Mission Statement

The CHUA Memristor Center (CMC) combines theoretical and experimental studies for the development of novel forms of computation based upon the nonlinear dynamics of memristors (and RRAMs).

The Center’s mission is to bundle research on (i) theory and modelling of RRAMs (memristors) with (ii) simulation studies and conceptual design of analogue and digital computing architectures and (iii) the setup of experimental demonstrators. The Center’s long-term goal is the design and manufacturing of memristor circuits and systems extending or improving the functionalities of state-of-the-art electronic computing systems. This requires a strong interaction between the three main topics theory, architecture and experiments, which are coupled in a continuous and causal loop.

The Center is an interdisciplinary consortium combining expertise and resources from various fields of research, including computer science, electrical engineering, physics, and chemistry. The aim of the consortium is to promote an intensive cooperation between theoretically-inclined researchers and experimentalists. In fact we believe that the scarce communication between these two communities impair advancement in memristor research. The activities shall involve distinguished international researchers.

The visibility of the Center shall be highlighted through various events, including regular academic seminars, national scientific workshops, yearly press conferences, annual internal meetings, and publications in peer-reviewed journals and proceedings of international conferences.

The CMC represents the ideal environment for the establishment of cooperation with industry and academics. The engagement of industry partners shall provide further verve into the project and provide market-oriented guidelines for the realization of the mission goals, which are summarized as follows:

1. Bridging the gap between communities of different disciplines physics, electrical engineering, chemistry, computer science  to create new opportunities, share knowledge, and combine expertise and resources to foster progressive advancement in memristor research.
2. Tailoring existing models of RRAM two-terminal elements to the specific memristive-centered computing systems of interest, and establishing a comprehensive theoretical foundation on memristor devices, circuits and systems.
3. Designing and manufacturing innovative circuits exploiting the peculiar nonlinear behaviour of memristors to target unconventional applications.
4. Investigating the full potential of RRAM nanostructures in extending or improving the functionalities of state-of-the-art systems, with a special focus on reconfigurable, energy-efficient, and real-time computing architectures.
5. Develop an appropriate software package for the simulation of memristor circuits and systems, in particular large-scale computing units.
6. Highlighting the CMC visibility through various means (academic seminars, scientific workshops, and joint publications).

Goals of the CMC

The goals of the CMC are:

• Establishing a comprehensive theoretical foundation on memristors
• Manufacturing innovative circuits
• Extending or improving the functionalities of computing architectures
• Developing software for the simulation of memristor circuits and systems
• Development of joint research projects, organization of workshops and publications

Memristors

Definition, history and classification

Memristors are two-terminal resistive devices with memory. In general, their nonlinear dynamic behaviour is mathematically modeled by means of a differential algebraic equation (DAE) set, in which an ordinary differential equation (ODE) governs the time evolution of the memory state, while an algebraic relation captures the state- and input-dependent Ohm law. The memristor, an acronym for memory resistor, was theoretically introduced in 1971 by L.O. Chua, whom the Chua Memristor Center (CMC) is dedicated to. The memristor introduced in the 1971 pioneering paper, presently referred to as ideal memristor, is the fourth fundamental two-terminal circuit element, the other three being the resistor, the capacitor, and the inductor, as shown in Fig. 1. The ideal memristor may be uniquely characterized by a nonlinear relation of the kind \(f(q, \varphi)=0\) between charge \(q\) and flux \(\varphi\), i.e. between the time integrals of current \(i\) and voltage \(v\) (the past history of these physical quantities is in fact at the origin for the device memory capability), or equivalently by a simple DAE set, reported in Fig. 2 for both the current and voltage input case. The topic of memristors remained an exclusive research field of theoreticians until the 2008 seminal paper from R.S. Williams and his team of engineers at Hewlett Packard (HP) Labs, which unveiled the first ever conscious discovery of memristor fingerprints (see Fig. 3) in nature over the course of studies on the resistive switching behaviour of a nano-scale film based upon titanium dioxide (refer to Fig. 4). Since then, the interest on memristors and their applications has been growing exponentially, with both academia and industry deploying a huge amount of funds and personnel to fabricate, model, and explore the full potential of these devices in electronics applications. In order to model real-world memristors, L.O. Chua recently generalized the DAE set of ideal memristors (see Figs. 5 and 6 for a complete classification). In the most general class of memristors, referred to as extended memristors, both the state evolution function, i.e. the right hand side of the state ODE, and the memristance (memductance) function in the Ohm law for the current (voltage) input case depend upon state and input. For the sake of completeness, extended memristors had been already proposed but named as memristive systems in a 1976 paper from L.O. Chua and Sung-Mo Kang.

Memristor applications

Real-world memristors promise to revolutionize the world of electronics in the years to come. Importantly, non-volatile memristor nano-devices, capable to retain the information embedded in their states for a practically-infinite time, may allow the design of novel, faster, denser, low power and high-endurance memories. Further, the remarkable similarity between the mechanisms behind the memristance programming of certain physical memristors and the synaptic weight modulation of biological synapses may exploited for the development of novel neuromorphic circuits operating according to biological principles.

However, this is only one side of the fascinating landscape of opportunities real-word memristor nano-devices may pave the way to. Exploiting the complex nonlinear dynamic behaviour of memristors, unconventional data computing paradigms may be implemented in circuit form. This may potentially lead to extend or complement the functionalities of purely-CMOS circuits. To name but one exciting example, some real-world memristors based upon niobium oxide deveopled at Hewlett Packard as well as at NaMLab may amplify infinitesimal signals provided they are biased on the negative differential resistance (NDR) region of their DC current-voltage characteristics. Their use in electronics may pave the way towards the development of novel power-efficient transistor-less circuits for bio-inspired data computing applications, as already demonstrated through the design of a neuristor-based cellular automaton endowed with universal computing capability from R.S. Williams and his research unit.

Furthermore, the ability of memristors to process signals and store data in the same physical locations may allow the conception of novel mem-computing machines outperforming state-of-the-art hardware systems suffering from the Von Neumann bottleneck, due to the impossibility for the processor to execute a program faster than the maximum rate at which instructions and data may be fetched from and written into the memory. For example, it was recently shown from R. Tetzlaff, A. Ascoli, and D. Ielmini how replacing the resistor of a purely-CMOS circuit implementation of a processing element (PE) of a standard Cellular Nonlinear Network (CNN) with an hafnium oxide-based memristor may allow to shrink considerably the cell IC size. In fact, given that memristor voltages and states are respectively used for data computing and storage, respectively, the inclusion of memory units within each PE becomes unnecessary, allowing to resolve the current mismatch between the densities of light sensor matrices and nonlinear dynamic arrays.

Certain memristors may also feature an excellent data sensing capability, which, combined with their miniaturized size, is of great interest in the current Internet-of-Things (IoT) era. For example, it has been shown that ultra-sensitive bio-sensors may be fabricated using these silicon nanowire-based field effect transistors, deprived of the gate terminal. The principle of detection in these innovative sensors is based upon the measurement of the voltage gap opening between the drain current minima in the drain current versus drain-to-source voltage loci in semi-logarithmic scale depending on the concentration of biological analytes bound to bio-receptors previously immobilized on the nanowire-based channel surface.

In view of the promising prospects offered by the introduction of memristors in circuit design, the future will certainly witness the development of novel miniaturized reconfigurable circuits and systems harnessing the memory, processing, and sensing functionalities of resistance switching memories to address open signal processing issues or to determine their solutions in a smarter and faster form and under a lower energy budget expenditure.

The HP Memristor

In 2008, the team of R. S. Williams at HP Labs in Palo Alto, CA, built the missing memristor. Watch the story or read the complete article at IEEE Spectrum here.

Some Research on Memristors

The diagram shows the fading memory effect in the shown nanoscale device. The Tantalum oxide microstructure is a Continuum-Memory Memristor. It means that the number of stable but not asymptotically stable states is infinite. When the memristor is switched off, the device may retain any state is may hold for a very long time thereafter. Nonetheless, the memristor may be stimulated so as to forget its past history.

Under AC periodic stimuli, the memristor ‘experiences’ memory loss, as demonstrated in this picture, showing a signal proportional to the current flowing through the device in response to a train of symmetric triangular pulses for a number of initial conditions. The information embedded within the initial condition is progressively lost and, at steady state, a unique asymptotic behavior appears.