Paul Meuffels and Rohit Soni
Forschungzentrum Jülich GmbH, Peter Grünberg Institut, Jülich, Germany
Nanoelektronik, Technische Fakultät, Christian-Albrechts-Universität zu Kiel, Kiel, Germany
In 2008, researchers at the Hewlett-Packard (HP) laboratories claimed to have found an analytical physical model for a genuine memristor device. 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. 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.
The width of the electrodes is not included in the current phenomenological models of memristance, but is included in the memory-conservation (mem-con) theory of memristance. An experimental study of the effect of changing the top electrode width was performed on titanium dioxide sol-gel memristors. It was demonstrated that both the on resistance, Ron, and the off resistance, Roff, decreased with increasing electrode size. The memory function part of the mem-con model could fit the relationship between Ron and electrode size. Similarly, the conservation function fits the change in Roff. The experimentally measured hysteresis did not fit the phenomenological model’s predictions. Instead the size of the hysteresis increased with increasing electrode size, and correlated well to decreasing Ron.
We have demonstrated that changing the size of an electrode affects the behavior of curved type memristors and has no effect on triangular switching ones. This suggests that the two types operate via different mechanisms. The size of the hysteresis increases with increasing electrode size, as a result of the decrease in the value of Ron with increasing electrode size.
The experimental results presented in this paper suggest that that a three-dimensional model of memristance is needed and that the Mem-Con model gives a good fit to the experimental data
Titanium dioxide sol-gel memristors have two different modes of operation, believed to be dependent on whether there is bulk memristance, i.e. memristance throughout the whole volume or filamentary memristance, i.e. memristance caused by the connection of conducting filaments. The mem-con theory of memristance is based on the drift of oxygen vacancies rather than that of conducting electrons and has been previously used to describe bulk memristance in several devices. Here, the mem-con theory is extended to model memristance caused by small filaments of low resistance titanium dioxide and it compares favorably to experimental results for filamentary memristance in sol-gel devices.
Several unique properties of biological systems, such as adaptation to natural environment, or of animals to learn patterns when appropriately trained, are features that are extremely useful, if emulated by electronic circuits, in applications ranging from robotics to solution of complex optimization problems, traffic control, etc. In this chapter, we discuss several examples of biologically-inspired circuits that take advantage of memory circuit elements, namely, electronic elements whose resistive, capacitive or inductive characteristics depend on their past dynamics. We provide several illustrations of what can be accomplished with these elements including learning circuits and related adaptive filters, neuromorphic and cellular computing circuits, analog massively-parallel computation architectures, etc. We also give examples of experimental realizations of memory circuit elements and discuss opportunities and challenges in this new field.
In conclusion, we have shown that the two-terminal electronic devices with memory
– memristive, memcapacitive and meminductive systems – are very useful to model
a variety of biological processes and systems. The electronic implementation of
all these mechanisms can clearly lead to a novel generation of ”smart” electronic
circuits that can find useful applications in diverse areas of science and technology.
In addition, these memelements and their networks, provide solid ground to test
various hypothesis and ideas regarding the functioning of the human (and animal)
brain both theoretically and experimentally. Theoretically because their flexibility in terms of what type and how many internal state variables responsible for memory,
or what network topology are required to reproduce certain biological functions can
lead to a better understanding of the microscopic mechanisms that are responsible
for such features in living organisms. Experimentally because with the continuing
miniaturization of electronic devices, memelements can be assembled into networks
with similar densities as the biological systems (e.g., the brain) they are designed to emulate. In particular, we anticipate potential applications for memcapacitive and
meminductive systems which offer such an important property as low energy
dissipation combined with information storage capabilities. We are thus confident
that the area of biologically-inspired electronics with memory circuit elements will
offer many research opportunities in several fields of science and technology
The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device’s terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular automata. Each cell gets info about states of its closest neighbours via incoming links. A link can be one ‘conductive’ or ‘non-conductive’ states. States of every link are updated depending on states of cells the link connects. Every cell of a memristive automaton takes three states: resting, excited (analog of positive polarity) and refractory (analog of negative polarity). A cell updates its state depending on states of its closest neighbours which are connected to the cell via ‘conductive’ links. We study behaviour of memristive automata in response to point-wise and spatially extended perturbations, structure of localised excitations coupled with topological defects, interfacial mobile excitations and growth of information pathways.
In our work we propose implementing fuzzy logic using memristors. Min and max operations are done by antipodally configured memristor circuits that may be assembled into computational circuits. We discuss computational power of such circuits with respect to m-efficiency and experimentally observed behavior of memristive devices. Circuits implemented with real devices are likely to manifest learning behavior. The circuits presented in the work may be applicable for instance in fuzzy classifiers.