The original paper by Chua, does not show any non-volatility. In fact, it makes a figure in the IV curve that has the shape of a tilted figure 8, passing through zero and it is a transient result. Not, a hard shut off with permanent storage as any RRAM shows. Sadly enough, the realization of such a figure is not from a single resistor and more from a circuit. In a very unphysical and naive attempt, HP engineers tried to add some physics to lumped circuits. A Junior level Physics book, like Halliday and Resnick could show them that equivalent circuits still must obey Maxwell's equation, for charge must be concerved. In any case, as we all know, there are 3 parameters in Maxwell's equatiosn - conductivity (sigma), permetivity(epsilon) and permeability(mu). All of these reflect 19 century physics in which the Currie-Weiss Mean Field Theory was the only semi-microscopic model. Untill quantum mechanics, such luped parameters led to V=IR etc. A simple diode, tells you that only in the linear low signal regime, ohm's law could be used - that is why we have h-parameters in bipolar transition etc. In the case of a resistor with memory - Memristor - the combination of very thin films (30 nm), oxygen vacancies and electron-hole pairs, including excitons create a messy business that is not really robust in storing anything and the IV curves are unsaturated at nearly zero current (i.e., the insulating phase). A simple, back of the envelop model for such a messy device is to consider that vacancies stay INSIDE of the material and not become a charge carrier through the contact. So, if charged, it just moves back and forth, facilitating mass transfer - a form of electromigration of Ti or O. A well know model for oxides is Vox(+2) + 2e(-) --> Vox(0). The equilibrium constant is k=exp(-Ea/KT) = [Vox(0)]/[Vox(+2)].n^2, where the [.] means concentration and n is the trapped electron concentration in oxygen vacancies. So, the Memmristor, at best is a trapped electron device with a differential voltage dV = I dR + R dI, if dR=0, it is just a resistor. The assertion that dR is not zero and is nonvolatile is a bit too much to swallow when for many years everyone knows that trapped electrons, magneto resistance etc, all have some meory effect. thus, with some algebra, you can easily see that the HP memristor is Ron /Roff = (1- n(trapped)/ n(total)), where n(total) comes from the injected electrons during operation. If all electrons are trapped (extreme case), Ron=0 (conductor) and if n(trapped)< n(total, the more common case, Roff>Ron (insulator). The physics is then only on charge trap - what is new in that? On top of everything, since Vox(+2) is also moving, no two switches are the same. Sorry HP, try quantum mechanics next time to understand electrons and holes and do not count on vacancies as a reliable device parameter.
The memristor concept is like an air castle. It looks like something but actually nothing. It seems like a new thing, but finally you found it still talked about the same thing. If you say it stands for nothing, they will tell you that it comprises everything.
Whereas the axiomatic definitions of ideal resistors, capacitors and inductors are in accordance with all laws of physics, this is not the case for ideal nonvolatile memristors (M. Di Ventra and Y. V. Pershin, "On the physical properties of memristive, memcapacitive, and meminductive systems", Nanotechnology, vol. 24, (2013) (http://iopscience.iop.org/0957-4484/24/25/255201)). Thus, there is also no place for real nonvolatile memristors by assuming that such real-world devices would exhibit some amount of capacitance or inductance. As the core element - the ideal nonvolatile memristor - is a physically impossible element, any equivalent circuit model including an ideal memristor component would also "operate" in conflict with physics.
Good queston. Although, according to Chua, there is a functional relationship between charge and flux (magnetic flux), which is the time integral of current and the time integral of voltage. The slope of this function is what he calls memristance. By this definition, a normal resistor is also a memristor. It just has a constant memristance (slope = 1). When memristance is constant, it is just defining Ohm's law.
These are theoretical electrical components. There will never be a real-world device, from HP or anyone else, that is purely a memristor, just as there will never be a device that is purely a capacitor or inductor. So, in that sense, if the application of current causes a change in resistance, then the term memristor could apply, just as we give the term resistor to a device even if it also ehibits some capacitance.
It is interesting to find several more Arxiv papers on the discussion of memristor. I'm wondering whether they have tried to a journal, or just posted there. The memristor paper machine guys might need to answer the questions before their continuing using such a word, even it is really mysterious to them.
It is also interesting to find the pour of memristor neural networks papers from the biology guys.
I have just finished reading a Nature Nanotech paper by HP in 2008, another key paper by HP on memristor.
The experiments there cannot even be regarded as a normal "design of experiments" concept, but such a paper can finally pass the peer-review process, and now with high citations. Any well-trained physicist will not accept the method and the superficial analysis described in this paper.
The resistive switching is a good concept for device development. Some very good results have been shown. There could be good future for ReRAM.
The "memristor", most of us even do not know what it is, should be kept as it was in 1970s, until a sound physical model has been shown. Any mathematicl modelling for a physical concept must be based on basic physical principles.
In my opinion, the misleading "memristor" concept will not help but hurt the development of ReRAM devices. Before the HP works, there were already some excellent pioneer works on resistive switching.
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