Wanted to correct an earlier statement I made. The memristor symposium video part 2 with what I called a "memristive AI demonstration" is acutally a simulation. It's not done with actual memristors, but with, presumably, software modules simulating memristive behavior. There was a little bit of language in the presentation I didn't catch. This is further reflected in this little blurb on the HP website:
"The research, by Greg Snider and Stan Williams of HP Labs, is a featured paper in the Jan. 24 issue of Nanotechnology, a publication of the British Institute of Physics ("Nano/CMOS Architectures Using Field-Programmable Nanowire Interconnect," www.iop.org/journals/nano). The research was conducted using classic modeling and simulation techniques, but Williams said HP is working on producing an actual chip using the approach, and could have a laboratory prototype completed within the year."
Also, I said the memristor part of the circuit simulates neuronal behavior, but it is synapses they substitute for -- not neurons. Neurons would have to be simulated with CMOS and, presumbably, software.
And finally, I haven't yet discovered what is memristive about the resistive devices in their synaptic role. I also have to go back to Williams' theoretical memristance discussions to see whether they are consistent with having memristor behavior in a write scheme that involves partial phase change.
I think I see what you're saying now. If a huge pulse of current is required to create the energy barrier (the phase change), then how can you use variable current to achieve a variety of different resistances -- memories?
I'll have to go back and check on that, because I acutally don't remember asking myself that question.
BTW, this IS possible in PRAM, but I don't remember any discussion like this with regard to ReRAM. But that doesn't mean it didn't happen! LOL
ReRAM elements are based on "resistance switching" effects which have been known for a long time. Usually, some electroforming step is required to activate "resistance switching" phenomena in oxide materials like TiO2 or Ta2O5. Electroforming is generally achieved by applying high electric fields which can lead to soft breakdown of the insulating oxide layers. Such fields can induce the formation of localized (filamentary), defect-rich and structurally/chemically altered regions that have much higher electrical conductivity than the surrounding insulating matrix. It can be assumed that resistance switching effects in metal oxides result from "reversible" physical/chemical phase transformations occurring somewhere along these defective, conducting filamentary paths. Such transformations can be brought forth by, for example, local Joule heating in combination with significant redistributions of mobile ionic species under electric field action.
The memristor was hypothetically envisioned as the fourth passive two-terminal electrical component. Memristor is a contraction of "memory resistor," because that is exactly how it would function: to remember its history. A memristor would be a two-terminal device whose resistance wouldn't be constant but would depend on the history of current that had previously flowed through the device, i.e., its present resistance would depend on how much electric charge has flowed in what direction through it in the past. When you turn off the voltage, the memristor would remember its most recent resistance until the next time you turn it on, whether that happens a day later or a year later. There is, however, on simple problem with this fourth passive two-terminal electrical component called "memristor": It cannot exist in physical reality!
"Moreover, the nonvolatile "memristor" concept raises some severe questions when viewed from the perspective of non-equilibrium thermodynamics /4, 5/. Nonvolatile information storage requires the existence of energy barriers that separate distinct memory states from each other. "Memristors" whose resistance (memory) states depend only on the current (like the HP memristor) or voltage history would thus be unable to protect their memory states against unavoidable fluctuations and therefore permanently suffer information loss:the proposed hypothetical concept provides no physical mechanism enabling such systems to retain memory states after the applied current or voltage stress is removed. Such elements can therefore not exist, as they would always be susceptible to a so-called "stochastic catastrophe" /5/. It is therefore pointless to tinker with this concept in order to describe physical phenomena like "resistance switching" effects."
The problem with memristor deniers is that they come from a math-physics-theory background and neglect to understand the practical details of memory operation. HP's TiOx RRAM uses high current density which causes a phase change. This change of phase represents an energy barrier. Transient fluctuations in voltage are infinitessimal compared to what is required to change phase which is in turn required to change logic state. It's the same energy barrier used in PRAM. By your account, there could not possibly be working prototypes, but there are. They even made a next-generation memristive AI machine. See the video:
A friendly reminder how HP's memristor ("The missing memristor found", NATURE) has been defined (according to "HP Memristor FAQ", http://www.hpl.hp.com/news/2008/apr-jun/memristor_faq.html):
"Memristance is a property of an electronic component. If charge flows in one direction through a circuit, the resistance of that component of the circuit will increase, and if charge flows in the opposite direction in the circuit, the resistance will decrease. If the flow of charge is stopped by turning off the applied voltage, the component will 'remember' the last resistance that it had, and when the flow of charge starts again the resistance of the circuit will be what it was when it was last active."
The weak point of the memristor concept is the dynamic state equation, i.e., the time response of the system to an externally applied electrical stress. Nonvolatile information storage by means of a material system requires the existence of energy barriers that separate distinct system's states from each other. At finite temperatures there exist, however, unavoidable fluctuations in all physical systems. If these energy barriers are not high enough, such fluctuations might be able to expel the system from its present state to another one.
A dynamic state equation of a system has to take into account stochastic terms related to such fluctuations (some type of a generalized Langevin-equation). This, however, was overlooked when the memristor concept was put forward; otherwise, it would immediately have become clear that the concept of purely current- or voltage-controlled memristors describes – from a thermodynamic point of view – nothing else but something like a frictionless "neutral equilibrium" system. Such a memristor system would always erratically "move" through its resistance state space – just under the influence of noise –, reminding somehow of a drunken sailor's random walk.
Re the assertion that ReRam must fail as a nonvolatile memory (your reference 5), a question: Surely there is an energetic barrier that resists e.g. the movement of oxygen ions in a TiO2 system. While given long enough with no field applied they will certainly diffuse back to equilibrium, this is also true of the electrons trapped in the gate of a flash memory cell. It seems to me that whether or not you consider a storage device to be nonvolatile just depends on your timescale. DRAMs are nonvolatile for a few seconds at room temp, while even diffused ROM will lose information to stochastic diffusion given enough time. Do you agree?
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.