Everything You Wish to Know About Memristors But Are Afraid to Ask

This paper classifies all memristors into three classes called Ideal, Generic, or Extended memristors. A subclass of Generic memristors is related to Ideal memristors via a one-to-one mathematical transformation, and is hence called Ideal Generic memristors. The concept of non-volatile memories is defined and clarified with illustrations. Several fundamental new concepts, including Continuum-memory memristor, POP (acronym for Power-Off Plot), DC V-I Plot, and Quasi DC V-I Plot, are rigorously defined and clarified with colorful illustrations. Among many colorful pictures the shoelace DC V-I Plot stands out as both stunning and illustrative. Even more impressive is that this bizarre shoelace plot has an exact analytical representation via 2 explicit functions of the state variable, derived by a novel parametric approach invented by the author

The Fourth Element: Characteristics, Modelling, and Electromagnetic Theory of the Memristor

In 2008, researchers at HP Labs published a paper in {\it Nature} reporting the realisation of a new basic circuit element that completes the missing link between charge and flux-linkage, which was postulated by Leon Chua in 1971. The HP memristor is based on a nanometer scale TiO$_2$ thin-film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and nonvolatile RAM (NVRAM), they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application specific integrated circuits (ASICs) and field programmable gate arrays (FPGAs). A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for Integrated Circuits (ICs). This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.Comment: 28 pages, 14 figures, Accepted as a regular paper - the Proceedings of Royal Society

Circuit elements with memory: memristors, memcapacitors and meminductors

We extend the notion of memristive systems to capacitive and inductive elements, namely capacitors and inductors whose properties depend on the state and history of the system. All these elements show pinched hysteretic loops in the two constitutive variables that define them: current-voltage for the memristor, charge-voltage for the memcapacitor, and current-flux for the meminductor. We argue that these devices are common at the nanoscale where the dynamical properties of electrons and ions are likely to depend on the history of the system, at least within certain time scales. These elements and their combination in circuits open up new functionalities in electronics and they are likely to find applications in neuromorphic devices to simulate learning, adaptive and spontaneous behavior

Reliable SPICE Simulations of Memristors, Memcapacitors and Meminductors

Memory circuit elements, namely memristive, memcapacitive and meminductive systems, are gaining considerable attention due to their ubiquity and use in diverse areas of science and technology. Their modeling within the most widely used environment, SPICE, is thus critical to make substantial progress in the design and analysis of complex circuits. Here, we present a collection of models of different memory circuit elements and provide a methodology for their accurate and reliable modeling in the SPICE environment. We also provide codes of these models written in the most popular SPICE versions (PSpice, LTspice, HSPICE) for the benefit of the reader. We expect this to be of great value to the growing community of scientists interested in the wide range of applications of memory circuit elements

Memcapacitors

Mestrado em Engenharia Eletrónica e TelecomunicaçõesThe present work aims to continue the study of memory devices, initiated with the prediction of the existence of memristors by Leon Chua in 1971, with the study and characterization of memcapacitors as a semiconductor two-terminal device, characterized by the non-linear relation between charge and voltage, which also present the ability to remember the voltage or charge that passes through the device, graphically represented by a graphic with hysteresis characteristics, also presenting a variable capacitance in function of the charge applied in its terminals. Here, a characterizationof the response functions to a sinusoidal periodic input with variable frequency to three mathematical models of memcapacitive systems is performed: given a memcapacitor in series with an ac input voltage source, the respective hysteresis charge-voltage plots are studied by simulations in the MATLAB environment. Next, a classification of the hysteresis plots in function of its geometry is performed, given that the crossing of such graph in the (0.0) point defines it as a type I or type II hysteresis loop. The analysis continues with the morphological identification of the area of the hysteresis curve of the first model, by varying amplitude and frequency of the input source, in such a way to compare the other models with the ideal one, as well as to take the critical frequencis from which the memcapacitance becomes constant, and thus the system becomes linear, by making the hysteresis curve to become a straight line. The area of the first model was taken by calculations with the Green theorem.O presente trabalho propõe-se a continuar o estudo dos dispositivos de memória, iniciado com a predição dos memristors por Leon Chua em 1971, por meio do estudo e caracterização dos memcapacitores como dispositivos semicondutores de dois terminais, caracterizados pela relação não linear entre carga e tensão, que apresentam capacidade de recordar a tensão ou corrente que passa pelo dispositivo, graficamente representado em forma de um gráfico com características de histerese, aprensentando também capacitância variável em função da carga aplicada em seus terminais. Aqui, uma caracterização das funções de resposta a uma entrada periódica sinusoidal com frequência variável, para três modelos matemáticos de sistemas memcapacitivos, é realizada: dado um memcapacitor em série com uma tensão de entrada ac, estuda-se as respectivas funções de histerese carga-tensão por meio de simulação em MATLAB. Em seguida, é realizada uma classificação das curvas de histerese em função da sua geometria, em que a passagem do gráfico no ponto (0,0), de origem dos planos, o define como tipo I ou tipo II. A análise prossegue com a identificação morfológica da área das curvas de histerese obtidas dos primeiro modelo teóricos em causa, variando-se, para isso, amplitude e frequência de entradas, de modo a se comparar os outros dois modelos restantes com este modelo ideal, ao mesmo tempo em que se deseja obter as frequências críticas de cada modelo, ou seja, as frequências e amplitudes a partir das quais a memcapacitância torna-se constante, e o sistema em causa, linear, fazendo então a curva de histerese degenerar para uma reta. A área do primeiro modelo foi calculada através de um algoritmo que calcula a área da curva por meio do Teorema de Green

Memristor Platforms for Pattern Recognition Memristor Theory, Systems and Applications

In the last decade a large scientific community has focused on the study of the memristor. The memristor is thought to be by many the best alternative to CMOS technology, which is gradually showing its flaws. Transistor technology has developed fast both under a research and an industrial point of view, reducing the size of its elements to the nano-scale. It has been possible to generate more and more complex machinery and to communicate with that same machinery thanks to the development of programming languages based on combinations of boolean operands. Alas as shown by Moore’s law, the steep curve of implementation and of development of CMOS is gradually reaching a plateau. It is clear the need of studying new elements that can combine the efficiency of transistors and at the same time increase the complexity of the operations. Memristors can be described as non-linear resistors capable of maintaining memory of the resistance state that they reached. From their first theoretical treatment by Professor Leon O. Chua in 1971, different research groups have devoted their expertise in studying the both the fabrication and the implementation of this new promising technology. In the following thesis a complete study on memristors and memristive elements is presented. The road map that characterizes this study departs from a deep understanding of the physics that govern memristors, focusing on the HP model by Dr. Stanley Williams. Other devices such as phase change memories (PCMs) and memristive biosensors made with Si nano-wires have been studied, developing emulators and equivalent circuitry, in order to describe their complex dynamics. This part sets the first milestone of a pathway that passes trough more complex implementations such as neuromorphic systems and neural networks based on memristors proving their computing efficiency. Finally it will be presented a memristror-based technology, covered by patent, demonstrating its efficacy for clinical applications. The presented system has been designed for detecting and assessing automatically chronic wounds, a syndrome that affects roughly 2% of the world population, through a Cellular Automaton which analyzes and processes digital images of ulcers. Thanks to its precision in measuring the lesions the proposed solution promises not only to increase healing rates, but also to prevent the worsening of the wounds that usually lead to amputation and death