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

Cerium oxide based resistive random access memory devices

Resistive Random Access Memory (RRAM) is an emerging technology of non-volatile memory (NVM). Although the observation of metal oxide that can undergo an abrupt insulator-metal transition into a conductive state has been known for over 40 years, researchers started investigating those materials for memory applications in late 1990s. It has been considered as the next generation memory technology to replace current flash memory because RRAM has demonstrated feasible switching characteristics and potential to build high density arrays and also RRAM is also compatible with contemporary CMOS processes, which means RRAM can be integrated into current CMOS chips. While the structure of RRAM is a simple metal-insulator-metal (MIM) device, there are numerous materials that exhibit resistive switching. The switching behavior is not only dependent on the switching layer materials but also dependent on the choice of metal electrodes and their interfacial properties. Many metal oxides such as hafnium oxide, titanium oxide, aluminum oxide, nickel oxide (NiO), tantalum oxide and etc. have been studied in details; however, some materials are unexplored such as cerium oxide. In addition to nonvolatile storage applications, RRAM is considered as one of essential elements for advancing neuromorphic computing because of its analog switching and retention characteristics. This thesis investigated CeO[subscript x]-based RRAMs, from its fundamental device characteristics to neuromorphic applications.Electrical and Computer Engineerin

Pattern Formation in a RD-MCNN with Locally Active Memristors

This chapter presents the mathematical investigation of the emergence of static patterns in a Reaction–Diffusion Memristor Cellular Nonlinear Network (RD-MCNN) structure via the application of the theory of local activity. The proposed RD-MCNN has a planar grid structure, which consists of identical memristive cells, and the couplings are established in a purely resistive fashion. The single cell has a compact design being composed of a locally active memristor in parallel with a capacitor, besides the bias circuitry, namely a DC voltage source and its series resistor. We first introduce the mathematical model of the locally active memristor and then study the main characteristics of its AC equivalent circuit. Later on, we perform a stability analysis to obtain the stability criteria for the single cell. Consequently, we apply the theory of local activity to extract the parameter space associated with locally active, edge-of-chaos, and sharp-edge-of-chaos domains, performing all the necessary calculations parametrically. The corresponding parameter space domains are represented in terms of intrinsic cell characteristics such as the DC operating point, the capacitance, and the coupling resistance. Finally, we simulate the proposed RD-MCNN structure where we demonstrate the emergence of pattern formation for various values of the design parameters

Firing multistability in a locally active memristive neuron model

Funding Information: This work is supported by The Major Research Project of the National Natural Science Foundation of China (91964108), The National Natural Science Foundation of China (61971185), The Open Fund Project of Key Laboratory in Hunan Universities (18K010). Publisher Copyright: © 2020, Springer Nature B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.The theoretical, numerical and experimental demonstrations of firing dynamics in isolated neuron are of great significance for the understanding of neural function in human brain. In this paper, a new type of locally active and non-volatile memristor with three stable pinched hysteresis loops is presented. Then, a novel locally active memristive neuron model is established by using the locally active memristor as a connecting autapse, and both firing patterns and multistability in this neuronal system are investigated. We have confirmed that, on the one hand, the constructed neuron can generate multiple firing patterns like periodic bursting, periodic spiking, chaotic bursting, chaotic spiking, stochastic bursting, transient chaotic bursting and transient stochastic bursting. On the other hand, the phenomenon of firing multistability with coexisting four kinds of firing patterns can be observed via changing its initial states. It is worth noting that the proposed neuron exhibits such firing multistability previously unobserved in single neuron model. Finally, an electric neuron is designed and implemented, which is extremely useful for the practical scientific and engineering applications. The results captured from neuron hardware experiments match well with the theoretical and numerical simulation results.Peer reviewedFinal Accepted Versio

Threshold Switching and Self-Oscillation in Niobium Oxide

Volatile threshold switching, or current controlled negative differential resistance (CC-NDR), has been observed in a range of transition metal oxides. Threshold switching devices exhibit a large non-linear change in electrical conductivity, switching from an insulating to a metallic state under external stimuli. Compact, scalable and low power threshold switching devices are of significant interest for use in existing and emerging technologies, including as a selector element in high-density memory arrays and as solid-state oscillators for hardware-based neuromorphic computing. This thesis explores the threshold switching in amorphous NbOx and the properties of individual and coupled oscillators based on this response. The study begins with an investigation of threshold switching in Pt/NbOx/TiN devices as a function device area, NbOx film thickness and temperature, which provides important insight into the structure of the self-assembled switching region. The devices exhibit combined threshold-memory behaviour after an initial voltage-controlled forming process, but exhibit symmetric threshold switching when the RESET and SET currents are kept below a critical value. In this mode, the threshold and hold voltages are shown to be independent of the device area and film thickness, and the threshold power, while independent of device area, is shown to decrease with increasing film thickness. These results are shown to be consistent with a structure in which the threshold switching volume is confined, both laterally and vertically, to the region between the residual memory filament and the electrode, and where the memory filament has a core-shell structure comprising a metallic core and a semiconducting shell. The veracity of this structure is demonstrated by comparing experimental results with the predictions of a resistor network model, and detailed finite element simulations. The next study focuses on electrical self-oscillation of an NbOx threshold switching device incorporated into a Pearson-Anson circuit configuration. Measurements confirm stable operation of the oscillator at source voltages as low as 1.06 V, and demonstrate frequency control in the range from 2.5 to 20.5 MHz with maximum frequency tuning range of 18 MHz/V. The oscillator exhibit three distinct oscillation regimes: sporadic spiking, stable oscillation and damped oscillation. The oscillation frequency, peak-to-peak amplitude and frequency are shown to be temperature and voltage dependent with stable oscillation achieved for temperatures up to ∼380 K. A physics-based threshold switching model with inclusion of device and circuit parameters is shown to explain the oscillation waveform and characteristic. The final study explores the oscillation dynamics of capacitively coupled Nb/Nb2O5 relaxation oscillators. The coupled system exhibits rich collective behaviour, from weak coupling to synchronisation, depending on the negative differential resistance response of the individual devices, the operating voltage and the coupling capacitance. These coupled oscillators are shown to exhibit stable frequency and phase locking states at source voltages as low as 2.2 V with MHz frequency tunable range. The numerical simulation of the coupled system highlights the role of source voltage, and circuit and device capacitance in controlling the coupling modes and dynamics

Low Power Memory/Memristor Devices and Systems

This reprint focusses on achieving low-power computation using memristive devices. The topic was designed as a convenient reference point: it contains a mix of techniques starting from the fundamental manufacturing of memristive devices all the way to applications such as physically unclonable functions, and also covers perspectives on, e.g., in-memory computing, which is inextricably linked with emerging memory devices such as memristors. Finally, the reprint contains a few articles representing how other communities (from typical CMOS design to photonics) are fighting on their own fronts in the quest towards low-power computation, as a comparison with the memristor literature. We hope that readers will enjoy discovering the articles within

A locally active discrete memristor model and its application in a hyperchaotic map

© 2022 Springer Nature Switzerland AG. Part of Springer Nature. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11071-021-07132-5The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.Peer reviewedFinal Accepted Versio

Filamentary Threshold Switching In Niobium Oxides

Two-terminal metal/oxide/metal (MOM) structures exhibit characteristic resistance changes, including non-volatile memory and volatile threshold switching responses when subjected to electrical stress (i.e., voltage or current stimuli), which are of interest as active elements in non-volatile memory arrays and neuromorphic computing. Recently, the threshold switching response in MOM devices based on vanadium oxides and niobium oxides have attracted particular attention due to their simple structure and reliability. Interestingly, specific phases of these oxides (e.g., VO2, NbO2 etc.) exhibit a metal-insulator transition (MIT) which causes dramatic changes in their intrinsic properties, including electrical and thermal conductivities, and often arguably reported as the dominant cause of the observed threshold switching response. While this response has been extensively studied for VO2, but the low transition temperature (~ 340K) limits their use only to low temperature microelectronics applications. In contrast, NbO2 has a much higher transition temperature ~ 1070 K, and NbO2 and other NbOx phases have drawn recent attention due to their reliable threshold switching characteristics. The resistance changes in MOM structures are often initiated by a one-step electroforming process that forms a filamentary conduction path. Knowledge about the structure, composition and spatial distribution of these filaments is essential for a full understanding of filamentary resistive/threshold-switching and for effective modelling and optimisation of associated devices. Additionally, NbOx-based devices exhibit a wide range of resistive and threshold switching responses that critically depend on operating condition, composition and device geometry. Thus, a proper understanding of these factors is important for achieving reliable switching with desired characteristics. This thesis focuses on understanding the electroforming process and subsequent threshold switching responses in NbOx by employing different techniques, including electrical testing, and thermo-reflectance imaging. At first, a simple means of detecting and spatially mapping conductive filaments in metal/oxide/metal cross-point devices is introduced and the utility of this technique is demonstrated to identify distinct modes of electroforming in low- and high-conductivity NbOx films. After that, the role of metal/oxide interface reactions on the post-forming characteristics of reactive-metal/Nb2O5/Pt devices is demonstrated. Specifically, devices are shown to exhibit stable threshold switching under negative bias but the response under positive bias depends on the choice of metal. Then, the threshold-switching and current-controlled negative differential resistance (NDR) characteristics of cross-point devices fabricated from undoped Nb2O5 and Ti-doped Nb2O5 are compared. In particular it is shown that doping offers an effective means of engineering the device response. Based on temperature dependent current-voltage characteristics and lumped-element modelling, these effects are attributed to doping-induced reductions in the device resistance and its rate of change with temperature. Finally, the physical origin of the discontinuous 'snapback' NDR is investigated. Specifically, it is shown that the snapback response is a direct consequence of current localisation and redistribution within the oxide film. Furthermore, it is demonstrated that material and device dependencies are consistent with predictions of a two-zone parallel memristor model of NDR which is based on a non-uniform current distribution after electroforming. These results advance the current understanding of threshold switching response in amorphous NbOx films, and provide a strong basis for engineering devices with specific NDR characteristics. Significantly, these results also resolve a long-standing controversy about the origin of the snapback response which has been a subject of considerable debate

Memristive Anodic Oxides: Production, Properties and Applications in Neuromorphic Computing

Memristive devices generally consist of metal oxide elements with specific structure and chemical composition, which are crucial to obtain the required variability in resistance. This makes the control of oxide properties vital. While CMOS compatible production technologies for metal oxides deposition generally involve physical or chemical deposition pathways, we here describe the possibility of using an electrochemical technique, anodic oxidation, as an alternative route to produce memristive oxides. In fact, anodization allows to form a very large range of oxides on the surface of valve metals, such as titanium, hafnium, niobium and tantalum, whose thickness, structure and functional properties depend on process parameters imposed. These oxides may be of interest to build neural networks based on memristive elements produced by anodic oxidation