. O. Chua, “Circuit elements with memory: Memristors,memcapacitors, and meminductors,” Proc. IEEE, vol. 97, no. 10, pp. 1717–1724, 2009.[12] R. Kubo, “Statistical-mechanical theory of irreversible processes. i. general theory and simpleapplications to magnetic and conduction problems,” J. Phys. Soc. Japan, vol. 12, no. 6, pp.570–586, 1957.[13] J. Martinez-Rincon, M. Di Ventra, and Y. V. Pershin, “Solid-state memcapacitive system withnegative and diverging capacitance,” Phys. Rev. B, vol. 81, p. 195430, 2010.[14] J. Martinez-Rincon and Y. V. Pershin, “Bistable non-volatile elastic membrane memcapacitorexhibiting chaotic behavior,” IEEE Trans. El. Dev., vol. 58, p. 1809, 2011.[15] J. Flak and J. K. Poikonen, “Solid-state memcapacitors and their applications,” in MemristorNetworks. Springer, 2014, pp. 585–601.[16] T. Schenk, U. Schroeder, M. Pesic, M. Popovici, Y. V. Pershin, and T. Mikolajick, “Electric fieldcycling behavior of ferroelectric hafnium oxide,” ACS Applied Materials & Interfaces, vol. 6,no. 22, pp. 19 744–19 751, 2014.[17] J. G. Simmons, “Generalized formula for electric tunnel effect between similar electrodesseparated by a thin insulating film,” J. Appl. Phys., vol. 34, no. 6, p. 1793, 1963.

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