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

Logaritmik Memristanslı TiO2 Memristör

An ideal memristor, which was claimed to be the fourth fundamental element of circuit design by Dr. Chua in 1971, is a nonlinear resistor and its properties cannot be mimicked with linear time-invariant circuit elements. A thin-film which behaves as if a memristor has been declared found experimentally by a HP research team lead by Stanley Williams in 2008. A quite explicit model of the memristor has also been given by the team. The HP memristor resistance can be found by summing the resistances of the doped and undoped regions. Assuming the doped region length is proportional to memristor charge, which is the integration of memristor current, the doped region has a constant drift speed, and a constant memristor cross-section, the HP memristor resistance has a linear charge dependency till it saturates. In this paper, it is shown that a memristor with a logarithmic charge dependency can be made using the principles given by the team and making some modifications to memristor geometry.İdeal bir memristör, 1971 yılında Dr. Chua tarafından devre tasarımı için dördüncü temel devre elemanı olarak iddia edilen nonlinear bir dirençtir ve özellikleri lineer zamanla-değişmeyen devre elemanları tarafından taklit edilememektedir. Memristör olarak davranan bir ince-filmin bulunduğu, 2008 senesinde Stanley Williams tarafından yönetilen bir HP araştırma timi tarafından ilan edilmiştir. Bu memristörün oldukça anlaşılabilir bir modeli de bu tim tarafından verilmiştir. Bu HP memristör direnci katkılanmış ve katkılanmamış bölgelerin dirençlerini ekleyerek bulunabilir. Katkılanmış bölge uzunluğunun akımın integrali olan memristör yüküne orantılı olduğu, katkılanmış bölgenin sabit bir sürüklenme hızına sahip olduğu ve memristör kesiti sabit olarak kabul edilirek, HP memristör direncinin, doyma gerçekleşene kadar, lineer yük bağımlılığı vardır. Bu makalede, logaritmik yük bağımlılığı olan bir memristörün HP timi tarafından verilen prensipleri kullanarak ve memristör geometrisine bazı değişiklikler yapılarak yapılabileceği gösterilmiştir

Memristor: Modeling, Simulation and Usage in Neuromorphic Computation

Memristor, the fourth passive circuit element, has attracted increased attention from various areas since the first real device was discovered in 2008. Its distinctive characteristic to record the historic profile of the voltage/current through itself creates great potential in future circuit design. Inspired by its high Scalability, ultra low power consumption and similar functionality to biology synapse, using memristor to build high density, high power efficiency neuromorphic circuits becomes one of most promising and also challenging applications. The challenges can be concluded into three levels: device level, circuit level and application level. At device level, we studied different memristor models and process variations, then we carried out three independent variation models to describe the variation and stochastic behavior of TiO2 memristors. These models can also extend to other memristor models. Meanwhile, these models are also compact enough for large-scale circuit simulation. At circuit level, inspired by the large-scale and unique requirement of memristor-based neuromorphic circuits, we designed a circuit simulator for efficient memristor cross-point array simulations. Out simulator is 4~5 orders of magnitude faster than tradition SPICE simulators. Both linear and nonlinear memristor cross-point arrays are studied for level-based and spike-based neuromorphic circuits, respectively. At application level, we first designed a few compact memristor-based neuromorphic components, including ``Macro cell'' for efficient and high definition weight storage, memristor-based stochastic neuron and memristor-based spatio temporal synapse. We then studied three typical neural network models and their hardware realization on memristor-based neuromorphic circuits: Brain-State-in-a-Box (BSB) model stands for level-based neural network, and STDP/ReSuMe models stand for spiking neural network for temporal learning. Our result demonstrates the high resilience to variation of memristor-based circuits and ultra-low power consumption. In this thesis, we have proposed a complete and detailed analysis for memristor-based neuromorphic circuit design from the device level to the application level. In each level, both theoretical analysis and experimental data versification are applied to ensure the completeness and accuracy of the work

Phase Noise Analyses and Measurements in the Hybrid Memristor-CMOS Phase-Locked Loop Design and Devices Beyond Bulk CMOS

Phase-locked loop (PLLs) has been widely used in analog or mixed-signal integrated circuits. Since there is an increasing market for low noise and high speed devices, PLLs are being employed in communications. In this dissertation, we investigated phase noise, tuning range, jitter, and power performances in different architectures of PLL designs. More energy efficient devices such as memristor, graphene, transition metal di-chalcogenide (TMDC) materials and their respective transistors are introduced in the design phase-locked loop. Subsequently, we modeled phase noise of a CMOS phase-locked loop from the superposition of noises from its building blocks which comprises of a voltage-controlled oscillator, loop filter, frequency divider, phase-frequency detector, and the auxiliary input reference clock. Similarly, a linear time-invariant model that has additive noise sources in frequency domain is used to analyze the phase noise. The modeled phase noise results are further compared with the corresponding phase-locked loop designs in different n-well CMOS processes. With the scaling of CMOS technology and the increase of the electrical field, the problem of short channel effects (SCE) has become dominant, which causes decay in subthreshold slope (SS) and positive and negative shifts in the threshold voltages of nMOS and pMOS transistors, respectively. Various devices are proposed to continue extending Moore\u27s law and the roadmap in semiconductor industry. We employed tunnel field effect transistor owing to its better performance in terms of SS, leakage current, power consumption etc. Applying an appropriate bias voltage to the gate-source region of TFET causes the valence band to align with the conduction band and injecting the charge carriers. Similarly, under reverse bias, the two bands are misaligned and there is no injection of carriers. We implemented graphene TFET and MoS2 in PLL design and the results show improvements in phase noise, jitter, tuning range, and frequency of operation. In addition, the power consumption is greatly reduced due to the low supply voltage of tunnel field effect transistor

BOOLEAN AND BRAIN-INSPIRED COMPUTING USING SPIN-TRANSFER TORQUE DEVICES

Several completely new approaches (such as spintronic, carbon nanotube, graphene, TFETs, etc.) to information processing and data storage technologies are emerging to address the time frame beyond current Complementary Metal-Oxide-Semiconductor (CMOS) roadmap. The high speed magnetization switching of a nano-magnet due to current induced spin-transfer torque (STT) have been demonstrated in recent experiments. Such STT devices can be explored in compact, low power memory and logic design. In order to truly leverage STT devices based computing, researchers require a re-think of circuit, architecture, and computing model, since the STT devices are unlikely to be drop-in replacements for CMOS. The potential of STT devices based computing will be best realized by considering new computing models that are inherently suited to the characteristics of STT devices, and new applications that are enabled by their unique capabilities, thereby attaining performance that CMOS cannot achieve. The goal of this research is to conduct synergistic exploration in architecture, circuit and device levels for Boolean and brain-inspired computing using nanoscale STT devices. Specifically, we first show that the non-volatile STT devices can be used in designing configurable Boolean logic blocks. We propose a spin-memristor threshold logic (SMTL) gate design, where memristive cross-bar array is used to perform current mode summation of binary inputs and the low power current mode spintronic threshold device carries out the energy efficient threshold operation. Next, for brain-inspired computing, we have exploited different spin-transfer torque device structures that can implement the hard-limiting and soft-limiting artificial neuron transfer functions respectively. We apply such STT based neuron (or ‘spin-neuron’) in various neural network architectures, such as hierarchical temporal memory and feed-forward neural network, for performing “human-like” cognitive computing, which show more than two orders of lower energy consumption compared to state of the art CMOS implementation. Finally, we show the dynamics of injection locked Spin Hall Effect Spin-Torque Oscillator (SHE-STO) cluster can be exploited as a robust multi-dimensional distance metric for associative computing, image/ video analysis, etc. Our simulation results show that the proposed system architecture with injection locked SHE-STOs and the associated CMOS interface circuits can be suitable for robust and energy efficient associative computing and pattern matching

Exploring Memristor Based Analog Design in Simscape

With conventional CMOS technologies approaching their scaling limits, researchers are actively investigating alternative technologies for ever increasing computing and mobile demand. A number of different technologies are currently being studied by different research groups. In the last decade, one-dimensional (1D) carbon nanotubes (CNT), graphene, which is a two-dimensional (2D) natural occurring carbon rolled in tubular form, and zero-dimensional (0D) fullerenes have been the subject of intensive research. In 2008, HP Labs announced a ground-breaking fabrication of memristors, the fourth fundamental element postulated by Chua at the University of California, Berkeley in 1971. In the last few years, the memristor has gained a lot of attention from the research community. In-depth studies of the memristor and its analog behavior have convinced the community that it has the potential in future nano-architectures for optimization of high-density memory and neuromorphic computing architectures. The objective of this thesis is to explore memristors for analog and mixed-signal system design using Simscape. This thesis presents a memristor model in the Simscape language. Simscape has been used as it has the potential for modeling large systems. A memristor based programmable oscillator is also presented with simulation results and characterization. In addition, simulation results of different memristor models are presented which are crucial for the detailed understanding of the memristor along with its properties

Emulator Circuits and Resistive Switching Parameters of Memristor

Chua predicted the existence of the fundamental circuit element, which provides the linkage of flux (ϕ) and charge (q). The new circuit element that is called memristor (memory + resistor) was demonstrated by Hewlett Packard (HP) researchers in 2008. Researchers focused on memristor fabrication, modeling, and its application with other circuit elements. Researchers could not find the commercially memristor devices in the market because of some fabrication difficulties. For this reason, researchers focused on the memristor modeling to analyze its characteristics with other circuit elements. This chapter presents a review of the general information of memristor and its device parameters. The chapter is continued with the details of memristor mathematical and SPICE models and memristor emulators based on the other circuit elements