Reliable Modeling of Ideal Generic Memristors via State-Space Transformation

The paper refers to problems of modeling and computer simulation of generic memristors caused by the so-called window functions, namely the stick effect, nonconvergence, and finding fundamentally incorrect solutions. A profoundly different modeling approach is proposed, which is mathematically equivalent to window-based modeling. However, due to its numerical stability, it definitely smoothes the above problems away

Memristors

This Edited Volume Memristors - Circuits and Applications of Memristor Devices is a collection of reviewed and relevant research chapters, offering a comprehensive overview of recent developments in the field of Engineering. The book comprises single chapters authored by various researchers and edited by an expert active in the physical sciences, engineering, and technology research areas. All chapters are complete in itself but united under a common research study topic. This publication aims at providing a thorough overview of the latest research efforts by international authors on physical sciences, engineering, and technology,and open new possible research paths for further novel developments

COMPARISON OF MEMRISTOR MODELS FOR MICROWAVE CIRCUIT SIMULATIONS IN TIME AND FREQUENCY DOMAIN

As reported in the open literature, there are many memristor models for the circuit-level simulations. Some of them are not particularly suitable for microwave circuit simulations. At RF/microwave frequencies, the memristor dynamics become an important issue for the transition process. In this paper we present a number of different SPICE memristor model groups. Each group is explained using representative models, which are analysed and compared from the microwave circuit analysis viewpoint. We consider the model behaviour at RF/microwave frequencies and the memristance setting issues. Results are compared and the best models are recommended

In-Memory Computing by Using Nano-ionic Memristive Devices

By reaching to the CMOS scaling limitation based on the Moore’s law and due to the increasing disparity between the processing units and memory performance, the quest is continued to find a suitable alternative to replace the conventional technology. The recently discovered two terminal element, memristor, is believed to be one of the most promising candidates for future very large scale integrated systems. This thesis is comprised of two main parts, (Part I) modeling the memristor devices, and (Part II) memristive computing. The first part is presented in one chapter and the second part of the thesis contains five chapters. The basics and fundamentals regarding the memristor functionality and memristive computing are presented in the introduction chapter. A brief detail of these two main parts is as follows: Part I: Modeling- This part presents an accurate model based on the charge transport mechanisms for nanoionic memristor devices. The main current mechanism in metal/insulator/metal (MIM) structures are assessed, a physic-based model is proposed and a SPICE model is presented and tested for four different fabricated devices. An accuracy comparison is done for various models for Ag/TiO2/ITO fabricated device. Also, the functionality of the model is tested for various input signals. Part II: Memristive computing- Memristive computing is about utilizing memristor to perform computational tasks. This part of the thesis is divided into neuromorphic, analog and digital computing schemes with memristor devices. – Neuromorphic computing- Two chapters of this thesis are about biologicalinspired memristive neural networks using STDP-based learning mechanism. The memristive implementation of two well-known spiking neuron models, Hudgkin-Huxley and Morris-Lecar, are assessed and utilized in the proposed memristive network. The synaptic connections are also memristor devices in this design. Unsupervised pattern classification tasks are done to ensure the right functionality of the system. – Analog computing- Memristor has analog memory property as it can be programmed to different memristance values. A novel memristive analog adder is designed by Continuous Valued Number System (CVNS) scheme and its circuit is comprised of addition and modulo blocks. The proposed analog adder design is explained and its functionality is tested for various numbers. It is shown that the CVNS scheme is compatible with memristive design and the environment resolution can be adjusted by the memristance ratio of the memristor devices. – Digital computing- Two chapters are dedicated for digital computing. In the first one, a development over IMPLY-based logic with memristor is provided to implement a 4:2 compressor circuit. In the second chapter, A novel resistive over a novel mirrored memristive crossbar platform. Different logic gates are designed with the proposed memristive logic method and the simulations are provided with Cadence to prove the functionality of the logic. The logic implementation over a mirrored memristive crossbars is also assessed

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

Applications of memristors in conventional analogue electronics

This dissertation presents the steps employed to activate and utilise analogue memristive devices in conventional analogue circuits and beyond. TiO2 memristors are mainly utilised in this study, and their large variability in operation in between similar devices is identified. A specialised memristor characterisation instrument is designed and built to mitigate this issue and to allow access to large numbers of devices at a time. Its performance is quantified against linear resistors, crossbars of linear resistors, stand-alone memristive elements and crossbars of memristors. This platform allows for a wide range of different pulsing algorithms to be applied on individual devices, or on crossbars of memristive elements, and is used throughout this dissertation. Different ways of achieving analogue resistive switching from any device state are presented. Results of these are used to devise a state-of-art biasing parameter finder which automatically extracts pulsing parameters that induce repeatable analogue resistive switching. IV measurements taken during analogue resistive switching are then utilised to model the internal atomic structure of two devices, via fittings by the Simmons tunnelling barrier model. These reveal that voltage pulses modulate a nano-tunnelling gap along a conical shape. Further retention measurements are performed which reveal that under certain conditions, TiO2 memristors become volatile at short time scales. This volatile behaviour is then implemented into a novel SPICE volatile memristor model. These characterisation methods of solid-state devices allowed for inclusion of TiO2 memristors in practical electronic circuits. Firstly, in the context of large analogue resistive crossbars, a crosspoint reading method is analysed and improved via a 3-step technique. Its scaling performance is then quantified via SPICE simulations. Next, the observed volatile dynamics of memristors are exploited in two separate sequence detectors, with applications in neuromorphic engineering. Finally, the memristor as a programmable resistive weight is exploited to synthesise a memristive programmable gain amplifier and a practical memristive automatic gain control circuit.Open Acces

Optimization of niobium oxide-based threshold switches for oscillator-based applications

In niobium oxide-based capacitors non-linear switching characteristics can be observed if the oxide properties are adjusted accordingly. Such non-linear threshold switching characteristics can be utilized in various non-linear circuit applications, which have the potential to pave the way for the application of new computing paradigms. Furthermore, the non-linearity also makes them an interesting candidate for the application as selector devices e.g. for non-volatile memory devices. To satisfy the requirements for those two areas of application, the threshold switching characteristics need to be adjusted to either obtain a maximized voltage extension of the negative differential resistance region in the quasi-static I-V characteristics, which enhances the non-linearity of the devices and results in improved robustness to device-to-device variability or to adapt the threshold voltage to a specific non-volatile memory cell. Those adaptations of the threshold switching characteristics were successfully achieved by deliberate modifications of the niobium oxide stack. Furthermore, the impact of the material stack on the dynamic behavior of the threshold switches in non-linear circuits as well as the impact of the electroforming routine on the threshold switching characteristics were analyzed. The optimized device stack was transferred from the micrometer-sized test structures to submicrometer-sized devices, which were packaged to enable easy integration in complex circuits. Based on those packaged threshold switching devices the behavior of single as well as of coupled relaxation oscillators was analyzed. Subsequently, the obtained results in combination with the measurement results for the statistic device-to-device variability were used as a basis to simulate the pattern formation in coupled relaxation oscillator networks as well as their performance in solving graph coloring problems. Furthermore, strategies to adapt the threshold voltage to the switching characteristics of a tantalum oxide-based non-volatile resistive switch and a non-volatile phase change cell, to enable their application as selector devices for the respective cells, were discussed.:Abstract I Zusammenfassung II List of Abbrevations VI List of Symbols VII 1 Motivation 1 2 Basics 5 2.1 Negative differential resistance and local activity in memristor devices 5 2.2 Threshold switches as selector devices 8 2.3 Switching effects observed in NbOx 13 2.3.1 Threshold switching caused by metal-insulator transition 13 2.3.2 Threshold switching caused by Frenkel-Poole conduction 18 2.3.3 Non-volatile resistive switching 32 3 Sample preparation 35 3.1 Deposition techniques 35 3.1.1 Evaporation 35 3.1.2 Sputtering 36 3.2 Micrometer-sized devices 36 3.3 Submicrometer-sized devices 37 3.3.1 Process flow 37 3.3.2 Reduction of the electrode resistance 39 3.3.3 Transfer from structuring via electron beam lithography to structuring via laser lithography 48 3.3.4 Packaging procedure 50 4 Investigation and optimization of the electrical device characteristic 51 4.1 Introduction 51 4.2 Measurement setup 52 4.3 Electroforming 53 4.3.1 Optimization of the electroforming process 53 4.3.2 Characterization of the formed filament 62 4.4 Dynamic device characteristics 67 4.4.1 Emergence and measurement of dynamic behavior 67 4.4.2 Impact of the dynamic device characteristics on quasi-static I-V characteristics 70 5 Optimization of the material stack 81 5.1 Introduction 81 5.2 Adjustment of the oxygen content in the bottom layer 82 5.3 Influence of the thickness of the oxygen-rich niobium oxide layer 92 5.4 Multilayer stacks 96 5.5 Device-to-device and Sample-to-sample variability 110 6 Applications of NbOx-based threshold switching devices 117 6.1 Introduction 117 6.2 Non-linear circuits 117 6.2.1 Coupled relaxation oscillators 117 6.2.2 Memristor Cellular Neural Network 121 6.2.3 Graph Coloring 127 6.3 Selector devices 132 7 Summary and Outlook 138 8 References 141 9 List of publications 154 10 Appendix 155 10.1 Parameter used for the LT Spice simulation of I-V curves for threshold switches with varying oxide thicknesses 155 10.2 Dependence of the oscillation frequency of the relaxation oscillator circuit on the capacitance and the applied source voltage 156 10.3 Calculation of the oscillation frequency of the relaxation oscillator circuit 157 10.4 Characteristics of the memristors and the cells utilized in the simulation of the memristor cellular neural network 164 10.5 Calculation of the impedance of the cell in the memristor cellular network 166 10.6 Example graphs from the 2nd DIMACS series 179 11 List of Figures 182 12 List of Tables 19

Reliability-aware circuit design to mitigate impact of device defects and variability in emerging memristor-based applications

In the last decades, semiconductor industry has fostered a fast downscale in technology, propelling the large scale integration of CMOS-based systems. The benefits in miniaturization are numerous, highlighting faster switching frequency, lower voltage supply and higher device density. However, this aggressive scaling trend it has not been without challenges, such as leakage currents, yield reduction or the increase in the overall system power dissipation. New materials, changes in the device structures and new architectures are key to keep the miniaturization trend. It is foreseen that 2D integration will eventually come to an insurmountable physical and economic limit, in which new strategic directions are required, such as the development of new device structures, 3D architectures or heterogeneous systems that takes advantage of the best of different technologies, both the ones already consolidated as well as emergent ones that provide performance and efficiency improvements in applications. In this context, memristor arises as one of several candidates in the race to find suitable emergent devices. Memristor, a blend of the words memory and resistor, is a passive device postulated by Leon Chua in 1971. In contrast with the other fundamental passive elements, memristors have the distinctive feature of modifying their resistance according to the charge that passes through these devices, and remaining unaltered when charge no longer flows. Although when it appeared no physical device implementation was acknowledged, HP Labs claimed in 2008 the manufacture of the first real memristor. This milestone triggered an unexpectedly high research activity about memristors, both in searching new materials and structures as well as in potential applications. Nowadays, memristors are not only appreciated in memory systems by their nonvolatile storage properties, but in many other fields, such as digital computing, signal processing circuits, or non-conventional applications like neuromorphic computing or chaotic circuits. In spite of their promising features, memristors show a primarily downside: they show significant device variation and limited lifetime due degradation compared with other alternatives. This Thesis explores the challenges that memristor variation and malfunction imposes in potential applications. The main goal is to propose circuits and strategies that either avoid reliability problems or take advantage of them. Throughout a collection of scenarios in which reliability issues are present, their impact is studied by means of simulations. This thesis is contextualized and their objectives are exposed in Chapter 1. In Chapter 2 the memristor is introduced, at both conceptual and experimental levels, and different compact levels are presented to be later used in simulations. Chapter 3 deepens in the phenomena that causes the lack of reliability in memristors, and models that include these defects in simulations are provided. The rest of the Thesis covers different applications. Therefore, Chapter 4 exhibits nonvolatile memory systems, and specifically an online test method for faulty cells. Digital computing is presented in Chapter 5, where a solution for the yield reduction in logic operations due to memristors variability is proposed. Lastly, Chapter 6 reviews applications in the analog domain, and it focuses in the exploitation of results observed in faulty memristor-based interconnect mediums for chaotic systems synchronization purposes. Finally, the Thesis concludes in Chapter 7 along with perspectives about future work.Este trabajo desarrolla un novedoso dispositivo condensador basado en el uso de la nanotecnología. El dispositivo parte del concepto existente de metal-aislador-metal (MIM), pero en lugar de una capa aislante continua, se utilizan nanopartículas dieléctricas. Las nanopartículas son principalmente de óxido de silicio (sílice) y poliestireno (PS) y los valores de diámetro son 255nm y 295nm respectivamente. Las nanopartículas contribuyen a una alta relación superficie/volumen y están fácilmente disponibles a bajo costo. La tecnología de depósito desarrollada en este trabajo se basa en la técnica de electrospray, que es una tecnología de fabricación ascendente (bottom-up) que permite el procesamiento por lotes y logra un buen compromiso entre una gran superficie y un bajo tiempo de depósito. Con el objetivo de aumentar la superficie de depósito, la configuración de electrospray ha sido ajustada para permitir áreas de depósito de 1cm2 a 25cm2. El dispositivo fabricado, los llamados condensadores de metal aislante de nanopartículas (NP-MIM) ofrecen valores de capacidad más altos que un condensador convencional similar con una capa aislante continua. En el caso de los NP-MIM de sílice, se alcanza un factor de hasta 1000 de mejora de la capacidad, mientras que los NP-MIM de poliestireno exhibe una ganancia de capacidad en el rango de 11. Además, los NP-MIM de sílice muestran comportamientos capacitivos en específicos rangos de frecuencias que depende de la humedad y el grosor de la capa de nanopartículas, mientras que los NP-MIM de poliestireno siempre mantienen su comportamiento capacitivo. Los dispositivos fabricados se han caracterizado mediante medidas de microscopía electrónica de barrido (SEM) complementadas con perforaciones de haz de iones focalizados (FIB) para caracterizar la topografía de los NP-MIMs. Los dispositivos también se han caracterizado por medidas de espectroscopia de impedancia, a diferentes temperaturas y humedades. El origen de la capacitancia aumentada está asociado en parte a la humedad en las interfaces de las nanopartículas. Se ha desarrollado un modelo de un circuito basado en elementos distribuidos para ajustar y predecir el comportamiento eléctrico de los NP-MIMs. En resumen, esta tesis muestra el diseño, fabricación, caracterización y modelización de un nuevo y prometedor condensador nanopartículas metal-aislante-metal que puede abrir el camino al desarrollo de una nueva tecnología de supercondensadores MIM

Reliability-aware circuit design to mitigate impact of device defects and variability in emerging memristor-based applications

In the last decades, semiconductor industry has fostered a fast downscale in technology, propelling the large scale integration of CMOS-based systems. The benefits in miniaturization are numerous, highlighting faster switching frequency, lower voltage supply and higher device density. However, this aggressive scaling trend it has not been without challenges, such as leakage currents, yield reduction or the increase in the overall system power dissipation. New materials, changes in the device structures and new architectures are key to keep the miniaturization trend. It is foreseen that 2D integration will eventually come to an insurmountable physical and economic limit, in which new strategic directions are required, such as the development of new device structures, 3D architectures or heterogeneous systems that takes advantage of the best of different technologies, both the ones already consolidated as well as emergent ones that provide performance and efficiency improvements in applications. In this context, memristor arises as one of several candidates in the race to find suitable emergent devices. Memristor, a blend of the words memory and resistor, is a passive device postulated by Leon Chua in 1971. In contrast with the other fundamental passive elements, memristors have the distinctive feature of modifying their resistance according to the charge that passes through these devices, and remaining unaltered when charge no longer flows. Although when it appeared no physical device implementation was acknowledged, HP Labs claimed in 2008 the manufacture of the first real memristor. This milestone triggered an unexpectedly high research activity about memristors, both in searching new materials and structures as well as in potential applications. Nowadays, memristors are not only appreciated in memory systems by their nonvolatile storage properties, but in many other fields, such as digital computing, signal processing circuits, or non-conventional applications like neuromorphic computing or chaotic circuits. In spite of their promising features, memristors show a primarily downside: they show significant device variation and limited lifetime due degradation compared with other alternatives. This Thesis explores the challenges that memristor variation and malfunction imposes in potential applications. The main goal is to propose circuits and strategies that either avoid reliability problems or take advantage of them. Throughout a collection of scenarios in which reliability issues are present, their impact is studied by means of simulations. This thesis is contextualized and their objectives are exposed in Chapter 1. In Chapter 2 the memristor is introduced, at both conceptual and experimental levels, and different compact levels are presented to be later used in simulations. Chapter 3 deepens in the phenomena that causes the lack of reliability in memristors, and models that include these defects in simulations are provided. The rest of the Thesis covers different applications. Therefore, Chapter 4 exhibits nonvolatile memory systems, and specifically an online test method for faulty cells. Digital computing is presented in Chapter 5, where a solution for the yield reduction in logic operations due to memristors variability is proposed. Lastly, Chapter 6 reviews applications in the analog domain, and it focuses in the exploitation of results observed in faulty memristor-based interconnect mediums for chaotic systems synchronization purposes. Finally, the Thesis concludes in Chapter 7 along with perspectives about future work.Este trabajo desarrolla un novedoso dispositivo condensador basado en el uso de la nanotecnología. El dispositivo parte del concepto existente de metal-aislador-metal (MIM), pero en lugar de una capa aislante continua, se utilizan nanopartículas dieléctricas. Las nanopartículas son principalmente de óxido de silicio (sílice) y poliestireno (PS) y los valores de diámetro son 255nm y 295nm respectivamente. Las nanopartículas contribuyen a una alta relación superficie/volumen y están fácilmente disponibles a bajo costo. La tecnología de depósito desarrollada en este trabajo se basa en la técnica de electrospray, que es una tecnología de fabricación ascendente (bottom-up) que permite el procesamiento por lotes y logra un buen compromiso entre una gran superficie y un bajo tiempo de depósito. Con el objetivo de aumentar la superficie de depósito, la configuración de electrospray ha sido ajustada para permitir áreas de depósito de 1cm2 a 25cm2. El dispositivo fabricado, los llamados condensadores de metal aislante de nanopartículas (NP-MIM) ofrecen valores de capacidad más altos que un condensador convencional similar con una capa aislante continua. En el caso de los NP-MIM de sílice, se alcanza un factor de hasta 1000 de mejora de la capacidad, mientras que los NP-MIM de poliestireno exhibe una ganancia de capacidad en el rango de 11. Además, los NP-MIM de sílice muestran comportamientos capacitivos en específicos rangos de frecuencias que depende de la humedad y el grosor de la capa de nanopartículas, mientras que los NP-MIM de poliestireno siempre mantienen su comportamiento capacitivo. Los dispositivos fabricados se han caracterizado mediante medidas de microscopía electrónica de barrido (SEM) complementadas con perforaciones de haz de iones focalizados (FIB) para caracterizar la topografía de los NP-MIMs. Los dispositivos también se han caracterizado por medidas de espectroscopia de impedancia, a diferentes temperaturas y humedades. El origen de la capacitancia aumentada está asociado en parte a la humedad en las interfaces de las nanopartículas. Se ha desarrollado un modelo de un circuito basado en elementos distribuidos para ajustar y predecir el comportamiento eléctrico de los NP-MIMs. En resumen, esta tesis muestra el diseño, fabricación, caracterización y modelización de un nuevo y prometedor condensador nanopartículas metal-aislante-metal que puede abrir el camino al desarrollo de una nueva tecnología de supercondensadores MIM.Postprint (published version